%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n014.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 10:53:26 EDT 2022 % Result : Unsatisfiable 38.11s 37.97s % Output : Proof 38.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.04/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n014.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 13 05:57:37 EDT 2022 % 0.13/0.34 % CPUTime : % 38.11/37.97 % SZS status Unsatisfiable % 38.11/37.97 % SZS output start Proof % 38.11/37.97 The input problem is unsatisfiable because % 38.11/37.97 % 38.11/37.97 [1] the following set of Horn clauses is unsatisfiable: % 38.11/37.97 % 38.11/37.97 multiply(identity, X) = X % 38.11/37.97 multiply(inverse(X), X) = identity % 38.11/37.97 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 38.11/37.97 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 38.11/37.97 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 38.11/37.97 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 38.11/37.97 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 38.11/37.97 least_upper_bound(X, X) = X % 38.11/37.97 greatest_lower_bound(X, X) = X % 38.11/37.97 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 38.11/37.97 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 38.11/37.97 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 38.11/37.97 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 38.11/37.97 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 38.11/37.97 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 38.11/37.97 least_upper_bound(a, c) = c % 38.11/37.97 least_upper_bound(b, c) = c % 38.11/37.97 greatest_lower_bound(least_upper_bound(a, b), c) = least_upper_bound(a, b) ==> \bottom % 38.11/37.97 % 38.11/37.97 This holds because % 38.11/37.97 % 38.11/37.97 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 38.11/37.97 % 38.11/37.97 E: % 38.11/37.97 f1(greatest_lower_bound(least_upper_bound(a, b), c)) = true__ % 38.11/37.97 f1(least_upper_bound(a, b)) = false__ % 38.11/37.97 greatest_lower_bound(X, X) = X % 38.11/37.97 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 38.11/37.97 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 38.11/37.97 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 38.11/37.97 least_upper_bound(X, X) = X % 38.11/37.97 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 38.11/37.97 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 38.11/37.97 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 38.11/37.97 least_upper_bound(a, c) = c % 38.11/37.97 least_upper_bound(b, c) = c % 38.11/37.97 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 38.11/37.97 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 38.11/37.97 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 38.11/37.97 multiply(identity, X) = X % 38.11/37.97 multiply(inverse(X), X) = identity % 38.11/37.97 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 38.11/37.97 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 38.11/37.97 G: % 38.11/37.97 true__ = false__ % 38.11/37.97 % 38.11/37.97 This holds because % 38.11/37.97 % 38.11/37.97 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 38.11/37.97 % 38.11/37.97 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 38.11/37.97 greatest_lower_bound(X1, multiply(X0, X1)) = multiply(greatest_lower_bound(identity, inverse(X0)), multiply(X0, X1)) % 38.11/37.97 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, Y1), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, Y1)), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(Y1, X2)), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(least_upper_bound(X1, identity), Y1), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(least_upper_bound(identity, X1), Y1), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, a) = greatest_lower_bound(a, greatest_lower_bound(c, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, a) = greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(X0, c), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, a) = greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(c, X0), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(X0, c))) % 38.11/37.97 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(c, X0))) % 38.11/37.97 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, c), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(c, X0), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, b) = greatest_lower_bound(c, greatest_lower_bound(b, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, b) = greatest_lower_bound(least_upper_bound(X0, c), greatest_lower_bound(b, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, b) = greatest_lower_bound(least_upper_bound(c, X0), greatest_lower_bound(b, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(X0, a)) = greatest_lower_bound(a, greatest_lower_bound(X0, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(X0, a)) = greatest_lower_bound(a, greatest_lower_bound(X0, greatest_lower_bound(c, Y0))) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(X0, a)) = greatest_lower_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(c, X0))) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) = greatest_lower_bound(b, greatest_lower_bound(X0, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) = greatest_lower_bound(c, greatest_lower_bound(Y0, greatest_lower_bound(b, X0))) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(a, Y0))) = greatest_lower_bound(Y0, greatest_lower_bound(a, X1)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(b, Y0))) = greatest_lower_bound(Y0, greatest_lower_bound(b, X1)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(a, Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(a, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(a, greatest_lower_bound(X1, Y0))) = greatest_lower_bound(Y0, greatest_lower_bound(X1, a)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(b, Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(b, Y0)) % 38.11/37.97 greatest_lower_bound(Y0, greatest_lower_bound(b, greatest_lower_bound(X1, Y0))) = greatest_lower_bound(Y0, greatest_lower_bound(X1, b)) % 