%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : HEN003-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 12:58:55 EDT 2022 % Result : Unsatisfiable 33.89s 33.51s % Output : Proof 33.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : HEN003-2 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n007.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Fri Jul 1 13:10:09 EDT 2022 % 0.12/0.33 % CPUTime : % 33.89/33.51 % SZS status Unsatisfiable % 33.89/33.51 % SZS output start Proof % 33.89/33.51 The input problem is unsatisfiable because % 33.89/33.51 % 33.89/33.51 [1] the following set of Horn clauses is unsatisfiable: % 33.89/33.51 % 33.89/33.51 less_equal(X, Y) ==> quotient(X, Y, zero) % 33.89/33.51 quotient(X, Y, zero) ==> less_equal(X, Y) % 33.89/33.51 quotient(X, Y, Z) ==> less_equal(Z, X) % 33.89/33.51 quotient(X, Y, V1) & quotient(Y, Z, V2) & quotient(X, Z, V3) & quotient(V3, V2, V4) & quotient(V1, Z, V5) ==> less_equal(V4, V5) % 33.89/33.51 less_equal(zero, X) % 33.89/33.51 less_equal(X, Y) & less_equal(Y, X) ==> X = Y % 33.89/33.51 less_equal(X, identity) % 33.89/33.51 quotient(X, Y, divide(X, Y)) % 33.89/33.51 quotient(X, Y, Z) & quotient(X, Y, W) ==> Z = W % 33.89/33.51 quotient(X, identity, zero) % 33.89/33.51 quotient(zero, X, zero) % 33.89/33.51 quotient(x, x, zero) ==> \bottom % 33.89/33.51 % 33.89/33.51 This holds because % 33.89/33.51 % 33.89/33.51 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 33.89/33.51 % 33.89/33.51 E: % 33.89/33.51 f1(less_equal(X, Y), X, Y) = true__ % 33.89/33.51 f1(true__, X, Y) = quotient(X, Y, zero) % 33.89/33.51 f10(less_equal(Y, X), X, Y) = Y % 33.89/33.51 f10(true__, X, Y) = f9(less_equal(X, Y), X, Y) % 33.89/33.51 f11(true__, Z, W) = Z % 33.89/33.51 f12(quotient(X, Y, W), X, Y, Z, W) = W % 33.89/33.51 f12(true__, X, Y, Z, W) = f11(quotient(X, Y, Z), Z, W) % 33.89/33.51 f13(quotient(x, x, zero)) = true__ % 33.89/33.51 f13(true__) = false__ % 33.89/33.51 f2(quotient(X, Y, zero), X, Y) = true__ % 33.89/33.51 f2(true__, X, Y) = less_equal(X, Y) % 33.89/33.51 f3(quotient(X, Y, Z), Z, X) = true__ % 33.89/33.51 f3(true__, Z, X) = less_equal(Z, X) % 33.89/33.51 f4(true__, V4, V5) = less_equal(V4, V5) % 33.89/33.51 f5(true__, X, Y, V1, V4, V5) = f4(quotient(X, Y, V1), V4, V5) % 33.89/33.51 f6(true__, Y, Z, V2, X, V1, V4, V5) = f5(quotient(Y, Z, V2), X, Y, V1, V4, V5) % 33.89/33.51 f7(true__, X, Z, V3, Y, V2, V1, V4, V5) = f6(quotient(X, Z, V3), Y, Z, V2, X, V1, V4, V5) % 33.89/33.51 f8(quotient(V1, Z, V5), V3, V2, V4, X, Z, Y, V1, V5) = true__ % 33.89/33.51 f8(true__, V3, V2, V4, X, Z, Y, V1, V5) = f7(quotient(V3, V2, V4), X, Z, V3, Y, V2, V1, V4, V5) % 33.89/33.51 f9(true__, X, Y) = X % 33.89/33.51 less_equal(X, identity) = true__ % 33.89/33.51 less_equal(zero, X) = true__ % 33.89/33.51 quotient(X, Y, divide(X, Y)) = true__ % 33.89/33.51 quotient(X, identity, zero) = true__ % 33.89/33.51 quotient(zero, X, zero) = true__ % 33.89/33.51 G: % 33.89/33.51 true__ = false__ % 33.89/33.51 % 33.89/33.51 This holds because % 33.89/33.51 % 33.89/33.51 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 33.89/33.51 % 33.89/33.51 f2(true__, Y3, Y4) = f5(true__, Y0, identity, zero, Y3, Y4) % 33.89/33.51 f5(true__, true__, identity, zero, Y3, Y4) = f5(true__, Y0, identity, zero, Y3, Y4) % 33.89/33.51 f6(true__, Y3, Y1, Y4, Y0, Y5, Y6, Y7) = f7(true__, Y0, Y1, divide(Y0, Y1), Y3, Y4, Y5, Y6, Y7) % 33.89/33.51 f6(true__, identity, identity, zero, true__, zero, Y3, Y4) = f6(true__, Y1, identity, zero, zero, zero, Y3, Y4) % 33.89/33.51 f6(true__, identity, identity, zero, true__, zero, Y3, Y4) = f6(true__, identity, identity, zero, Y0, zero, Y3, Y4) % 33.89/33.51 f6(true__, true__, identity, zero, zero, zero, Y3, Y4) = f6(true__, Y1, identity, zero, zero, zero, Y3, Y4) % 33.89/33.51 f6(true__, zero, identity, zero, Y3, Y4, Y5, Y6) = f6(true__, zero, Y1, zero, Y3, Y4, Y5, Y6) % 33.89/33.51 f7(true__, X2, identity, zero, identity, zero, zero, Y0, Y1) = f7(true__, Y2, identity, zero, Y3, zero, divide(Y2, Y3), Y0, Y1) % 33.89/33.51 f7(true__, X2, identity, zero, identity, zero, zero, Y0, Y1) = f7(true__, Y2, identity, zero, identity, zero, zero, Y0, Y1) % 