/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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MAYBE
We consider the system theBenchmark.

We are asked to determine termination of the following first-order TRS.

  0 : [] --> o 
  U11 : [o] --> o 
  U21 : [o] --> o 
  U31 : [o] --> o 
  U41 : [o * o] --> o 
  U42 : [o] --> o 
  U51 : [o * o] --> o 
  U52 : [o] --> o 
  U61 : [o * o] --> o 
  U62 : [o] --> o 
  U71 : [o * o * o] --> o 
  U72 : [o * o] --> o 
  U81 : [o] --> o 
  U91 : [o * o * o * o] --> o 
  U92 : [o * o * o * o] --> o 
  U93 : [o * o * o * o] --> o 
  active : [o] --> o 
  cons : [o * o] --> o 
  isNat : [o] --> o 
  isNatIList : [o] --> o 
  isNatList : [o] --> o 
  length : [o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  take : [o * o] --> o 
  top : [o] --> o 
  tt : [] --> o 
  zeros : [] --> o 

  active(zeros) => mark(cons(0, zeros)) 
  active(U11(tt)) => mark(tt) 
  active(U21(tt)) => mark(tt) 
  active(U31(tt)) => mark(tt) 
  active(U41(tt, X)) => mark(U42(isNatIList(X))) 
  active(U42(tt)) => mark(tt) 
  active(U51(tt, X)) => mark(U52(isNatList(X))) 
  active(U52(tt)) => mark(tt) 
  active(U61(tt, X)) => mark(U62(isNatIList(X))) 
  active(U62(tt)) => mark(tt) 
  active(U71(tt, X, Y)) => mark(U72(isNat(Y), X)) 
  active(U72(tt, X)) => mark(s(length(X))) 
  active(U81(tt)) => mark(nil) 
  active(U91(tt, X, Y, Z)) => mark(U92(isNat(Y), X, Y, Z)) 
  active(U92(tt, X, Y, Z)) => mark(U93(isNat(Z), X, Y, Z)) 
  active(U93(tt, X, Y, Z)) => mark(cons(Z, take(Y, X))) 
  active(isNat(0)) => mark(tt) 
  active(isNat(length(X))) => mark(U11(isNatList(X))) 
  active(isNat(s(X))) => mark(U21(isNat(X))) 
  active(isNatIList(X)) => mark(U31(isNatList(X))) 
  active(isNatIList(zeros)) => mark(tt) 
  active(isNatIList(cons(X, Y))) => mark(U41(isNat(X), Y)) 
  active(isNatList(nil)) => mark(tt) 
  active(isNatList(cons(X, Y))) => mark(U51(isNat(X), Y)) 
  active(isNatList(take(X, Y))) => mark(U61(isNat(X), Y)) 
  active(length(nil)) => mark(0) 
  active(length(cons(X, Y))) => mark(U71(isNatList(Y), Y, X)) 
  active(take(0, X)) => mark(U81(isNatIList(X))) 
  active(take(s(X), cons(Y, Z))) => mark(U91(isNatIList(Z), Z, X, Y)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(U11(X)) => U11(active(X)) 
  active(U21(X)) => U21(active(X)) 
  active(U31(X)) => U31(active(X)) 
  active(U41(X, Y)) => U41(active(X), Y) 
  active(U42(X)) => U42(active(X)) 
  active(U51(X, Y)) => U51(active(X), Y) 
  active(U52(X)) => U52(active(X)) 
  active(U61(X, Y)) => U61(active(X), Y) 
  active(U62(X)) => U62(active(X)) 
  active(U71(X, Y, Z)) => U71(active(X), Y, Z) 
  active(U72(X, Y)) => U72(active(X), Y) 
  active(s(X)) => s(active(X)) 
  active(length(X)) => length(active(X)) 
  active(U81(X)) => U81(active(X)) 
  active(U91(X, Y, Z, U)) => U91(active(X), Y, Z, U) 
  active(U92(X, Y, Z, U)) => U92(active(X), Y, Z, U) 
