/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] --> o U11 : [o * o * o] --> o U21 : [o * o] --> o U31 : [o * o] --> o U41 : [o * o] --> o U51 : [o * o * o] --> o U61 : [o * o] --> o U71 : [o * o] --> o U81 : [o * o * o * o] --> o U82 : [o * o] --> o U91 : [o * o] --> o a!6220!6220U101 : [o * o * o] --> o a!6220!6220U11 : [o * o * o] --> o a!6220!6220U21 : [o * o] --> o a!6220!6220U31 : [o * o] --> o a!6220!6220U41 : [o * o] --> o a!6220!6220U51 : [o * o * o] --> o a!6220!6220U61 : [o * o] --> o a!6220!6220U71 : [o * o] --> o a!6220!6220U81 : [o * o * o * o] --> o a!6220!6220U82 : [o * o] --> o a!6220!6220U91 : [o * o] --> o a!6220!6220afterNth : [o * o] --> o a!6220!6220and : [o * o] --> o a!6220!6220fst : [o] --> o a!6220!6220head : [o] --> o a!6220!6220isLNat : [o] --> o a!6220!6220isNatural : [o] --> o a!6220!6220isPLNat : [o] --> o a!6220!6220natsFrom : [o] --> o a!6220!6220sel : [o * o] --> o a!6220!6220snd : [o] --> o a!6220!6220splitAt : [o * o] --> o a!6220!6220tail : [o] --> o a!6220!6220take : [o * o] --> o afterNth : [o * o] --> o and : [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 a!6220!6220U101(tt, X, Y) => a!6220!6220fst(a!6220!6220splitAt(mark(X), mark(Y))) a!6220!6220U11(tt, X, Y) => a!6220!6220snd(a!6220!6220splitAt(mark(X), mark(Y))) a!6220!6220U21(tt, X) => mark(X) a!6220!6220U31(tt, X) => mark(X) a!6220!6220U41(tt, X) => cons(mark(X), natsFrom(s(X))) a!6220!6220U51(tt, X, Y) => a!6220!6220head(a!6220!6220afterNth(mark(X), mark(Y))) a!6220!6220U61(tt, X) => mark(X) a!6220!6220U71(tt, X) => pair(nil, mark(X)) a!6220!6220U81(tt, X, Y, Z) => a!6220!6220U82(a!6220!6220splitAt(mark(X), mark(Z)), Y) a!6220!6220U82(pair(X, Y), Z) => pair(cons(mark(Z), X), mark(Y)) a!6220!6220U91(tt, X) => mark(X) a!6220!6220afterNth(X, Y) => a!6220!6220U11(a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)), X, Y) a!6220!6220and(tt, X) => mark(X) a!6220!6220fst(pair(X, Y)) => a!6220!6220U21(a!6220!6220and(a!6220!6220isLNat(X), isLNat(Y)), X) a!6220!6220head(cons(X, Y)) => a!6220!6220U31(a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)), X) a!6220!6220isLNat(nil) => tt a!6220!6220isLNat(afterNth(X, Y)) => a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)) a!6220!6220isLNat(cons(X, Y)) => a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)) a!6220!6220isLNat(fst(X)) => a!6220!6220isPLNat(X) a!6220!6220isLNat(natsFrom(X)) => a!6220!6220isNatural(X) a!6220!6220isLNat(snd(X)) => a!6220!6220isPLNat(X) a!6220!6220isLNat(tail(X)) => a!6220!6220isLNat(X) a!6220!6220isLNat(take(X, Y)) => a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)) a!6220!6220isNatural(0) => tt