%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP191-2 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 10:54:00 EDT 2022 % Result : Unsatisfiable 165.86s 165.36s % Output : Proof 165.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRP191-2 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.07/0.14 % Command : moca.sh %s % 0.13/0.35 % Computer : n006.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon Jun 13 23:59:41 EDT 2022 % 0.13/0.35 % CPUTime : % 165.86/165.36 % SZS status Unsatisfiable % 165.86/165.36 % SZS output start Proof % 165.86/165.36 The input problem is unsatisfiable because % 165.86/165.36 % 165.86/165.36 [1] the following set of Horn clauses is unsatisfiable: % 165.86/165.36 % 165.86/165.36 multiply(identity, X) = X % 165.86/165.36 multiply(inverse(X), X) = identity % 165.86/165.36 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 165.86/165.36 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 165.86/165.36 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 165.86/165.36 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 165.86/165.36 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 165.86/165.36 least_upper_bound(X, X) = X % 165.86/165.36 greatest_lower_bound(X, X) = X % 165.86/165.36 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 165.86/165.36 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 165.86/165.36 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 165.86/165.36 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 165.86/165.36 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 165.86/165.36 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 165.86/165.36 greatest_lower_bound(a, b) = b % 165.86/165.36 least_upper_bound(inverse(a), inverse(b)) = inverse(b) ==> \bottom % 165.86/165.36 % 165.86/165.36 This holds because % 165.86/165.36 % 165.86/165.36 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 165.86/165.36 % 165.86/165.36 E: % 165.86/165.36 f1(inverse(b)) = false__ % 165.86/165.36 f1(least_upper_bound(inverse(a), inverse(b))) = true__ % 165.86/165.36 greatest_lower_bound(X, X) = X % 165.86/165.36 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 165.86/165.36 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 165.86/165.36 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 165.86/165.36 greatest_lower_bound(a, b) = b % 165.86/165.36 least_upper_bound(X, X) = X % 165.86/165.36 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 165.86/165.36 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 165.86/165.36 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 165.86/165.36 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 165.86/165.36 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 165.86/165.36 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 165.86/165.36 multiply(identity, X) = X % 165.86/165.36 multiply(inverse(X), X) = identity % 165.86/165.36 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 165.86/165.36 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 165.86/165.36 G: % 165.86/165.36 true__ = false__ % 165.86/165.36 % 165.86/165.36 This holds because % 165.86/165.36 % 165.86/165.36 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 165.86/165.36 % 165.86/165.36 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 165.86/165.36 greatest_lower_bound(X1, multiply(X0, X1)) = multiply(greatest_lower_bound(identity, inverse(X0)), multiply(X0, X1)) % 165.86/165.36 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, Y1), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, Y1)), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(Y1, X2)), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(least_upper_bound(X1, identity), Y1), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(a, Y0)) % 165.86/165.36 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, least_upper_bound(X1, a)), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, least_upper_bound(a, X1)), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(a, X0), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(X0, identity), a), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(identity, X0), a), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(X0, a)) = greatest_lower_bound(a, greatest_lower_bound(X0, greatest_lower_bound(a, Y0))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) = greatest_lower_bound(b, greatest_lower_bound(X0, Y0)) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) = greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(a, Y0))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) = greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(b, Y0))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) = greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(a, X0))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(b, Y0))) = greatest_lower_bound(Y0, greatest_lower_bound(b, X1)) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(Y1, b)) = greatest_lower_bound(Y1, greatest_lower_bound(b, greatest_lower_bound(Y1, Y0))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) = greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(Y0, a))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) = greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(b, Y0))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) = greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(X0, a))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) = greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(X0, b))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) = greatest_lower_bound(b, greatest_lower_bound(a, greatest_lower_bound(X0, Y0))) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(b, Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(b, Y0)) % 165.86/165.36 greatest_lower_bound(Y0, greatest_lower_bound(b, greatest_lower_bound(X1, Y0))) = greatest_lower_bound(Y0, greatest_lower_bound(X1, b)) % 165.86/165.36 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(a, inverse(b)), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), Y0) % 165.86/165.36 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, inverse(inverse(X0))), Y0) % 165.86/165.36 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(identity, multiply(X0, X1)), Y0) % 165.86/165.36 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(multiply(X0, X1), identity), Y0) % 165.86/165.36 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 165.86/165.36 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 165.86/165.36 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 165.86/165.36 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 165.86/165.36 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 165.86/165.36 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1) % 165.86/165.36 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1) % 165.86/165.36 greatest_lower_bound(Y1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), X1), Y1)) = multiply(greatest_lower_bound(X1, identity), Y1) % 165.86/165.36 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 165.86/165.36 greatest_lower_bound(a, greatest_lower_bound(X2, greatest_lower_bound(b, X1))) = greatest_lower_bound(b, greatest_lower_bound(X1, X2)) % 165.86/165.36 greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(a, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(b, X0)) % 165.86/165.36 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X2, a), Y0)) = greatest_lower_bound(Y0, b) % 165.86/165.36 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(X0, identity)) % 165.86/165.36 greatest_lower_bound(identity, greatest_lower_bound(multiply(b, inverse(a)), Y2)) = greatest_lower_bound(Y2, multiply(b, inverse(a))) % 165.86/165.36 greatest_lower_bound(identity, multiply(X0, inverse(X1))) = multiply(greatest_lower_bound(X0, X1), inverse(X1)) % 165.86/165.36 greatest_lower_bound(identity, multiply(X0, inverse(b))) = multiply(greatest_lower_bound(b, X0), inverse(b)) % 165.86/165.36 greatest_lower_bound(identity, multiply(X1, inverse(X0))) = multiply(greatest_lower_bound(X0, X1), inverse(X0)) % 165.86/165.36 greatest_lower_bound(identity, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1) % 165.86/165.36 greatest_lower_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), greatest_lower_bound(Y1, Y2)) % 165.86/165.36 greatest_lower_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), greatest_lower_bound(Y1, Y2)) % 165.86/165.36 greatest_lower_bound(least_upper_bound(a, X0), greatest_lower_bound(Y1, least_upper_bound(X0, a))) = greatest_lower_bound(Y1, least_upper_bound(a, X0)) % 165.86/165.36 greatest_lower_bound(least_upper_bound(a, X0), greatest_lower_bound(least_upper_bound(X0, a), Y2)) = greatest_lower_bound(Y2, least_upper_bound(a, X0)) % 165.86/165.36 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(X1, inverse(X0))) % 165.86/165.36 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(inverse(X0), X1)) % 165.86/165.36 greatest_lower_bound(multiply(Y0, Y1), identity) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1) % 165.86/165.36 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 165.86/165.36 least_upper_bound(X1, multiply(X0, X1)) = multiply(least_upper_bound(identity, inverse(X0)), multiply(X0, X1)) % 165.86/165.36 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, Y1), Y0)) % 165.86/165.36 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)), Y0)) % 165.86/165.36 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)), Y0)) % 165.86/165.36 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(multiply(greatest_lower_bound(X1, identity), Y1), Y0)) % 165.86/165.36 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(multiply(greatest_lower_bound(identity, X1), Y1), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(X0, b))) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(X0, greatest_lower_bound(X1, b)))) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(X0, greatest_lower_bound(b, X1)))) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(b, X0))) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, multiply(greatest_lower_bound(X0, identity), b))) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X0), b))) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, b), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(b, X1)), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(X0, identity), b), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(X1, identity), a), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(identity, X0), b), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(identity, X1), a), Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(b, least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(X0, b), least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(b, X1)), least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(b, X0), least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(multiply(greatest_lower_bound(X0, identity), b), least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, a) = least_upper_bound(multiply(greatest_lower_bound(identity, X0), b), least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, identity) = least_upper_bound(identity, least_upper_bound(multiply(b, inverse(a)), Y0)) % 