%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 10:53:39 EDT 2022 % Result : Unsatisfiable 158.63s 158.33s % Output : Proof 158.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.07/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n022.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Mon Jun 13 12:03:33 EDT 2022 % 0.14/0.36 % CPUTime : % 158.63/158.33 % SZS status Unsatisfiable % 158.63/158.33 % SZS output start Proof % 158.63/158.33 The input problem is unsatisfiable because % 158.63/158.33 % 158.63/158.33 [1] the following set of Horn clauses is unsatisfiable: % 158.63/158.33 % 158.63/158.33 multiply(identity, X) = X % 158.63/158.33 multiply(inverse(X), X) = identity % 158.63/158.33 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 158.63/158.33 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 158.63/158.33 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 158.63/158.33 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 158.63/158.33 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 158.63/158.33 least_upper_bound(X, X) = X % 158.63/158.33 greatest_lower_bound(X, X) = X % 158.63/158.33 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 158.63/158.33 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 158.63/158.33 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 158.63/158.33 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 158.63/158.33 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 158.63/158.33 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 158.63/158.33 greatest_lower_bound(inverse(a), inverse(b)) = inverse(a) % 158.63/158.33 greatest_lower_bound(a, b) = b ==> \bottom % 158.63/158.33 % 158.63/158.33 This holds because % 158.63/158.33 % 158.63/158.33 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 158.63/158.33 % 158.63/158.33 E: % 158.63/158.33 f1(b) = false__ % 158.63/158.33 f1(greatest_lower_bound(a, b)) = true__ % 158.63/158.33 greatest_lower_bound(X, X) = X % 158.63/158.33 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 158.63/158.33 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 158.63/158.33 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 158.63/158.33 greatest_lower_bound(inverse(a), inverse(b)) = inverse(a) % 158.63/158.33 least_upper_bound(X, X) = X % 158.63/158.33 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 158.63/158.33 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 158.63/158.33 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 158.63/158.33 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 158.63/158.33 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 158.63/158.33 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 158.63/158.33 multiply(identity, X) = X % 158.63/158.33 multiply(inverse(X), X) = identity % 158.63/158.33 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 158.63/158.33 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 158.63/158.33 G: % 158.63/158.33 true__ = false__ % 158.63/158.33 % 158.63/158.33 This holds because % 158.63/158.33 % 158.63/158.33 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 158.63/158.33 % 158.63/158.33 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 158.63/158.33 greatest_lower_bound(X1, multiply(X0, X1)) = multiply(greatest_lower_bound(identity, inverse(X0)), multiply(X0, X1)) % 158.63/158.33 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, Y1), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, Y1)), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(Y1, X2)), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, a), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(inverse(multiply(b, inverse(a))), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(a, inverse(b)), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(X0), least_upper_bound(X0, X1)), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(X0), least_upper_bound(X1, X0)), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(least_upper_bound(X0, inverse(X1)), X1), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(a), greatest_lower_bound(Y0, least_upper_bound(X0, inverse(b)))) % 158.63/158.33 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(a), greatest_lower_bound(Y0, least_upper_bound(inverse(b), X0))) % 158.63/158.33 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(a), greatest_lower_bound(least_upper_bound(X0, inverse(b)), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(a), greatest_lower_bound(least_upper_bound(inverse(b), X0), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), Y0) % 158.63/158.33 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, inverse(inverse(X0))), Y0) % 158.63/158.33 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(identity, multiply(X0, X1)), Y0) % 158.63/158.33 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(multiply(X0, X1), identity), Y0) % 158.63/158.33 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 158.63/158.33 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 158.63/158.33 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 158.63/158.33 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 158.63/158.33 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 158.63/158.33 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1) % 158.63/158.33 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1) % 158.63/158.33 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 158.63/158.33 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(X0, identity)) % 158.63/158.33 greatest_lower_bound(identity, greatest_lower_bound(multiply(b, inverse(a)), Y2)) = greatest_lower_bound(Y2, multiply(b, inverse(a))) % 158.63/158.33 greatest_lower_bound(identity, multiply(X0, inverse(X1))) = multiply(greatest_lower_bound(X0, X1), inverse(X1)) % 158.63/158.33 greatest_lower_bound(identity, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1) % 158.63/158.33 greatest_lower_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), greatest_lower_bound(Y1, Y2)) % 158.63/158.33 greatest_lower_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), greatest_lower_bound(Y1, Y2)) % 158.63/158.33 greatest_lower_bound(inverse(b), greatest_lower_bound(Y0, inverse(a))) = greatest_lower_bound(inverse(a), Y0) % 158.63/158.33 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)) % 158.63/158.33 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(X1, inverse(X0))) % 158.63/158.33 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(inverse(X0), X1)) % 158.63/158.33 greatest_lower_bound(multiply(Y0, Y1), identity) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1) % 158.63/158.33 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 158.63/158.33 least_upper_bound(X1, multiply(X0, X1)) = multiply(least_upper_bound(identity, inverse(X0)), multiply(X0, X1)) % 158.63/158.33 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, Y1), Y0)) % 158.63/158.33 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)), Y0)) % 158.63/158.33 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)), Y0)) % 158.63/158.33 least_upper_bound(Y0, a) = least_upper_bound(b, least_upper_bound(a, Y0)) % 158.63/158.33 least_upper_bound(Y0, identity) = least_upper_bound(identity, least_upper_bound(inverse(multiply(inverse(b), a)), Y0)) % 158.63/158.35 least_upper_bound(Y0, identity) = least_upper_bound(identity, least_upper_bound(multiply(b, inverse(a)), Y0)) % 