33.89/33.51 f7(true__, Y3, identity, zero, zero, zero, Y4, Y5, Y6) = f7(true__, Y3, Y1, divide(Y3, Y1), zero, zero, Y4, Y5, Y6) % 33.89/33.51 f7(true__, divide(Y1, X1), Y1, zero, zero, zero, Y2, Y3, Y4) = f7(true__, divide(Y1, X1), identity, zero, zero, zero, Y2, Y3, Y4) % 33.89/33.51 f7(true__, true__, identity, zero, identity, zero, zero, Y3, Y4) = f7(true__, Y0, identity, zero, Y1, zero, divide(Y0, Y1), Y3, Y4) % 33.89/33.51 f7(true__, true__, identity, zero, identity, zero, zero, Y3, Y4) = f7(true__, Y0, identity, zero, identity, zero, zero, Y3, Y4) % 33.89/33.51 f7(true__, zero, X3, zero, zero, zero, Y0, Y1, Y2) = f7(true__, zero, Y3, zero, zero, zero, Y0, Y1, Y2) % 33.89/33.51 f7(true__, zero, X4, zero, zero, zero, Y3, Y4, Y5) = f7(true__, zero, identity, zero, zero, zero, Y3, Y4, Y5) % 33.89/33.51 f7(true__, zero, X4, zero, zero, zero, Y3, Y4, Y5) = f7(true__, zero, true__, zero, zero, zero, Y3, Y4, Y5) % 33.89/33.51 f7(true__, zero, Y0, zero, divide(Y0, Y1), zero, Y3, Y4, Y5) = f7(true__, zero, identity, zero, divide(Y0, Y1), zero, Y3, Y4, Y5) % 33.89/33.51 f7(true__, zero, Y1, zero, Y0, divide(Y0, Y1), Y3, Y4, Y5) = f7(true__, zero, identity, zero, Y0, zero, Y3, Y4, Y5) % 33.89/33.51 f8(true__, zero, zero, zero, zero, X2, zero, Y0, Y1) = f8(true__, zero, zero, zero, zero, Y2, zero, Y0, Y1) % 33.89/33.51 f8(true__, zero, zero, zero, zero, identity, zero, Y4, Y5) = f8(true__, zero, zero, zero, zero, Y1, zero, Y4, Y5) % 33.89/33.51 f8(true__, zero, zero, zero, zero, true__, zero, Y4, Y5) = f8(true__, zero, zero, zero, zero, Y1, zero, Y4, Y5) % 33.89/33.51 divide(X0, X0) -> zero % 33.89/33.51 divide(Y0, identity) -> zero % 33.89/33.51 divide(divide(X0, X0), zero) -> zero % 33.89/33.51 divide(divide(Y1, X1), Y1) -> zero % 33.89/33.51 divide(divide(divide(Y0, Y1), zero), divide(divide(Y0, zero), Y1)) -> zero % 33.89/33.51 divide(divide(divide(Y0, divide(Y0, zero)), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(Y1, Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(X0, X0), Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(X0, X0), zero), Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(divide(X0, X0), X1), zero), Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(divide(X0, X0), zero), Y1), zero), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), Y1), zero), zero) -> zero % 33.89/33.51 divide(divide(divide(divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1), zero), zero) -> zero % 33.89/33.51 divide(zero, Y1) -> zero % 33.89/33.51 f1(f2(true__, Y0, Y1), Y0, Y1) -> true__ % 33.89/33.51 f1(f7(true__, X2, identity, zero, X3, zero, divide(X2, X3), Y1, Y2), Y1, Y2) -> true__ % 33.89/33.51 f1(f7(true__, X2, identity, zero, identity, zero, zero, Y0, Y1), Y0, Y1) -> true__ % 33.89/33.51 f1(f7(true__, Y0, X4, divide(Y0, X4), zero, zero, divide(Y0, zero), Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(X0, X0), Y1, divide(divide(X0, X0), Y1), zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(X0, X0), identity, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(X0, X0), zero, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(Y1, X1), Y1, zero, zero, zero, divide(divide(Y1, X1), zero), Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(X0, X0), zero), Y1, divide(divide(divide(X0, X0), zero), Y1), zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(X0, X0), zero), zero, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, zero, zero, divide(divide(divide(X0, X1), zero), zero), Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(divide(X0, X0), X1), zero), identity, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), identity, zero, zero, zero, zero, Y2, Y3), Y2, Y3) -> true__ % 33.89/33.51 f1(f8(true__, divide(Y0, Y1), zero, divide(divide(Y0, Y1), zero), Y0, Y1, zero, divide(Y0, zero), Y3), divide(divide(Y0, Y1), zero), Y3) -> true__ % 33.89/33.51 f1(less_equal(X, Y), X, Y) -> true__ % 33.89/33.51 f1(true__, Y0, identity) -> true__ % 33.89/33.51 f1(true__, Y1, Y1) -> true__ % 33.89/33.51 f1(true__, divide(X0, X0), zero) -> true__ % 33.89/33.51 f1(true__, divide(Y2, X1), Y2) -> true__ % 33.89/33.51 