/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U101 : [o * o * o] --> o U102 : [o * o * o] --> o U103 : [o * o * o] --> o U104 : [o * o * o] --> o U11 : [o * o * o] --> o U12 : [o * o * o] --> o U13 : [o * o * o] --> o U14 : [o * o * o] --> o U15 : [o * o] --> o U16 : [o] --> o U21 : [o * o] --> o U22 : [o * o] --> o U23 : [o] --> o U31 : [o * o * o] --> o U32 : [o * o * o] --> o U33 : [o * o * o] --> o U34 : [o * o * o] --> o U35 : [o * o] --> o U36 : [o] --> o U41 : [o * o] --> o U42 : [o] --> o U51 : [o] --> o U61 : [o * o] --> o U62 : [o] --> o U71 : [o * o] --> o U72 : [o * o] --> o U81 : [o * o * o] --> o U82 : [o * o * o] --> o U83 : [o * o * o] --> o U84 : [o * o * o] --> o U91 : [o * o] --> o U92 : [o] --> o active : [o] --> o isNat : [o] --> o isNatKind : [o] --> o mark : [o] --> o ok : [o] --> o plus : [o * o] --> o proper : [o] --> o s : [o] --> o top : [o] --> o tt : [] --> o x : [o * o] --> o active(U101(tt, X, Y)) => mark(U102(isNatKind(X), X, Y)) active(U102(tt, X, Y)) => mark(U103(isNat(Y), X, Y)) active(U103(tt, X, Y)) => mark(U104(isNatKind(Y), X, Y)) active(U104(tt, X, Y)) => mark(plus(x(Y, X), Y)) active(U11(tt, X, Y)) => mark(U12(isNatKind(X), X, Y)) active(U12(tt, X, Y)) => mark(U13(isNatKind(Y), X, Y)) active(U13(tt, X, Y)) => mark(U14(isNatKind(Y), X, Y)) active(U14(tt, X, Y)) => mark(U15(isNat(X), Y)) active(U15(tt, X)) => mark(U16(isNat(X))) active(U16(tt)) => mark(tt) active(U21(tt, X)) => mark(U22(isNatKind(X), X)) active(U22(tt, X)) => mark(U23(isNat(X))) active(U23(tt)) => mark(tt) active(U31(tt, X, Y)) => mark(U32(isNatKind(X), X, Y)) active(U32(tt, X, Y)) => mark(U33(isNatKind(Y), X, Y)) active(U33(tt, X, Y)) => mark(U34(isNatKind(Y), X, Y)) active(U34(tt, X, Y)) => mark(U35(isNat(X), Y)) active(U35(tt, X)) => mark(U36(isNat(X))) active(U36(tt)) => mark(tt) active(U41(tt, X)) => mark(U42(isNatKind(X))) active(U42(tt)) => mark(tt) active(U51(tt)) => mark(tt) active(U61(tt, X)) => mark(U62(isNatKind(X))) active(U62(tt)) => mark(tt) active(U71(tt, X)) => mark(U72(isNatKind(X), X)) active(U72(tt, X)) => mark(X) active(U81(tt, X, Y)) => mark(U82(isNatKind(X), X, Y)) active(U82(tt, X, Y)) => mark(U83(isNat(Y), X, Y)) active(U83(tt, X, Y)) => mark(U84(isNatKind(Y), X, Y)) active(U84(tt, X, Y)) => mark(s(plus(Y, X))) active(U91(tt, X)) => mark(U92(isNatKind(X))) active(U92(tt)) => mark(0) active(isNat(0)) => mark(tt) active(isNat(plus(X, Y))) => mark(U11(isNatKind(X), X, Y)) active(isNat(s(X))) => mark(U21(isNatKind(X), X)) active(isNat(x(X, Y))) => mark(U31(isNatKind(X), X, Y)) active(isNatKind(0)) => mark(tt) active(isNatKind(plus(X, Y))) => mark(U41(isNatKind(X), Y)) active(isNatKind(s(X))) => mark(U51(isNatKind(X))) active(isNatKind(x(X, Y))) => mark(U61(isNatKind(X), Y)) active(plus(X, 0)) => mark(U71(isNat(X), X)) active(plus(X, s(Y))) => mark(U81(isNat(Y), Y, X)) active(x(X, 