165.86/165.36 least_upper_bound(Y0, inverse(b)) = least_upper_bound(inverse(b), least_upper_bound(inverse(a), Y0)) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(X0, a)) = least_upper_bound(a, least_upper_bound(X0, Y0)) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(X0, a)) = least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(a, X0))) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(X0, b)) = least_upper_bound(b, least_upper_bound(X0, least_upper_bound(b, Y0))) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(X1, least_upper_bound(a, Y0))) = least_upper_bound(Y0, least_upper_bound(a, X1)) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(Y1, a)) = least_upper_bound(Y1, least_upper_bound(a, least_upper_bound(Y1, Y0))) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(a, Y1)) = least_upper_bound(Y1, least_upper_bound(a, Y0)) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(a, least_upper_bound(X1, Y0))) = least_upper_bound(Y0, least_upper_bound(X1, a)) % 165.86/165.36 least_upper_bound(Y0, least_upper_bound(b, X0)) = least_upper_bound(b, least_upper_bound(X0, least_upper_bound(b, Y0))) % 165.86/165.36 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, inverse(inverse(X0))), Y0) % 165.86/165.36 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), Y0) % 165.86/165.36 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(identity, multiply(X0, X1)), Y0) % 165.86/165.36 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(multiply(X0, X1), identity), Y0) % 165.86/165.36 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1))) % 165.86/165.36 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0)) % 165.86/165.36 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1))) % 165.86/165.36 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0)) % 165.86/165.36 least_upper_bound(Y1, least_upper_bound(Y0, Y2)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 165.86/165.36 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1) % 165.86/165.36 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1) % 165.86/165.36 least_upper_bound(Y2, least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 165.86/165.36 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(X0, a))) = least_upper_bound(a, least_upper_bound(X0, X1)) % 165.86/165.36 least_upper_bound(b, greatest_lower_bound(least_upper_bound(X1, b), a)) = greatest_lower_bound(a, least_upper_bound(X1, b)) % 165.86/165.36 least_upper_bound(b, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, b)), a)) = greatest_lower_bound(a, least_upper_bound(X1, least_upper_bound(X2, b))) % 165.86/165.36 least_upper_bound(b, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(b, X2)), a)) = greatest_lower_bound(a, least_upper_bound(X1, least_upper_bound(b, X2))) % 165.86/165.36 least_upper_bound(b, greatest_lower_bound(multiply(least_upper_bound(X1, identity), b), a)) = greatest_lower_bound(a, multiply(least_upper_bound(X1, identity), b)) % 165.86/165.36 least_upper_bound(b, greatest_lower_bound(multiply(least_upper_bound(identity, X1), b), a)) = greatest_lower_bound(a, multiply(least_upper_bound(identity, X1), b)) % 165.86/165.39 least_upper_bound(b, least_upper_bound(X2, least_upper_bound(a, X1))) = least_upper_bound(X1, least_upper_bound(X2, a)) % 165.86/165.39 least_upper_bound(greatest_lower_bound(X0, a), least_upper_bound(greatest_lower_bound(b, X0), Y2)) = least_upper_bound(Y2, greatest_lower_bound(X0, a)) % 165.86/165.39 least_upper_bound(greatest_lower_bound(X0, b), least_upper_bound(greatest_lower_bound(X0, a), Y2)) = least_upper_bound(Y2, greatest_lower_bound(X0, a)) % 165.86/165.39 least_upper_bound(greatest_lower_bound(Y0, b), least_upper_bound(multiply(greatest_lower_bound(false__, identity), greatest_lower_bound(Y0, b)), greatest_lower_bound(Y0, a))) = greatest_lower_bound(a, Y0) % 165.86/165.39 least_upper_bound(greatest_lower_bound(a, X0), least_upper_bound(Y1, greatest_lower_bound(X0, b))) = least_upper_bound(Y1, greatest_lower_bound(a, X0)) % 165.86/165.39 least_upper_bound(greatest_lower_bound(a, X0), least_upper_bound(greatest_lower_bound(X0, b), Y2)) = least_upper_bound(Y2, greatest_lower_bound(a, X0)) % 165.86/165.39 least_upper_bound(greatest_lower_bound(b, X0), least_upper_bound(greatest_lower_bound(a, X0), Y2)) = least_upper_bound(Y2, greatest_lower_bound(a, X0)) % 165.86/165.39 least_upper_bound(greatest_lower_bound(b, Y0), greatest_lower_bound(Y0, a)) = greatest_lower_bound(a, Y0) % 165.86/165.39 least_upper_bound(greatest_lower_bound(b, Y1), least_upper_bound(greatest_lower_bound(Y1, b), Y2)) = least_upper_bound(Y2, greatest_lower_bound(b, Y1)) % 165.86/165.39 least_upper_bound(identity, least_upper_bound(X0, least_upper_bound(identity, Y2))) = least_upper_bound(Y2, least_upper_bound(X0, identity)) % 165.86/165.39 least_upper_bound(identity, least_upper_bound(multiply(a, inverse(b)), Y2)) = least_upper_bound(Y2, multiply(a, inverse(b))) % 165.86/165.39 least_upper_bound(identity, least_upper_bound(multiply(inverse(b), a), Y2)) = least_upper_bound(Y2, multiply(inverse(b), a)) % 165.86/165.39 least_upper_bound(identity, multiply(X0, inverse(X1))) = multiply(least_upper_bound(X0, X1), inverse(X1)) % 165.86/165.39 least_upper_bound(identity, multiply(X0, inverse(a))) = multiply(least_upper_bound(a, X0), inverse(a)) % 165.86/165.39 least_upper_bound(identity, multiply(X1, inverse(X0))) = multiply(least_upper_bound(X0, X1), inverse(X0)) % 165.86/165.39 least_upper_bound(identity, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1) % 165.86/165.39 least_upper_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), least_upper_bound(Y1, Y2)) % 165.86/165.39 least_upper_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), least_upper_bound(Y1, Y2)) % 165.86/165.39 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(X1, inverse(X0))) % 165.86/165.39 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(inverse(X0), X1)) % 165.86/165.39 least_upper_bound(multiply(Y0, Y1), identity) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1) % 165.86/165.39 multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1)) % 165.86/165.39 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1)) % 165.86/165.39 multiply(greatest_lower_bound(X1, identity), greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(X1, greatest_lower_bound(Y0, Y1)))) % 165.86/165.39 multiply(greatest_lower_bound(identity, X1), greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(X1, greatest_lower_bound(Y0, Y1)))) % 165.86/165.39 multiply(least_upper_bound(X1, identity), least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, multiply(X1, least_upper_bound(Y0, Y1)))) % 165.86/165.39 multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1)) % 165.86/165.39 multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1)) % 165.86/165.39 multiply(least_upper_bound(identity, X1), least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, multiply(X1, least_upper_bound(Y0, Y1)))) % 165.86/165.39 f1(inverse(b)) -> false__ % 165.86/165.39 f1(least_upper_bound(inverse(a), inverse(b))) -> true__ % 165.86/165.39 f1(least_upper_bound(inverse(b), inverse(a))) -> true__ % 165.86/165.39 greatest_lower_bound(X, X) -> X % 165.86/165.39 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X % 165.86/165.39 greatest_lower_bound(X0, greatest_lower_bound(a, least_upper_bound(Y1, greatest_lower_bound(a, X0)))) -> greatest_lower_bound(X0, a) % 165.86/165.39 greatest_lower_bound(X0, greatest_lower_bound(inverse(a), least_upper_bound(Y1, inverse(b)))) -> greatest_lower_bound(X0, inverse(a)) % 165.86/165.39 greatest_lower_bound(X1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(X1, false__)), inverse(multiply(inverse(X1), least_upper_bound(Y1, identity))))) -> inverse(multiply(inverse(X1), least_upper_bound(Y1, identity))) % 165.86/165.39 greatest_lower_bound(X1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(X1, false__)), inverse(multiply(inverse(X1), least_upper_bound(identity, Y1))))) -> inverse(multiply(inverse(X1), least_upper_bound(identity, Y1))) % 165.86/165.39 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(Y1)), X1)) -> multiply(greatest_lower_bound(Y1, identity), multiply(inverse(Y1), X1)) % 165.86/165.39 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(Y1)), X1)) -> multiply(greatest_lower_bound(identity, Y1), multiply(inverse(Y1), X1)) % 165.86/165.39 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(least_upper_bound(Y1, identity))), X1)) -> multiply(inverse(least_upper_bound(Y1, identity)), X1) % 165.86/165.39 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(least_upper_bound(identity, Y1))), X1)) -> multiply(inverse(least_upper_bound(identity, Y1)), X1) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(greatest_lower_bound(Y0, Y1), X1))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(Y2, least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y2) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(b, Y0)) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(a, X1), Y0))) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, Y0), Y2)) -> greatest_lower_bound(Y0, Y2) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(Y0, X1), Y2)) -> greatest_lower_bound(Y0, Y2) % 165.86/165.39 greatest_lower_bound(Y0, greatest_lower_bound(multiply(least_upper_bound(identity, X1), Y0), Y2)) -> greatest_lower_bound(Y0, Y2) % 165.86/165.39 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y0))) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y0, X2))) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, Y0)))) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(Y0, X2)))) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y0))) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y0))) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X1)), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 