158.63/158.35 least_upper_bound(Y0, identity) = least_upper_bound(identity, least_upper_bound(multiply(greatest_lower_bound(X0, inverse(X1)), X1), Y0)) % 158.63/158.35 least_upper_bound(Y0, least_upper_bound(X0, a)) = least_upper_bound(a, least_upper_bound(X0, Y0)) % 158.63/158.35 least_upper_bound(Y0, least_upper_bound(X0, a)) = least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(a, X0))) % 158.63/158.35 least_upper_bound(Y0, least_upper_bound(a, Y1)) = least_upper_bound(Y1, least_upper_bound(a, Y0)) % 158.63/158.35 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, inverse(inverse(X0))), Y0) % 158.63/158.35 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), Y0) % 158.63/158.35 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(identity, multiply(X0, X1)), Y0) % 158.63/158.35 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(multiply(X0, X1), identity), Y0) % 158.63/158.35 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1))) % 158.63/158.35 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0)) % 158.63/158.35 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1))) % 158.63/158.35 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0)) % 158.63/158.35 least_upper_bound(Y1, least_upper_bound(Y0, Y2)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 158.63/158.35 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1) % 158.63/158.35 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1) % 158.63/158.35 least_upper_bound(Y2, least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 158.63/158.35 least_upper_bound(b, least_upper_bound(X0, least_upper_bound(a, Y2))) = least_upper_bound(Y2, least_upper_bound(X0, a)) % 158.63/158.35 least_upper_bound(identity, least_upper_bound(X0, least_upper_bound(identity, Y2))) = least_upper_bound(Y2, least_upper_bound(X0, identity)) % 158.63/158.35 least_upper_bound(identity, least_upper_bound(multiply(a, inverse(b)), Y2)) = least_upper_bound(Y2, multiply(a, inverse(b))) % 158.63/158.35 least_upper_bound(identity, least_upper_bound(multiply(inverse(b), a), Y2)) = least_upper_bound(Y2, multiply(inverse(b), a)) % 158.63/158.35 least_upper_bound(identity, multiply(X0, inverse(X1))) = multiply(least_upper_bound(X0, X1), inverse(X1)) % 158.63/158.35 least_upper_bound(identity, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1) % 158.63/158.35 least_upper_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), least_upper_bound(Y1, Y2)) % 158.63/158.35 least_upper_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), least_upper_bound(Y1, Y2)) % 158.63/158.35 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(X1, inverse(X0))) % 158.63/158.35 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(inverse(X0), X1)) % 158.63/158.35 least_upper_bound(multiply(Y0, Y1), identity) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1) % 158.63/158.35 multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1)) % 158.63/158.35 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1)) % 158.63/158.35 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)))) % 158.63/158.35 multiply(greatest_lower_bound(X2, greatest_lower_bound(identity, X1)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1)) % 158.63/158.35 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)))) % 158.63/158.35 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)))) % 158.63/158.35 multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1)) % 158.63/158.35 multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1)) % 158.63/158.35 multiply(least_upper_bound(X2, least_upper_bound(identity, X1)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1)) % 158.63/158.35 multiply(least_upper_bound(Y1, multiply(X0, Y1)), Y2) = multiply(least_upper_bound(identity, X0), multiply(Y1, Y2)) % 158.63/158.35 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)))) % 158.63/158.35 f1(b) -> false__ % 158.63/158.35 f1(greatest_lower_bound(a, b)) -> true__ % 158.63/158.35 f1(greatest_lower_bound(b, a)) -> true__ % 158.63/158.35 greatest_lower_bound(X, X) -> X % 158.63/158.35 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X % 158.63/158.35 greatest_lower_bound(X1, inverse(multiply(inverse(X1), least_upper_bound(Y1, identity)))) -> inverse(multiply(inverse(X1), least_upper_bound(Y1, identity))) % 158.63/158.35 greatest_lower_bound(X1, inverse(multiply(inverse(X1), least_upper_bound(identity, Y1)))) -> inverse(multiply(inverse(X1), least_upper_bound(identity, Y1))) % 158.63/158.35 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) -> multiply(greatest_lower_bound(Y1, identity), multiply(inverse(Y1), X1)) % 158.63/158.35 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) -> multiply(greatest_lower_bound(identity, Y1), multiply(inverse(Y1), X1)) % 158.63/158.35 greatest_lower_bound(X1, multiply(inverse(least_upper_bound(Y1, identity)), X1)) -> multiply(inverse(least_upper_bound(Y1, identity)), X1) % 158.63/158.35 greatest_lower_bound(X1, multiply(inverse(least_upper_bound(identity, Y1)), X1)) -> multiply(inverse(least_upper_bound(identity, Y1)), X1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, greatest_lower_bound(Y0, Y1))))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, least_upper_bound(greatest_lower_bound(Y0, Y1), X2)))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(greatest_lower_bound(Y0, Y1), X1))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(least_upper_bound(X1, identity), greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(least_upper_bound(identity, X1), greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(Y2, least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y2) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, Y0), Y2)) -> greatest_lower_bound(Y0, Y2) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, Y0)), Y2)) -> greatest_lower_bound(Y0, Y2) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(Y0, X2)), Y2)) -> greatest_lower_bound(Y0, Y2) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(Y0, X1), Y2)) -> greatest_lower_bound(Y0, Y2) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(multiply(least_upper_bound(X1, identity), Y0), Y2)) -> greatest_lower_bound(Y0, Y2) % 158.63/158.35 greatest_lower_bound(Y0, greatest_lower_bound(multiply(least_upper_bound(identity, X1), Y0), Y2)) -> greatest_lower_bound(Y0, Y2) % 158.63/158.35 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y0))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y0, X2))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, Y0)))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(Y0, X2)))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y0))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y0))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X1)), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 158.63/158.35 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 158.63/158.35 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, multiply(X1, least_upper_bound(Y0, Y1))) % 158.63/158.35 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 158.63/158.35 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, multiply(X1, least_upper_bound(Y0, Y1))) % 158.63/158.35 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), least_upper_bound(Y0, Y1))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y0)) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y0)) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0 % 158.63/158.35 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), least_upper_bound(Y0, Y1))) -> Y0 % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(X1, multiply(greatest_lower_bound(X2, identity), Y1))) -> greatest_lower_bound(X1, multiply(greatest_lower_bound(X2, identity), Y1)) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, Y1))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y1)))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y1, X2)))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(Y1, X1))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y1))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y1))) -> greatest_lower_bound(Y0, Y1) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2) % 158.63/158.35 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), X1)) -> greatest_lower_bound(Y1, X1) % 158.63/158.35 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)) % 158.63/158.35 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)) % 158.63/158.35 greatest_lower_bound(Y1, multiply(a, multiply(inverse(b), Y1))) -> Y1 % 158.63/158.35 greatest_lower_bound(Y1, multiply(b, multiply(inverse(a), Y1))) -> multiply(b, multiply(inverse(a), Y1)) % 158.63/158.35 greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1)) -> multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) % 158.63/158.35 greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1)) -> multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) % 158.63/158.35 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1) % 158.63/158.35 greatest_lower_bound(Y1, multiply(inverse(b), multiply(a, Y1))) -> Y1 % 158.63/158.35 greatest_lower_bound(a, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(Y1, a) % 158.63/158.35 greatest_lower_bound(b, a) -> b % 158.63/158.35 greatest_lower_bound(b, greatest_lower_bound(X0, b)) -> greatest_lower_bound(b, X0) % 158.63/158.35 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(X0, a))) -> greatest_lower_bound(Y0, b) % 158.63/158.35 greatest_lower_bound(b, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(Y1, b) % 158.63/158.35 greatest_lower_bound(b, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(b, Y1) % 158.63/158.35 greatest_lower_bound(b, greatest_lower_bound(a, Y2)) -> greatest_lower_bound(b, Y2) % 158.63/158.35 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, a), Y2)) -> greatest_lower_bound(b, Y2) % 158.63/158.35 greatest_lower_bound(b, least_upper_bound(Y1, a)) -> b % 158.63/158.35 greatest_lower_bound(b, least_upper_bound(Y1, least_upper_bound(Y2, a))) -> b % 158.63/158.35 greatest_lower_bound(b, least_upper_bound(Y1, least_upper_bound(a, Y0))) -> b % 158.63/158.35 greatest_lower_bound(b, least_upper_bound(a, Y0)) -> b % 158.63/158.35 greatest_lower_bound(b, multiply(inverse(b), multiply(a, a))) -> b % 158.63/158.35 greatest_lower_bound(b, multiply(least_upper_bound(X1, identity), a)) -> b % 158.63/158.35 greatest_lower_bound(b, multiply(least_upper_bound(identity, X1), a)) -> b % 158.63/158.35 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z)) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) -> greatest_lower_bound(X0, greatest_lower_bound(identity, Y2)) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(X0, identity)) -> greatest_lower_bound(X0, identity) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(Y0, inverse(multiply(b, inverse(a))))) -> greatest_lower_bound(Y0, identity) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(a, inverse(b)))) -> greatest_lower_bound(Y0, identity) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(X0), least_upper_bound(X0, X1)))) -> greatest_lower_bound(Y0, identity) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(X0), least_upper_bound(X1, X0)))) -> greatest_lower_bound(Y0, identity) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(b), a))) -> greatest_lower_bound(Y0, identity) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(least_upper_bound(X0, inverse(X1)), X1))) -> greatest_lower_bound(Y0, identity) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(Y1, identity)) -> greatest_lower_bound(identity, Y1) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(multiply(a, inverse(b)), Y2)) -> greatest_lower_bound(identity, Y2) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(multiply(b, inverse(a)), Y2)) -> greatest_lower_bound(multiply(b, inverse(a)), Y2) % 158.63/158.35 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y2)) -> greatest_lower_bound(identity, Y2) % 158.63/158.35 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(Y1, identity), inverse(Y1)) % 158.63/158.35 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(identity, Y1), inverse(Y1)) % 158.63/158.35 greatest_lower_bound(identity, inverse(a)) -> multiply(greatest_lower_bound(identity, a), inverse(a)) % 158.63/158.35 greatest_lower_bound(identity, inverse(b)) -> multiply(greatest_lower_bound(identity, b), inverse(b)) % 158.63/158.35 greatest_lower_bound(identity, inverse(identity)) -> identity % 158.63/158.35 greatest_lower_bound(identity, inverse(inverse(Y0))) -> greatest_lower_bound(identity, Y0) % 158.63/158.35 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, identity))) -> inverse(least_upper_bound(Y1, identity)) % 158.63/158.35 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, least_upper_bound(Y2, identity)))) -> inverse(least_upper_bound(Y1, least_upper_bound(Y2, identity))) % 158.63/158.35 greatest_lower_bound(identity, inverse(least_upper_bound(identity, Y1))) -> inverse(least_upper_bound(identity, Y1)) % 158.63/158.35 greatest_lower_bound(identity, inverse(multiply(X0, greatest_lower_bound(X1, inverse(X0))))) -> identity % 158.63/158.35 greatest_lower_bound(identity, inverse(multiply(X0, greatest_lower_bound(inverse(X0), X1)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(Y0, inverse(identity))) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(greatest_lower_bound(identity, inverse(identity))))) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(inverse(identity)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(least_upper_bound(identity, inverse(identity))))) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(inverse(identity), Y1)) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(inverse(inverse(identity)), Y1)) -> identity % 158.63/158.35 greatest_lower_bound(identity, least_upper_bound(inverse(least_upper_bound(identity, inverse(identity))), Y1)) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(X1, inverse(X0)))) -> multiply(X0, greatest_lower_bound(X1, inverse(X0))) % 158.63/158.35 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), X1))) -> multiply(X0, greatest_lower_bound(inverse(X0), X1)) % 158.63/158.35 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(X0)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(inverse(inverse(X0)))))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(X0), Y1))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(inverse(inverse(X0))), Y1))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1))) % 158.63/158.35 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1))) % 158.63/158.35 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, Y0)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(Y0, X1)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(a, inverse(b))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(b, inverse(a))) -> multiply(b, inverse(a)) % 