  active(U93(X, Y, Z, U)) => U93(active(X), Y, Z, U) 
  active(take(X, Y)) => take(active(X), Y) 
  active(take(X, Y)) => take(X, active(Y)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  U11(mark(X)) => mark(U11(X)) 
  U21(mark(X)) => mark(U21(X)) 
  U31(mark(X)) => mark(U31(X)) 
  U41(mark(X), Y) => mark(U41(X, Y)) 
  U42(mark(X)) => mark(U42(X)) 
  U51(mark(X), Y) => mark(U51(X, Y)) 
  U52(mark(X)) => mark(U52(X)) 
  U61(mark(X), Y) => mark(U61(X, Y)) 
  U62(mark(X)) => mark(U62(X)) 
  U71(mark(X), Y, Z) => mark(U71(X, Y, Z)) 
  U72(mark(X), Y) => mark(U72(X, Y)) 
  s(mark(X)) => mark(s(X)) 
  length(mark(X)) => mark(length(X)) 
  U81(mark(X)) => mark(U81(X)) 
  U91(mark(X), Y, Z, U) => mark(U91(X, Y, Z, U)) 
  U92(mark(X), Y, Z, U) => mark(U92(X, Y, Z, U)) 
  U93(mark(X), Y, Z, U) => mark(U93(X, Y, Z, U)) 
  take(mark(X), Y) => mark(take(X, Y)) 
  take(X, mark(Y)) => mark(take(X, Y)) 
  proper(zeros) => ok(zeros) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(U11(X)) => U11(proper(X)) 
  proper(tt) => ok(tt) 
  proper(U21(X)) => U21(proper(X)) 
  proper(U31(X)) => U31(proper(X)) 
  proper(U41(X, Y)) => U41(proper(X), proper(Y)) 
  proper(U42(X)) => U42(proper(X)) 
  proper(isNatIList(X)) => isNatIList(proper(X)) 
  proper(U51(X, Y)) => U51(proper(X), proper(Y)) 
  proper(U52(X)) => U52(proper(X)) 
  proper(isNatList(X)) => isNatList(proper(X)) 
  proper(U61(X, Y)) => U61(proper(X), proper(Y)) 
  proper(U62(X)) => U62(proper(X)) 
  proper(U71(X, Y, Z)) => U71(proper(X), proper(Y), proper(Z)) 
  proper(U72(X, Y)) => U72(proper(X), proper(Y)) 
  proper(isNat(X)) => isNat(proper(X)) 
  proper(s(X)) => s(proper(X)) 
  proper(length(X)) => length(proper(X)) 
  proper(U81(X)) => U81(proper(X)) 
  proper(nil) => ok(nil) 
  proper(U91(X, Y, Z, U)) => U91(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(U92(X, Y, Z, U)) => U92(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(U93(X, Y, Z, U)) => U93(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(take(X, Y)) => take(proper(X), proper(Y)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  U11(ok(X)) => ok(U11(X)) 
  U21(ok(X)) => ok(U21(X)) 
  U31(ok(X)) => ok(U31(X)) 
  U41(ok(X), ok(Y)) => ok(U41(X, Y)) 
  U42(ok(X)) => ok(U42(X)) 
  isNatIList(ok(X)) => ok(isNatIList(X)) 
  U51(ok(X), ok(Y)) => ok(U51(X, Y)) 
  U52(ok(X)) => ok(U52(X)) 
  isNatList(ok(X)) => ok(isNatList(X)) 
  U61(ok(X), ok(Y)) => ok(U61(X, Y)) 
  U62(ok(X)) => ok(U62(X)) 
  U71(ok(X), ok(Y), ok(Z)) => ok(U71(X, Y, Z)) 
  U72(ok(X), ok(Y)) => ok(U72(X, Y)) 
  isNat(ok(X)) => ok(isNat(X)) 
  s(ok(X)) => ok(s(X)) 
  length(ok(X)) => ok(length(X)) 
  U81(ok(X)) => ok(U81(X)) 
  U91(ok(X), ok(Y), ok(Z), ok(U)) => ok(U91(X, Y, Z, U)) 
  U92(ok(X), ok(Y), ok(Z), ok(U)) => ok(U92(X, Y, Z, U)) 
  U93(ok(X), ok(Y), ok(Z), ok(U)) => ok(U93(X, Y, Z, U)) 
  take(ok(X), ok(Y)) => ok(take(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))