f1(true__, divide(divide(X0, divide(X0, zero)), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(Y0, Y1), zero), divide(divide(Y0, zero), Y1)) -> true__ % 33.89/33.51 f1(true__, divide(divide(Y1, Y1), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(X0, X0), X1), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(divide(X0, X0), zero), Y1), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), Y1), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), Y1), zero), zero) -> true__ % 33.89/33.51 f1(true__, divide(divide(divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1), zero), zero) -> true__ % 33.89/33.51 f1(true__, zero, Y1) -> true__ % 33.89/33.51 f10(f2(true__, Y0, Y1), Y1, Y0) -> Y0 % 33.89/33.51 f10(f7(true__, X2, identity, zero, X3, zero, divide(X2, X3), Y1, Y2), Y2, Y1) -> Y1 % 33.89/33.51 f10(f7(true__, X2, identity, zero, identity, zero, zero, Y0, Y1), Y1, Y0) -> Y0 % 33.89/33.51 f10(f7(true__, Y0, X4, divide(Y0, X4), zero, zero, divide(Y0, zero), Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(X0, X0), Y1, divide(divide(X0, X0), Y1), zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(X0, X0), identity, zero, zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(X0, X0), zero, zero, zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(X0, X1), X0, zero, zero, zero, divide(divide(X0, X1), zero), Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(X0, X0), zero), Y1, divide(divide(divide(X0, X0), zero), Y1), zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(X0, X0), zero), zero, zero, zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, zero, zero, divide(divide(divide(X0, X1), zero), zero), Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(divide(X0, X0), X1), zero), identity, zero, zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, zero, zero, zero, Y2, Y3), Y3, Y2) -> Y2 % 33.89/33.51 f10(less_equal(Y, X), X, Y) -> Y % 33.89/33.51 f10(true__, X, Y) -> f9(less_equal(X, Y), X, Y) % 33.89/33.51 f11(f1(true__, Y0, Y1), zero, Y3) -> f12(true__, Y0, Y1, zero, Y3) % 33.89/33.51 f11(quotient(X, Y, Z), Z, W) -> f12(true__, X, Y, Z, W) % 33.89/33.51 f11(true__, Z, W) -> Z % 33.89/33.51 f12(f1(true__, Y0, Y1), Y0, Y1, Y3, zero) -> zero % 33.89/33.51 f12(quotient(X, Y, W), X, Y, Z, W) -> W % 33.89/33.51 f12(true__, Y0, Y1, Y3, divide(Y0, Y1)) -> divide(Y0, Y1) % 33.89/33.51 f12(true__, Y0, Y1, divide(Y0, Y1), Y3) -> divide(Y0, Y1) % 33.89/33.51 f12(true__, Y0, identity, Y3, zero) -> zero % 33.89/33.51 f12(true__, Y0, identity, zero, Y3) -> zero % 33.89/33.51 f12(true__, Y1, Y1, Y2, zero) -> zero % 33.89/33.51 f12(true__, Y1, Y1, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(X0, X0), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(X0, X0), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(Y1, X1), Y1, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(Y1, X1), Y1, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(X0, X0), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(X0, X0), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(X0, divide(X0, zero)), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(X0, divide(X0, zero)), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(X0, X0), X1), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(X0, X0), X1), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(X0, X0), X1), zero), Y1), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1), zero), zero, Y2, zero) -> zero % 33.89/33.51 f12(true__, divide(divide(divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1), zero), zero, zero, Y2) -> zero % 33.89/33.51 f12(true__, zero, Y1, Y3, zero) -> zero % 33.89/33.51 f12(true__, zero, Y1, zero, Y3) -> zero % 33.89/33.51 f13(f1(true__, x, x)) -> true__ % 33.89/33.51 f13(quotient(x, x, zero)) -> true__ % 33.89/33.51 f13(true__) -> false__ % 33.89/33.51 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__ % 33.89/33.51 f2(quotient(X, Y, zero), X, Y) -> true__ % 33.89/33.51 f2(true__, Y0, identity) -> true__ % 33.89/33.51 f2(true__, zero, Y1) -> true__ % 33.89/33.51 f3(f1(true__, Y0, Y1), zero, Y0) -> true__ % 33.89/33.51 f3(quotient(X, Y, Z), Z, X) -> true__ % 33.89/33.51 f3(true__, Z, X) -> less_equal(Z, X) % 