158.63/158.35 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, X1), inverse(X1))) -> multiply(greatest_lower_bound(X0, X1), inverse(X1)) % 158.63/158.35 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> multiply(greatest_lower_bound(X0, inverse(X1)), X1) % 158.63/158.35 greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, X0), inverse(X0))) -> multiply(greatest_lower_bound(identity, X0), inverse(X0)) % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> multiply(inverse(X0), greatest_lower_bound(X0, X1)) % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(X0), greatest_lower_bound(X1, X0))) -> multiply(inverse(X0), greatest_lower_bound(X1, X0)) % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(Y0), least_upper_bound(X1, least_upper_bound(Y0, X2)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(Y0), multiply(least_upper_bound(identity, X1), Y0))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(b), a)) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(X0, a))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(a, X0))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(X0, a), inverse(least_upper_bound(a, X0)))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(X0, identity), least_upper_bound(identity, Y1))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, X0), inverse(X0))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, identity), inverse(Y0))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(Y1, Y0), inverse(Y1))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(a, Y0), inverse(a))) -> identity % 158.63/158.35 greatest_lower_bound(identity, multiply(least_upper_bound(identity, X0), inverse(X0))) -> identity % 158.63/158.35 greatest_lower_bound(inverse(X1), inverse(multiply(X1, least_upper_bound(Y1, identity)))) -> inverse(multiply(X1, least_upper_bound(Y1, identity))) % 158.63/158.35 greatest_lower_bound(inverse(X1), inverse(multiply(X1, least_upper_bound(identity, Y1)))) -> inverse(multiply(X1, least_upper_bound(identity, Y1))) % 158.63/158.35 greatest_lower_bound(inverse(a), greatest_lower_bound(X0, least_upper_bound(Y1, inverse(b)))) -> greatest_lower_bound(inverse(a), X0) % 158.73/158.35 greatest_lower_bound(inverse(a), greatest_lower_bound(inverse(b), Y2)) -> greatest_lower_bound(inverse(a), Y2) % 158.73/158.35 greatest_lower_bound(inverse(a), inverse(b)) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(a), least_upper_bound(X1, inverse(b))) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(a), least_upper_bound(X1, least_upper_bound(X2, inverse(b)))) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(a), least_upper_bound(X1, least_upper_bound(inverse(b), X2))) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(a), least_upper_bound(inverse(b), X1)) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(a), multiply(least_upper_bound(X1, identity), inverse(b))) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(a), multiply(least_upper_bound(identity, X1), inverse(b))) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(b), greatest_lower_bound(Y0, inverse(a))) -> greatest_lower_bound(Y0, inverse(a)) % 158.73/158.35 greatest_lower_bound(inverse(b), greatest_lower_bound(Y1, inverse(b))) -> greatest_lower_bound(Y1, inverse(b)) % 158.73/158.35 greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y2)) -> greatest_lower_bound(inverse(a), Y2) % 158.73/158.35 greatest_lower_bound(inverse(b), inverse(a)) -> inverse(a) % 158.73/158.35 greatest_lower_bound(inverse(least_upper_bound(Y2, identity)), least_upper_bound(Y1, identity)) -> inverse(least_upper_bound(Y2, identity)) % 158.73/158.35 greatest_lower_bound(inverse(least_upper_bound(identity, Y2)), least_upper_bound(Y1, identity)) -> inverse(least_upper_bound(identity, Y2)) % 158.73/158.35 greatest_lower_bound(inverse(multiply(X1, inverse(b))), multiply(a, inverse(X1))) -> inverse(multiply(X1, inverse(b))) % 158.73/158.35 greatest_lower_bound(inverse(multiply(inverse(b), a)), least_upper_bound(Y1, identity)) -> inverse(multiply(inverse(b), a)) % 158.73/158.35 greatest_lower_bound(least_upper_bound(X0, X1), least_upper_bound(X0, least_upper_bound(X1, Y1))) -> least_upper_bound(X0, X1) % 158.73/158.35 greatest_lower_bound(least_upper_bound(X0, identity), least_upper_bound(Y1, least_upper_bound(identity, X0))) -> least_upper_bound(X0, identity) % 158.73/158.35 greatest_lower_bound(least_upper_bound(X0, identity), least_upper_bound(identity, X0)) -> least_upper_bound(X0, identity) % 158.73/158.35 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X1, least_upper_bound(Y1, X2))) -> least_upper_bound(X1, X2) % 158.73/158.35 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X2, least_upper_bound(Y1, X1))) -> least_upper_bound(X1, X2) % 158.73/158.35 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) % 158.73/158.35 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) % 158.73/158.35 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) % 158.73/158.35 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)) % 158.73/158.35 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)) % 158.73/158.35 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)) % 158.73/158.35 greatest_lower_bound(least_upper_bound(Y0, inverse(b)), inverse(a)) -> inverse(a) % 158.73/158.35 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) % 158.73/158.35 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) % 158.73/158.35 greatest_lower_bound(least_upper_bound(Y2, X1), greatest_lower_bound(Y1, least_upper_bound(Y2, X1))) -> greatest_lower_bound(Y1, least_upper_bound(Y2, X1)) % 158.73/158.35 greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(X0, a)) -> least_upper_bound(a, X0) % 158.73/158.35 greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(Y1, least_upper_bound(X0, a))) -> least_upper_bound(a, X0) % 158.73/158.35 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) % 158.73/158.35 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) % 158.73/158.35 greatest_lower_bound(least_upper_bound(greatest_lower_bound(Y2, X1), X2), least_upper_bound(Y1, least_upper_bound(Y2, X2))) -> least_upper_bound(greatest_lower_bound(Y2, X1), X2) % 158.73/158.35 greatest_lower_bound(least_upper_bound(inverse(b), Y0), inverse(a)) -> inverse(a) % 158.73/158.35 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z)) % 158.73/158.35 greatest_lower_bound(multiply(X0, greatest_lower_bound(X1, X2)), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X0, X2), Y2)) % 158.73/158.35 greatest_lower_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(greatest_lower_bound(multiply(X0, X1), Y2), Y1) % 158.73/158.35 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y2))) -> multiply(X1, Y2) % 158.73/158.35 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y2))) -> multiply(X1, Y2) % 158.73/158.35 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X) % 158.73/158.35 greatest_lower_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(greatest_lower_bound(Y0, multiply(X0, X1)), Y1) % 158.73/158.35 greatest_lower_bound(multiply(b, inverse(a)), least_upper_bound(Y1, identity)) -> multiply(b, inverse(a)) % 158.73/158.35 greatest_lower_bound(multiply(b, multiply(inverse(a), Y2)), least_upper_bound(Y1, Y2)) -> multiply(b, multiply(inverse(a), Y2)) % 158.73/158.35 