38.11/37.97 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(a), c), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, inverse(c)) = greatest_lower_bound(inverse(a), greatest_lower_bound(inverse(c), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), Y0) % 38.11/37.97 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, inverse(inverse(X0))), Y0) % 38.11/37.97 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(identity, multiply(X0, X1)), Y0) % 38.11/37.97 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 38.11/37.97 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 38.11/37.97 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 38.11/37.97 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 38.11/37.97 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 38.11/37.97 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1) % 38.11/37.97 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1) % 38.11/37.97 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 38.11/37.97 greatest_lower_bound(a, greatest_lower_bound(X0, greatest_lower_bound(c, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(a, X0)) % 38.11/37.97 greatest_lower_bound(c, greatest_lower_bound(X0, greatest_lower_bound(b, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(X0, b)) % 38.11/37.97 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(X0, identity)) % 38.11/37.97 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(c), b), Y2)) = greatest_lower_bound(Y2, multiply(inverse(c), b)) % 38.11/37.97 greatest_lower_bound(identity, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1) % 38.11/37.98 greatest_lower_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), greatest_lower_bound(Y1, Y2)) % 38.11/37.98 greatest_lower_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), greatest_lower_bound(Y1, Y2)) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, c), greatest_lower_bound(least_upper_bound(c, X0), Y2)) = greatest_lower_bound(Y2, least_upper_bound(X0, c)) % 38.11/37.98 greatest_lower_bound(multiply(Y0, Y1), identity) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1) % 38.11/37.98 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 38.11/37.98 least_upper_bound(X1, multiply(X0, X1)) = multiply(least_upper_bound(identity, inverse(X0)), multiply(X0, X1)) % 38.11/37.98 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, Y1), Y0)) % 38.11/37.98 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)), Y0)) % 38.11/37.98 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)), Y0)) % 38.11/37.98 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(multiply(greatest_lower_bound(X1, identity), Y1), Y0)) % 38.11/37.98 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(multiply(greatest_lower_bound(identity, X1), Y1), Y0)) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(c, least_upper_bound(Y0, greatest_lower_bound(a, X0))) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(c, least_upper_bound(b, Y0)) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(c, least_upper_bound(greatest_lower_bound(X0, a), Y0)) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(c, least_upper_bound(greatest_lower_bound(X0, b), Y0)) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(c, least_upper_bound(greatest_lower_bound(a, X0), Y0)) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(c, least_upper_bound(greatest_lower_bound(b, X0), Y0)) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(greatest_lower_bound(X0, a), least_upper_bound(c, Y0)) % 38.11/37.98 least_upper_bound(Y0, c) = least_upper_bound(greatest_lower_bound(a, X0), least_upper_bound(c, Y0)) % 38.11/37.98 least_upper_bound(Y0, identity) = least_upper_bound(identity, least_upper_bound(multiply(inverse(c), b), Y0)) % 38.11/37.98 least_upper_bound(Y0, inverse(b)) = least_upper_bound(inverse(c), least_upper_bound(inverse(b), Y0)) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(X0, c)) = least_upper_bound(c, least_upper_bound(Y0, least_upper_bound(b, X0))) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(X1, least_upper_bound(c, Y0))) = least_upper_bound(Y0, least_upper_bound(c, X1)) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(Y2, c)) = least_upper_bound(c, least_upper_bound(Y2, Y0)) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(c, X0)) = least_upper_bound(X0, least_upper_bound(c, Y0)) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(c, X0)) = least_upper_bound(a, least_upper_bound(Y0, least_upper_bound(X0, c))) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(c, X0)) = least_upper_bound(c, least_upper_bound(X0, least_upper_bound(Y0, b))) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(c, X0)) = least_upper_bound(c, least_upper_bound(b, least_upper_bound(X0, Y0))) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(c, least_upper_bound(X1, Y0))) = least_upper_bound(Y0, least_upper_bound(X1, c)) % 38.11/37.98 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, inverse(inverse(X0))), Y0) % 38.11/37.98 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), Y0) % 38.11/37.98 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(identity, multiply(X0, X1)), Y0) % 38.11/37.98 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(multiply(X0, X1), identity), Y0) % 38.11/37.98 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1))) % 38.11/37.98 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0)) % 38.11/37.98 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1))) % 38.11/37.98 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0)) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y0, Y2)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 38.11/37.98 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1) % 38.11/37.98 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1) % 38.11/37.98 least_upper_bound(Y2, least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 38.11/37.98 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(X2, c))) = least_upper_bound(c, least_upper_bound(X1, X2)) % 38.11/37.98 