33.89/33.51 f4(f1(true__, Y0, Y1), Y3, Y4) -> f7(true__, Y0, identity, zero, Y1, zero, zero, Y3, Y4) % 33.89/33.51 f4(quotient(X, Y, V1), V4, V5) -> f5(true__, X, Y, V1, V4, V5) % 33.89/33.51 f4(true__, V4, V5) -> less_equal(V4, V5) % 33.89/33.51 f5(f1(true__, Y0, Y1), Y3, Y0, Y4, Y5, Y6) -> f6(true__, Y0, Y1, zero, Y3, Y4, Y5, Y6) % 33.89/33.51 f5(quotient(Y, Z, V2), X, Y, V1, V4, V5) -> f6(true__, Y, Z, V2, X, V1, V4, V5) % 33.89/33.51 f5(true__, Y2, identity, zero, Y0, identity) -> true__ % 33.89/33.51 f5(true__, Y2, identity, zero, zero, Y1) -> true__ % 33.89/33.51 f5(true__, Y3, Y0, Y4, Y5, Y6) -> f6(true__, Y0, identity, zero, Y3, Y4, Y5, Y6) % 33.89/33.51 f5(true__, zero, Y1, zero, Y3, Y4) -> f5(true__, true__, identity, zero, Y3, Y4) % 33.89/33.51 f6(f1(true__, Y0, Y1), Y3, Y1, Y4, Y0, Y5, Y6, Y7) -> f7(true__, Y0, Y1, zero, Y3, Y4, Y5, Y6, Y7) % 33.89/33.51 f6(quotient(X, Z, V3), Y, Z, V2, X, V1, V4, V5) -> f7(true__, X, Z, V3, Y, V2, V1, V4, V5) % 33.89/33.51 f6(true__, Y0, Y1, divide(Y0, Y1), Y3, Y4, Y5, Y6) -> f7(true__, Y3, identity, zero, Y0, zero, Y4, Y5, Y6) % 33.89/33.51 f6(true__, Y2, Y1, Y3, divide(Y1, X1), Y4, Y5, Y6) -> f7(true__, divide(Y1, X1), Y1, zero, Y2, Y3, Y4, Y5, Y6) % 33.89/33.51 f6(true__, Y2, zero, Y3, divide(divide(X0, X0), zero), Y4, Y5, Y6) -> f7(true__, divide(divide(X0, X0), zero), zero, zero, Y2, Y3, Y4, Y5, Y6) % 33.89/33.51 f6(true__, Y3, Y1, Y4, zero, Y5, Y6, Y7) -> f7(true__, zero, Y1, zero, Y3, Y4, Y5, Y6, Y7) % 33.89/33.51 f6(true__, Y3, identity, Y4, Y0, Y5, Y6, Y7) -> f7(true__, Y0, identity, zero, Y3, Y4, Y5, Y6, Y7) % 33.89/33.51 f6(true__, divide(Y1, X1), Y1, zero, Y2, Y3, Y4, Y5) -> f7(true__, Y2, identity, zero, divide(Y1, X1), zero, Y3, Y4, Y5) % 33.89/33.51 f6(true__, divide(divide(X0, X0), zero), zero, zero, Y2, Y3, Y4, Y5) -> f7(true__, Y2, identity, zero, divide(divide(X0, X0), zero), zero, Y3, Y4, Y5) % 33.89/33.51 f6(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, Y2, Y3, Y4, Y5) -> f7(true__, Y2, identity, zero, divide(divide(X0, X1), zero), zero, Y3, Y4, Y5) % 33.92/33.51 f6(true__, identity, identity, zero, Y0, zero, Y3, Y4) -> f6(true__, true__, identity, zero, zero, zero, Y3, Y4) % 33.92/33.51 f6(true__, identity, identity, zero, Y2, zero, Y0, identity) -> true__ % 33.92/33.51 f6(true__, identity, identity, zero, Y2, zero, zero, Y1) -> true__ % 33.92/33.51 f6(true__, identity, identity, zero, true__, zero, divide(Y0, Y1), Y0) -> true__ % 33.92/33.51 f6(true__, zero, Y1, zero, Y3, Y4, Y5, Y6) -> f7(true__, Y3, identity, zero, zero, zero, Y4, Y5, Y6) % 33.92/33.51 f7(f1(true__, Y0, Y1), Y3, Y4, Y0, Y5, Y1, Y6, zero, Y7) -> f8(true__, Y0, Y1, zero, Y3, Y4, Y5, Y6, Y7) % 33.92/33.51 f7(quotient(V3, V2, V4), X, Z, V3, Y, V2, V1, V4, V5) -> f8(true__, V3, V2, V4, X, Z, Y, V1, V5) % 33.92/33.51 f7(true__, Y0, Y1, divide(Y0, Y1), zero, zero, divide(Y0, zero), zero, Y2) -> true__ % 33.92/33.51 f7(true__, Y0, Y1, divide(Y0, Y1), zero, zero, divide(Y0, zero), zero, divide(Y3, X1)) -> true__ % 33.92/33.51 f7(true__, Y0, Y1, divide(Y0, Y1), zero, zero, divide(Y0, zero), zero, zero) -> true__ % 33.92/33.51 f7(true__, Y0, Y4, divide(Y0, Y4), zero, zero, divide(Y0, zero), Y2, identity) -> true__ % 33.92/33.51 f7(true__, Y0, Y4, divide(Y0, Y4), zero, zero, divide(Y0, zero), divide(Y3, X3), Y3) -> true__ % 33.92/33.51 f7(true__, Y1, identity, zero, Y1, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, Y1, identity, zero, Y1, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, Y2, Y3, divide(Y1, X1), Y4, Y1, Y5, zero, Y6) -> f8(true__, divide(Y1, X1), Y1, zero, Y2, Y3, Y4, Y5, Y6) % 33.92/33.51 f7(true__, Y2, identity, zero, Y3, zero, divide(Y2, Y3), Y0, identity) -> true__ % 33.92/33.51 f7(true__, Y2, identity, zero, Y3, zero, divide(Y2, Y3), divide(Y1, X1), Y1) -> true__ % 33.92/33.51 f7(true__, Y2, identity, zero, identity, zero, zero, Y0, identity) -> true__ % 33.92/33.51 f7(true__, Y2, identity, zero, identity, zero, zero, divide(Y1, X1), Y1) -> true__ % 33.92/33.51 f7(true__, Y2, identity, zero, identity, zero, zero, zero, Y1) -> true__ % 33.92/33.51 f7(true__, Y3, Y4, Y0, Y5, Y1, Y6, divide(Y0, Y1), Y7) -> f8(true__, Y0, Y1, divide(Y0, Y1), Y3, Y4, Y5, Y6, Y7) % 