greatest_lower_bound(multiply(greatest_lower_bound(X0, X2), X1), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X2, X1), Y2)) % 158.73/158.35 greatest_lower_bound(multiply(inverse(b), X1), inverse(multiply(inverse(X1), a))) -> inverse(multiply(inverse(X1), a)) % 158.73/158.35 greatest_lower_bound(multiply(inverse(b), inverse(X1)), inverse(multiply(X1, a))) -> inverse(multiply(X1, a)) % 158.73/158.35 greatest_lower_bound(multiply(inverse(least_upper_bound(Y2, identity)), X1), least_upper_bound(Y1, X1)) -> multiply(inverse(least_upper_bound(Y2, identity)), X1) % 158.73/158.35 greatest_lower_bound(multiply(inverse(least_upper_bound(identity, Y2)), X1), least_upper_bound(Y1, X1)) -> multiply(inverse(least_upper_bound(identity, Y2)), X1) % 158.73/158.35 greatest_lower_bound(multiply(least_upper_bound(X1, identity), inverse(b)), inverse(a)) -> inverse(a) % 158.73/158.35 greatest_lower_bound(multiply(least_upper_bound(identity, X1), inverse(b)), inverse(a)) -> inverse(a) % 158.73/158.35 inverse(greatest_lower_bound(identity, inverse(identity))) -> identity % 158.73/158.35 inverse(greatest_lower_bound(identity, least_upper_bound(X0, inverse(identity)))) -> identity % 158.73/158.35 inverse(identity) -> identity % 158.73/158.35 inverse(inverse(Y0)) -> Y0 % 158.73/158.35 inverse(inverse(identity)) -> identity % 158.73/158.35 inverse(least_upper_bound(identity, greatest_lower_bound(X0, inverse(identity)))) -> identity % 158.73/158.35 inverse(least_upper_bound(identity, inverse(identity))) -> identity % 158.73/158.35 inverse(multiply(X1, Y0)) -> multiply(inverse(Y0), inverse(X1)) % 158.73/158.35 inverse(multiply(X1, a)) -> multiply(inverse(a), inverse(X1)) % 158.73/158.35 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1)) % 158.73/158.35 inverse(multiply(inverse(X1), Y0)) -> multiply(inverse(Y0), X1) % 158.73/158.35 inverse(multiply(inverse(X1), a)) -> multiply(inverse(a), X1) % 158.73/158.35 inverse(multiply(inverse(X1), inverse(Y0))) -> multiply(Y0, X1) % 158.73/158.35 least_upper_bound(X, X) -> X % 158.73/158.35 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X % 158.73/158.35 least_upper_bound(X0, least_upper_bound(X1, least_upper_bound(a, greatest_lower_bound(Y1, b)))) -> least_upper_bound(X0, least_upper_bound(X1, a)) % 158.73/158.35 least_upper_bound(X0, least_upper_bound(a, greatest_lower_bound(Y1, b))) -> least_upper_bound(X0, a) % 158.73/158.35 least_upper_bound(X0, least_upper_bound(inverse(b), greatest_lower_bound(Y1, inverse(a)))) -> least_upper_bound(X0, inverse(b)) % 158.73/158.35 least_upper_bound(X1, inverse(multiply(inverse(X1), greatest_lower_bound(Y1, identity)))) -> inverse(multiply(inverse(X1), greatest_lower_bound(Y1, identity))) % 158.73/158.35 least_upper_bound(X1, inverse(multiply(inverse(X1), greatest_lower_bound(identity, Y1)))) -> inverse(multiply(inverse(X1), greatest_lower_bound(identity, Y1))) % 158.73/158.35 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(Y1, identity), multiply(inverse(Y1), X1)) % 158.73/158.35 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(identity, Y1), multiply(inverse(Y1), X1)) % 158.73/158.35 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(Y1, identity)), X1)) -> multiply(inverse(greatest_lower_bound(Y1, identity)), X1) % 158.73/158.35 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(identity, Y1)), X1)) -> multiply(inverse(greatest_lower_bound(identity, Y1)), X1) % 158.73/158.35 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))) -> Y0 % 158.73/158.35 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))) -> Y0 % 158.73/158.35 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0 % 158.73/158.35 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0)))) -> Y0 % 158.73/158.35 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2)))) -> Y0 % 158.73/158.35 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y0))) -> Y0 % 158.73/158.35 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y0))) -> Y0 % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, least_upper_bound(Y0, Y1))))) -> least_upper_bound(Y0, Y1) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(least_upper_bound(Y0, Y1), X2)))) -> least_upper_bound(Y0, Y1) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(least_upper_bound(Y0, Y1), X1))) -> least_upper_bound(Y0, Y1) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y1, multiply(greatest_lower_bound(X1, identity), least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y1, multiply(greatest_lower_bound(identity, X1), least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(Y2, greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, Y2) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(a, Y0)) -> least_upper_bound(Y0, a) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0)), Y2)) -> least_upper_bound(Y0, Y2) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2)), Y2)) -> least_upper_bound(Y0, Y2) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y0, X1), Y2)) -> least_upper_bound(Y0, Y2) % 158.73/158.35 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y1, Y0), Y2)) -> least_upper_bound(Y0, Y2) % 158.73/158.36 least_upper_bound(Y0, least_upper_bound(multiply(greatest_lower_bound(X1, identity), Y0), Y2)) -> least_upper_bound(Y0, Y2) % 158.73/158.36 least_upper_bound(Y0, least_upper_bound(multiply(greatest_lower_bound(identity, X1), Y0), Y2)) -> least_upper_bound(Y0, Y2) % 158.73/158.36 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y0)) -> Y0 % 158.73/158.36 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y0)) -> Y0 % 158.73/158.36 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> Y0 % 158.73/158.36 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), greatest_lower_bound(Y0, Y1))) -> Y0 % 158.73/158.36 least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> Y0 % 158.73/158.36 least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), greatest_lower_bound(Y0, Y1))) -> Y0 % 158.73/158.36 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 158.73/158.36 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))) % 158.73/158.36 least_upper_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 158.73/158.36 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0)) % 158.73/158.36 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))) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(X1, multiply(least_upper_bound(X2, identity), Y1))) -> least_upper_bound(X1, multiply(least_upper_bound(X2, identity), Y1)) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, Y1))) -> least_upper_bound(Y0, Y1) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> least_upper_bound(Y0, Y1) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> least_upper_bound(Y0, Y1) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(Y1, X1))) -> least_upper_bound(Y0, Y1) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1))) -> least_upper_bound(Y0, Y1) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1))) -> least_upper_bound(Y0, Y1) % 158.73/158.36 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2) % 158.73/158.36 least_upper_bound(Y1, multiply(a, multiply(inverse(b), Y1))) -> multiply(a, multiply(inverse(b), Y1)) % 158.73/158.36 least_upper_bound(Y1, multiply(b, multiply(inverse(a), Y1))) -> Y1 % 158.73/158.36 least_upper_bound(Y1, multiply(inverse(b), multiply(a, Y1))) -> multiply(inverse(b), multiply(a, Y1)) % 