165.86/165.39 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 165.86/165.39 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 165.86/165.39 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y0)) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y0)) -> Y0 % 165.86/165.39 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0 % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, Y1))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y1)))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y1, X2)))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(Y1, X1))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y1))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y1))) -> greatest_lower_bound(Y0, Y1) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), X1)) -> greatest_lower_bound(Y1, X1) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)) % 165.86/165.39 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)) % 165.86/165.39 greatest_lower_bound(Y1, multiply(a, multiply(inverse(b), Y1))) -> Y1 % 165.86/165.39 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1) % 165.86/165.39 greatest_lower_bound(Y1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1) % 165.86/165.39 greatest_lower_bound(Y1, multiply(inverse(b), multiply(a, Y1))) -> Y1 % 165.86/165.39 greatest_lower_bound(a, b) -> b % 165.86/165.39 greatest_lower_bound(a, greatest_lower_bound(X1, greatest_lower_bound(X2, b))) -> greatest_lower_bound(b, greatest_lower_bound(X1, X2)) % 165.86/165.39 greatest_lower_bound(a, greatest_lower_bound(X1, greatest_lower_bound(b, X2))) -> greatest_lower_bound(b, greatest_lower_bound(X1, X2)) % 165.86/165.39 greatest_lower_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(X0, a))) -> greatest_lower_bound(Y0, greatest_lower_bound(X0, a)) % 165.86/165.39 greatest_lower_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(b, X0))) -> greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) % 165.86/165.39 greatest_lower_bound(a, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(Y1, a) % 165.86/165.39 greatest_lower_bound(a, greatest_lower_bound(b, Y2)) -> greatest_lower_bound(b, Y2) % 165.86/165.39 greatest_lower_bound(a, multiply(greatest_lower_bound(X1, identity), b)) -> multiply(greatest_lower_bound(identity, X1), b) % 165.86/165.39 greatest_lower_bound(a, multiply(greatest_lower_bound(identity, X1), b)) -> multiply(greatest_lower_bound(identity, X1), b) % 165.86/165.39 greatest_lower_bound(b, a) -> b % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X0, b)) -> greatest_lower_bound(X0, b) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X0, b)) -> greatest_lower_bound(b, X0) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(multiply(least_upper_bound(false__, identity), b), greatest_lower_bound(X0, greatest_lower_bound(multiply(least_upper_bound(false__, identity), X0), a))))) -> greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(false__, identity), b), X0)) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X0, least_upper_bound(Y1, a))) -> greatest_lower_bound(b, X0) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X0, least_upper_bound(Y1, greatest_lower_bound(a, X0)))) -> greatest_lower_bound(b, X0) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X1, greatest_lower_bound(X2, a))) -> greatest_lower_bound(X1, greatest_lower_bound(X2, b)) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X1, greatest_lower_bound(X2, a))) -> greatest_lower_bound(b, greatest_lower_bound(X1, X2)) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(X1, greatest_lower_bound(a, X2))) -> greatest_lower_bound(b, greatest_lower_bound(X1, X2)) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, a)) -> greatest_lower_bound(b, Y0) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(X0, b))) -> greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(a, X0))) -> greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(X0, least_upper_bound(X1, a)))) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(X0, least_upper_bound(a, X1)))) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(a, X0))) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, multiply(least_upper_bound(X0, identity), a))) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X0), a))) -> greatest_lower_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(a, Y0)) -> greatest_lower_bound(b, Y0) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(a, greatest_lower_bound(X0, Y2))) -> greatest_lower_bound(b, greatest_lower_bound(X0, Y2)) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X2, a), Y0)) -> greatest_lower_bound(b, Y0) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(a, Y1), Y0)) -> greatest_lower_bound(b, Y0) % 165.86/165.39 greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(false__, identity), b), X0)) -> greatest_lower_bound(b, X0) % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(X0, a)) -> b % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(X1, least_upper_bound(a, X2))) -> b % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, a)))) -> b % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(Y0, least_upper_bound(X1, least_upper_bound(a, X2)))) -> b % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), a))) -> b % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), a))) -> b % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(Y1, least_upper_bound(X0, a))) -> b % 165.86/165.39 greatest_lower_bound(b, least_upper_bound(a, X1)) -> b % 165.86/165.39 greatest_lower_bound(b, multiply(greatest_lower_bound(X1, identity), a)) -> greatest_lower_bound(b, multiply(X1, a)) % 165.86/165.39 greatest_lower_bound(b, multiply(greatest_lower_bound(identity, X1), a)) -> greatest_lower_bound(b, multiply(X1, a)) % 165.86/165.39 greatest_lower_bound(b, multiply(inverse(b), multiply(a, a))) -> b % 165.86/165.39 greatest_lower_bound(b, multiply(least_upper_bound(X1, identity), a)) -> b % 165.86/165.39 greatest_lower_bound(b, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), a)) -> b % 165.86/165.39 greatest_lower_bound(b, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), a)) -> b % 165.86/165.39 greatest_lower_bound(b, multiply(least_upper_bound(identity, X1), a)) -> b % 165.86/165.39 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z)) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) -> greatest_lower_bound(X0, greatest_lower_bound(identity, Y2)) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(X0, identity)) -> greatest_lower_bound(X0, identity) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(a, inverse(b)))) -> greatest_lower_bound(Y0, identity) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(b), a))) -> greatest_lower_bound(Y0, identity) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(Y1, identity)) -> greatest_lower_bound(identity, Y1) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(multiply(a, inverse(b)), Y2)) -> greatest_lower_bound(identity, Y2) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(multiply(b, inverse(a)), Y2)) -> greatest_lower_bound(multiply(b, inverse(a)), Y2) % 165.86/165.39 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y2)) -> greatest_lower_bound(identity, Y2) % 165.86/165.39 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(Y1, identity), inverse(Y1)) % 165.86/165.39 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(identity, Y1), inverse(Y1)) % 165.86/165.39 greatest_lower_bound(identity, inverse(identity)) -> identity % 165.86/165.39 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, identity))) -> inverse(least_upper_bound(Y1, identity)) % 165.86/165.39 greatest_lower_bound(identity, inverse(least_upper_bound(identity, Y1))) -> inverse(least_upper_bound(identity, Y1)) % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(Y0, inverse(identity))) -> identity % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(greatest_lower_bound(identity, inverse(identity))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(inverse(identity)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(least_upper_bound(identity, inverse(identity))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)) -> identity % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(inverse(identity), Y1)) -> identity % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(inverse(inverse(identity)), Y1)) -> identity % 165.86/165.39 greatest_lower_bound(identity, least_upper_bound(inverse(least_upper_bound(identity, inverse(identity))), Y1)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(X1, inverse(X0)))) -> multiply(X0, greatest_lower_bound(X1, inverse(X0))) % 165.86/165.39 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), X1))) -> multiply(X0, greatest_lower_bound(inverse(X0), X1)) % 165.86/165.39 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(X0)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(inverse(inverse(X0)))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(X0), Y1))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(inverse(inverse(X0))), Y1))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1))) % 165.86/165.39 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1))) % 165.86/165.39 greatest_lower_bound(identity, multiply(X1, multiply(X0, least_upper_bound(Y1, multiply(inverse(X0), inverse(X1)))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X1, multiply(X0, least_upper_bound(multiply(inverse(X0), inverse(X1)), Y1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X1, multiply(inverse(X0), least_upper_bound(Y1, multiply(X0, inverse(X1)))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(X1, multiply(inverse(X0), least_upper_bound(multiply(X0, inverse(X1)), Y1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, Y0)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(Y0, X1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(a, inverse(b))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, greatest_lower_bound(X1, b))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, greatest_lower_bound(b, X1))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(b, X0)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(a, inverse(multiply(greatest_lower_bound(X0, identity), b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(a, inverse(multiply(greatest_lower_bound(identity, X0), b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, X1), inverse(X0))) -> multiply(greatest_lower_bound(X0, X1), inverse(X0)) % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, X1), inverse(X1))) -> multiply(greatest_lower_bound(X0, X1), inverse(X1)) % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, a), inverse(greatest_lower_bound(X0, b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, a), inverse(greatest_lower_bound(b, X0)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, b), inverse(a))) -> multiply(greatest_lower_bound(X0, b), inverse(a)) % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> multiply(greatest_lower_bound(X0, inverse(X1)), X1) % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(a, X0), inverse(greatest_lower_bound(X0, b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(a, X0), inverse(greatest_lower_bound(b, X0)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(a))) -> multiply(greatest_lower_bound(b, X0), inverse(a)) % 