33.92/33.51 f7(true__, Y3, Y4, Y0, Y5, identity, Y6, zero, Y7) -> f8(true__, Y0, identity, zero, Y3, Y4, Y5, Y6, Y7) % 33.92/33.51 f7(true__, Y3, Y4, zero, Y5, Y1, Y6, zero, Y7) -> f8(true__, zero, Y1, zero, Y3, Y4, Y5, Y6, Y7) % 33.92/33.51 f7(true__, divide(X0, X0), Y1, divide(divide(X0, X0), Y1), zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(X0, X0), Y1, divide(divide(X0, X0), Y1), zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(X0, X0), Y1, divide(divide(X0, X0), Y1), zero, zero, zero, zero, Y2) -> true__ % 33.92/33.51 f7(true__, divide(X0, X0), identity, zero, zero, zero, zero, Y2, Y3) -> f7(true__, true__, identity, zero, identity, zero, zero, Y2, Y3) % 33.92/33.51 f7(true__, divide(X0, X0), identity, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(X0, X0), identity, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(X0, X0), zero, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(X0, X0), zero, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(Y1, X1), Y1, zero, zero, zero, divide(divide(Y1, X1), zero), Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(Y1, X1), Y1, zero, zero, zero, divide(divide(Y1, X1), zero), divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(Y1, X1), identity, zero, Y1, zero, zero, Y2, Y3) -> f7(true__, true__, identity, zero, identity, zero, zero, Y2, Y3) % 33.92/33.51 f7(true__, divide(Y1, Y1), Y1, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X0), zero), Y1, divide(divide(divide(X0, X0), zero), Y1), zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X0), zero), Y1, divide(divide(divide(X0, X0), zero), Y1), zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X0), zero), Y1, divide(divide(divide(X0, X0), zero), Y1), zero, zero, zero, zero, Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X0), zero), identity, zero, zero, zero, zero, Y2, Y3) -> f7(true__, true__, identity, zero, identity, zero, zero, Y2, Y3) % 33.92/33.51 f7(true__, divide(divide(X0, X0), zero), zero, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X0), zero), zero, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, zero, zero, divide(divide(divide(X0, X1), zero), zero), Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, zero, zero, divide(divide(divide(X0, X1), zero), zero), divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(X0, X1), zero), identity, zero, divide(divide(X0, zero), X1), zero, zero, Y2, Y3) -> f7(true__, true__, identity, zero, identity, zero, zero, Y2, Y3) % 33.92/33.51 f7(true__, divide(divide(divide(X0, X0), X1), zero), Y1, divide(divide(divide(divide(X0, X0), X1), zero), Y1), zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X0), X1), zero), Y1, divide(divide(divide(divide(X0, X0), X1), zero), Y1), zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X0), X1), zero), Y1, divide(divide(divide(divide(X0, X0), X1), zero), Y1), zero, zero, zero, zero, Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X0), X1), zero), identity, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X0), X1), zero), identity, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X0), X1), zero), zero, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X0), X1), zero), zero, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1, divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1), zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1, divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1), zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1, divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), Y1), zero, zero, zero, zero, Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, zero, zero, Y2, Y3) -> f7(true__, true__, identity, zero, identity, zero, zero, Y2, Y3) % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, zero, zero, zero, Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, zero, zero, Y2, Y3) -> f7(true__, true__, identity, zero, identity, zero, zero, Y2, Y3) % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), identity, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), identity, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1, divide(divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1), zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1, divide(divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), Y1), zero, zero, zero, zero, Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), identity, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), identity, zero, zero, zero, zero, divide(Y2, Y3), Y2) -> true__ % 33.92/33.51 f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), zero, zero, zero, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, identity, zero, zero, Y1, Y1) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, identity, zero, zero, divide(X0, X0), zero) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, identity, zero, zero, divide(Y0, Y1), Y0) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(X0, X0), zero), zero) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(X0, X1), zero), divide(divide(X0, zero), X1)) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(divide(X0, X0), X1), zero), zero) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(divide(divide(X0, X0), zero), X1), zero), zero) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), zero) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), zero) -> true__ % 33.92/33.51 f7(true__, true__, identity, zero, true__, zero, divide(true__, true__), divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), zero) -> true__ % 33.92/33.51 f7(true__, zero, X4, zero, zero, zero, zero, Y1, Y2) -> f7(true__, true__, identity, zero, identity, zero, zero, Y1, Y2) % 33.92/33.51 f7(true__, zero, Y0, zero, Y0, zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, Y0, zero, divide(Y0, Y1), zero, zero, Y3, identity) -> true__ % 33.92/33.51 f7(true__, zero, Y4, zero, Y0, divide(Y0, Y4), zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, Y4, zero, identity, divide(identity, Y4), zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, Y4, zero, identity, divide(identity, Y4), zero, divide(Y3, X2), Y3) -> true__ % 33.92/33.51 f7(true__, zero, divide(divide(X0, zero), X1), zero, divide(divide(X0, X1), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, identity, zero, Y1, zero, zero, Y3, Y4) -> f7(true__, true__, identity, zero, identity, zero, zero, Y3, Y4) % 33.92/33.51 f7(true__, zero, zero, zero, divide(X0, X0), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, zero, zero, divide(divide(X0, X0), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, zero, zero, divide(divide(divide(X0, X0), X1), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, zero, zero, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, zero, zero, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, zero, zero, divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, zero, zero, divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f7(true__, zero, zero, zero, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), zero, zero, Y2, identity) -> true__ % 33.92/33.51 f8(f1(true__, Y0, Y1), Y3, Y4, Y5, Y6, Y1, Y7, Y0, zero) -> true__ % 33.92/33.51 f8(quotient(V1, Z, V5), V3, V2, V4, X, Z, Y, V1, V5) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y4, zero) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, zero, Y5, divide(X0, X0), zero) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, zero, Y5, divide(divide(divide(X0, X0), X1), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, zero, Y5, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, zero, Y5, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, zero, Y5, divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, zero, Y5, divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y0, Y1, Y2, Y3, zero, Y5, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y2, Y3, Y4, Y5, Y1, Y6, divide(Y1, X1), zero) -> true__ % 33.92/33.51 f8(true__, Y2, Y3, Y4, Y5, divide(divide(X0, zero), X1), Y6, divide(divide(X0, X1), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y2, Y3, Y4, Y5, zero, Y6, divide(divide(X0, X0), zero), zero) -> true__ % 33.92/33.51 f8(true__, Y3, Y4, Y5, Y6, Y1, Y7, Y0, divide(Y0, Y1)) -> true__ % 33.92/33.51 f8(true__, Y3, Y4, Y5, Y6, Y1, Y7, zero, zero) -> true__ % 