/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 U103 : [o] --> o U11 : [o * o * o] --> o U111 : [o * o] --> o U112 : [o] --> o U121 : [o * o] --> o U122 : [o] --> o U131 : [o * o * o] --> o U132 : [o * o] --> o U133 : [o] --> o U141 : [o * o * o] --> o U142 : [o * o] --> o U143 : [o] --> o U151 : [o * o * o] --> o U152 : [o * o] --> o U153 : [o] --> o U161 : [o * o] --> o U171 : [o * o * o] --> o U181 : [o * o] --> o U191 : [o * o] --> o U201 : [o * o * o * o] --> o U202 : [o * o] --> o U21 : [o * o] --> o U211 : [o * o] --> o U221 : [o * o * o] --> o U31 : [o * 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 U62 : [o] --> o U71 : [o * o] --> o U72 : [o] --> o U81 : [o * o] --> o U82 : [o] --> o U91 : [o * o] --> o U92 : [o] --> o active : [o] --> o afterNth : [o * o] --> o and : [o * o] --> o cons : [o * o] --> o fst : [o] --> o head : [o] --> o isLNat : [o] --> o isLNatKind : [o] --> o isNatural : [o] --> o isNaturalKind : [o] --> o isPLNat : [o] --> o isPLNatKind : [o] --> o mark : [o] --> o natsFrom : [o] --> o nil : [] --> o ok : [o] --> o pair : [o * o] --> o proper : [o] --> o s : [o] --> o sel : [o * o] --> o snd : [o] --> o splitAt : [o * o] --> o tail : [o] --> o take : [o * o] --> o top : [o] --> o tt : [] --> o active(U101(tt, X, Y)) => mark(U102(isNatural(X), Y)) active(U102(tt, X)) => mark(U103(isLNat(X))) active(U103(tt)) => mark(tt) active(U11(tt, X, Y)) => mark(snd(splitAt(X, Y))) active(U111(tt, X)) => mark(U112(isLNat(X))) active(U112(tt)) => mark(tt) active(U121(tt, X)) => mark(U122(isNatural(X))) active(U122(tt)) => mark(tt) active(U131(tt, X, Y)) => mark(U132(isNatural(X), Y)) active(U132(tt, X)) => mark(U133(isLNat(X))) active(U133(tt)) => mark(tt) active(U141(tt, X, Y)) => mark(U142(isLNat(X), Y)) active(U142(tt, X)) => mark(U143(isLNat(X))) active(U143(tt)) => mark(tt) active(U151(tt, X, Y)) => mark(U152(isNatural(X), Y)) active(U152(tt, X)) => mark(U153(isLNat(X))) active(U153(tt)) => mark(tt) active(U161(tt, X)) => mark(cons(X, natsFrom(s(X)))) active(U171(tt, X, Y)) => mark(head(afterNth(X, Y))) active(U181(tt, X)) => mark(X) active(U191(tt, X)) => mark(pair(nil, X)) active(U201(tt, X, Y, Z)) => mark(U202(splitAt(X, Z), Y)) active(U202(pair(X, Y), Z)) => mark(pair(cons(Z, X), Y)) active(U21(tt, X)) => mark(X) active(U211(tt, X)) => mark(X) active(U221(tt, X, Y)) => mark(fst(splitAt(X, Y))) active(U31(tt, X)) => mark(X) active(U41(tt, X, Y)) => mark(U42(isNatural(X), Y)) active(U42(tt, X)) => mark(U43(isLNat(X))) active(U43(tt)) => mark(tt) active(U51(tt, X, Y)) => mark(U52(isNatural(X), Y)) active(U52(tt, X)) => mark(U53(isLNat(X))) active(U53(tt)) => mark(tt) active(U61(tt, X)) => mark(U62(isPLNat(X))) active(U62(tt)) => mark(tt) active(U71(tt, X)) => mark(U72(isNatural(X))) active(U72(tt)) => mark(tt) active(U81(tt, X)) => mark(U82(isPLNat(X))) active(U82(tt)) => mark(tt) active(U91(tt, X)) => mark(U92(isLNat(X))) active(U92(tt)) => mark(tt) active(afterNth(X, Y)) => mark(U11(and(and(isNatural(X), isNaturalKind(X)), and(isLNat(Y), isLNatKind(Y))), X, Y)) active(and(tt, X)) => mark(X) active(fst(pair(X, Y))) => mark(U21(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), X)) active(head(cons(X, Y))) => mark(U31(and(and(isNatural(X), isNaturalKind(X)), and(isLNat(Y), isLNatKind(Y))), X)) active(isLNat(nil)) => mark(tt) active(isLNat(afterNth(X, Y))) => mark(U41(and(isNaturalKind(X), isLNatKind(Y)), X, Y)) active(isLNat(cons(X, Y))) => mark(U51(and(isNaturalKind(X), isLNatKind(Y)), X, Y)) active(isLNat(fst(X))) => mark(U61(isPLNatKind(X), X)) active(isLNat(natsFrom(X))) => mark(U71(isNaturalKind(X), X)) active(isLNat(snd(X))) => mark(U81(isPLNatKind(X), X)) active(isLNat(tail(X))) => mark(U91(isLNatKind(X), X)) active(isLNat(take(X, Y))) => mark(U101(and(isNaturalKind(X), isLNatKind(Y)), X, Y)) active(isLNatKind(nil)) => mark(tt) active(isLNatKind(afterNth(X, Y))) => mark(and(isNaturalKind(X), isLNatKind(Y))) active(isLNatKind(cons(X, Y))) => mark(and(isNaturalKind(X), isLNatKind(Y))) active(isLNatKind(fst(X))) => mark(isPLNatKind(X)) active(isLNatKind(natsFrom(X))) => mark(isNaturalKind(X)) active(isLNatKind(snd(X))) => mark(isPLNatKind(X)) active(isLNatKind(tail(X))) => mark(isLNatKind(X)) active(isLNatKind(take(X, Y))) => mark(and(isNaturalKind(X), isLNatKind(Y))) active(isNatural(0)) => mark(tt) active(isNatural(head(X))) => mark(U111(isLNatKind(X), X)) active(isNatural(s(X))) => mark(U121(isNaturalKind(X), X)) active(isNatural(sel(X, Y))) => mark(U131(and(isNaturalKind(X), isLNatKind(Y)), X, Y)) active(isNaturalKind(0)) => mark(tt) active(isNaturalKind(head(X))) => mark(isLNatKind(X)) active(isNaturalKind(s(X))) => mark(isNaturalKind(X)) active(isNaturalKind(sel(X, Y))) => mark(and(isNaturalKind(X), isLNatKind(Y))) active(isPLNat(pair(X, Y))) => mark(U141(and(isLNatKind(X), isLNatKind(Y)), X, Y)) active(isPLNat(splitAt(X, Y))) => mark(U151(and(isNaturalKind(X), isLNatKind(Y)), X, Y)) active(isPLNatKind(pair(X, Y))) => mark(and(isLNatKind(X), isLNatKind(Y))) active(isPLNatKind(splitAt(X, Y))) => mark(and(isNaturalKind(X), isLNatKind(Y))) active(natsFrom(X)) => mark(U161(and(isNatural(X), isNaturalKind(X)), X)) active(sel(X, Y)) => mark(U171(and(and(isNatural(X), isNaturalKind(X)), and(isLNat(Y), isLNatKind(Y))), X, Y)) active(snd(pair(X, Y))) => mark(U181(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), Y)) active(splitAt(0, X)) => mark(U191(and(isLNat(X), isLNatKind(X)), X)) active(splitAt(s(X), cons(Y, Z))) => mark(U201(and(and(isNatural(X), isNaturalKind(X)), and(and(isNatural(Y), isNaturalKind(Y)), and(isLNat(Z), isLNatKind(Z)))), X, Y, Z)) active(tail(cons(X, Y))) => mark(U211(and(and(isNatural(X), isNaturalKind(X)), and(isLNat(Y), isLNatKind(Y))), Y)) active(take(X, Y)) => mark(U221(and(and(isNatural(X), isNaturalKind(X)), and(isLNat(Y), isLNatKind(Y))), X, Y)) active(U101(X, Y, Z)) => U101(active(X), Y, Z) active(U102(X, Y)) => U102(active(X), Y) active(U103(X)) => U103(active(X)) active(U11(X, Y, Z)) => U11(active(X), Y, Z) active(snd(X)) => snd(active(X)) active(splitAt(X, Y)) => splitAt(active(X), Y) active(splitAt(X, Y)) => splitAt(X, active(Y)) active(U111(X, Y)) => U111(active(X), Y) active(U112(X)) => U112(active(X)) active(U121(X, Y)) => U121(active(X), Y) active(U122(X)) => U122(active(X)) active(U131(X, Y, Z)) => U131(active(X), Y, Z) active(U132(X, Y)) => U132(active(X), Y) active(U133(X)) => U133(active(X)) active(U141(X, Y, Z)) => U141(active(X), Y, Z) active(U142(X, Y)) => U142(active(X), Y) active(U143(X)) => U143(active(X)) active(U151(X, Y, Z)) => U151(active(X), Y, Z) active(U152(X, Y)) => U152(active(X), Y) active(U153(X)) => U153(active(X)) active(U161(X, Y)) => U161(active(X), Y) active(cons(X, Y)) => cons(active(X), Y) active(natsFrom(X)) => natsFrom(active(X)) active(s(X)) => s(active(X)) active(U171(X, Y, Z)) => U171(active(X), Y, Z) active(head(X)) => head(active(X)) active(afterNth(X, Y)) => afterNth(active(X), Y) active(afterNth(X, Y)) => afterNth(X, active(Y)) active(U181(X, Y)) => U181(active(X), Y) active(U191(X, Y)) => U191(active(X), Y) active(pair(X, Y)) => pair(active(X), Y) active(pair(X, Y)) => pair(X, active(Y)) active(U201(X, Y, Z, U)) => U201(active(X), Y, Z, U) active(U202(X, Y)) => U202(active(X), Y) active(U21(X, Y)) => U21(active(X), Y) active(U211(X, Y)) => U211(active(X), Y) active(U221(X, Y, Z)) => U221(active(X), Y, Z) active(fst(X)) => fst(active(X)) active(U31(X, Y)) => U31(active(X), Y) active(U41(X, Y, Z)) => U41(active(X), Y, Z) active(U42(X, Y)) => U42(active(X), Y) active(U43(X)) => U43(active(X)) active(U51(X, Y, Z)) => U51(active(X), Y, Z) active(U52(X, Y)) => U52(active(X), Y) active(U53(X)) => U53(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)) => U72(active(X)) active(U81(X, Y)) => U81(active(X), Y) active(U82(X)) => U82(active(X)) active(U91(X, Y)) => U91(active(X), Y) active(U92(X)) => U92(active(X)) active(and(X, Y)) => and(active(X), Y) active(tail(X)) => tail(active(X)) active(take(X, Y)) => take(active(X), Y) active(take(X, Y)) => take(X, active(Y)) active(sel(X, Y)) => sel(active(X), Y) active(sel(X, Y)) => sel(X, active(Y)) U101(mark(X), Y, Z) => mark(U101(X, Y, Z)) U102(mark(X), Y) => mark(U102(X, Y)) U103(mark(X)) => mark(U103(X)) U11(mark(X), Y, Z) => mark(U11(X, Y, Z)) snd(mark(X)) => mark(snd(X)) splitAt(mark(X), Y) => mark(splitAt(X, Y)) splitAt(X, mark(Y)) => mark(splitAt(X, Y)) U111(mark(X), Y) => mark(U111(X, Y)) U112(mark(X)) => mark(U112(X)) U121(mark(X), Y) => mark(U121(X, Y)) U122(mark(X)) => mark(U122(X)) U131(mark(X), Y, Z) => mark(U131(X, Y, Z)) U132(mark(X), Y) => mark(U132(X, Y)) U133(mark(X)) => mark(U133(X)) U141(mark(X), Y, Z) => mark(U141(X, Y, Z)) U142(mark(X), Y) => mark(U142(X, Y)) U143(mark(X)) => mark(U143(X)) U151(mark(X), Y, Z) => mark(U151(X, Y, Z)) U152(mark(X), Y) => mark(U152(X, Y)) U153(mark(X)) => mark(U153(X)) U161(mark(X), Y) => mark(U161(X, Y)) cons(mark(X), Y) => mark(cons(X, Y)) natsFrom(mark(X)) => mark(natsFrom(X)) s(mark(X)) => mark(s(X)) U171(mark(X), Y, Z) => mark(U171(X, Y, Z)) head(mark(X)) => mark(head(X)) afterNth(mark(X), Y) => mark(afterNth(X, Y)) afterNth(X, mark(Y)) => mark(afterNth(X, Y)) U181(mark(X), Y) => mark(U181(X, Y)) U191(mark(X), Y) => mark(U191(X, Y)) pair(mark(X), Y) => mark(pair(X, Y)) pair(X, mark(Y)) => mark(pair(X, Y)) U201(mark(X), Y, Z, U) => mark(U201(X, Y, Z, U)) U202(mark(X), Y) => mark(U202(X, Y)) U21(mark(X), Y) => mark(U21(X, Y)) U211(mark(X), Y) => mark(U211(X, Y)) U221(mark(X), Y, Z) => mark(U221(X, Y, Z)) fst(mark(X)) => mark(fst(X)) U31(mark(X), Y) => mark(U31(X, Y)) U41(mark(X), Y, Z) => mark(U41(X, Y, Z)) U42(mark(X), Y) => mark(U42(X, Y)) U43(mark(X)) => mark(U43(X)) U51(mark(X), Y, Z) => mark(U51(X, Y, Z)) U52(mark(X), Y) => mark(U52(X, Y)) U53(mark(X)) => mark(U53(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)) => mark(U72(X)) U81(mark(X), Y) => mark(U81(X, Y)) U82(mark(X)) => mark(U82(X)) U91(mark(X), Y) => mark(U91(X, Y)) U92(mark(X)) => mark(U92(X)) and(mark(X), Y) => mark(and(X, Y)) tail(mark(X)) => mark(tail(X)) take(mark(X), Y) => mark(take(X, Y)) take(X, mark(Y)) => mark(take(X, Y)) sel(mark(X), Y) => mark(sel(X, Y)) sel(X, mark(Y)) => mark(sel(X, Y)) proper(U101(X, Y, Z)) => U101(proper(X), proper(Y), proper(Z)) proper(tt) => ok(tt) proper(U102(X, Y)) => U102(proper(X), proper(Y)) proper(isNatural(X)) => isNatural(proper(X)) proper(U103(X)) => U103(proper(X)) proper(isLNat(X)) => isLNat(proper(X)) proper(U11(X, Y, Z)) => U11(proper(X), proper(Y), proper(Z)) proper(snd(X)) => snd(proper(X)) proper(splitAt(X, Y)) => splitAt(proper(X), proper(Y)) proper(U111(X, Y)) => U111(proper(X), proper(Y)) proper(U112(X)) => U112(proper(X)) proper(U121(X, Y)) => U121(proper(X), proper(Y)) proper(U122(X)) => U122(proper(X)) proper(U131(X, Y, Z)) => U131(proper(X), proper(Y), proper(Z)) proper(U132(X, Y)) => U132(proper(X), proper(Y)) proper(U133(X)) => U133(proper(X)) proper(U141(X, Y, Z)) => U141(proper(X), proper(Y), proper(Z)) proper(U142(X, Y)) => U142(proper(X), proper(Y)) proper(U143(X)) => U143(proper(X)) proper(U151(X, Y, Z)) => U151(proper(X), proper(Y), proper(Z)) proper(U152(X, Y)) => U152(proper(X), proper(Y)) proper(U153(X)) => U153(proper(X)) proper(U161(X, Y)) => U161(proper(X), proper(Y)) proper(cons(X, Y)) => cons(proper(X), proper(Y)) proper(natsFrom(X)) => natsFrom(proper(X)) proper(s(X)) => s(proper(X)) proper(U171(X, Y, Z)) => U171(proper(X), proper(Y), proper(Z)) proper(head(X)) => head(proper(X)) proper(afterNth(X, Y)) => afterNth(proper(X), proper(Y)) proper(U181(X, Y)) => U181(proper(X), proper(Y)) proper(U191(X, Y)) => U191(proper(X), proper(Y)) proper(pair(X, Y)) => pair(proper(X), proper(Y)) proper(nil) => ok(nil) proper(U201(X, Y, Z, U)) => U201(proper(X), proper(Y), proper(Z), proper(U)) proper(U202(X, Y)) => U202(proper(X), proper(Y)) proper(U21(X, Y)) => U21(proper(X), proper(Y)) proper(U211(X, Y)) => U211(proper(X), proper(Y)) proper(U221(X, Y, Z)) => U221(proper(X), proper(Y), proper(Z)) proper(fst(X)) => fst(proper(X)) proper(U31(X, Y)) => U31(proper(X), proper(Y)) proper(U41(X, Y, Z)) => U41(proper(X), proper(Y), proper(Z)) proper(U42(X, Y)) => U42(proper(X), proper(Y)) proper(U43(X)) => U43(proper(X)) proper(U51(X, Y, Z)) => U51(proper(X), proper(Y), proper(Z)) proper(U52(X, Y)) => U52(proper(X), proper(Y)) proper(U53(X)) => U53(proper(X)) proper(U61(X, Y)) => U61(proper(X), proper(Y)) proper(U62(X)) => U62(proper(X)) proper(isPLNat(X)) => isPLNat(proper(X)) proper(U71(X, Y)) => U71(proper(X), proper(Y)) proper(U72(X)) => U72(proper(X)) proper(U81(X, Y)) => U81(proper(X), proper(Y)) proper(U82(X)) => U82(proper(X)) proper(U91(X, Y)) => U91(proper(X), proper(Y)) proper(U92(X)) => U92(proper(X)) proper(and(X, Y)) => and(proper(X), proper(Y)) proper(isNaturalKind(X)) => isNaturalKind(proper(X)) proper(isLNatKind(X)) => isLNatKind(proper(X)) proper(isPLNatKind(X)) => isPLNatKind(proper(X)) proper(tail(X)) => tail(proper(X)) proper(take(X, Y)) => take(proper(X), proper(Y)) proper(0) => ok(0) proper(sel(X, Y)) => sel(proper(X), proper(Y)) U101(ok(X), ok(Y), ok(Z)) => ok(U101(X, Y, Z)) U102(ok(X), ok(Y)) => ok(U102(X, Y)) isNatural(ok(X)) => ok(isNatural(X)) U103(ok(X)) => ok(U103(X)) isLNat(ok(X)) => ok(isLNat(X)) U11(ok(X), ok(Y), ok(Z)) => ok(U11(X, Y, Z)) snd(ok(X)) => ok(snd(X)) splitAt(ok(X), ok(Y)) => ok(splitAt(X, Y)) U111(ok(X), ok(Y)) => ok(U111(X, Y)) U112(ok(X)) => ok(U112(X)) U121(ok(X), ok(Y)) => ok(U121(X, Y)) U122(ok(X)) => ok(U122(X)) U131(ok(X), ok(Y), ok(Z)) => ok(U131(X, Y, Z)) U132(ok(X), ok(Y)) => ok(U132(X, Y)) U133(ok(X)) => ok(U133(X)) U141(ok(X), ok(Y), ok(Z)) => ok(U141(X, Y, Z)) U142(ok(X), ok(Y)) => ok(U142(X, Y)) U143(ok(X)) => ok(U143(X)) U151(ok(X), ok(Y), ok(Z)) => ok(U151(X, Y, Z)) U152(ok(X), ok(Y)) => ok(U152(X, Y)) U153(ok(X)) => ok(U153(X)) U161(ok(X), ok(Y)) => ok(U161(X, Y)) cons(ok(X), ok(Y)) => ok(cons(X, Y)) natsFrom(ok(X)) => ok(natsFrom(X)) s(ok(X)) => ok(s(X)) U171(ok(X), ok(Y), ok(Z)) => ok(U171(X, Y, Z)) head(ok(X)) => ok(head(X)) afterNth(ok(X), ok(Y)) => ok(afterNth(X, Y)) U181(ok(X), ok(Y)) => ok(U181(X, Y)) U191(ok(X), ok(Y)) => ok(U191(X, Y)) pair(ok(X), ok(Y)) => ok(pair(X, Y)) U201(ok(X), ok(Y), ok(Z), ok(U)) => ok(U201(X, Y, Z, U)) U202(ok(X), ok(Y)) => ok(U202(X, Y)) U21(ok(X), ok(Y)) => ok(U21(X, Y)) U211(ok(X), ok(Y)) => ok(U211(X, Y)) U221(ok(X), ok(Y), ok(Z)) => ok(U221(X, Y, Z)) fst(ok(X)) => ok(fst(X)) U31(ok(X), ok(Y)) => ok(U31(X, Y)) U41(ok(X), ok(Y), ok(Z)) => ok(U41(X, Y, Z)) U42(ok(X), ok(Y)) => ok(U42(X, Y)) U43(ok(X)) => ok(U43(X)) U51(ok(X), ok(Y), ok(Z)) => ok(U51(X, Y, Z)) U52(ok(X), ok(Y)) => ok(U52(X, Y)) U53(ok(X)) => ok(U53(X)) U61(ok(X), ok(Y)) => ok(U61(X, Y)) U62(ok(X)) => ok(U62(X)) isPLNat(ok(X)) => ok(isPLNat(X)) U71(ok(X), ok(Y)) => ok(U71(X, Y)) U72(ok(X)) => ok(U72(X)) U81(ok(X), ok(Y)) => ok(U81(X, Y)) U82(ok(X)) => ok(U82(X)) U91(ok(X), ok(Y)) => ok(U91(X, Y)) U92(ok(X)) => ok(U92(X)) and(ok(X), ok(Y)) => ok(and(X, Y)) isNaturalKind(ok(X)) => ok(isNaturalKind(X)) isLNatKind(ok(X)) => ok(isLNatKind(X)) isPLNatKind(ok(X)) => ok(isPLNatKind(X)) tail(ok(X)) => ok(tail(X)) take(ok(X), ok(Y)) => ok(take(X, Y)) sel(ok(X), ok(Y)) => ok(sel(X, Y)) top(mark(X)) => top(proper(X)) top(ok(X)) => top(active(X))