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(c, X2))) = least_upper_bound(c, least_upper_bound(X1, X2)) % 38.11/37.98 least_upper_bound(a, least_upper_bound(X2, least_upper_bound(c, X1))) = least_upper_bound(c, least_upper_bound(X1, X2)) % 38.11/37.98 least_upper_bound(a, least_upper_bound(Y0, c)) = least_upper_bound(c, Y0) % 38.11/37.98 least_upper_bound(b, least_upper_bound(X2, least_upper_bound(c, X1))) = least_upper_bound(c, least_upper_bound(X1, X2)) % 38.11/37.98 least_upper_bound(c, least_upper_bound(X0, least_upper_bound(b, Y2))) = least_upper_bound(Y2, least_upper_bound(c, X0)) % 38.11/37.98 least_upper_bound(greatest_lower_bound(false__, a), multiply(least_upper_bound(identity, X0), c)) = multiply(least_upper_bound(X0, identity), c) % 38.11/37.98 least_upper_bound(identity, least_upper_bound(X0, least_upper_bound(identity, Y2))) = least_upper_bound(Y2, least_upper_bound(X0, identity)) % 38.11/37.98 least_upper_bound(identity, least_upper_bound(multiply(inverse(a), c), Y2)) = least_upper_bound(Y2, multiply(inverse(a), c)) % 38.11/37.98 least_upper_bound(identity, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1) % 38.11/37.98 least_upper_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), least_upper_bound(Y1, Y2)) % 38.11/37.98 least_upper_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), least_upper_bound(Y1, Y2)) % 38.11/37.98 least_upper_bound(multiply(Y0, Y1), identity) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1) % 38.11/37.98 multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1)) % 38.11/37.98 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1)) % 38.11/37.98 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)))) % 38.11/37.98 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)))) % 38.11/37.98 multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1)) % 38.11/37.98 multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), c) = least_upper_bound(greatest_lower_bound(false__, a), multiply(least_upper_bound(identity, X1), c)) % 38.11/37.98 multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1)) % 38.11/37.98 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)))) % 38.11/37.98 f1(greatest_lower_bound(c, least_upper_bound(a, b))) -> true__ % 38.11/37.98 f1(greatest_lower_bound(least_upper_bound(a, b), c)) -> true__ % 38.11/37.98 f1(least_upper_bound(a, b)) -> false__ % 38.11/37.98 greatest_lower_bound(X, X) -> X % 38.11/37.98 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X % 38.11/37.98 greatest_lower_bound(X0, greatest_lower_bound(b, greatest_lower_bound(X1, least_upper_bound(Y1, c)))) -> greatest_lower_bound(X0, greatest_lower_bound(b, X1)) % 38.11/37.98 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) -> multiply(greatest_lower_bound(Y1, identity), multiply(inverse(Y1), X1)) % 38.11/37.98 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) -> multiply(greatest_lower_bound(identity, Y1), multiply(inverse(Y1), X1)) % 38.11/37.98 greatest_lower_bound(X1, multiply(inverse(least_upper_bound(Y1, identity)), X1)) -> multiply(inverse(least_upper_bound(Y1, identity)), X1) % 38.11/37.98 greatest_lower_bound(X1, multiply(inverse(least_upper_bound(identity, Y1)), X1)) -> multiply(inverse(least_upper_bound(identity, Y1)), X1) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(greatest_lower_bound(Y0, Y1), X1))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(Y2, least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y2) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(a, Y0)) -> greatest_lower_bound(Y0, a) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(b, Y0)) -> greatest_lower_bound(Y0, b) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X1, c), Y0))) -> greatest_lower_bound(Y0, b) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, Y0), Y2)) -> greatest_lower_bound(Y0, Y2) % 38.11/37.98 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(Y0, X1), Y2)) -> greatest_lower_bound(Y0, Y2) % 38.11/37.98 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y0))) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y0, X2))) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y0))) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y0))) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 38.11/37.98 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 38.11/37.98 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y0)) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y0)) -> Y0 % 38.11/37.98 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0 % 38.11/37.98 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, Y1))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y1)))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y1, X2)))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(Y1, X1))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y1))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y1))) -> greatest_lower_bound(Y0, Y1) % 38.11/37.98 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2) % 38.11/37.98 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1) % 38.11/37.98 greatest_lower_bound(Y1, multiply(inverse(a), multiply(c, Y1))) -> Y1 % 38.11/37.98 greatest_lower_bound(Y1, multiply(inverse(c), multiply(b, Y1))) -> multiply(inverse(c), multiply(b, Y1)) % 38.11/37.98 greatest_lower_bound(a, c) -> a % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(X0, a)) -> greatest_lower_bound(X0, a) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(X0, a)) -> greatest_lower_bound(a, X0) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(X0, greatest_lower_bound(c, X0))) -> greatest_lower_bound(a, X0) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(X1, greatest_lower_bound(X2, c))) -> greatest_lower_bound(X1, greatest_lower_bound(X2, a)) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, a) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(Y0, least_upper_bound(X0, c))) -> greatest_lower_bound(Y0, a) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(Y0, least_upper_bound(c, X0))) -> greatest_lower_bound(Y0, a) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(c, Y2)) -> greatest_lower_bound(a, Y2) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(X0, c), Y2)) -> greatest_lower_bound(a, Y2) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(X0, c), b)) -> greatest_lower_bound(a, b) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(c, X0), Y2)) -> greatest_lower_bound(a, Y2) % 