/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 U102 : [o] --> o U11 : [o * o * o] --> o U111 : [o] --> o U12 : [o * o * o] --> o U121 : [o] --> o U131 : [o * o] --> o U132 : [o] --> o U141 : [o * o] --> o U142 : [o] --> o U151 : [o * o] --> o U152 : [o] --> o U161 : [o * o] --> o U171 : [o * o * o] --> o U172 : [o * o * o] --> o U181 : [o * o] --> o U182 : [o * o] --> o U191 : [o * o] --> o U201 : [o * o * o * o] --> o U202 : [o * o * o * o] --> o U203 : [o * o * o * o] --> o U204 : [o * o] --> o U21 : [o * o * o] --> o U211 : [o * o] --> o U212 : [o * o] --> o U22 : [o * o] --> o U221 : [o * o * o] --> o U222 : [o * o * o] --> o U31 : [o * o * o] --> o U32 : [o * o] --> o U41 : [o * o] --> o U42 : [o] --> o U51 : [o * o] --> o U52 : [o] --> o U61 : [o] --> o U71 : [o] --> o U81 : [o] --> o U91 : [o] --> o active : [o] --> o afterNth : [o * o] --> o cons : [o * o] --> o fst : [o] --> o head : [o] --> o isLNat : [o] --> o isNatural : [o] --> o isPLNat : [o] --> o mark : [o] --> o natsFrom : [o] --> o nil : [] --> o pair : [o * o] --> o s : [o] --> o sel : [o * o] --> o snd : [o] --> o splitAt : [o * o] --> o tail : [o] --> o take : [o * o] --> o tt : [] --> o active(U101(tt, X)) => mark(U102(isLNat(X))) active(U102(tt)) => mark(tt) active(U11(tt, X, Y)) => mark(U12(isLNat(Y), X, Y)) active(U111(tt)) => mark(tt) active(U12(tt, X, Y)) => mark(snd(splitAt(X, Y))) active(U121(tt)) => mark(tt) active(U131(tt, X)) => mark(U132(isLNat(X))) active(U132(tt)) => mark(tt) active(U141(tt, X)) => mark(U142(isLNat(X))) active(U142(tt)) => mark(tt) active(U151(tt, X)) => mark(U152(isLNat(X))) active(U152(tt)) => mark(tt) active(U161(tt, X)) => mark(cons(X, natsFrom(s(X)))) active(U171(tt, X, Y)) => mark(U172(isLNat(Y), X, Y)) active(U172(tt, X, Y)) => mark(head(afterNth(X, Y))) active(U181(tt, X)) => mark(U182(isLNat(X), X)) active(U182(tt, X)) => mark(X) active(U191(tt, X)) => mark(pair(nil, X)) active(U201(tt, X, Y, Z)) => mark(U202(isNatural(Y), X, Y, Z)) active(U202(tt, X, Y, Z)) => mark(U203(isLNat(Z), X, Y, Z)) active(U203(tt, X, Y, Z)) => mark(U204(splitAt(X, Z), Y)) active(U204(pair(X, Y), Z)) => mark(pair(cons(Z, X), Y)) active(U21(tt, X, Y)) => mark(U22(isLNat(Y), X)) active(U211(tt, X)) => mark(U212(isLNat(X), X)) active(U212(tt, X)) => mark(X) active(U22(tt, X)) => mark(X) active(U221(tt, X, Y)) => mark(U222(isLNat(Y), X, Y)) active(U222(tt, X, Y)) => mark(fst(splitAt(X, Y))) active(U31(tt, X, Y)) => mark(U32(isLNat(Y), X)) active(U32(tt, X)) => mark(X) active(U41(tt, X)) => mark(U42(isLNat(X))) active(U42(tt)) => mark(tt) active(U51(tt, X)) => mark(U52(isLNat(X))) active(U52(tt)) => mark(tt) active(U61(tt)) => mark(tt) active(U71(tt)) => mark(tt) active(U81(tt)) => mark(tt) active(U91(tt)) => mark(tt) active(afterNth(X, Y)) => mark(U11(isNatural(X), X, Y)) active(fst(pair(X, Y))) => mark(U21(isLNat(X), X, Y)) active(head(cons(X, Y))) => mark(U31(isNatural(X), X, Y)) active(isLNat(nil)) => mark(tt) active(isLNat(afterNth(X, Y))) => mark(U41(isNatural(X), Y)) active(isLNat(cons(X, Y))) => mark(U51(isNatural(X), Y)) active(isLNat(fst(X))) => mark(U61(isPLNat(X))) active(isLNat(natsFrom(X))) => mark(U71(isNatural(X))) active(isLNat(snd(X))) => mark(U81(isPLNat(X))) active(isLNat(tail(X))) => mark(U91(isLNat(X))) active(isLNat(take(X, Y))) => mark(U101(isNatural(X), Y)) active(isNatural(0)) => mark(tt) active(isNatural(head(X))) => mark(U111(isLNat(X))) active(isNatural(s(X))) => mark(U121(isNatural(X))) active(isNatural(sel(X, Y))) => mark(U131(isNatural(X), Y)) active(isPLNat(pair(X, Y))) => mark(U141(isLNat(X), Y)) active(isPLNat(splitAt(X, Y))) => mark(U151(isNatural(X), Y)) active(natsFrom(X)) => mark(U161(isNatural(X), X)) active(sel(X, Y)) => mark(U171(isNatural(X), X, Y)) active(snd(pair(X, Y))) => mark(U181(isLNat(X), Y)) active(splitAt(0, X)) => mark(U191(isLNat(X), X)) active(splitAt(s(X), cons(Y, Z))) => mark(U201(isNatural(X), X, Y, Z)) active(tail(cons(X, Y))) => mark(U211(isNatural(X), Y)) active(take(X, Y)) => mark(U221(isNatural(X), X, Y)) mark(U101(X, Y)) => active(U101(mark(X), Y)) mark(tt) => active(tt) mark(U102(X)) => active(U102(mark(X))) mark(isLNat(X)) => active(isLNat(X)) mark(U11(X, Y, Z)) => active(U11(mark(X), Y, Z)) mark(U12(X, Y, Z)) => active(U12(mark(X), Y, Z)) mark(U111(X)) => active(U111(mark(X))) mark(snd(X)) => active(snd(mark(X))) mark(splitAt(X, Y)) => active(splitAt(mark(X), mark(Y))) mark(U121(X)) => active(U121(mark(X))) mark(U131(X, Y)) => active(U131(mark(X), Y)) mark(U132(X)) => active(U132(mark(X))) mark(U141(X, Y)) => active(U141(mark(X), Y)) mark(U142(X)) => active(U142(mark(X))) mark(U151(X, Y)) => active(U151(mark(X), Y)) mark(U152(X)) => active(U152(mark(X))) mark(U161(X, Y)) => active(U161(mark(X), Y)) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(natsFrom(X)) => active(natsFrom(mark(X))) mark(s(X)) => active(s(mark(X))) mark(U171(X, Y, Z)) => active(U171(mark(X), Y, Z)) mark(U172(X, Y, Z)) => active(U172(mark(X), Y, Z)) mark(head(X)) => active(head(mark(X))) mark(afterNth(X, Y)) => active(afterNth(mark(X), mark(Y))) mark(U181(X, Y)) => active(U181(mark(X), Y)) mark(U182(X, Y)) => active(U182(mark(X), Y)) mark(U191(X, Y)) => active