165.86/165.39 greatest_lower_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(b))) -> multiply(greatest_lower_bound(b, X0), inverse(b)) % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> multiply(inverse(X0), greatest_lower_bound(X0, X1)) % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X0), greatest_lower_bound(X1, X0))) -> multiply(inverse(X0), greatest_lower_bound(X1, X0)) % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X1), multiply(X0, least_upper_bound(Y1, multiply(inverse(X0), X1))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X1), multiply(X0, least_upper_bound(multiply(inverse(X0), X1), Y1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X1), multiply(inverse(X0), least_upper_bound(Y1, multiply(X0, X1))))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(X1), multiply(inverse(X0), least_upper_bound(multiply(X0, X1), Y1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(a), greatest_lower_bound(X0, b))) -> multiply(inverse(a), greatest_lower_bound(X0, b)) % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(a), greatest_lower_bound(b, X0))) -> multiply(inverse(a), greatest_lower_bound(b, X0)) % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), a)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(X0, a))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(X0, least_upper_bound(X1, a)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(X0, least_upper_bound(a, X1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(a, X0))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), multiply(inverse(b), multiply(a, a)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), multiply(inverse(b), multiply(a, b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), multiply(least_upper_bound(X0, identity), a))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(b), multiply(least_upper_bound(identity, X0), a))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X0, greatest_lower_bound(X1, b))), a)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X0, greatest_lower_bound(b, X1))), a)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(Y0, b)), a)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(b, X0)), a)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(multiply(greatest_lower_bound(X0, identity), b)), a)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(inverse(multiply(greatest_lower_bound(identity, X0), b)), a)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(X0, a), inverse(b))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(X0, a), inverse(least_upper_bound(a, X0)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(X0, identity), multiply(a, inverse(b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(X0, least_upper_bound(X1, a)), inverse(b))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(X0, least_upper_bound(a, X1)), inverse(b))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(X1, least_upper_bound(Y1, X2)), inverse(Y1))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, X0), inverse(X0))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(X1, X0)), multiply(inverse(X0), inverse(X1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(X1, inverse(X0))), multiply(X0, inverse(X1)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(inverse(X1), X0)), multiply(inverse(X0), X1))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(inverse(X1), inverse(X0))), multiply(X0, X1))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(Y1, Y0), inverse(Y1))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(a, X0), inverse(b))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(a, Y0), inverse(a))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(b, X0), inverse(least_upper_bound(X0, b)))) -> identity % 165.86/165.39 greatest_lower_bound(identity, multiply(least_upper_bound(identity, X0), multiply(a, inverse(b)))) -> identity % 165.86/165.39 greatest_lower_bound(inverse(X1), inverse(multiply(X1, least_upper_bound(Y1, identity)))) -> inverse(multiply(X1, least_upper_bound(Y1, identity))) % 165.86/165.39 greatest_lower_bound(inverse(X1), inverse(multiply(X1, least_upper_bound(identity, Y1)))) -> inverse(multiply(X1, least_upper_bound(identity, Y1))) % 165.86/165.39 greatest_lower_bound(inverse(a), least_upper_bound(Y1, inverse(b))) -> inverse(a) % 165.86/165.39 greatest_lower_bound(inverse(b), greatest_lower_bound(Y0, inverse(a))) -> greatest_lower_bound(Y0, inverse(a)) % 165.86/165.39 greatest_lower_bound(inverse(b), greatest_lower_bound(Y1, inverse(b))) -> greatest_lower_bound(Y1, inverse(b)) % 165.86/165.39 greatest_lower_bound(inverse(b), greatest_lower_bound(Y1, inverse(b))) -> greatest_lower_bound(inverse(b), Y1) % 165.86/165.39 greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y2)) -> greatest_lower_bound(inverse(a), Y2) % 165.86/165.39 greatest_lower_bound(inverse(b), greatest_lower_bound(multiply(least_upper_bound(false__, identity), inverse(b)), inverse(a))) -> inverse(a) % 165.86/165.39 greatest_lower_bound(inverse(b), inverse(a)) -> inverse(a) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, X1), least_upper_bound(X0, least_upper_bound(X1, Y1))) -> least_upper_bound(X0, X1) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(Y1, least_upper_bound(b, X0))) -> least_upper_bound(X0, b) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(b, X0)) -> least_upper_bound(X0, b) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(X0, a)) -> least_upper_bound(X0, greatest_lower_bound(X1, b)) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(a, X0)) -> least_upper_bound(X0, greatest_lower_bound(X1, b)) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(b, X1)), least_upper_bound(X0, a)) -> least_upper_bound(X0, greatest_lower_bound(b, X1)) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(b, X1)), least_upper_bound(Y1, least_upper_bound(X0, a))) -> least_upper_bound(X0, greatest_lower_bound(b, X1)) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, identity), least_upper_bound(Y1, least_upper_bound(identity, X0))) -> least_upper_bound(X0, identity) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X0, identity), least_upper_bound(identity, X0)) -> least_upper_bound(X0, identity) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X1, least_upper_bound(Y1, X2))) -> least_upper_bound(X1, X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X2, least_upper_bound(Y1, X1))) -> least_upper_bound(X1, X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, Y2)))) -> least_upper_bound(X1, X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(Y2, X2)))) -> least_upper_bound(X1, X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X2, least_upper_bound(Y2, X1)))) -> least_upper_bound(X1, X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, Y1), least_upper_bound(X1, greatest_lower_bound(X2, Y1))) -> least_upper_bound(X1, greatest_lower_bound(X2, Y1)) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, Y1), least_upper_bound(X1, greatest_lower_bound(Y1, X2))) -> least_upper_bound(X1, greatest_lower_bound(Y1, X2)) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, a), least_upper_bound(Y1, least_upper_bound(a, least_upper_bound(X1, Y2)))) -> least_upper_bound(X1, a) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, a), least_upper_bound(a, least_upper_bound(X1, Y1))) -> least_upper_bound(X1, a) % 165.86/165.39 greatest_lower_bound(least_upper_bound(X1, greatest_lower_bound(Y1, X2)), least_upper_bound(Y1, X1)) -> least_upper_bound(X1, greatest_lower_bound(Y1, X2)) % 165.86/165.39 greatest_lower_bound(least_upper_bound(Y0, a), least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0) % 165.86/165.39 greatest_lower_bound(least_upper_bound(Y1, X2), least_upper_bound(greatest_lower_bound(X1, Y1), X2)) -> least_upper_bound(greatest_lower_bound(X1, Y1), X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(Y1, X2), least_upper_bound(greatest_lower_bound(Y1, X1), X2)) -> least_upper_bound(greatest_lower_bound(Y1, X1), X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(X0, a)) -> least_upper_bound(a, X0) % 165.86/165.39 greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(Y1, least_upper_bound(X0, a))) -> least_upper_bound(a, X0) % 165.86/165.39 greatest_lower_bound(least_upper_bound(a, X1), least_upper_bound(X1, least_upper_bound(a, Y1))) -> least_upper_bound(a, X1) % 165.86/165.39 greatest_lower_bound(least_upper_bound(a, X1), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(a, Y2)))) -> least_upper_bound(a, X1) % 165.86/165.39 greatest_lower_bound(least_upper_bound(b, Y0), least_upper_bound(Y0, b)) -> least_upper_bound(Y0, b) % 165.86/165.39 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X0, b), X1), least_upper_bound(X1, a)) -> least_upper_bound(greatest_lower_bound(X0, b), X1) % 165.86/165.39 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1, Y1), X2), least_upper_bound(X2, Y1)) -> least_upper_bound(greatest_lower_bound(X1, Y1), X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1, Y2), X2), least_upper_bound(Y1, least_upper_bound(X2, Y2))) -> least_upper_bound(greatest_lower_bound(X1, Y2), X2) % 165.86/165.39 greatest_lower_bound(least_upper_bound(greatest_lower_bound(b, X0), X1), least_upper_bound(a, X1)) -> least_upper_bound(greatest_lower_bound(b, X0), X1) % 165.86/165.39 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z)) % 165.86/165.39 greatest_lower_bound(multiply(X0, greatest_lower_bound(X1, X2)), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X0, X2), Y2)) % 165.86/165.39 