38.11/37.98 greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(false__, c), b)) -> greatest_lower_bound(a, b) % 38.11/37.98 greatest_lower_bound(a, least_upper_bound(X1, least_upper_bound(X2, c))) -> a % 38.11/37.98 greatest_lower_bound(a, least_upper_bound(Y0, c)) -> a % 38.11/37.98 greatest_lower_bound(a, least_upper_bound(Y1, least_upper_bound(c, X0))) -> a % 38.11/37.98 greatest_lower_bound(a, least_upper_bound(c, X0)) -> a % 38.11/37.98 greatest_lower_bound(a, multiply(greatest_lower_bound(X1, identity), c)) -> greatest_lower_bound(a, multiply(X1, c)) % 38.11/37.98 greatest_lower_bound(a, multiply(greatest_lower_bound(identity, X1), c)) -> greatest_lower_bound(a, multiply(X1, c)) % 38.11/37.98 greatest_lower_bound(a, multiply(inverse(a), multiply(c, c))) -> a % 38.11/37.98 greatest_lower_bound(a, multiply(least_upper_bound(X1, identity), c)) -> a % 38.11/37.98 greatest_lower_bound(a, multiply(least_upper_bound(identity, X1), c)) -> a % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(X0, least_upper_bound(Y1, c))) -> greatest_lower_bound(b, X0) % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(c, Y1))) -> greatest_lower_bound(b, Y0) % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(Y1, b)) -> greatest_lower_bound(Y1, b) % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(Y0, c), b)) -> b % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(Y1, c), Y0)) -> greatest_lower_bound(b, Y0) % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(c, X0), Y2)) -> greatest_lower_bound(b, Y2) % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(c, X0), b)) -> b % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(multiply(X0, b), least_upper_bound(Y1, c))) -> multiply(greatest_lower_bound(X0, identity), b) % 38.11/37.98 greatest_lower_bound(b, greatest_lower_bound(multiply(X0, b), least_upper_bound(Y1, c))) -> multiply(greatest_lower_bound(identity, X0), b) % 38.11/37.98 greatest_lower_bound(b, least_upper_bound(X1, least_upper_bound(X2, c))) -> b % 38.11/37.98 greatest_lower_bound(b, least_upper_bound(X1, least_upper_bound(c, X2))) -> b % 38.11/37.98 greatest_lower_bound(b, least_upper_bound(Y0, c)) -> b % 38.11/37.98 greatest_lower_bound(b, least_upper_bound(c, X0)) -> b % 38.11/37.98 greatest_lower_bound(b, multiply(least_upper_bound(X1, identity), c)) -> b % 38.11/37.98 greatest_lower_bound(b, multiply(least_upper_bound(identity, X1), c)) -> b % 38.11/37.98 greatest_lower_bound(c, b) -> b % 38.11/37.98 greatest_lower_bound(c, greatest_lower_bound(X0, greatest_lower_bound(b, X1))) -> greatest_lower_bound(X0, greatest_lower_bound(b, X1)) % 38.11/37.98 greatest_lower_bound(c, greatest_lower_bound(X1, greatest_lower_bound(X2, b))) -> greatest_lower_bound(X1, greatest_lower_bound(X2, b)) % 38.11/37.98 greatest_lower_bound(c, greatest_lower_bound(Y0, b)) -> greatest_lower_bound(Y0, b) % 38.11/37.98 greatest_lower_bound(c, greatest_lower_bound(Y1, c)) -> greatest_lower_bound(Y1, c) % 38.11/37.98 greatest_lower_bound(c, greatest_lower_bound(Y1, c)) -> greatest_lower_bound(c, Y1) % 38.11/37.98 greatest_lower_bound(c, greatest_lower_bound(b, Y2)) -> greatest_lower_bound(b, Y2) % 38.11/37.98 greatest_lower_bound(c, least_upper_bound(a, b)) -> least_upper_bound(a, b) % 38.11/37.98 greatest_lower_bound(c, multiply(greatest_lower_bound(X0, identity), b)) -> multiply(greatest_lower_bound(X0, identity), b) % 38.11/37.98 greatest_lower_bound(c, multiply(greatest_lower_bound(identity, X0), b)) -> multiply(greatest_lower_bound(identity, X0), b) % 38.11/37.98 greatest_lower_bound(c, multiply(inverse(c), multiply(b, b))) -> multiply(inverse(c), multiply(b, b)) % 38.11/37.98 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z)) % 38.11/37.98 greatest_lower_bound(identity, greatest_lower_bound(X0, identity)) -> greatest_lower_bound(X0, identity) % 38.11/37.98 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(a), c))) -> greatest_lower_bound(Y0, identity) % 38.11/37.98 greatest_lower_bound(identity, greatest_lower_bound(Y1, identity)) -> greatest_lower_bound(identity, Y1) % 38.11/37.98 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(a), c), Y2)) -> greatest_lower_bound(identity, Y2) % 38.11/37.98 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(Y1, identity), inverse(Y1)) % 38.11/37.98 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(identity, Y1), inverse(Y1)) % 38.11/37.98 greatest_lower_bound(identity, inverse(identity)) -> identity % 38.11/37.98 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, identity))) -> inverse(least_upper_bound(Y1, identity)) % 38.11/37.98 greatest_lower_bound(identity, inverse(least_upper_bound(identity, Y1))) -> inverse(least_upper_bound(identity, Y1)) % 38.11/37.98 greatest_lower_bound(identity, least_upper_bound(Y0, inverse(identity))) -> identity % 38.11/37.98 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1))) % 38.11/37.98 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1))) % 38.11/37.98 greatest_lower_bound(identity, multiply(inverse(a), c)) -> identity % 38.11/37.98 greatest_lower_bound(identity, multiply(inverse(c), b)) -> multiply(inverse(c), b) % 38.11/37.98 greatest_lower_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> identity % 38.11/37.98 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, X0), inverse(X0))) -> identity % 38.11/37.98 greatest_lower_bound(inverse(a), greatest_lower_bound(Y0, inverse(c))) -> greatest_lower_bound(Y0, inverse(c)) % 38.11/37.98 greatest_lower_bound(inverse(a), inverse(c)) -> inverse(c) % 38.11/37.98 greatest_lower_bound(inverse(c), inverse(b)) -> inverse(c) % 38.11/37.98 