0)) => mark(U91(isNat(X), X)) active(x(X, s(Y))) => mark(U101(isNat(Y), Y, X)) active(U101(X, Y, Z)) => U101(active(X), Y, Z) active(U102(X, Y, Z)) => U102(active(X), Y, Z) active(U103(X, Y, Z)) => U103(active(X), Y, Z) active(U104(X, Y, Z)) => U104(active(X), Y, Z) active(plus(X, Y)) => plus(active(X), Y) active(plus(X, Y)) => plus(X, active(Y)) active(x(X, Y)) => x(active(X), Y) active(x(X, Y)) => x(X, active(Y)) active(U11(X, Y, Z)) => U11(active(X), Y, Z) active(U12(X, Y, Z)) => U12(active(X), Y, Z) active(U13(X, Y, Z)) => U13(active(X), Y, Z) active(U14(X, Y, Z)) => U14(active(X), Y, Z) active(U15(X, Y)) => U15(active(X), Y) active(U16(X)) => U16(active(X)) active(U21(X, Y)) => U21(active(X), Y) active(U22(X, Y)) => U22(active(X), Y) active(U23(X)) => U23(active(X)) active(U31(X, Y, Z)) => U31(active(X), Y, Z) active(U32(X, Y, Z)) => U32(active(X), Y, Z) active(U33(X, Y, Z)) => U33(active(X), Y, Z) active(U34(X, Y, Z)) => U34(active(X), Y, Z) active(U35(X, Y)) => U35(active(X), Y) active(U36(X)) => U36(active(X)) active(U41(X, Y)) => U41(active(X), Y) active(U42(X)) => U42(active(X)) active(U51(X)) => U51(active(X)) active(U61(X, Y)) => U61(active(X), Y) active(U62(X)) => U62(active(X)) active(U71(X, Y)) => U71(active(X), Y) active(U72(X, Y)) => U72(active(X), Y) active(U81(X, Y, Z)) => U81(active(X), Y, Z) active(U82(X, Y, Z)) => U82(active(X), Y, Z) active(U83(X, Y, Z)) => U83(active(X), Y, Z) active(U84(X, Y, Z)) => U84(active(X), Y, Z) active(s(X)) => s(active(X)) active(U91(X, Y)) => U91(active(X), Y) active(U92(X)) => U92(active(X)) U101(mark(X), Y, Z) => mark(U101(X, Y, Z)) U102(mark(X), Y, Z) => mark(U102(X, Y, Z)) U103(mark(X), Y, Z) => mark(U103(X, Y, Z)) U104(mark(X), Y, Z) => mark(U104(X, Y, Z)) plus(mark(X), Y) => mark(plus(X, Y)) plus(X, mark(Y)) => mark(plus(X, Y)) x(mark(X), Y) => mark(x(X, Y)) x(X, mark(Y)) => mark(x(X, Y)) U11(mark(X), Y, Z) => mark(U11(X, Y, Z)) U12(mark(X), Y, Z) => mark(U12(X, Y, Z)) U13(mark(X), Y, Z) => mark(U13(X, Y, Z)) U14(mark(X), Y, Z) => mark(U14(X, Y, Z)) U15(mark(X), Y) => mark(U15(X, Y)) U16(mark(X)) => mark(U16(X)) U21(mark(X), Y) => mark(U21(X, Y)) U22(mark(X), Y) => mark(U22(X, Y)) U23(mark(X)) => mark(U23(X)) U31(mark(X), Y, Z) => mark(U31(X, Y, Z)) U32(mark(X), Y, Z) => mark(U32(X, Y, Z)) U33(mark(X), Y, Z) => mark(U33(X, Y, Z)) U34(mark(X), Y, Z) => mark(U34(X, Y, Z)) U35(mark(X), Y) => mark(U35(X, Y)) U36(mark(X)) => mark(U36(X)) U41(mark(X), Y) => mark(U41(X, Y)) U42(mark(X)) => mark(U42(X)) U51(mark(X)) => mark(U51(X)) U61(mark(X), Y) => mark(U61(X, Y)) U62(mark(X)) => mark(U62(X)) U71(mark(X), Y) => mark(U71(X, Y)) U72(mark(X), Y) => mark(U72(X, Y)) U81(mark(X), Y, Z) => mark(U81(X, Y, Z)) U82(mark(X), Y, Z) => mark(U82(X, Y, Z)) U83(mark(X), Y, Z) => mark(U83(X, Y, Z)) U84(mark(X), Y, Z) => mark(U84(X, Y, Z)) s(mark(X)) => mark(s(X)) U91(mark(X), Y) => mark(U91(X, Y)) U92(mark(X)) => mark(U92(X)) proper(U101(X, Y, Z)) => U101(proper(X), proper(Y), proper(Z)) proper(tt) => ok(tt) proper(U102(X, Y, Z)) => U102(proper(X), proper(Y), proper(Z)) proper(isNatKind(X)) => isNatKind(proper(X)) proper(U103(X, Y, Z)) => U103(proper(X), proper(Y), proper(Z)) proper(isNat(X)) => isNat(proper(X)) proper(U104(X, Y, Z)) => U104(proper(X), proper(Y), proper(Z)) proper(plus(X, Y)) => plus(proper(X), proper(Y)) proper(x(X, Y)) => x(proper(X), proper(Y)) proper(U11(X, Y, Z)) => U11(proper(X), proper(Y), proper(Z)) proper(U12(X, Y, Z)) => U12(proper(X), proper(Y), proper(Z)) proper(U13(X, Y, Z)) => U13(proper(X), proper(Y), proper(Z)) proper(U14(X, Y, Z)) => U14(proper(X), proper(Y), proper(Z)) proper(U15(X, Y)) => U15(proper(X), proper(Y)) proper(U16(X)) => U16(proper(X)) proper(U21(X, Y)) => U21(proper(X), proper(Y)) proper(U22(X, Y)) => U22(proper(X), proper(Y)) proper(U23(X)) => U23(proper(X)) proper(U31(X, Y, Z)) => U31(proper(X), proper(Y), proper(Z)) proper(U32(X, Y, Z)) => U32(proper(X), proper(Y), proper(Z)) proper(U33(X, Y, Z)) => U33(proper(X), proper(Y), proper(Z)) proper(U34(X, Y, Z)) => U34(proper(X), proper(Y), proper(Z)) proper(U35(X, Y)) => U35(proper(X), proper(Y)) proper(U36(X)) => U36(proper(X)) proper(U41(X, Y)) => U41(proper(X), proper(Y)) proper(U42(X)) => U42(proper(X)) proper(U51(X)) => U51(proper(X)) proper(U61(X, Y)) => U61(proper(X), proper(Y)) proper(U62(X)) => U62(proper(X)) proper(U71(X, Y)) => U71(proper(X), proper(Y)) proper(U72(X, Y)) => U72(proper(X), proper(Y)) proper(U81(X, Y, Z)) => U81(proper(X), proper(Y), proper(Z)) proper(U82(X, Y, Z)) => U82(proper(X), proper(Y), proper(Z)) proper(U83(X, Y, Z)) => U83(proper(X), proper(Y), proper(Z)) proper(U84(X, Y, Z)) => U84(proper(X), proper(Y), proper(Z)) proper(s(X)) => s(proper(X)) proper(U91(X, Y)) => U91(proper(X), proper(Y)) proper(U92(X)) => U92(proper(X)) proper(0) => ok(0) U101(ok(X), ok(Y), ok(Z)) => ok(U101(X, Y, Z)) U102(ok(X), ok(Y), ok(Z)) => ok(U102(X, Y, Z)) isNatKind(ok(X)) => ok(isNatKind(X)) U103(ok(X), ok(Y), ok(Z)) => ok(U103(X, Y, Z)) isNat(ok(X)) => ok(isNat(X)) U104(ok(X), ok(Y), ok(Z)) => ok(U104(X, Y, Z)) plus(ok(X), ok(Y)) => ok(plus(X, Y)) x(ok(X), ok(Y)) => ok(x(X, Y)) U11(ok(X), ok(Y), ok(Z)) => ok(U11(X, Y, Z)) U12(ok(X), ok(Y), ok(Z)) => ok(U12(X, Y, Z)) U13(ok(X), ok(Y), ok(Z)) => ok(U13(X, Y, Z)) U14(ok(X), ok(Y), ok(Z)) => ok(U14(X, Y, Z)) U15(ok(X), ok(Y)) => ok(U15(X, Y)) U16(ok(X)) => ok(U16(X)) U21(ok(X), ok(Y)) => ok(U21(X, Y)) U22(ok(X), ok(Y)) => ok(U22(X, Y)) U23(ok(X)) => ok(U23(X)) U31(ok(X), ok(Y), ok(Z)) => ok(U31(X, Y, Z)) U32(ok(X), ok(Y), ok(Z)) => ok(U32(X, Y, Z)) U33(ok(X), ok(Y), ok(Z)) => ok(U33(X, Y, Z)) U34(ok(X), ok(Y), ok(Z)) => ok(U34(X, Y, Z)) U35(ok(X), ok(Y)) => ok(U35(X, Y)) U36(ok(X)) => ok(U36(X)) U41(ok(X), ok(Y)) => ok(U41(X, Y)) U42(ok(X)) => ok(U42(X)) U51(ok(X)) => ok(U51(X)) U61(ok(X), ok(Y)) => ok(U61(X, Y)) U62(ok(X)) => ok(U62(X)) U71(ok(X), ok(Y)) => ok(U71(X, Y)) U72(ok(X), ok(Y)) => ok(U72(X, Y)) U81(ok(X), ok(Y), ok(Z)) => ok(U81(X, Y, Z)) U82(ok(X), ok(Y), ok(Z)) => ok(U82(X, Y, Z)) U83(ok(X), ok(Y), ok(Z)) => ok(U83(X, Y, Z)) U84(ok(X), ok(Y), ok(Z)) => ok(U84(X, Y, Z)) s(ok(X)) => ok(s(X)) U91(ok(X), ok(Y)) => ok(U91(X, Y)) U92(ok(X)) => ok(U92(X)) top(mark(X)) => top(proper(X)) top(ok(X)) => top(active(X))