158.73/158.36 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) % 158.73/158.36 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) % 158.73/158.36 least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y1)) -> multiply(least_upper_bound(identity, X1), Y1) % 158.73/158.36 least_upper_bound(a, greatest_lower_bound(Y1, b)) -> a % 158.73/158.36 least_upper_bound(a, greatest_lower_bound(Y1, greatest_lower_bound(Y2, b))) -> a % 158.73/158.36 least_upper_bound(a, greatest_lower_bound(b, Y2)) -> a % 158.73/158.36 least_upper_bound(b, a) -> a % 158.73/158.36 least_upper_bound(b, least_upper_bound(X0, least_upper_bound(X1, a))) -> least_upper_bound(X0, least_upper_bound(X1, a)) % 158.73/158.36 least_upper_bound(b, least_upper_bound(X0, least_upper_bound(a, Y2))) -> least_upper_bound(X0, least_upper_bound(a, Y2)) % 158.73/158.36 least_upper_bound(b, least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 158.73/158.36 least_upper_bound(b, least_upper_bound(Y1, b)) -> least_upper_bound(Y1, b) % 158.73/158.36 least_upper_bound(b, least_upper_bound(Y1, b)) -> least_upper_bound(b, Y1) % 158.73/158.36 least_upper_bound(b, least_upper_bound(a, Y2)) -> least_upper_bound(a, Y2) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X0, X1), greatest_lower_bound(X0, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X0, X1) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(X0, b))) -> greatest_lower_bound(X0, a) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> greatest_lower_bound(X0, a) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, a) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(X0, a)) -> greatest_lower_bound(X0, a) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X0, identity), greatest_lower_bound(Y1, greatest_lower_bound(identity, X0))) -> greatest_lower_bound(X0, identity) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X0, identity), greatest_lower_bound(identity, X0)) -> greatest_lower_bound(X0, identity) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))) -> greatest_lower_bound(X1, X2) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))) -> greatest_lower_bound(X1, X2) % 158.73/158.36 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) % 158.73/158.36 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) % 158.73/158.36 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) % 158.73/158.36 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)) % 158.73/158.36 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)) % 158.73/158.36 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)) % 158.73/158.36 least_upper_bound(greatest_lower_bound(X1, least_upper_bound(Y2, X2)), greatest_lower_bound(Y1, greatest_lower_bound(X1, Y2))) -> greatest_lower_bound(X1, least_upper_bound(Y2, X2)) % 158.73/158.36 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) % 158.73/158.36 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) % 158.73/158.36 least_upper_bound(greatest_lower_bound(Y2, X1), least_upper_bound(Y1, greatest_lower_bound(Y2, X1))) -> least_upper_bound(Y1, greatest_lower_bound(Y2, X1)) % 158.73/158.36 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> greatest_lower_bound(a, X0) % 158.73/158.36 least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(a, X0)) -> greatest_lower_bound(a, X0) % 158.73/158.36 least_upper_bound(greatest_lower_bound(inverse(b), X0), greatest_lower_bound(inverse(a), X0)) -> greatest_lower_bound(inverse(b), X0) % 158.73/158.36 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) % 158.73/158.36 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) % 158.73/158.36 least_upper_bound(greatest_lower_bound(least_upper_bound(Y2, X1), X2), greatest_lower_bound(Y1, greatest_lower_bound(Y2, X2))) -> greatest_lower_bound(least_upper_bound(Y2, X1), X2) % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(Y0, inverse(identity))) -> identity % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(Y1, inverse(greatest_lower_bound(identity, inverse(identity))))) -> identity % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(Y1, inverse(inverse(identity)))) -> identity % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(Y1, inverse(least_upper_bound(identity, inverse(identity))))) -> identity % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)) -> identity % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(inverse(identity), Y1)) -> identity % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(inverse(inverse(identity)), Y1)) -> identity % 158.73/158.36 least_upper_bound(identity, greatest_lower_bound(inverse(least_upper_bound(identity, inverse(identity))), Y1)) -> identity % 158.73/158.36 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(Y1, identity), inverse(Y1)) % 158.73/158.36 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(identity, Y1), inverse(Y1)) % 158.73/158.36 least_upper_bound(identity, inverse(a)) -> multiply(least_upper_bound(identity, a), inverse(a)) % 158.73/158.36 least_upper_bound(identity, inverse(b)) -> multiply(least_upper_bound(identity, b), inverse(b)) % 158.73/158.36 least_upper_bound(identity, inverse(greatest_lower_bound(Y1, greatest_lower_bound(Y2, identity)))) -> inverse(greatest_lower_bound(Y1, greatest_lower_bound(Y2, identity))) % 158.73/158.36 least_upper_bound(identity, inverse(greatest_lower_bound(Y1, identity))) -> inverse(greatest_lower_bound(Y1, identity)) % 158.73/158.36 least_upper_bound(identity, inverse(greatest_lower_bound(identity, Y1))) -> inverse(greatest_lower_bound(identity, Y1)) % 158.73/158.36 least_upper_bound(identity, inverse(identity)) -> identity % 158.73/158.36 least_upper_bound(identity, inverse(inverse(Y0))) -> least_upper_bound(identity, Y0) % 158.73/158.36 least_upper_bound(identity, inverse(multiply(X0, least_upper_bound(X1, inverse(X0))))) -> identity % 158.73/158.36 least_upper_bound(identity, inverse(multiply(X0, least_upper_bound(inverse(X0), X1)))) -> identity % 158.73/158.36 least_upper_bound(identity, inverse(multiply(inverse(b), a))) -> identity % 158.73/158.36 least_upper_bound(identity, least_upper_bound(X0, identity)) -> least_upper_bound(X0, identity) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(X0, least_upper_bound(identity, Y2))) -> least_upper_bound(X0, least_upper_bound(identity, Y2)) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(Y0, inverse(multiply(inverse(b), a)))) -> least_upper_bound(Y0, identity) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(Y0, multiply(b, inverse(a)))) -> least_upper_bound(Y0, identity) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(Y0, multiply(greatest_lower_bound(X0, inverse(X1)), X1))) -> least_upper_bound(Y0, identity) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(Y1, identity)) -> least_upper_bound(identity, Y1) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(multiply(a, inverse(b)), Y2)) -> least_upper_bound(multiply(a, inverse(b)), Y2) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(multiply(b, inverse(a)), Y2)) -> least_upper_bound(identity, Y2) % 158.73/158.36 least_upper_bound(identity, least_upper_bound(multiply(inverse(b), a), Y2)) -> least_upper_bound(multiply(inverse(b), a), Y2) % 158.73/158.36 