greatest_lower_bound(inverse(c), least_upper_bound(Y1, inverse(b))) -> inverse(c) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, X1), least_upper_bound(X0, least_upper_bound(X1, Y1))) -> least_upper_bound(X0, X1) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(Y1, least_upper_bound(a, X0))) -> least_upper_bound(X0, a) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(a, X0)) -> least_upper_bound(X0, a) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(Y1, least_upper_bound(X0, c))) -> least_upper_bound(X0, b) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(Y1, least_upper_bound(c, X0))) -> least_upper_bound(X0, b) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(c, X0)) -> least_upper_bound(X0, b) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, c), greatest_lower_bound(Y0, b)) -> greatest_lower_bound(Y0, b) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, c), least_upper_bound(X0, b)) -> least_upper_bound(X0, b) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, c), least_upper_bound(Y1, least_upper_bound(c, X0))) -> least_upper_bound(X0, c) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X0, c), least_upper_bound(c, X0)) -> least_upper_bound(X0, c) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X1, least_upper_bound(Y1, X2))) -> least_upper_bound(X1, X2) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X2, least_upper_bound(Y1, X1))) -> least_upper_bound(X1, X2) % 38.11/37.98 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) % 38.11/37.98 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)) % 38.11/37.98 greatest_lower_bound(least_upper_bound(X1, c), least_upper_bound(c, least_upper_bound(X1, Y1))) -> least_upper_bound(X1, c) % 38.11/37.98 greatest_lower_bound(least_upper_bound(Y0, c), b) -> b % 38.11/37.98 greatest_lower_bound(least_upper_bound(Y0, least_upper_bound(Y1, c)), b) -> b % 38.11/37.98 greatest_lower_bound(least_upper_bound(Y0, least_upper_bound(c, Y1)), b) -> b % 38.11/37.98 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) % 38.11/37.98 greatest_lower_bound(least_upper_bound(Y1, c), greatest_lower_bound(b, Y0)) -> greatest_lower_bound(b, Y0) % 38.11/37.98 greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(X0, c)) -> least_upper_bound(b, X0) % 38.11/37.98 greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(Y1, least_upper_bound(X0, c))) -> least_upper_bound(b, X0) % 38.11/37.98 greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(Y1, least_upper_bound(c, X0))) -> least_upper_bound(b, X0) % 38.11/37.98 greatest_lower_bound(least_upper_bound(c, X0), greatest_lower_bound(Y0, b)) -> greatest_lower_bound(Y0, b) % 38.11/37.98 greatest_lower_bound(least_upper_bound(c, X0), greatest_lower_bound(b, Y2)) -> greatest_lower_bound(b, Y2) % 38.11/37.98 greatest_lower_bound(least_upper_bound(c, X0), least_upper_bound(b, X0)) -> least_upper_bound(b, X0) % 38.11/37.98 greatest_lower_bound(least_upper_bound(c, X1), least_upper_bound(X1, least_upper_bound(c, Y1))) -> least_upper_bound(c, X1) % 38.11/37.98 greatest_lower_bound(least_upper_bound(c, Y0), b) -> b % 38.11/37.98 greatest_lower_bound(least_upper_bound(c, Y1), least_upper_bound(Y1, c)) -> least_upper_bound(c, Y1) % 38.11/37.98 greatest_lower_bound(least_upper_bound(c, Y2), least_upper_bound(Y1, least_upper_bound(Y2, c))) -> least_upper_bound(c, Y2) % 38.11/37.98 greatest_lower_bound(least_upper_bound(false__, c), b) -> b % 38.11/37.98 greatest_lower_bound(least_upper_bound(false__, c), greatest_lower_bound(X0, b)) -> greatest_lower_bound(X0, b) % 38.11/37.98 greatest_lower_bound(least_upper_bound(false__, c), greatest_lower_bound(b, X1)) -> greatest_lower_bound(b, X1) % 38.11/37.98 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X0, a), X1), least_upper_bound(X1, c)) -> least_upper_bound(greatest_lower_bound(X0, a), X1) % 38.11/37.98 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X0, b), X1), least_upper_bound(X1, c)) -> least_upper_bound(greatest_lower_bound(X0, b), X1) % 38.11/37.98 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) % 38.11/37.98 greatest_lower_bound(least_upper_bound(greatest_lower_bound(b, X0), X1), least_upper_bound(X1, c)) -> least_upper_bound(greatest_lower_bound(b, X0), X1) % 38.11/37.98 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z)) % 38.11/37.98 greatest_lower_bound(multiply(X0, greatest_lower_bound(X1, X2)), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X0, X2), Y2)) % 38.11/37.98 greatest_lower_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(greatest_lower_bound(multiply(X0, X1), Y2), Y1) % 38.11/37.98 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y2))) -> multiply(X1, Y2) % 38.11/37.98 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y2))) -> multiply(X1, Y2) % 38.11/37.98 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X) % 38.11/37.98 greatest_lower_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(greatest_lower_bound(Y0, multiply(X0, X1)), Y1) % 38.11/37.98 greatest_lower_bound(multiply(greatest_lower_bound(X0, X2), X1), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X2, X1), Y2)) % 38.11/37.98 greatest_lower_bound(multiply(inverse(c), b), least_upper_bound(Y1, identity)) -> multiply(inverse(c), b) % 38.11/37.98 greatest_lower_bound(multiply(inverse(c), multiply(b, Y2)), least_upper_bound(Y1, Y2)) -> multiply(inverse(c), multiply(b, Y2)) % 38.11/37.98 greatest_lower_bound(multiply(inverse(c), multiply(b, b)), least_upper_bound(Y1, c)) -> multiply(inverse(c), multiply(b, b)) % 38.11/37.98 greatest_lower_bound(multiply(least_upper_bound(Y0, identity), c), b) -> b % 38.11/37.98 greatest_lower_bound(multiply(least_upper_bound(identity, Y0), c), b) -> b % 38.11/37.98 greatest_lower_bound(multiply(least_upper_bound(identity, c), c), b) -> b % 38.11/37.98 inverse(greatest_lower_bound(identity, inverse(identity))) -> identity % 38.11/37.98 inverse(identity) -> identity % 38.11/37.98 inverse(inverse(Y0)) -> Y0 % 38.11/37.98 inverse(inverse(identity)) -> identity % 38.11/37.98 inverse(least_upper_bound(identity, inverse(identity))) -> identity % 38.11/37.98 least_upper_bound(X, X) -> X % 38.11/37.98 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X % 38.11/37.98 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(Y1, identity), multiply(inverse(Y1), X1)) % 