33.92/33.51 f8(true__, Y3, Y4, Y5, Y6, identity, Y7, Y0, zero) -> true__ % 33.92/33.51 f8(true__, divide(Y0, Y1), zero, divide(divide(Y0, Y1), zero), Y0, Y1, zero, divide(Y0, zero), divide(Y0, Y1)) -> true__ % 33.92/33.51 f8(true__, divide(Y0, Y1), zero, divide(divide(Y0, Y1), zero), Y0, Y1, zero, divide(Y0, zero), identity) -> true__ % 33.92/33.51 f8(true__, divide(divide(X0, X0), zero), zero, zero, divide(X0, X0), zero, zero, divide(divide(X0, X0), zero), identity) -> true__ % 33.92/33.51 f8(true__, divide(divide(divide(X0, X0), zero), Y1), zero, divide(divide(divide(divide(X0, X0), zero), Y1), zero), divide(divide(X0, X0), zero), Y1, zero, zero, identity) -> true__ % 33.92/33.51 f8(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, divide(divide(divide(X0, X0), zero), X1), zero, zero, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity) -> true__ % 33.92/33.51 f8(true__, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero), divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, zero, zero, identity) -> true__ % 33.92/33.51 f8(true__, zero, divide(identity, Y4), zero, zero, Y4, identity, zero, Y3) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, Y1, identity, Y1, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, Y2, identity, Y3, divide(Y2, Y3), Y1) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, Y2, identity, identity, zero, Y1) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(X0, X0), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(X0, X0), zero, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(Y1, X1), Y1, zero, divide(divide(Y1, X1), zero), Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(Y1, X1), Y1, zero, divide(divide(Y1, X1), zero), divide(Y2, Y3)) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(Y1, X1), Y1, zero, divide(divide(Y1, X1), zero), identity) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(Y1, X1), Y1, zero, divide(divide(Y1, X1), zero), zero) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(Y1, X1), identity, Y1, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(Y1, Y1), Y1, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(Y1, Y1), Y1, zero, zero, identity) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(X0, X0), zero), divide(X0, X0), zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(X0, X0), zero), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(X0, X0), zero), zero, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, divide(divide(divide(X0, X1), zero), zero), Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(X0, X1), zero), identity, divide(divide(X0, zero), X1), zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(X0, X0), X1), zero), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(X0, X0), X1), zero), zero, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero, zero, identity) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), zero, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(divide(X0, X0), zero), X1), zero), divide(divide(divide(X0, X0), zero), X1), zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(divide(divide(X0, X0), X1), zero), X2), zero), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), X2), zero), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), identity, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), zero, zero, zero, Y2) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, true__, identity, identity, zero, Y0) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, zero, Y2, zero, Y0, divide(Y0, true__)) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, zero, Y2, zero, Y0, zero) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, zero, Y2, zero, divide(identity, X6), zero) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, zero, Y2, zero, zero, Y1) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, zero, Y3, zero, Y1, divide(Y1, Y0)) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, zero, identity, Y2, zero, Y1) -> true__ % 33.92/33.51 f8(true__, zero, zero, zero, zero, true__, zero, Y1, divide(Y1, Y0)) -> true__ % 33.92/33.51 f9(f2(true__, Y1, zero), Y1, zero) -> zero % 33.92/33.51 