(U191(mark(X), Y)) mark(pair(X, Y)) => active(pair(mark(X), mark(Y))) mark(nil) => active(nil) mark(U201(X, Y, Z, U)) => active(U201(mark(X), Y, Z, U)) mark(U202(X, Y, Z, U)) => active(U202(mark(X), Y, Z, U)) mark(isNatural(X)) => active(isNatural(X)) mark(U203(X, Y, Z, U)) => active(U203(mark(X), Y, Z, U)) mark(U204(X, Y)) => active(U204(mark(X), Y)) mark(U21(X, Y, Z)) => active(U21(mark(X), Y, Z)) mark(U22(X, Y)) => active(U22(mark(X), Y)) mark(U211(X, Y)) => active(U211(mark(X), Y)) mark(U212(X, Y)) => active(U212(mark(X), Y)) mark(U221(X, Y, Z)) => active(U221(mark(X), Y, Z)) mark(U222(X, Y, Z)) => active(U222(mark(X), Y, Z)) mark(fst(X)) => active(fst(mark(X))) mark(U31(X, Y, Z)) => active(U31(mark(X), Y, Z)) mark(U32(X, Y)) => active(U32(mark(X), Y)) mark(U41(X, Y)) => active(U41(mark(X), Y)) mark(U42(X)) => active(U42(mark(X))) mark(U51(X, Y)) => active(U51(mark(X), Y)) mark(U52(X)) => active(U52(mark(X))) mark(U61(X)) => active(U61(mark(X))) mark(U71(X)) => active(U71(mark(X))) mark(U81(X)) => active(U81(mark(X))) mark(U91(X)) => active(U91(mark(X))) mark(isPLNat(X)) => active(isPLNat(X)) mark(tail(X)) => active(tail(mark(X))) mark(take(X, Y)) => active(take(mark(X), mark(Y))) mark(0) => active(0) mark(sel(X, Y)) => active(sel(mark(X), mark(Y))) U101(mark(X), Y) => U101(X, Y) U101(X, mark(Y)) => U101(X, Y) U101(active(X), Y) => U101(X, Y) U101(X, active(Y)) => U101(X, Y) U102(mark(X)) => U102(X) U102(active(X)) => U102(X) isLNat(mark(X)) => isLNat(X) isLNat(active(X)) => isLNat(X) U11(mark(X), Y, Z) => U11(X, Y, Z) U11(X, mark(Y), Z) => U11(X, Y, Z) U11(X, Y, mark(Z)) => U11(X, Y, Z) U11(active(X), Y, Z) => U11(X, Y, Z) U11(X, active(Y), Z) => U11(X, Y, Z) U11(X, Y, active(Z)) => U11(X, Y, Z) U12(mark(X), Y, Z) => U12(X, Y, Z) U12(X, mark(Y), Z) => U12(X, Y, Z) U12(X, Y, mark(Z)) => U12(X, Y, Z) U12(active(X), Y, Z) => U12(X, Y, Z) U12(X, active(Y), Z) => U12(X, Y, Z) U12(X, Y, active(Z)) => U12(X, Y, Z) U111(mark(X)) => U111(X) U111(active(X)) => U111(X) snd(mark(X)) => snd(X) snd(active(X)) => snd(X) splitAt(mark(X), Y) => splitAt(X, Y) splitAt(X, mark(Y)) => splitAt(X, Y) splitAt(active(X), Y) => splitAt(X, Y) splitAt(X, active(Y)) => splitAt(X, Y) U121(mark(X)) => U121(X) U121(active(X)) => U121(X) U131(mark(X), Y) => U131(X, Y) U131(X, mark(Y)) => U131(X, Y) U131(active(X), Y) => U131(X, Y) U131(X, active(Y)) => U131(X, Y) U132(mark(X)) => U132(X) U132(active(X)) => U132(X) U141(mark(X), Y) => U141(X, Y) U141(X, mark(Y)) => U141(X, Y) U141(active(X), Y) => U141(X, Y) U141(X, active(Y)) => U141(X, Y) U142(mark(X)) => U142(X) U142(active(X)) => U142(X) U151(mark(X), Y) => U151(X, Y) U151(X, mark(Y)) => U151(X, Y) U151(active(X), Y) => U151(X, Y) U151(X, active(Y)) => U151(X, Y) U152(mark(X)) => U152(X) U152(active(X)) => U152(X) U161(mark(X), Y) => U161(X, Y) U161(X, mark(Y)) => U161(X, Y) U161(active(X), Y) => U161(X, Y) U161(X, active(Y)) => U161(X, Y) 