38.11/37.98 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(identity, Y1), multiply(inverse(Y1), X1)) % 38.11/37.98 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(Y1, identity)), X1)) -> multiply(inverse(greatest_lower_bound(Y1, identity)), X1) % 38.11/37.98 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(identity, Y1)), X1)) -> multiply(inverse(greatest_lower_bound(identity, Y1)), X1) % 38.11/37.98 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))) -> Y0 % 38.11/37.98 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))) -> Y0 % 38.11/37.98 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0 % 38.11/37.98 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0)))) -> Y0 % 38.11/37.98 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2)))) -> Y0 % 38.11/37.98 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y0))) -> Y0 % 38.11/37.98 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y0))) -> Y0 % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(least_upper_bound(Y0, Y1), X1))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(Y2, greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, Y2) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(c, Y0)) -> least_upper_bound(Y0, c) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y0, X1), Y2)) -> least_upper_bound(Y0, Y2) % 38.11/37.98 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y1, Y0), Y2)) -> least_upper_bound(Y0, Y2) % 38.11/37.98 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y0)) -> Y0 % 38.11/37.98 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y0)) -> Y0 % 38.11/37.98 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> Y0 % 38.11/37.98 least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> Y0 % 38.11/37.98 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 38.11/37.98 least_upper_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 38.11/37.98 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, Y1))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(Y1, X1))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1))) -> least_upper_bound(Y0, Y1) % 38.11/37.98 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2) % 38.11/37.98 least_upper_bound(Y1, multiply(inverse(a), multiply(c, Y1))) -> multiply(inverse(a), multiply(c, Y1)) % 38.11/37.98 least_upper_bound(Y1, multiply(inverse(c), multiply(b, Y1))) -> Y1 % 38.11/37.98 least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y1)) -> multiply(least_upper_bound(identity, X1), Y1) % 38.11/37.98 least_upper_bound(a, c) -> c % 38.11/37.98 least_upper_bound(a, least_upper_bound(X0, least_upper_bound(X1, c))) -> least_upper_bound(X0, least_upper_bound(X1, c)) % 38.11/37.98 least_upper_bound(a, least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c) % 38.11/37.98 least_upper_bound(a, least_upper_bound(Y0, least_upper_bound(c, X0))) -> least_upper_bound(Y0, least_upper_bound(c, X0)) % 38.11/37.98 least_upper_bound(a, least_upper_bound(Y1, a)) -> least_upper_bound(Y1, a) % 38.11/37.98 least_upper_bound(a, least_upper_bound(Y1, a)) -> least_upper_bound(a, Y1) % 38.11/37.98 least_upper_bound(a, least_upper_bound(c, Y2)) -> least_upper_bound(c, Y2) % 38.11/37.98 least_upper_bound(a, multiply(least_upper_bound(X1, identity), c)) -> multiply(least_upper_bound(identity, X1), c) % 38.11/37.98 least_upper_bound(a, multiply(least_upper_bound(identity, X1), c)) -> multiply(least_upper_bound(identity, X1), c) % 38.11/37.98 least_upper_bound(b, c) -> c % 38.11/37.98 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(X2, c))) -> least_upper_bound(c, least_upper_bound(X1, X2)) % 38.11/37.98 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(c, X2))) -> least_upper_bound(c, least_upper_bound(X1, X2)) % 38.11/37.98 least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(c, X0))) -> least_upper_bound(Y0, least_upper_bound(c, X0)) % 38.11/37.98 least_upper_bound(b, least_upper_bound(Y1, b)) -> least_upper_bound(Y1, b) % 38.11/37.98 least_upper_bound(b, least_upper_bound(c, Y2)) -> least_upper_bound(c, Y2) % 38.11/37.98 least_upper_bound(b, multiply(least_upper_bound(X1, identity), c)) -> multiply(least_upper_bound(identity, X1), c) % 38.11/37.98 least_upper_bound(b, multiply(least_upper_bound(identity, X1), c)) -> multiply(least_upper_bound(identity, X1), c) % 38.11/37.98 least_upper_bound(c, b) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(X0, b)) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(X1, greatest_lower_bound(X2, a))) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(X1, greatest_lower_bound(a, X2))) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(X1, greatest_lower_bound(b, X2))) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(Y1, a)) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(Y1, greatest_lower_bound(X0, b))) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(Y1, least_upper_bound(a, b))) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(a, Y0)) -> c % 38.11/37.98 least_upper_bound(c, greatest_lower_bound(b, X1)) -> c % 38.11/37.98 least_upper_bound(c, least_upper_bound(X0, c)) -> least_upper_bound(X0, c) % 38.11/37.98 least_upper_bound(c, least_upper_bound(X0, greatest_lower_bound(Y1, a))) -> least_upper_bound(c, X0) % 38.11/37.98 least_upper_bound(c, least_upper_bound(X0, greatest_lower_bound(Y1, b))) -> least_upper_bound(c, X0) % 38.11/37.98 least_upper_bound(c, least_upper_bound(X1, least_upper_bound(X2, b))) -> least_upper_bound(X1, least_upper_bound(X2, c)) % 38.11/37.98 least_upper_bound(c, least_upper_bound(Y0, b)) -> least_upper_bound(Y0, c) % 38.11/37.98 least_upper_bound(c, least_upper_bound(Y0, b)) -> least_upper_bound(c, Y0) % 38.11/37.98 least_upper_bound(c, least_upper_bound(Y0, greatest_lower_bound(b, X0))) -> least_upper_bound(Y0, c) % 38.11/37.98 least_upper_bound(c, least_upper_bound(Y0, least_upper_bound(b, X0))) -> least_upper_bound(Y0, least_upper_bound(c, X0)) % 38.11/37.98 least_upper_bound(c, least_upper_bound(Y1, c)) -> least_upper_bound(c, Y1) % 38.11/37.98 