f9(f2(true__, identity, Y0), identity, Y0) -> Y0 % 33.92/33.51 f9(f7(true__, X2, identity, zero, X3, zero, divide(X2, X3), Y1, zero), Y1, zero) -> zero % 33.92/33.51 f9(f7(true__, X2, identity, zero, X3, zero, divide(X2, X3), identity, Y1), identity, Y1) -> Y1 % 33.92/33.51 f9(f7(true__, X2, identity, zero, identity, zero, zero, Y0, divide(Y0, Y1)), Y0, divide(Y0, Y1)) -> divide(Y0, Y1) % 33.92/33.51 f9(f7(true__, X2, identity, zero, identity, zero, zero, Y0, zero), Y0, zero) -> zero % 33.92/33.51 f9(f7(true__, X2, identity, zero, identity, zero, zero, identity, Y0), identity, Y0) -> Y0 % 33.92/33.51 f9(f7(true__, Y0, X4, divide(Y0, X4), zero, zero, divide(Y0, zero), Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, Y0, X4, divide(Y0, X4), zero, zero, divide(Y0, zero), identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(X0, X0), Y1, divide(divide(X0, X0), Y1), zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(X0, X0), Y1, divide(divide(X0, X0), Y1), zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(X0, X0), identity, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(X0, X0), identity, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(X0, X0), zero, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(X0, X0), zero, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(Y1, X1), Y1, zero, zero, zero, divide(divide(Y1, X1), zero), Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(Y1, X1), Y1, zero, zero, zero, divide(divide(Y1, X1), zero), identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(X0, X0), zero), Y1, divide(divide(divide(X0, X0), zero), Y1), zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(X0, X0), zero), Y1, divide(divide(divide(X0, X0), zero), Y1), zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(X0, X0), zero), zero, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(X0, X0), zero), zero, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, zero, zero, divide(divide(divide(X0, X1), zero), zero), Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(X0, X1), zero), divide(divide(X0, zero), X1), zero, zero, zero, divide(divide(divide(X0, X1), zero), zero), identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(divide(X0, X0), X1), zero), identity, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(divide(X0, X0), X1), zero), identity, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(divide(X0, X1), divide(divide(X0, zero), X1)), zero), identity, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1, divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), Y1), zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), identity, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(X0, X0), zero), X1), zero), zero, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), identity, zero, zero, zero, zero, Y2, zero), Y2, zero) -> zero % 33.92/33.51 f9(f7(true__, divide(divide(divide(divide(divide(divide(X0, X0), zero), X1), zero), X2), zero), identity, zero, zero, zero, zero, identity, Y2), identity, Y2) -> Y2 % 33.92/33.51 f9(f7(true__, true__, identity, zero, identity, zero, zero, Y2, divide(Y2, X1)), Y2, divide(Y2, X1)) -> divide(Y2, X1) % 33.92/33.51 f9(f7(true__, zero, X4, zero, identity, divide(identity, X4), zero, Y1, zero), Y1, zero) -> zero % 33.92/33.51 f9(f8(true__, divide(Y0, Y1), zero, divide(divide(Y0, Y1), zero), Y0, Y1, zero, divide(Y0, zero), zero), divide(divide(Y0, Y1), zero), zero) -> zero % 33.92/33.51 f9(true__, X, Y) -> X % 33.92/33.51 false__ -> true__ % 33.92/33.51 less_equal(X, Y) -> f2(true__, X, Y) % 33.92/33.51 less_equal(X, identity) -> true__ % 33.92/33.51 less_equal(zero, X) -> true__ % 33.92/33.51 quotient(X, Y, divide(X, Y)) -> true__ % 33.92/33.51 quotient(X, Y, zero) -> f1(true__, X, Y) % 33.92/33.51 quotient(X, identity, zero) -> true__ % 33.92/33.51 quotient(zero, X, zero) -> true__ % 33.92/33.51 with the LPO induced by % 33.92/33.51 x > f13 > f11 > f12 > divide > f10 > f9 > f4 > f3 > less_equal > f2 > f5 > f6 > f7 > f8 > quotient > f1 > zero > identity > false__ > true__ % 33.92/33.51 % 33.92/33.51 % SZS output end Proof % 33.92/33.51 %------------------------------------------------------------------------------