greatest_lower_bound(multiply(X0, inverse(least_upper_bound(X0, X1))), least_upper_bound(Y1, identity)) -> multiply(X0, inverse(least_upper_bound(X0, X1))) % 165.86/165.39 greatest_lower_bound(multiply(X0, inverse(least_upper_bound(X1, X0))), least_upper_bound(Y1, identity)) -> multiply(X0, inverse(least_upper_bound(X1, X0))) % 165.86/165.39 greatest_lower_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(greatest_lower_bound(multiply(X0, X1), Y2), Y1) % 165.86/165.39 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y2))) -> multiply(X1, Y2) % 165.86/165.39 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y2))) -> multiply(X1, Y2) % 165.86/165.39 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X) % 165.86/165.39 greatest_lower_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(greatest_lower_bound(Y0, multiply(X0, X1)), Y1) % 165.86/165.39 greatest_lower_bound(multiply(b, inverse(a)), greatest_lower_bound(multiply(X0, inverse(a)), least_upper_bound(Y1, identity))) -> multiply(greatest_lower_bound(b, X0), inverse(a)) % 165.86/165.39 greatest_lower_bound(multiply(b, inverse(a)), least_upper_bound(Y1, identity)) -> multiply(b, inverse(a)) % 165.86/165.39 greatest_lower_bound(multiply(b, inverse(least_upper_bound(X0, a))), least_upper_bound(Y1, identity)) -> multiply(b, inverse(least_upper_bound(X0, a))) % 165.86/165.39 greatest_lower_bound(multiply(b, inverse(least_upper_bound(a, X0))), least_upper_bound(Y1, identity)) -> multiply(b, inverse(least_upper_bound(a, X0))) % 165.86/165.39 greatest_lower_bound(multiply(b, multiply(inverse(a), Y2)), least_upper_bound(Y1, Y2)) -> multiply(b, multiply(inverse(a), Y2)) % 165.86/165.39 greatest_lower_bound(multiply(greatest_lower_bound(X0, X2), X1), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X2, X1), Y2)) % 165.86/165.39 greatest_lower_bound(multiply(inverse(a), X0), greatest_lower_bound(multiply(inverse(a), b), least_upper_bound(Y1, identity))) -> multiply(inverse(a), greatest_lower_bound(X0, b)) % 165.86/165.39 greatest_lower_bound(multiply(inverse(a), b), greatest_lower_bound(multiply(inverse(a), X0), least_upper_bound(Y1, identity))) -> multiply(inverse(a), greatest_lower_bound(b, X0)) % 165.86/165.39 inverse(greatest_lower_bound(identity, inverse(identity))) -> identity % 165.86/165.39 inverse(identity) -> identity % 165.86/165.39 inverse(inverse(Y0)) -> Y0 % 165.86/165.39 inverse(inverse(identity)) -> identity % 165.86/165.39 inverse(least_upper_bound(identity, inverse(identity))) -> identity % 165.86/165.39 inverse(multiply(X1, Y0)) -> multiply(inverse(Y0), inverse(X1)) % 165.86/165.39 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1)) % 165.86/165.39 inverse(multiply(inverse(X1), Y0)) -> multiply(inverse(Y0), X1) % 165.86/165.39 inverse(multiply(inverse(X1), inverse(Y0))) -> multiply(Y0, X1) % 165.86/165.39 least_upper_bound(X, X) -> X % 165.86/165.39 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X % 165.86/165.39 least_upper_bound(X0, least_upper_bound(a, least_upper_bound(X1, greatest_lower_bound(Y1, b)))) -> least_upper_bound(X0, least_upper_bound(a, X1)) % 165.86/165.39 least_upper_bound(X1, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X1, false__)), inverse(multiply(inverse(X1), greatest_lower_bound(Y1, identity))))) -> inverse(multiply(inverse(X1), greatest_lower_bound(Y1, identity))) % 165.86/165.39 least_upper_bound(X1, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X1, false__)), inverse(multiply(inverse(X1), greatest_lower_bound(identity, Y1))))) -> inverse(multiply(inverse(X1), greatest_lower_bound(identity, Y1))) % 165.86/165.39 least_upper_bound(X1, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X1, false__)), multiply(inverse(Y1), X1))) -> multiply(least_upper_bound(identity, Y1), multiply(inverse(Y1), X1)) % 165.86/165.39 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(Y1, identity), multiply(inverse(Y1), X1)) % 165.86/165.39 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(identity, Y1), multiply(inverse(Y1), X1)) % 165.86/165.39 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(Y1, identity)), X1)) -> multiply(inverse(greatest_lower_bound(Y1, identity)), X1) % 165.86/165.39 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(identity, Y1)), X1)) -> multiply(inverse(greatest_lower_bound(identity, Y1)), X1) % 165.86/165.39 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(Y1)), X1)) -> multiply(least_upper_bound(Y1, identity), multiply(inverse(Y1), X1)) % 165.86/165.39 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(Y1)), X1)) -> multiply(least_upper_bound(identity, Y1), multiply(inverse(Y1), X1)) % 165.86/165.39 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(greatest_lower_bound(Y1, identity))), X1)) -> multiply(inverse(greatest_lower_bound(Y1, identity)), X1) % 165.86/165.39 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(greatest_lower_bound(identity, Y1))), X1)) -> multiply(inverse(greatest_lower_bound(identity, Y1)), X1) % 165.86/165.39 least_upper_bound(X2, least_upper_bound(a, least_upper_bound(X2, least_upper_bound(greatest_lower_bound(X1, a), X2)))) -> least_upper_bound(a, X2) % 165.86/165.39 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))) -> Y0 % 165.86/165.39 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))) -> Y0 % 165.86/165.39 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0 % 165.86/165.39 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0)))) -> Y0 % 165.86/165.39 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2)))) -> Y0 % 165.86/165.40 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(b, Y0)))) -> Y0 % 165.86/165.40 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y0))) -> Y0 % 165.86/165.40 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y0))) -> Y0 % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(least_upper_bound(Y0, Y1), X1))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(Y2, greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, Y2) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(a, Y0)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(a, least_upper_bound(greatest_lower_bound(X1, b), Y0))) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(X1, b), least_upper_bound(a, Y0))) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y0, X1), Y2)) -> least_upper_bound(Y0, Y2) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y1, Y0), Y2)) -> least_upper_bound(Y0, Y2) % 165.86/165.40 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(b, X1), least_upper_bound(a, Y0))) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y0)) -> Y0 % 165.86/165.40 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y0)) -> Y0 % 165.86/165.40 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> Y0 % 165.86/165.40 least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> Y0 % 165.86/165.40 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 165.86/165.40 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, multiply(X1, greatest_lower_bound(Y0, Y1))) % 165.86/165.40 least_upper_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 165.86/165.40 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 165.86/165.40 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, multiply(X1, greatest_lower_bound(Y0, Y1))) % 165.86/165.40 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, Y1))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(Y1, X1))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1))) -> least_upper_bound(Y0, Y1) % 165.86/165.40 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2) % 165.86/165.40 least_upper_bound(Y1, multiply(b, multiply(inverse(a), Y1))) -> Y1 % 165.86/165.40 least_upper_bound(Y1, multiply(inverse(b), multiply(a, Y1))) -> multiply(inverse(b), multiply(a, Y1)) % 165.86/165.40 least_upper_bound(Y1, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1)) -> multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1) % 165.86/165.40 least_upper_bound(Y1, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1)) -> multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1) % 165.86/165.40 least_upper_bound(Y1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), multiply(inverse(b), a)), Y1)) -> multiply(inverse(b), multiply(a, Y1)) % 165.86/165.40 least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y1)) -> multiply(least_upper_bound(identity, X1), Y1) % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(X1, greatest_lower_bound(X2, b))) -> a % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(Y0, b)) -> a % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, b)))) -> a % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(b, X2)))) -> a % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), b))) -> a % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), b))) -> a % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> a % 165.86/165.40 least_upper_bound(a, greatest_lower_bound(b, X0)) -> a % 165.86/165.40 least_upper_bound(a, least_upper_bound(X0, greatest_lower_bound(Y1, b))) -> least_upper_bound(a, X0) % 165.86/165.40 least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(b, Y1))) -> least_upper_bound(a, Y0) % 165.86/165.40 least_upper_bound(a, least_upper_bound(Y1, a)) -> least_upper_bound(Y1, a) % 165.86/165.40 least_upper_bound(a, least_upper_bound(greatest_lower_bound(Y1, b), Y0)) -> least_upper_bound(a, Y0) % 165.86/165.40 least_upper_bound(a, least_upper_bound(greatest_lower_bound(b, X0), Y2)) -> least_upper_bound(a, Y2) % 165.86/165.40 least_upper_bound(a, least_upper_bound(multiply(X0, a), greatest_lower_bound(Y1, b))) -> multiply(least_upper_bound(X0, identity), a) % 165.86/165.40 least_upper_bound(a, least_upper_bound(multiply(X0, a), greatest_lower_bound(Y1, b))) -> multiply(least_upper_bound(identity, X0), a) % 165.86/165.40 least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(false__, identity), a), X1)) -> least_upper_bound(a, X1) % 165.86/165.40 least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(false__, identity), a), greatest_lower_bound(Y0, greatest_lower_bound(b, Y1)))) -> a % 165.86/165.40 least_upper_bound(a, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), b)) -> a % 165.86/165.40 least_upper_bound(a, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), b)) -> a % 165.86/165.40 least_upper_bound(a, multiply(greatest_lower_bound(X1, identity), b)) -> a % 165.86/165.40 least_upper_bound(a, multiply(greatest_lower_bound(identity, X1), b)) -> a % 165.86/165.40 least_upper_bound(b, a) -> a % 165.86/165.40 least_upper_bound(b, greatest_lower_bound(a, least_upper_bound(X1, b))) -> greatest_lower_bound(a, least_upper_bound(X1, b)) % 165.86/165.40 least_upper_bound(b, greatest_lower_bound(a, least_upper_bound(b, X1))) -> greatest_lower_bound(a, least_upper_bound(b, X1)) % 165.86/165.40 least_upper_bound(b, greatest_lower_bound(least_upper_bound(X1, b), a)) -> greatest_lower_bound(least_upper_bound(X1, b), a) % 165.86/165.40 least_upper_bound(b, greatest_lower_bound(least_upper_bound(b, X1), a)) -> greatest_lower_bound(least_upper_bound(b, X1), a) % 165.86/165.40 least_upper_bound(b, least_upper_bound(X0, least_upper_bound(a, X1))) -> least_upper_bound(X0, least_upper_bound(a, X1)) % 165.86/165.40 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(X2, a))) -> least_upper_bound(X1, least_upper_bound(X2, a)) % 165.86/165.40 least_upper_bound(b, least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(X0, b))) -> least_upper_bound(Y0, least_upper_bound(X0, b)) % 165.86/165.40 least_upper_bound(b, least_upper_bound(Y1, b)) -> least_upper_bound(Y1, b) % 165.86/165.40 least_upper_bound(b, least_upper_bound(Y1, b)) -> least_upper_bound(b, Y1) % 165.86/165.40 least_upper_bound(b, least_upper_bound(a, Y2)) -> least_upper_bound(a, Y2) % 165.86/165.40 least_upper_bound(b, multiply(inverse(b), multiply(a, a))) -> multiply(inverse(b), multiply(a, a)) % 165.86/165.40 least_upper_bound(b, multiply(least_upper_bound(X0, identity), a)) -> multiply(least_upper_bound(X0, identity), a) % 165.86/165.40 least_upper_bound(b, multiply(least_upper_bound(identity, X0), a)) -> multiply(least_upper_bound(identity, X0), a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, X1), greatest_lower_bound(X0, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X0, X1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(X0, b))) -> greatest_lower_bound(X0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> greatest_lower_bound(X0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(X0, a)) -> greatest_lower_bound(X0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> greatest_lower_bound(X0, b) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, b) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, b), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, b), least_upper_bound(multiply(greatest_lower_bound(false__, identity), greatest_lower_bound(X0, b)), greatest_lower_bound(X0, a))) -> greatest_lower_bound(X0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(b, X1)), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, identity), greatest_lower_bound(Y1, greatest_lower_bound(identity, X0))) -> greatest_lower_bound(X0, identity) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, identity), greatest_lower_bound(identity, X0)) -> greatest_lower_bound(X0, identity) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X0, least_upper_bound(X1, a)), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, least_upper_bound(X1, a)) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))) -> greatest_lower_bound(X1, X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))) -> greatest_lower_bound(X1, X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y2)))) -> greatest_lower_bound(X1, X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y2, X2)))) -> greatest_lower_bound(X1, X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X2, greatest_lower_bound(Y2, X1)))) -> greatest_lower_bound(X1, X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, Y1), greatest_lower_bound(X1, least_upper_bound(X2, Y1))) -> greatest_lower_bound(X1, least_upper_bound(X2, Y1)) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, Y1), greatest_lower_bound(X1, least_upper_bound(Y1, X2))) -> greatest_lower_bound(X1, least_upper_bound(Y1, X2)) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, b), greatest_lower_bound(Y1, greatest_lower_bound(b, greatest_lower_bound(X1, Y2)))) -> greatest_lower_bound(X1, b) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, b), greatest_lower_bound(b, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X1, b) % 165.86/165.40 least_upper_bound(greatest_lower_bound(X1, least_upper_bound(Y1, X2)), greatest_lower_bound(Y1, X1)) -> greatest_lower_bound(X1, least_upper_bound(Y1, X2)) % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, b), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, b), greatest_lower_bound(a, Y0)) -> greatest_lower_bound(a, Y0) % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, b))), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(b, X2))), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, greatest_lower_bound(Y1, b)), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, greatest_lower_bound(b, Y1)), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), b)), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), b)), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y1, X2), greatest_lower_bound(least_upper_bound(X1, Y1), X2)) -> greatest_lower_bound(least_upper_bound(X1, Y1), X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y1, X2), greatest_lower_bound(least_upper_bound(Y1, X1), X2)) -> greatest_lower_bound(least_upper_bound(Y1, X1), X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(Y1, b), least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0) % 165.86/165.40 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(X0, b)) -> greatest_lower_bound(a, X0) % 165.86/165.40 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(Y1, greatest_lower_bound(X0, b))) -> greatest_lower_bound(a, X0) % 165.86/165.40 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> greatest_lower_bound(a, X0) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(a, X0)) -> greatest_lower_bound(a, X0) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, X0), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, X1), greatest_lower_bound(X1, greatest_lower_bound(b, Y1))) -> greatest_lower_bound(b, X1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, X1), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(b, Y2)))) -> greatest_lower_bound(b, X1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, X1), greatest_lower_bound(least_upper_bound(X0, a), X1)) -> greatest_lower_bound(least_upper_bound(X0, a), X1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, Y0), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, Y0), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, Y1), greatest_lower_bound(Y1, b)) -> greatest_lower_bound(b, Y1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, Y1), least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0) % 165.86/165.40 least_upper_bound(greatest_lower_bound(b, Y2), greatest_lower_bound(Y1, greatest_lower_bound(Y2, b))) -> greatest_lower_bound(b, Y2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(false__, b), a) -> a % 165.86/165.40 least_upper_bound(greatest_lower_bound(false__, b), least_upper_bound(a, X1)) -> least_upper_bound(a, X1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(false__, b), multiply(least_upper_bound(X1, identity), a)) -> multiply(least_upper_bound(identity, X1), a) % 165.86/165.40 least_upper_bound(greatest_lower_bound(least_upper_bound(X0, a), X1), greatest_lower_bound(X1, b)) -> greatest_lower_bound(least_upper_bound(X0, a), X1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(least_upper_bound(X0, a), X1), greatest_lower_bound(Y1, greatest_lower_bound(X1, b))) -> greatest_lower_bound(least_upper_bound(X0, a), X1) % 165.86/165.40 least_upper_bound(greatest_lower_bound(least_upper_bound(X1, Y1), X2), greatest_lower_bound(X2, Y1)) -> greatest_lower_bound(least_upper_bound(X1, Y1), X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(least_upper_bound(X1, Y2), X2), greatest_lower_bound(Y1, greatest_lower_bound(X2, Y2))) -> greatest_lower_bound(least_upper_bound(X1, Y2), X2) % 165.86/165.40 least_upper_bound(greatest_lower_bound(least_upper_bound(a, X0), X1), greatest_lower_bound(X1, b)) -> greatest_lower_bound(least_upper_bound(a, X0), X1) % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(Y0, inverse(identity))) -> identity % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(Y1, inverse(greatest_lower_bound(identity, inverse(identity))))) -> identity % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(Y1, inverse(inverse(identity)))) -> identity % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(Y1, inverse(least_upper_bound(identity, inverse(identity))))) -> identity % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)) -> identity % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(inverse(identity), Y1)) -> identity % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(inverse(inverse(identity)), Y1)) -> identity % 165.86/165.40 least_upper_bound(identity, greatest_lower_bound(inverse(least_upper_bound(identity, inverse(identity))), Y1)) -> identity % 165.86/165.40 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(Y1, identity), inverse(Y1)) % 165.86/165.40 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(identity, Y1), inverse(Y1)) % 165.86/165.40 least_upper_bound(identity, inverse(greatest_lower_bound(Y1, identity))) -> inverse(greatest_lower_bound(Y1, identity)) % 165.86/165.40 least_upper_bound(identity, inverse(greatest_lower_bound(identity, Y1))) -> inverse(greatest_lower_bound(identity, Y1)) % 165.86/165.40 least_upper_bound(identity, inverse(identity)) -> identity % 165.86/165.40 least_upper_bound(identity, least_upper_bound(X0, identity)) -> least_upper_bound(X0, identity) % 165.86/165.40 least_upper_bound(identity, least_upper_bound(X0, least_upper_bound(identity, Y2))) -> least_upper_bound(X0, least_upper_bound(identity, Y2)) % 165.86/165.40 least_upper_bound(identity, least_upper_bound(Y0, multiply(b, inverse(a)))) -> least_upper_bound(Y0, identity) % 165.86/165.40 least_upper_bound(identity, least_upper_bound(Y1, identity)) -> least_upper_bound(identity, Y1) % 165.86/165.40 least_upper_bound(identity, least_upper_bound(multiply(a, inverse(b)), Y2)) -> least_upper_bound(multiply(a, inverse(b)), Y2) % 165.86/165.40 least_upper_bound(identity, least_upper_bound(multiply(b, inverse(a)), Y2)) -> least_upper_bound(identity, Y2) % 165.86/165.40 least_upper_bound(identity, least_upper_bound(multiply(inverse(b), a), Y2)) -> least_upper_bound(multiply(inverse(b), a), Y2) % 165.86/165.40 