least_upper_bound(c, least_upper_bound(b, Y0)) -> least_upper_bound(c, Y0) % 38.11/37.98 least_upper_bound(c, least_upper_bound(b, least_upper_bound(X0, Y2))) -> least_upper_bound(c, least_upper_bound(X0, Y2)) % 38.11/37.98 least_upper_bound(c, least_upper_bound(greatest_lower_bound(Y1, a), Y0)) -> least_upper_bound(c, Y0) % 38.11/37.98 least_upper_bound(c, least_upper_bound(greatest_lower_bound(Y1, b), Y0)) -> least_upper_bound(c, Y0) % 38.11/37.98 least_upper_bound(c, least_upper_bound(greatest_lower_bound(b, Y1), Y0)) -> least_upper_bound(c, Y0) % 38.11/37.98 least_upper_bound(c, multiply(greatest_lower_bound(X1, identity), a)) -> c % 38.11/37.98 least_upper_bound(c, multiply(greatest_lower_bound(X1, identity), b)) -> c % 38.11/37.98 least_upper_bound(c, multiply(greatest_lower_bound(identity, X1), a)) -> c % 38.11/37.98 least_upper_bound(c, multiply(greatest_lower_bound(identity, X1), b)) -> c % 38.11/37.98 least_upper_bound(c, multiply(inverse(c), multiply(b, b))) -> c % 38.11/37.98 least_upper_bound(c, multiply(least_upper_bound(X1, identity), b)) -> least_upper_bound(c, multiply(X1, b)) % 38.11/37.98 least_upper_bound(c, multiply(least_upper_bound(identity, X1), b)) -> least_upper_bound(c, multiply(X1, b)) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, X1), greatest_lower_bound(X0, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X0, X1) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(X0, c)) -> greatest_lower_bound(X0, c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(a, X0))) -> greatest_lower_bound(X0, a) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(a, X0)) -> greatest_lower_bound(X0, a) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, a), least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, c), greatest_lower_bound(Y1, greatest_lower_bound(X0, a))) -> greatest_lower_bound(X0, c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, c), greatest_lower_bound(Y1, greatest_lower_bound(c, X0))) -> greatest_lower_bound(X0, c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, c), greatest_lower_bound(c, X0)) -> greatest_lower_bound(X0, c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, least_upper_bound(X1, c)), greatest_lower_bound(X0, b)) -> greatest_lower_bound(X0, least_upper_bound(X1, c)) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X0, least_upper_bound(c, X1)), greatest_lower_bound(X0, b)) -> greatest_lower_bound(X0, least_upper_bound(c, X1)) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))) -> greatest_lower_bound(X1, X2) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))) -> greatest_lower_bound(X1, X2) % 38.11/37.98 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) % 38.11/37.98 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) % 38.11/37.98 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)) % 38.11/37.98 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)) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X1, a), greatest_lower_bound(a, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X1, a) % 38.11/37.98 least_upper_bound(greatest_lower_bound(X1, b), greatest_lower_bound(b, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X1, b) % 38.11/37.98 least_upper_bound(greatest_lower_bound(Y0, a), c) -> c % 38.11/37.98 least_upper_bound(greatest_lower_bound(Y0, greatest_lower_bound(a, X1)), c) -> c % 38.11/37.98 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) % 38.11/37.98 least_upper_bound(greatest_lower_bound(Y1, a), least_upper_bound(c, Y0)) -> least_upper_bound(c, Y0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(Y2, greatest_lower_bound(X0, a)), c) -> c % 38.11/37.98 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(c, X0)) -> greatest_lower_bound(c, X0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(a, X0), least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(a, X1), greatest_lower_bound(X1, greatest_lower_bound(a, Y1))) -> greatest_lower_bound(a, X1) % 38.11/37.98 least_upper_bound(greatest_lower_bound(a, Y0), c) -> c % 38.11/37.98 least_upper_bound(greatest_lower_bound(a, Y1), greatest_lower_bound(Y1, a)) -> greatest_lower_bound(a, Y1) % 38.11/37.98 least_upper_bound(greatest_lower_bound(a, Y2), greatest_lower_bound(Y1, greatest_lower_bound(Y2, a))) -> greatest_lower_bound(a, Y2) % 38.11/37.98 least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(X0, b)) -> greatest_lower_bound(b, X0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(Y1, greatest_lower_bound(X0, b))) -> greatest_lower_bound(b, X0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(b, X1), greatest_lower_bound(X1, greatest_lower_bound(b, Y1))) -> greatest_lower_bound(b, X1) % 38.11/37.98 least_upper_bound(greatest_lower_bound(c, X0), greatest_lower_bound(X0, a)) -> greatest_lower_bound(c, X0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(c, X0), greatest_lower_bound(Y1, greatest_lower_bound(X0, a))) -> greatest_lower_bound(c, X0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(c, X0), greatest_lower_bound(Y1, greatest_lower_bound(a, X0))) -> greatest_lower_bound(c, X0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(false__, a), least_upper_bound(c, X0)) -> least_upper_bound(c, X0) % 38.11/37.98 least_upper_bound(greatest_lower_bound(false__, a), multiply(least_upper_bound(identity, X0), c)) -> multiply(least_upper_bound(identity, X0), c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(false__, a), multiply(least_upper_bound(identity, c), c)) -> multiply(least_upper_bound(identity, c), c) % 38.11/37.98 least_upper_bound(greatest_lower_bound(least_upper_bound(X0, c), X1), greatest_lower_bound(X1, a)) -> greatest_lower_bound(least_upper_bound(X0, c), X1) % 38.11/37.98 least_upper_bound(greatest_lower_bound(least_upper_bound(X0, c), X1), greatest_lower_bound(X1, b)) -> greatest_lower_bound(least_upper_bound(X0, c), X1) % 38.11/37.98 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) % 38.11/37.98 least_upper_bound(greatest_lower_bound(least_upper_bound(c, X0), X1), greatest_lower_bound(X1, a)) -> greatest_lower_bound(least_upper_bound(c, X0), X1) % 38.11/37.98 