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) natsFrom(mark(X)) => natsFrom(X) natsFrom(active(X)) => natsFrom(X) s(mark(X)) => s(X) s(active(X)) => s(X) U171(mark(X), Y, Z) => U171(X, Y, Z) U171(X, mark(Y), Z) => U171(X, Y, Z) U171(X, Y, mark(Z)) => U171(X, Y, Z) U171(active(X), Y, Z) => U171(X, Y, Z) U171(X, active(Y), Z) => U171(X, Y, Z) U171(X, Y, active(Z)) => U171(X, Y, Z) U172(mark(X), Y, Z) => U172(X, Y, Z) U172(X, mark(Y), Z) => U172(X, Y, Z) U172(X, Y, mark(Z)) => U172(X, Y, Z) U172(active(X), Y, Z) => U172(X, Y, Z) U172(X, active(Y), Z) => U172(X, Y, Z) U172(X, Y, active(Z)) => U172(X, Y, Z) head(mark(X)) => head(X) head(active(X)) => head(X) afterNth(mark(X), Y) => afterNth(X, Y) afterNth(X, mark(Y)) => afterNth(X, Y) afterNth(active(X), Y) => afterNth(X, Y) afterNth(X, active(Y)) => afterNth(X, Y) U181(mark(X), Y) => U181(X, Y) U181(X, mark(Y)) => U181(X, Y) U181(active(X), Y) => U181(X, Y) U181(X, active(Y)) => U181(X, Y) U182(mark(X), Y) => U182(X, Y) U182(X, mark(Y)) => U182(X, Y) U182(active(X), Y) => U182(X, Y) U182(X, active(Y)) => U182(X, Y) U191(mark(X), Y) => U191(X, Y) U191(X, mark(Y)) => U191(X, Y) U191(active(X), Y) => U191(X, Y) U191(X, active(Y)) => U191(X, Y) pair(mark(X), Y) => pair(X, Y) pair(X, mark(Y)) => pair(X, Y) pair(active(X), Y) => pair(X, Y) pair(X, active(Y)) => pair(X, Y) U201(mark(X), Y, Z, U) => U201(X, Y, Z, U) U201(X, mark(Y), Z, U) => U201(X, Y, Z, U) U201(X, Y, mark(Z), U) => U201(X, Y, Z, U) U201(X, Y, Z, mark(U)) => U201(X, Y, Z, U) U201(active(X), Y, Z, U) => U201(X, Y, Z, U) U201(X, active(Y), Z, U) => U201(X, Y, Z, U) U201(X, Y, active(Z), U) => U201(X, Y, Z, U) U201(X, Y, Z, active(U)) => U201(X, Y, Z, U) U202(mark(X), Y, Z, U) => U202(X, Y, Z, U) U202(X, mark(Y), Z, U) => U202(X, Y, Z, U) U202(X, Y, mark(Z), U) => U202(X, Y, Z, U) U202(X, Y, Z, mark(U)) => U202(X, Y, Z, U) U202(active(X), Y, Z, U) => U202(X, Y, Z, U) U202(X, active(Y), Z, U) => U202(X, Y, Z, U) U202(X, Y, active(Z), U) => U202(X, Y, Z, U) U202(X, Y, Z, active(U)) => U202(X, Y, Z, U) isNatural(mark(X)) => isNatural(X) isNatural(active(X)) => isNatural(X) U203(mark(X), Y, Z, U) => U203(X, Y, Z, U) U203(X, mark(Y), Z, U) => U203(X, Y, Z, U) U203(X, Y, mark(Z), U) => U203(X, Y, Z, U) U203(X, Y, Z, mark(U)) => U203(X, Y, Z, U) U203(active(X), Y, Z, U) => U203(X, Y, Z, U) U203(X, active(Y), Z, U) => U203(X, Y, Z, U) U203(X, Y, active(Z), U) => U203(X, Y, Z, U) U203(X, Y, Z, active(U)) => U203(X, Y, Z, U) U204(mark(X), Y) => U204(X, Y) U204(X, mark(Y)) => U204(X, Y) U204(active(X), Y) => U204(X, Y) U204(X, active(Y)) => U204(X, Y) U21(mark(X), Y, Z) => U21(X, Y, Z) U21(X, mark(Y), Z) => U21(X, Y, Z) U21(X, Y, mark(Z)) => U21(X, Y, Z) U21(active(X), Y, Z) => U21(X, Y, Z) U21(X, active(Y), Z) => U21(X, Y, Z) U21(X, Y, active(Z)) => U21(X, Y, Z) U22(mark(X), Y) => U22(X, Y) U22(X, mark(Y)) => U22(X, Y) U22(active(X), Y) => U22(X, Y) U22(X, active(Y)) => U22(X, Y) U211(mark(X), Y) => U211(X, Y) U211(X, mark(Y)) => U211(X, Y) U211(active(X), Y) => U211(X, Y) U211(X, active(Y)) => U211(X, Y) U212(mark(X), Y) => U212(X, Y) U212(X, mark(Y)) => U212(X, Y) U212(active(X), Y) => U212(X, Y) U212(X, active(Y)) => U212(X, Y) U221(mark(X), Y, Z) => U221(X, Y, Z) U221(X, mark(Y), Z) => U221(X, Y, Z) U221(X, Y, mark(Z)) => U221(X, Y, Z) U221(active(X), Y, Z) => U221(X, Y, Z) U221(X, active(Y), Z) => U221(X, Y, Z) U221(X, Y, active(Z)) => U221(X, Y, Z) U222(mark(X), Y, Z) => U222(X, Y, Z) U222(X, mark(Y), Z) => U222(X, Y, Z) U222(X, Y, mark(Z)) => U222(X, Y, Z) U222(active(X), Y, Z) => U222(X, Y, Z) U222(X, active(Y), Z) => U222(X, Y, Z) U222(X, Y, active(Z)) => U222(X, Y, Z) fst(mark(X)) => fst(X) fst(active(X)) => fst(X) U31(mark(X), Y, Z) => U31(X, Y, Z) U31(X, mark(Y), Z) => U31(X, Y, Z) U31(X, Y, mark(Z)) => U31(X, Y, Z) U31(active(X), Y, Z) => U31(X, Y, Z) U31(X, active(Y), Z) => U31(X, Y, Z) U31(X, Y, active(Z)) => U31(X, Y, Z) U32(mark(X), Y) => U32(X, Y) U32(X, mark(Y)) => U32(X, Y) U32(active(X), Y) => U32(X, Y) U32(X, active(Y)) => U32(X, Y) U41(mark(X), Y) => U41(X, Y) U41(X, mark(Y)) => U41(X, Y) U41(active(X), Y) => U41(X, Y) U41(X, active(Y)) => U41(X, Y) U42(mark(X)) => U42(X) U42(active(X)) => U42(X) U51(mark(X), Y) => U51(X, Y) U51(X, mark(Y)) => U51(X, Y) U51(active(X), Y) => U51(X, Y) U51(X, active(Y)) => U51(X, Y) U52(mark(X)) => U52(X) U52(active(X)) => U52(X) U61(mark(X)) => U61(X) U61(active(X)) => U61(X) U71(mark(X)) => U71(X) U71(active(X)) => U71(X) U81(mark(X)) => U81(X) U81(active(X)) => U81(X) U91(mark(X)) => U91(X) U91(active(X)) => U91(X) isPLNat(mark(X)) => isPLNat(X) isPLNat(active(X)) => isPLNat(X) tail(mark(X)) => tail(X) tail(active(X)) => tail(X) 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) sel(mark(X), Y) => sel(X, Y) sel(X, mark(Y)) => sel(X, Y) sel(active(X), Y) => sel(X, Y) sel(X, active(Y)) => sel(X, Y)