least_upper_bound(identity, multiply(X0, greatest_lower_bound(Y1, inverse(X0)))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(X0, greatest_lower_bound(Y1, inverse(inverse(inverse(X0)))))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), Y1))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(X0, greatest_lower_bound(inverse(inverse(inverse(X0))), Y1))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(X0, least_upper_bound(X1, inverse(X0)))) -> multiply(X0, least_upper_bound(X1, inverse(X0))) % 158.73/158.36 least_upper_bound(identity, multiply(X0, least_upper_bound(inverse(X0), X1))) -> multiply(X0, least_upper_bound(inverse(X0), X1)) % 158.73/158.36 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, Y0)))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, least_upper_bound(X2, Y0))))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, least_upper_bound(Y0, X2))))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(Y0, X1)))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(a, inverse(b))) -> multiply(a, inverse(b)) % 158.73/158.36 least_upper_bound(identity, multiply(b, inverse(a))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(X0, a)))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(greatest_lower_bound(X0, identity), greatest_lower_bound(identity, Y1))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, X0), inverse(X0))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, identity), inverse(Y0))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(greatest_lower_bound(Y1, Y0), inverse(Y1))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(greatest_lower_bound(a, X0)))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(greatest_lower_bound(identity, X0), inverse(X0))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(inverse(X0), greatest_lower_bound(X1, X0))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> multiply(inverse(X0), least_upper_bound(X0, X1)) % 158.73/158.36 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> multiply(inverse(X0), least_upper_bound(X1, X0)) % 158.73/158.36 least_upper_bound(identity, multiply(inverse(Y0), multiply(greatest_lower_bound(identity, X1), Y0))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(inverse(b), a)) -> multiply(inverse(b), a) % 158.73/158.36 least_upper_bound(identity, multiply(inverse(b), least_upper_bound(greatest_lower_bound(false__, b), a))) -> multiply(inverse(b), a) % 158.73/158.36 least_upper_bound(identity, multiply(inverse(least_upper_bound(X0, inverse(b))), inverse(a))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(inverse(least_upper_bound(inverse(b), X0)), inverse(a))) -> identity % 158.73/158.36 least_upper_bound(identity, multiply(least_upper_bound(X0, X1), inverse(X1))) -> multiply(least_upper_bound(X0, X1), inverse(X1)) % 158.73/158.36 least_upper_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> multiply(least_upper_bound(X0, inverse(X1)), X1) % 158.73/158.36 least_upper_bound(identity, multiply(least_upper_bound(identity, X0), inverse(X0))) -> multiply(least_upper_bound(identity, X0), inverse(X0)) % 158.73/158.36 least_upper_bound(inverse(X1), inverse(multiply(X1, greatest_lower_bound(Y1, identity)))) -> inverse(multiply(X1, greatest_lower_bound(Y1, identity))) % 158.73/158.36 least_upper_bound(inverse(X1), inverse(multiply(X1, greatest_lower_bound(identity, Y1)))) -> inverse(multiply(X1, greatest_lower_bound(identity, Y1))) % 158.73/158.36 least_upper_bound(inverse(a), least_upper_bound(Y1, inverse(a))) -> least_upper_bound(Y1, inverse(a)) % 158.73/158.36 least_upper_bound(inverse(b), greatest_lower_bound(Y1, greatest_lower_bound(Y2, inverse(a)))) -> inverse(b) % 158.73/158.36 least_upper_bound(inverse(b), greatest_lower_bound(Y1, inverse(a))) -> inverse(b) % 158.73/158.36 least_upper_bound(inverse(b), greatest_lower_bound(inverse(a), Y0)) -> inverse(b) % 158.73/158.36 least_upper_bound(inverse(b), inverse(a)) -> inverse(b) % 158.73/158.36 least_upper_bound(inverse(b), least_upper_bound(X0, greatest_lower_bound(Y1, inverse(a)))) -> least_upper_bound(inverse(b), X0) % 158.73/158.36 least_upper_bound(inverse(b), least_upper_bound(X0, inverse(a))) -> least_upper_bound(inverse(b), X0) % 158.73/158.36 least_upper_bound(inverse(b), least_upper_bound(Y0, inverse(a))) -> least_upper_bound(Y0, inverse(b)) % 158.73/158.36 least_upper_bound(inverse(b), least_upper_bound(inverse(a), Y2)) -> least_upper_bound(inverse(b), Y2) % 158.73/158.36 least_upper_bound(inverse(greatest_lower_bound(Y2, identity)), greatest_lower_bound(Y1, identity)) -> inverse(greatest_lower_bound(Y2, identity)) % 158.73/158.36 least_upper_bound(inverse(greatest_lower_bound(identity, Y2)), greatest_lower_bound(Y1, identity)) -> inverse(greatest_lower_bound(identity, Y2)) % 158.73/158.36 least_upper_bound(inverse(multiply(b, inverse(a))), greatest_lower_bound(Y1, identity)) -> inverse(multiply(b, inverse(a))) % 158.73/158.36 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z)) % 158.73/158.36 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z)) % 158.73/158.36 least_upper_bound(multiply(X0, least_upper_bound(X1, X2)), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X0, X2), Y2)) % 158.73/158.36 least_upper_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(least_upper_bound(multiply(X0, X1), Y2), Y1) % 158.73/158.36 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y2))) -> multiply(X1, Y2) % 158.73/158.36 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y2))) -> multiply(X1, Y2) % 158.73/158.36 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X) % 158.73/158.36 least_upper_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(least_upper_bound(Y0, multiply(X0, X1)), Y1) % 158.73/158.36 least_upper_bound(multiply(a, inverse(b)), greatest_lower_bound(Y1, identity)) -> multiply(a, inverse(b)) % 158.73/158.36 least_upper_bound(multiply(a, multiply(inverse(b), Y2)), greatest_lower_bound(Y1, Y2)) -> multiply(a, multiply(inverse(b), Y2)) % 158.73/158.36 least_upper_bound(multiply(b, X1), inverse(multiply(inverse(X1), inverse(a)))) -> inverse(multiply(inverse(X1), inverse(a))) % 158.73/158.36 least_upper_bound(multiply(b, inverse(X1)), inverse(multiply(X1, inverse(a)))) -> inverse(multiply(X1, inverse(a))) % 158.73/158.36 least_upper_bound(multiply(inverse(b), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(b), a) % 158.73/158.36 least_upper_bound(multiply(inverse(b), multiply(a, Y2)), greatest_lower_bound(Y1, Y2)) -> multiply(inverse(b), multiply(a, Y2)) % 158.73/158.36 least_upper_bound(multiply(inverse(greatest_lower_bound(identity, Y2)), X1), greatest_lower_bound(Y1, X1)) -> multiply(inverse(greatest_lower_bound(identity, Y2)), X1) % 158.73/158.36 least_upper_bound(multiply(least_upper_bound(X0, X2), X1), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X2, X1), Y2)) % 158.73/158.36 multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0) % 158.73/158.36 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0 % 158.73/158.36 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))) % 158.73/158.36 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))) % 158.73/158.36 multiply(Y0, inverse(Y0)) -> identity % 158.73/158.36 multiply(Y0, inverse(inverse(inverse(Y0)))) -> identity % 158.73/158.36 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity % 158.73/158.36 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1 % 158.73/158.36 multiply(Y0, multiply(inverse(Y0), X1)) -> X1 % 158.73/158.36 multiply(Y0, multiply(inverse(multiply(X1, Y0)), X1)) -> identity % 158.73/158.36 