/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 U11 : [o * o] --> o U12 : [o] --> o U21 : [o * o] --> o U22 : [o] --> o U31 : [o * o] --> o U32 : [o] --> o U41 : [o * o * o] --> o U42 : [o * o] --> o U43 : [o] --> o U51 : [o * o * o] --> o U52 : [o * o] --> o U53 : [o] --> o U61 : [o * o * o] --> o U62 : [o * o] --> o U63 : [o] --> o U71 : [o * o] --> o U81 : [o] --> o U91 : [o * o * o * o] --> o active : [o] --> o and : [o * o] --> o cons : [o * o] --> o isNat : [o] --> o isNatIList : [o] --> o isNatIListKind : [o] --> o isNatKind : [o] --> o isNatList : [o] --> o length : [o] --> o mark : [o] --> o nil : [] --> o s : [o] --> o take : [o * o] --> o tt : [] --> o zeros : [] --> o active(zeros) => mark(cons(0, zeros)) active(U11(tt, X)) => mark(U12(isNatList(X))) active(U12(tt)) => mark(tt) active(U21(tt, X)) => mark(U22(isNat(X))) active(U22(tt)) => mark(tt) active(U31(tt, X)) => mark(U32(isNatList(X))) active(U32(tt)) => mark(tt) active(U41(tt, X, Y)) => mark(U42(isNat(X), Y)) active(U42(tt, X)) => mark(U43(isNatIList(X))) active(U43(tt)) => mark(tt) active(U51(tt, X, Y)) => mark(U52(isNat(X), Y)) active(U52(tt, X)) => mark(U53(isNatList(X))) active(U53(tt)) => mark(tt) active(U61(tt, X, Y)) => mark(U62(isNat(X), Y)) active(U62(tt, X)) => mark(U63(isNatIList(X))) active(U63(tt)) => mark(tt) active(U71(tt, X)) => mark(s(length(X))) active(U81(tt)) => mark(nil) active(U91(tt, X, Y, Z)) => mark(cons(Z, take(Y, X))) active(and(tt, X)) => mark(X) active(isNat(0)) => mark(tt) active(isNat(length(X))) => mark(U11(isNatIListKind(X), X)) active(isNat(s(X))) => mark(U21(isNatKind(X), X)) active(isNatIList(X)) => mark(U31(isNatIListKind(X), X)) active(isNatIList(zeros)) => mark(tt) active(isNatIList(cons(X, Y))) => mark(U41(and(isNatKind(X), isNatIListKind(Y)), X, Y)) active(isNatIListKind(nil)) => mark(tt) active(isNatIListKind(zeros)) => mark(tt) active(isNatIListKind(cons(X, Y))) => mark(and(isNatKind(X), isNatIListKind(Y))) active(isNatIListKind(take(X, Y))) => mark(and(isNatKind(X), isNatIListKind(Y))) active(isNatKind(0)) => mark(tt) active(isNatKind(length(X))) => mark(isNatIListKind(X)) active(isNatKind(s(X))) => mark(isNatKind(X)) active(isNatList(nil)) => mark(tt) active(isNatList(cons(X, Y))) => mark(U51(and(isNatKind(X), isNatIListKind(Y)), X, Y)) active(isNatList(take(X, Y))) => mark(U61(and(isNatKind(X), isNatIListKind(Y)), X, Y)) active(length(nil)) => mark(0) active(length(cons(X, Y))) => mark(U71(and(and(isNatList(Y), isNatIListKind(Y)), and(isNat(X), isNatKind(X))), Y)) active(take(0, X)) => mark(U81(and(isNatIList(X), isNatIListKind(X)))) active(take(s(X), cons(Y, Z))) => mark(U91(and(and(isNatIList(Z), isNatIListKind(Z)), and(and(isNat(X), isNatKind(X)), and(isNat(Y), isNatKind(Y)))), Z, X, Y)) mark(zeros) => active(zeros) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(0) => active(0) mark(U11(X, Y)) => active(U11(mark(X), Y)) mark(tt) => active(tt) mark(U12(X)) => active(U12(mark(X))) mark(isNatList(X)) => active(isNatList(X)) mark(U21(X, Y)) => active(U21(mark(X), Y)) mark(U22(X)) => active(U22(mark(X))) mark(isNat(X)) => active(isNat(X)) mark(U31(X, Y)) => active(U31(mark(X), Y)) mark(U32(X)) => active(U32(mark(X))) mark(U41(X, Y, Z)) => active(U41(mark(X), Y, Z)) mark(U42(X, Y)) => active(U42(mark(X), Y)) mark(U43(X)) => active(U43(mark(X))) mark(isNatIList(X)) => active(isNatIList(X)) mark(U51(X, Y, Z)) => active(U51(mark(X), Y, Z)) mark(U52(X, Y)) => active(U52(mark(X), Y)) mark(U53(X)) => active(U53(mark(X))) mark(U61(X, Y, Z)) => active