a!6220!6220isNatural(head(X)) => a!6220!6220isLNat(X) a!6220!6220isNatural(s(X)) => a!6220!6220isNatural(X) a!6220!6220isNatural(sel(X, Y)) => a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)) a!6220!6220isPLNat(pair(X, Y)) => a!6220!6220and(a!6220!6220isLNat(X), isLNat(Y)) a!6220!6220isPLNat(splitAt(X, Y)) => a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)) a!6220!6220natsFrom(X) => a!6220!6220U41(a!6220!6220isNatural(X), X) a!6220!6220sel(X, Y) => a!6220!6220U51(a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)), X, Y) a!6220!6220snd(pair(X, Y)) => a!6220!6220U61(a!6220!6220and(a!6220!6220isLNat(X), isLNat(Y)), Y) a!6220!6220splitAt(0, X) => a!6220!6220U71(a!6220!6220isLNat(X), X) a!6220!6220splitAt(s(X), cons(Y, Z)) => a!6220!6220U81(a!6220!6220and(a!6220!6220isNatural(X), and(isNatural(Y), isLNat(Z))), X, Y, Z) a!6220!6220tail(cons(X, Y)) => a!6220!6220U91(a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)), Y) a!6220!6220take(X, Y) => a!6220!6220U101(a!6220!6220and(a!6220!6220isNatural(X), isLNat(Y)), X, Y) mark(U101(X, Y, Z)) => a!6220!6220U101(mark(X), Y, Z) mark(fst(X)) => a!6220!6220fst(mark(X)) mark(splitAt(X, Y)) => a!6220!6220splitAt(mark(X), mark(Y)) mark(U11(X, Y, Z)) => a!6220!6220U11(mark(X), Y, Z) mark(snd(X)) => a!6220!6220snd(mark(X)) mark(U21(X, Y)) => a!6220!6220U21(mark(X), Y) mark(U31(X, Y)) => a!6220!6220U31(mark(X), Y) mark(U41(X, Y)) => a!6220!6220U41(mark(X), Y) mark(natsFrom(X)) => a!6220!6220natsFrom(mark(X)) mark(U51(X, Y, Z)) => a!6220!6220U51(mark(X), Y, Z) mark(head(X)) => a!6220!6220head(mark(X)) mark(afterNth(X, Y)) => a!6220!6220afterNth(mark(X), mark(Y)) mark(U61(X, Y)) => a!6220!6220U61(mark(X), Y) mark(U71(X, Y)) => a!6220!6220U71(mark(X), Y) mark(U81(X, Y, Z, U)) => a!6220!6220U81(mark(X), Y, Z, U) mark(U82(X, Y)) => a!6220!6220U82(mark(X), Y) mark(U91(X, Y)) => a!6220!6220U91(mark(X), Y) mark(and(X, Y)) => a!6220!6220and(mark(X), Y) mark(isNatural(X)) => a!6220!6220isNatural(X) mark(isLNat(X)) => a!6220!6220isLNat(X) mark(isPLNat(X)) => a!6220!6220isPLNat(X) mark(tail(X)) => a!6220!6220tail(mark(X)) mark(take(X, Y)) => a!6220!6220take(mark(X), mark(Y)) mark(sel(X, Y)) => a!6220!6220sel(mark(X), mark(Y)) mark(tt) => tt mark(cons(X, Y)) => cons(mark(X), Y) mark(s(X)) => s(mark(X)) mark(pair(X, Y)) => pair(mark(X), mark(Y)) mark(nil) => nil mark(0) => 0 a!6220!6220U101(X, Y, Z) => U101(X, Y, Z) a!6220!6220fst(X) => fst(X) a!6220!6220splitAt(X, Y) => splitAt(X, Y) a!6220!6220U11(X, Y, Z) => U11(X, Y, Z) a!6220!6220snd(X) => snd(X) a!6220!6220U21(X, Y) => U21(X, Y) a!6220!6220U31(X, Y) => U31(X, Y) a!6220!6220U41(X, Y) => U41(X, Y) a!6220!6220natsFrom(X) => natsFrom(X) a!6220!6220U51(X, Y, Z) => U51(X, Y, Z) a!6220!6220head(X) => head(X) a!6220!6220afterNth(X, Y) => afterNth(X, Y) a!6220!6220U61(X, Y) => U61(X, Y) a!6220!6220U71(X, Y) => U71(X, Y) a!6220!6220U81(X, Y, Z, U) => U81(X, Y, Z, U) a!6220!6220U82(X, Y) => U82(X, Y) a!6220!6220U91(X, Y) => U91(X, Y) a!6220!6220and(X, Y) => and(X, Y) a!6220!6220isNatural(X) => isNatural(X) a!6220!6220isLNat(X) => isLNat(X) a!6220!6220isPLNat(X) => isPLNat(X) a!6220!6220tail(X) => tail(X) a!6220!6220take(X, Y) => take(X, Y) a!6220!6220sel(X, Y) => sel(X, Y)