multiply(Y0, multiply(inverse(multiply(inverse(X1), Y0)), inverse(X1))) -> identity % 158.73/158.36 multiply(Y1, identity) -> Y1 % 158.73/158.36 multiply(a, inverse(a)) -> identity % 158.73/158.36 multiply(b, inverse(b)) -> identity % 158.73/158.36 multiply(greatest_lower_bound(identity, X0), inverse(greatest_lower_bound(X0, identity))) -> identity % 158.73/158.36 multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), inverse(greatest_lower_bound(X0, identity))) -> identity % 158.73/158.36 multiply(greatest_lower_bound(identity, inverse(a)), least_upper_bound(b, a)) -> greatest_lower_bound(identity, least_upper_bound(b, a)) % 158.73/158.36 multiply(greatest_lower_bound(identity, inverse(identity)), Y0) -> Y0 % 158.73/158.36 multiply(greatest_lower_bound(identity, inverse(inverse(X0))), identity) -> greatest_lower_bound(identity, X0) % 158.73/158.36 multiply(greatest_lower_bound(identity, inverse(multiply(greatest_lower_bound(X0, inverse(X1)), X1))), identity) -> identity % 158.73/158.36 multiply(greatest_lower_bound(identity, inverse(multiply(inverse(X0), greatest_lower_bound(X0, X1)))), identity) -> identity % 158.73/158.36 multiply(greatest_lower_bound(identity, inverse(multiply(inverse(X0), greatest_lower_bound(X1, X0)))), identity) -> identity % 158.73/158.36 multiply(greatest_lower_bound(identity, least_upper_bound(X0, inverse(identity))), identity) -> identity % 158.73/158.36 multiply(greatest_lower_bound(inverse(Y1), Y2), Y1) -> greatest_lower_bound(identity, multiply(Y2, Y1)) % 158.73/158.36 multiply(identity, X) -> X % 158.73/158.36 multiply(inverse(X), X) -> identity % 158.73/158.36 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 158.73/158.36 multiply(inverse(a), greatest_lower_bound(b, a)) -> multiply(inverse(a), b) % 158.73/158.36 multiply(inverse(a), least_upper_bound(b, a)) -> identity % 158.73/158.36 multiply(inverse(a), multiply(least_upper_bound(b, a), Y2)) -> Y2 % 158.73/158.36 multiply(inverse(greatest_lower_bound(X0, a)), least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(X0, a))) -> identity % 158.73/158.36 multiply(inverse(greatest_lower_bound(X0, a)), least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(X0, a))) -> identity % 158.73/158.36 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 158.73/158.36 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(identity, X0)) -> identity % 158.73/158.36 multiply(inverse(greatest_lower_bound(X0, identity)), least_upper_bound(greatest_lower_bound(identity, X0), greatest_lower_bound(X0, identity))) -> identity % 158.73/158.36 multiply(inverse(greatest_lower_bound(X0, inverse(Y1))), greatest_lower_bound(multiply(X0, Y1), identity)) -> Y1 % 158.73/158.36 multiply(inverse(greatest_lower_bound(a, X0)), least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(a, X0))) -> identity % 158.73/158.36 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(X0, identity)) -> identity % 158.73/158.36 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 158.73/158.36 multiply(inverse(greatest_lower_bound(identity, inverse(identity))), Y1) -> Y1 % 158.73/158.36 multiply(inverse(greatest_lower_bound(inverse(Y1), X1)), greatest_lower_bound(identity, multiply(X1, Y1))) -> Y1 % 158.73/158.36 multiply(inverse(identity), Y1) -> Y1 % 158.73/158.36 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1) % 158.73/158.36 multiply(inverse(inverse(Y1)), identity) -> Y1 % 158.73/158.36 multiply(inverse(least_upper_bound(X0, identity)), greatest_lower_bound(least_upper_bound(identity, X0), least_upper_bound(X0, identity))) -> identity % 158.73/158.36 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1 % 158.73/158.36 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(identity, X0)) -> identity % 158.73/158.36 multiply(inverse(least_upper_bound(X0, inverse(Y1))), least_upper_bound(multiply(X0, Y1), identity)) -> Y1 % 158.73/158.36 multiply(inverse(least_upper_bound(X0, least_upper_bound(X1, a))), least_upper_bound(b, least_upper_bound(X0, least_upper_bound(X1, a)))) -> identity % 158.73/158.36 multiply(inverse(least_upper_bound(a, X0)), greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(a, X0))) -> identity % 158.73/158.36 multiply(inverse(least_upper_bound(identity, X0)), least_upper_bound(X0, identity)) -> identity % 158.73/158.36 multiply(inverse(least_upper_bound(identity, X0)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1 % 158.73/158.36 multiply(inverse(least_upper_bound(identity, inverse(identity))), Y1) -> Y1 % 158.73/158.36 multiply(inverse(least_upper_bound(inverse(Y1), X1)), least_upper_bound(identity, multiply(X1, Y1))) -> Y1 % 158.73/158.36 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1 % 158.73/158.36 multiply(inverse(multiply(X1, Y1)), X1) -> inverse(Y1) % 158.73/158.36 multiply(inverse(multiply(X1, inverse(Y1))), X1) -> Y1 % 158.73/158.36 multiply(inverse(multiply(b, multiply(inverse(a), Y1))), greatest_lower_bound(Y1, multiply(b, multiply(inverse(a), Y1)))) -> identity % 158.73/158.36 multiply(inverse(multiply(greatest_lower_bound(X1, identity), Y1)), greatest_lower_bound(Y1, multiply(X1, Y1))) -> identity % 158.73/158.36 multiply(inverse(multiply(inverse(X1), Y1)), inverse(X1)) -> inverse(Y1) % 158.73/158.36 multiply(inverse(multiply(inverse(X1), inverse(Y1))), inverse(X1)) -> Y1 % 158.73/158.36 multiply(inverse(multiply(inverse(b), multiply(a, Y1))), least_upper_bound(Y1, multiply(inverse(b), multiply(a, Y1)))) -> identity % 158.73/158.36 multiply(inverse(multiply(least_upper_bound(X1, identity), Y1)), least_upper_bound(Y1, multiply(X1, Y1))) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, X0), inverse(least_upper_bound(X0, identity))) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, greatest_lower_bound(X0, inverse(identity))), identity) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, inverse(a)), least_upper_bound(b, a)) -> least_upper_bound(identity, least_upper_bound(b, a)) % 158.73/158.36 multiply(least_upper_bound(identity, inverse(identity)), Y0) -> Y0 % 158.73/158.36 multiply(least_upper_bound(identity, inverse(inverse(X0))), identity) -> least_upper_bound(identity, X0) % 158.73/158.36 multiply(least_upper_bound(identity, inverse(multiply(inverse(X0), least_upper_bound(X0, X1)))), identity) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, inverse(multiply(inverse(X0), least_upper_bound(X1, X0)))), identity) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, inverse(multiply(inverse(b), a))), identity) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, inverse(multiply(least_upper_bound(X0, inverse(X1)), X1))), identity) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), inverse(least_upper_bound(X0, identity))) -> identity % 158.73/158.36 multiply(least_upper_bound(identity, least_upper_bound(X1, least_upper_bound(X2, identity))), inverse(least_upper_bound(X1, least_upper_bound(X2, identity)))) -> identity % 158.73/158.36 multiply(least_upper_bound(inverse(Y1), Y2), Y1) -> least_upper_bound(identity, multiply(Y2, Y1)) % 158.73/158.36 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 158.73/158.36 true__ -> false__ % 158.73/158.36 with the LPO induced by % 158.73/158.36 a > f1 > b > inverse > identity > greatest_lower_bound > least_upper_bound > multiply > true__ > false__ % 158.73/158.36 % 158.73/158.36 % SZS output end Proof % 158.73/158.36 %------------------------------------------------------------------------------