least_upper_bound(identity, multiply(X0, greatest_lower_bound(Y1, inverse(X0)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(X0, greatest_lower_bound(Y1, inverse(inverse(inverse(X0)))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), Y1))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(X0, greatest_lower_bound(inverse(inverse(inverse(X0))), Y1))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(X0, least_upper_bound(X1, inverse(X0)))) -> multiply(X0, least_upper_bound(X1, inverse(X0))) % 165.86/165.40 least_upper_bound(identity, multiply(X0, least_upper_bound(inverse(X0), X1))) -> multiply(X0, least_upper_bound(inverse(X0), X1)) % 165.86/165.40 least_upper_bound(identity, multiply(X1, multiply(X0, greatest_lower_bound(Y1, multiply(inverse(X0), inverse(X1)))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(X1, multiply(X0, greatest_lower_bound(multiply(inverse(X0), inverse(X1)), Y1)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(X1, multiply(inverse(X0), greatest_lower_bound(Y1, multiply(X0, inverse(X1)))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(X1, multiply(inverse(X0), greatest_lower_bound(multiply(X0, inverse(X1)), Y1)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, Y0)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, least_upper_bound(X2, Y0))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, least_upper_bound(Y0, X2))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(Y0, X1)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(a, inverse(b))) -> multiply(a, inverse(b)) % 165.86/165.40 least_upper_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, b)))) -> multiply(a, inverse(greatest_lower_bound(X0, b))) % 165.86/165.40 least_upper_bound(identity, multiply(a, inverse(greatest_lower_bound(b, X0)))) -> multiply(a, inverse(greatest_lower_bound(b, X0))) % 165.86/165.40 least_upper_bound(identity, multiply(b, inverse(a))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(X0, a)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(X0, least_upper_bound(X1, a))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(X0, least_upper_bound(a, X1))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(a, X0)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(b, inverse(multiply(least_upper_bound(X0, identity), a)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(b, inverse(multiply(least_upper_bound(identity, X0), a)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X0, b), inverse(a))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X0, b), inverse(greatest_lower_bound(X0, a)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X0, b), inverse(greatest_lower_bound(a, X0)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), inverse(a))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X0, greatest_lower_bound(b, X1)), inverse(a))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X0, identity), multiply(b, inverse(a)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)), inverse(Y1))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, X0), inverse(X0))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, b), inverse(greatest_lower_bound(b, Y0)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(X1, X0)), multiply(inverse(X0), inverse(X1)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(X1, inverse(X0))), multiply(X0, inverse(X1)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(inverse(X1), X0)), multiply(inverse(X0), X1))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(inverse(X1), inverse(X0))), multiply(X0, X1))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(Y1, Y0), inverse(Y1))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(a))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(greatest_lower_bound(X0, a)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(greatest_lower_bound(X0, b)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(greatest_lower_bound(a, X0)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(b, Y0), inverse(b))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(greatest_lower_bound(identity, X0), multiply(b, inverse(a)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X0), greatest_lower_bound(X1, X0))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> multiply(inverse(X0), least_upper_bound(X0, X1)) % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> multiply(inverse(X0), least_upper_bound(X1, X0)) % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X1), multiply(X0, greatest_lower_bound(Y1, multiply(inverse(X0), X1))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X1), multiply(X0, greatest_lower_bound(multiply(inverse(X0), X1), Y1)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X1), multiply(inverse(X0), greatest_lower_bound(Y1, multiply(X0, X1))))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(X1), multiply(inverse(X0), greatest_lower_bound(multiply(X0, X1), Y1)))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(a), greatest_lower_bound(Y0, b))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(a), greatest_lower_bound(b, X0))) -> identity % 165.86/165.40 least_upper_bound(identity, multiply(inverse(b), a)) -> multiply(inverse(b), a) % 165.86/165.40 least_upper_bound(identity, multiply(inverse(b), least_upper_bound(X0, a))) -> multiply(inverse(b), least_upper_bound(X0, a)) % 165.86/165.40 least_upper_bound(identity, multiply(inverse(b), least_upper_bound(a, X0))) -> multiply(inverse(b), least_upper_bound(a, X0)) % 165.86/165.40 least_upper_bound(identity, multiply(inverse(greatest_lower_bound(X0, b)), a)) -> multiply(inverse(greatest_lower_bound(X0, b)), a) % 165.86/165.40 least_upper_bound(identity, multiply(inverse(greatest_lower_bound(b, X0)), a)) -> multiply(inverse(greatest_lower_bound(b, X0)), a) % 165.86/165.40 least_upper_bound(identity, multiply(least_upper_bound(X0, X1), inverse(X0))) -> multiply(least_upper_bound(X0, X1), inverse(X0)) % 165.86/165.40 least_upper_bound(identity, multiply(least_upper_bound(X0, X1), inverse(X1))) -> multiply(least_upper_bound(X0, X1), inverse(X1)) % 165.86/165.40 least_upper_bound(identity, multiply(least_upper_bound(X0, a), inverse(b))) -> multiply(least_upper_bound(X0, a), inverse(b)) % 165.86/165.40 least_upper_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> multiply(least_upper_bound(X0, inverse(X1)), X1) % 165.86/165.40 least_upper_bound(identity, multiply(least_upper_bound(a, X0), inverse(a))) -> multiply(least_upper_bound(a, X0), inverse(a)) % 165.86/165.40 least_upper_bound(identity, multiply(least_upper_bound(a, X0), inverse(b))) -> multiply(least_upper_bound(a, X0), inverse(b)) % 165.86/165.40 least_upper_bound(inverse(X1), inverse(multiply(X1, greatest_lower_bound(Y1, identity)))) -> inverse(multiply(X1, greatest_lower_bound(Y1, identity))) % 165.86/165.40 least_upper_bound(inverse(X1), inverse(multiply(X1, greatest_lower_bound(identity, Y1)))) -> inverse(multiply(X1, greatest_lower_bound(identity, Y1))) % 165.86/165.40 least_upper_bound(inverse(a), least_upper_bound(Y1, inverse(a))) -> least_upper_bound(Y1, inverse(a)) % 165.86/165.40 least_upper_bound(inverse(b), greatest_lower_bound(Y1, inverse(a))) -> inverse(b) % 165.86/165.40 least_upper_bound(inverse(b), greatest_lower_bound(inverse(a), Y0)) -> inverse(b) % 165.86/165.40 least_upper_bound(inverse(b), inverse(a)) -> inverse(b) % 165.86/165.40 least_upper_bound(inverse(b), least_upper_bound(Y0, inverse(a))) -> least_upper_bound(Y0, inverse(b)) % 165.86/165.40 least_upper_bound(inverse(b), least_upper_bound(Y1, inverse(a))) -> least_upper_bound(inverse(b), Y1) % 165.86/165.40 least_upper_bound(inverse(b), least_upper_bound(inverse(a), Y2)) -> least_upper_bound(inverse(b), Y2) % 165.86/165.40 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z)) % 165.86/165.40 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z)) % 165.86/165.40 least_upper_bound(multiply(X0, inverse(b)), least_upper_bound(multiply(a, inverse(b)), greatest_lower_bound(Y1, identity))) -> multiply(least_upper_bound(X0, a), inverse(b)) % 165.86/165.40 least_upper_bound(multiply(X0, inverse(greatest_lower_bound(X0, X1))), greatest_lower_bound(Y1, identity)) -> multiply(X0, inverse(greatest_lower_bound(X0, X1))) % 165.86/165.40 least_upper_bound(multiply(X0, inverse(greatest_lower_bound(X1, X0))), greatest_lower_bound(Y1, identity)) -> multiply(X0, inverse(greatest_lower_bound(X1, X0))) % 165.86/165.40 least_upper_bound(multiply(X0, least_upper_bound(X1, X2)), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X0, X2), Y2)) % 165.86/165.40 least_upper_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(least_upper_bound(multiply(X0, X1), Y2), Y1) % 165.86/165.40 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y2))) -> multiply(X1, Y2) % 165.86/165.40 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y2))) -> multiply(X1, Y2) % 165.86/165.40 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X) % 165.86/165.40 least_upper_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(least_upper_bound(Y0, multiply(X0, X1)), Y1) % 165.86/165.40 least_upper_bound(multiply(a, inverse(b)), greatest_lower_bound(Y1, identity)) -> multiply(a, inverse(b)) % 165.86/165.40 least_upper_bound(multiply(a, inverse(b)), least_upper_bound(multiply(X0, inverse(b)), greatest_lower_bound(Y1, identity))) -> multiply(least_upper_bound(a, X0), inverse(b)) % 165.86/165.40 least_upper_bound(multiply(a, inverse(greatest_lower_bound(X0, b))), greatest_lower_bound(Y1, identity)) -> multiply(a, inverse(greatest_lower_bound(X0, b))) % 165.86/165.40 least_upper_bound(multiply(a, inverse(greatest_lower_bound(b, X0))), greatest_lower_bound(Y1, identity)) -> multiply(a, inverse(greatest_lower_bound(b, X0))) % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(X0, identity), b), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), b), a) -> a % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), b), a) -> a % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, b)), b), a) -> a % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(X1, identity), greatest_lower_bound(Y0, b)), a) -> a % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(Y0, identity), b), a) -> a % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(identity, X0), b), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(identity, X1), greatest_lower_bound(Y0, b)), a) -> a % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(identity, Y0), b), a) -> a % 165.86/165.40 least_upper_bound(multiply(greatest_lower_bound(identity, b), b), a) -> a % 165.86/165.40 least_upper_bound(multiply(inverse(b), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(b), a) % 