(U61(mark(X), Y, Z)) mark(U62(X, Y)) => active(U62(mark(X), Y)) mark(U63(X)) => active(U63(mark(X))) mark(U71(X, Y)) => active(U71(mark(X), Y)) mark(s(X)) => active(s(mark(X))) mark(length(X)) => active(length(mark(X))) mark(U81(X)) => active(U81(mark(X))) mark(nil) => active(nil) mark(U91(X, Y, Z, U)) => active(U91(mark(X), Y, Z, U)) mark(take(X, Y)) => active(take(mark(X), mark(Y))) mark(and(X, Y)) => active(and(mark(X), Y)) mark(isNatIListKind(X)) => active(isNatIListKind(X)) mark(isNatKind(X)) => active(isNatKind(X)) cons(mark(X), Y) => cons(X, Y) cons(X, mark(Y)) => cons(X, Y) cons(active(X), Y) => cons(X, Y) cons(X, active(Y)) => cons(X, Y) U11(mark(X), Y) => U11(X, Y) U11(X, mark(Y)) => U11(X, Y) U11(active(X), Y) => U11(X, Y) U11(X, active(Y)) => U11(X, Y) U12(mark(X)) => U12(X) U12(active(X)) => U12(X) isNatList(mark(X)) => isNatList(X) isNatList(active(X)) => isNatList(X) U21(mark(X), Y) => U21(X, Y) U21(X, mark(Y)) => U21(X, Y) U21(active(X), Y) => U21(X, Y) U21(X, active(Y)) => U21(X, Y) U22(mark(X)) => U22(X) U22(active(X)) => U22(X) isNat(mark(X)) => isNat(X) isNat(active(X)) => isNat(X) U31(mark(X), Y) => U31(X, Y) U31(X, mark(Y)) => U31(X, Y) U31(active(X), Y) => U31(X, Y) U31(X, active(Y)) => U31(X, Y) U32(mark(X)) => U32(X) U32(active(X)) => U32(X) U41(mark(X), Y, Z) => U41(X, Y, Z) U41(X, mark(Y), Z) => U41(X, Y, Z) U41(X, Y, mark(Z)) => U41(X, Y, Z) U41(active(X), Y, Z) => U41(X, Y, Z) U41(X, active(Y), Z) => U41(X, Y, Z) U41(X, Y, active(Z)) => U41(X, Y, Z) U42(mark(X), Y) => U42(X, Y) U42(X, mark(Y)) => U42(X, Y) U42(active(X), Y) => U42(X, Y) U42(X, active(Y)) => U42(X, Y) U43(mark(X)) => U43(X) U43(active(X)) => U43(X) isNatIList(mark(X)) => isNatIList(X) isNatIList(active(X)) => isNatIList(X) U51(mark(X), Y, Z) => U51(X, Y, Z) U51(X, mark(Y), Z) => U51(X, Y, Z) U51(X, Y, mark(Z)) => U51(X, Y, Z) U51(active(X), Y, Z) => U51(X, Y, Z) U51(X, active(Y), Z) => U51(X, Y, Z) U51(X, Y, active(Z)) => U51(X, Y, Z) U52(mark(X), Y) => U52(X, Y) U52(X, mark(Y)) => U52(X, Y) U52(active(X), Y) => U52(X, Y) U52(X, active(Y)) => U52(X, Y) U53(mark(X)) => U53(X) U53(active(X)) => U53(X) U61(mark(X), Y, Z) => U61(X, Y, Z) U61(X, mark(Y), Z) => U61(X, Y, Z) U61(X, Y, mark(Z)) => U61(X, Y, Z) U61(active(X), Y, Z) => U61(X, Y, Z) U61(X, active(Y), Z) => U61(X, Y, Z) U61(X, Y, active(Z)) => U61(X, Y, Z) U62(mark(X), Y) => U62(X, Y) U62(X, mark(Y)) => U62(X, Y) U62(active(X), Y) => U62(X, Y) U62(X, active(Y)) => U62(X, Y) U63(mark(X)) => U63(X) U63(active(X)) => U63(X) U71(mark(X), Y) => U71(X, Y) U71(X, mark(Y)) => U71(X, Y) U71(active(X), Y) => U71(X, Y) U71(X, active(Y)) => U71(X, Y) s(mark(X)) => s(X) s(active(X)) => s(X) length(mark(X)) => length(X) length(active(X)) => length(X) U81(mark(X)) => U81(X) U81(active(X)) => U81(X) U91(mark(X), Y, Z, U) => U91(X, Y, Z, U) U91(X, mark(Y), Z, U) => U91(X, Y, Z, U) U91(X, Y, mark(Z), U) => U91(X, Y, Z, U) U91(X, Y, Z, mark(U)) => U91(X, Y, Z, U) U91(active(X), Y, Z, U) => U91(X, Y, Z, U) U91(X, active(Y), Z, U) => U91(X, Y, Z, U) U91(X, Y, active(Z), U) => U91(X, Y, Z, U) U91(X, Y, Z, active(U)) => U91(X, Y, Z, U) take(mark(X), Y) => take(X, Y) take(X, mark(Y)) => take(X, Y) take(active(X), Y) => take(X, Y) take(X, active(Y)) => take(X, Y) and(mark(X), Y) => and(X, Y) and(X, mark(Y)) => and(X, Y) and(active(X), Y) => and(X, Y) and(X, active(Y)) => and(X, Y) isNatIListKind(mark(X)) => isNatIListKind(X) isNatIListKind(active(X)) => isNatIListKind(X) isNatKind(mark(X)) => isNatKind(X) isNatKind(active(X)) => isNatKind(X)