least_upper_bound(greatest_lower_bound(least_upper_bound(c, X0), X1), greatest_lower_bound(X1, b)) -> greatest_lower_bound(least_upper_bound(c, X0), X1) % 38.11/37.98 least_upper_bound(identity, greatest_lower_bound(Y0, inverse(identity))) -> identity % 38.11/37.98 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(Y1, identity), inverse(Y1)) % 38.11/37.98 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(identity, Y1), inverse(Y1)) % 38.11/37.98 least_upper_bound(identity, inverse(greatest_lower_bound(Y1, identity))) -> inverse(greatest_lower_bound(Y1, identity)) % 38.11/37.98 least_upper_bound(identity, inverse(greatest_lower_bound(identity, Y1))) -> inverse(greatest_lower_bound(identity, Y1)) % 38.11/37.98 least_upper_bound(identity, inverse(identity)) -> identity % 38.11/37.98 least_upper_bound(identity, least_upper_bound(X0, identity)) -> least_upper_bound(X0, identity) % 38.11/37.98 least_upper_bound(identity, least_upper_bound(Y0, multiply(inverse(c), b))) -> least_upper_bound(Y0, identity) % 38.11/37.98 least_upper_bound(identity, least_upper_bound(Y1, identity)) -> least_upper_bound(identity, Y1) % 38.11/37.98 least_upper_bound(identity, least_upper_bound(multiply(inverse(c), b), Y2)) -> least_upper_bound(identity, Y2) % 38.11/37.98 least_upper_bound(identity, multiply(X1, inverse(multiply(greatest_lower_bound(Y1, identity), X1)))) -> multiply(X1, inverse(multiply(greatest_lower_bound(Y1, identity), X1))) % 38.11/37.98 least_upper_bound(identity, multiply(X1, inverse(multiply(greatest_lower_bound(identity, Y1), X1)))) -> multiply(X1, inverse(multiply(greatest_lower_bound(identity, Y1), X1))) % 38.11/37.98 least_upper_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> identity % 38.11/37.98 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, X0), inverse(X0))) -> identity % 38.11/37.98 least_upper_bound(identity, multiply(inverse(a), c)) -> multiply(inverse(a), c) % 38.11/37.98 least_upper_bound(identity, multiply(inverse(c), b)) -> identity % 38.11/37.98 least_upper_bound(inverse(a), greatest_lower_bound(Y1, inverse(c))) -> inverse(a) % 38.11/37.98 least_upper_bound(inverse(a), inverse(c)) -> inverse(a) % 38.11/37.98 least_upper_bound(inverse(c), inverse(b)) -> inverse(b) % 38.11/37.98 least_upper_bound(inverse(c), least_upper_bound(Y0, inverse(b))) -> least_upper_bound(Y0, inverse(b)) % 38.11/37.98 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z)) % 38.11/37.98 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z)) % 38.11/37.98 least_upper_bound(multiply(X0, least_upper_bound(X1, X2)), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X0, X2), Y2)) % 38.11/37.98 least_upper_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(least_upper_bound(multiply(X0, X1), Y2), Y1) % 38.11/37.98 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y2))) -> multiply(X1, Y2) % 38.11/37.98 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y2))) -> multiply(X1, Y2) % 38.11/37.98 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X) % 38.11/37.98 least_upper_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(least_upper_bound(Y0, multiply(X0, X1)), Y1) % 38.11/37.98 least_upper_bound(multiply(inverse(a), c), greatest_lower_bound(Y1, identity)) -> multiply(inverse(a), c) % 38.11/37.98 least_upper_bound(multiply(inverse(a), multiply(c, Y2)), greatest_lower_bound(Y1, Y2)) -> multiply(inverse(a), multiply(c, Y2)) % 38.11/37.98 least_upper_bound(multiply(least_upper_bound(X0, X2), X1), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X2, X1), Y2)) % 38.11/37.98 multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0) % 38.11/37.98 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0 % 38.11/37.98 multiply(Y0, inverse(Y0)) -> identity % 38.11/37.98 multiply(Y0, inverse(inverse(inverse(Y0)))) -> identity % 38.11/37.98 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity % 38.11/37.98 multiply(Y0, multiply(inverse(Y0), X1)) -> X1 % 38.11/37.98 multiply(Y1, identity) -> Y1 % 38.11/37.98 multiply(greatest_lower_bound(identity, inverse(identity)), Y0) -> Y0 % 38.11/37.98 multiply(greatest_lower_bound(identity, inverse(inverse(X0))), identity) -> greatest_lower_bound(identity, X0) % 38.11/37.98 multiply(greatest_lower_bound(inverse(Y1), Y2), Y1) -> greatest_lower_bound(identity, multiply(Y2, Y1)) % 38.11/37.98 multiply(greatest_lower_bound(inverse(a), inverse(c)), X1) -> multiply(inverse(c), X1) % 38.11/37.98 multiply(identity, X) -> X % 38.11/37.98 multiply(inverse(X), X) -> identity % 38.11/37.98 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 38.11/37.98 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 38.11/37.98 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 38.11/37.98 multiply(inverse(greatest_lower_bound(identity, inverse(identity))), Y1) -> Y1 % 38.11/37.98 multiply(inverse(identity), Y1) -> Y1 % 38.11/37.98 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1) % 38.11/37.98 multiply(inverse(inverse(Y1)), identity) -> Y1 % 38.11/37.98 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1 % 38.11/37.98 multiply(inverse(least_upper_bound(identity, X0)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1 % 38.11/37.98 multiply(inverse(least_upper_bound(identity, inverse(identity))), Y1) -> Y1 % 38.11/37.98 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1 % 38.11/37.98 multiply(least_upper_bound(identity, inverse(identity)), Y0) -> Y0 % 38.11/37.98 multiply(least_upper_bound(identity, inverse(inverse(X0))), identity) -> least_upper_bound(identity, X0) % 38.11/37.98 multiply(least_upper_bound(inverse(Y1), Y2), Y1) -> least_upper_bound(identity, multiply(Y2, Y1)) % 38.11/37.98 multiply(least_upper_bound(inverse(c), inverse(b)), X1) -> multiply(inverse(b), X1) % 38.11/37.98 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 38.11/37.98 true__ -> false__ % 38.11/37.98 with the LPO induced by % 38.11/37.98 f1 > b > c > a > inverse > identity > least_upper_bound > greatest_lower_bound > multiply > true__ > false__ % 38.11/37.98 % 38.11/37.98 % SZS output end Proof % 38.11/37.98 %------------------------------------------------------------------------------