165.86/165.40 least_upper_bound(multiply(inverse(b), a), least_upper_bound(multiply(inverse(b), X0), greatest_lower_bound(Y1, identity))) -> multiply(inverse(b), least_upper_bound(a, X0)) % 165.86/165.40 least_upper_bound(multiply(inverse(b), multiply(a, Y2)), greatest_lower_bound(Y1, Y2)) -> multiply(inverse(b), multiply(a, Y2)) % 165.86/165.40 least_upper_bound(multiply(inverse(b), multiply(a, a)), greatest_lower_bound(Y1, b)) -> multiply(inverse(b), multiply(a, a)) % 165.86/165.40 least_upper_bound(multiply(inverse(greatest_lower_bound(X0, b)), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(greatest_lower_bound(X0, b)), a) % 165.86/165.40 least_upper_bound(multiply(inverse(greatest_lower_bound(b, X0)), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(greatest_lower_bound(b, X0)), a) % 165.86/165.40 least_upper_bound(multiply(least_upper_bound(X0, X2), X1), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X2, X1), Y2)) % 165.86/165.40 multiply(X1, greatest_lower_bound(inverse(X1), inverse(multiply(least_upper_bound(Y1, identity), X1)))) -> inverse(least_upper_bound(Y1, identity)) % 165.86/165.40 multiply(X1, greatest_lower_bound(inverse(X1), inverse(multiply(least_upper_bound(identity, Y1), X1)))) -> inverse(least_upper_bound(identity, Y1)) % 165.86/165.40 multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0) % 165.86/165.40 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0 % 165.86/165.40 multiply(X1, least_upper_bound(inverse(X1), inverse(multiply(greatest_lower_bound(Y1, identity), X1)))) -> multiply(X1, inverse(multiply(greatest_lower_bound(Y1, identity), X1))) % 165.86/165.40 multiply(X1, least_upper_bound(inverse(X1), inverse(multiply(greatest_lower_bound(identity, Y1), X1)))) -> multiply(X1, inverse(multiply(greatest_lower_bound(identity, Y1), X1))) % 165.86/165.40 multiply(Y0, inverse(Y0)) -> identity % 165.86/165.40 multiply(Y0, inverse(inverse(inverse(Y0)))) -> identity % 165.86/165.40 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity % 165.86/165.40 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1 % 165.86/165.40 multiply(Y0, multiply(inverse(Y0), X1)) -> X1 % 165.86/165.40 multiply(Y1, identity) -> Y1 % 165.86/165.40 multiply(greatest_lower_bound(X0, b), inverse(greatest_lower_bound(b, X0))) -> identity % 165.86/165.40 multiply(greatest_lower_bound(X0, identity), inverse(greatest_lower_bound(identity, X0))) -> identity % 165.86/165.40 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X1)), b) -> multiply(greatest_lower_bound(identity, X1), b) % 165.86/165.40 multiply(greatest_lower_bound(Y0, multiply(X1, Y0)), multiply(inverse(Y0), inverse(greatest_lower_bound(X1, identity)))) -> identity % 165.86/165.40 multiply(greatest_lower_bound(b, X0), inverse(greatest_lower_bound(X0, b))) -> identity % 165.86/165.40 multiply(greatest_lower_bound(identity, X0), inverse(greatest_lower_bound(X0, identity))) -> identity % 165.86/165.40 multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), inverse(greatest_lower_bound(X0, identity))) -> identity % 165.86/165.40 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, greatest_lower_bound(X2, identity))), Y1) -> multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) % 165.86/165.40 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, greatest_lower_bound(identity, X2))), Y1) -> multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) % 165.86/165.40 multiply(greatest_lower_bound(identity, inverse(identity)), Y0) -> Y0 % 165.86/165.40 multiply(greatest_lower_bound(identity, inverse(inverse(X0))), identity) -> greatest_lower_bound(identity, X0) % 165.86/165.40 multiply(greatest_lower_bound(inverse(Y1), Y2), Y1) -> greatest_lower_bound(identity, multiply(Y2, Y1)) % 165.86/165.40 multiply(greatest_lower_bound(inverse(b), greatest_lower_bound(multiply(least_upper_bound(false__, identity), inverse(b)), inverse(a))), X1) -> multiply(inverse(a), X1) % 165.86/165.40 multiply(greatest_lower_bound(inverse(b), inverse(a)), X1) -> multiply(inverse(a), X1) % 165.86/165.40 multiply(greatest_lower_bound(least_upper_bound(identity, X0), least_upper_bound(X0, identity)), inverse(least_upper_bound(X0, identity))) -> identity % 165.86/165.40 multiply(identity, X) -> X % 165.86/165.40 multiply(inverse(X), X) -> identity % 165.86/165.40 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 165.86/165.40 multiply(inverse(greatest_lower_bound(X0, a)), least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(X0, a))) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(X0, a)), least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(X0, a))) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(X0, b)), greatest_lower_bound(b, X0)) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 165.86/165.40 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(identity, X0)) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(X0, identity)), least_upper_bound(greatest_lower_bound(identity, X0), greatest_lower_bound(X0, identity))) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(X0, inverse(Y1))), greatest_lower_bound(multiply(X0, Y1), identity)) -> Y1 % 165.86/165.40 multiply(inverse(greatest_lower_bound(a, X0)), least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(a, X0))) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(a, X0)), least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(a, X0))) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(b, Y1)), greatest_lower_bound(Y1, b)) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(false__, identity), a), multiply(inverse(b), multiply(a, b))))), b) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(b, multiply(greatest_lower_bound(least_upper_bound(false__, identity), multiply(inverse(b), a)), a))), b) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(X0, identity)) -> identity % 165.86/165.40 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 165.86/165.40 multiply(inverse(greatest_lower_bound(identity, inverse(identity))), Y1) -> Y1 % 165.86/165.40 multiply(inverse(identity), Y1) -> Y1 % 165.86/165.40 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1) % 165.86/165.40 multiply(inverse(inverse(Y1)), identity) -> Y1 % 165.86/165.40 multiply(inverse(least_upper_bound(X0, b)), greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(X0, b))) -> identity % 165.86/165.40 multiply(inverse(least_upper_bound(X0, identity)), greatest_lower_bound(least_upper_bound(identity, X0), least_upper_bound(X0, identity))) -> identity % 165.86/165.40 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1 % 165.86/165.40 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(identity, X0)) -> identity % 165.86/165.40 multiply(inverse(least_upper_bound(X0, inverse(Y1))), least_upper_bound(multiply(X0, Y1), identity)) -> Y1 % 165.86/165.40 multiply(inverse(least_upper_bound(a, X0)), greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(a, X0))) -> identity % 165.86/165.40 multiply(inverse(least_upper_bound(identity, X0)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1 % 165.86/165.40 multiply(inverse(least_upper_bound(identity, inverse(identity))), Y1) -> Y1 % 165.86/165.40 multiply(inverse(least_upper_bound(inverse(Y1), X1)), least_upper_bound(identity, multiply(X1, Y1))) -> Y1 % 165.86/165.40 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1 % 165.86/165.40 multiply(inverse(multiply(X1, Y1)), X1) -> inverse(Y1) % 165.86/165.40 multiply(inverse(multiply(X1, inverse(Y1))), X1) -> Y1 % 165.86/165.40 multiply(inverse(multiply(greatest_lower_bound(X1, identity), Y1)), greatest_lower_bound(Y1, multiply(X1, Y1))) -> identity % 165.86/165.40 multiply(inverse(multiply(inverse(X1), Y1)), inverse(X1)) -> inverse(Y1) % 165.86/165.40 multiply(inverse(multiply(inverse(X1), inverse(Y1))), inverse(X1)) -> Y1 % 165.86/165.40 multiply(inverse(multiply(least_upper_bound(X1, identity), Y1)), least_upper_bound(Y1, multiply(X1, Y1))) -> identity % 165.86/165.40 multiply(least_upper_bound(X0, b), inverse(least_upper_bound(b, X0))) -> identity % 165.86/165.40 multiply(least_upper_bound(X0, identity), inverse(least_upper_bound(identity, X0))) -> identity % 165.86/165.40 multiply(least_upper_bound(X0, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X0, false__)), Y1)), inverse(least_upper_bound(X0, Y1))) -> identity % 165.86/165.40 multiply(least_upper_bound(X0, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X0, false__)), Y1)), inverse(least_upper_bound(Y1, X0))) -> identity % 165.86/165.40 multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), a) -> multiply(least_upper_bound(identity, X1), a) % 165.86/165.40 multiply(least_upper_bound(Y0, multiply(X1, Y0)), multiply(inverse(Y0), inverse(least_upper_bound(X1, identity)))) -> identity % 165.86/165.40 multiply(least_upper_bound(a, X0), inverse(least_upper_bound(X0, a))) -> identity % 165.86/165.40 multiply(least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), X0)), inverse(least_upper_bound(X0, b))) -> identity % 165.86/165.40 multiply(least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), X1)), inverse(least_upper_bound(b, X1))) -> identity % 165.86/165.40 multiply(least_upper_bound(greatest_lower_bound(identity, X0), greatest_lower_bound(X0, identity)), inverse(greatest_lower_bound(X0, identity))) -> identity % 165.86/165.40 multiply(least_upper_bound(identity, X0), inverse(least_upper_bound(X0, identity))) -> identity % 165.86/165.40 multiply(least_upper_bound(identity, inverse(identity)), Y0) -> Y0 % 165.86/165.40 multiply(least_upper_bound(identity, inverse(inverse(X0))), identity) -> least_upper_bound(identity, X0) % 165.86/165.40 multiply(least_upper_bound(identity, inverse(multiply(inverse(b), a))), identity) -> identity % 165.86/165.40 multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), inverse(least_upper_bound(X0, identity))) -> identity % 165.86/165.40 multiply(least_upper_bound(identity, multiply(a, inverse(b))), multiply(b, inverse(a))) -> identity % 165.86/165.40 multiply(least_upper_bound(inverse(Y1), Y2), Y1) -> least_upper_bound(identity, multiply(Y2, Y1)) % 165.86/165.40 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 165.86/165.40 true__ -> false__ % 165.86/165.40 with the LPO induced by % 165.86/165.40 a > f1 > b > inverse > identity > greatest_lower_bound > least_upper_bound > multiply > true__ > false__ % 165.86/165.40 % 165.86/165.40 % SZS output end Proof % 165.86/165.40 %------------------------------------------------------------------------------