/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] --> 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 
  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 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  top : [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)) => mark(s(length(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(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(length(nil)) => mark(0) 
  active(length(cons(X, Y))) => mark(U61(and(and(isNatList(Y), isNatIListKind(Y)), and(isNat(X), isNatKind(X))), Y)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(U11(X, Y)) => U11(active(X), Y) 
  active(U12(X)) => U12(active(X)) 
  active(U21(X, Y)) => U21(active(X), Y) 
  active(U22(X)) => U22(active(X)) 
  active(U31(X, Y)) => U31(active(X), Y) 
  active(U32(X)) => U32(active(X)) 
  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(s(X)) => s(active(X)) 
  active(length(X)) => length(active(X)) 
  active(and(X, Y)) => and(active(X), Y) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  U11(mark(X), Y) => mark(U11(X, Y)) 
  U12(mark(X)) => mark(U12(X)) 
  U21(mark(X), Y) => mark(U21(X, Y)) 
  U22(mark(X)) => mark(U22(X)) 
  U31(mark(X), Y) => mark(U31(X, Y)) 
  U32(mark(X)) => mark(U32(X)) 
  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)) 
  s(mark(X)) => mark(s(X)) 
  length(mark(X)) => mark(length(X)) 
  and(mark(X), Y) => mark(and(X, Y)) 
  proper(zeros) => ok(zeros) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(U11(X, Y)) => U11(proper(X), proper(Y)) 
  proper(tt) => ok(tt) 
  proper(U12(X)) => U12(proper(X)) 
  proper(isNatList(X)) => isNatList(proper(X)) 
  proper(U21(X, Y)) => U21(proper(X), proper(Y)) 
  proper(U22(X)) => U22(proper(X)) 
  proper(isNat(X)) => isNat(proper(X)) 
  proper(U31(X, Y)) => U31(proper(X), proper(Y)) 
  proper(U32(X)) => U32(proper(X)) 
  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(isNatIList(X)) => isNatIList(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(s(X)) => s(proper(X)) 
  proper(length(X)) => length(proper(X)) 
  proper(and(X, Y)) => and(proper(X), proper(Y)) 
  proper(isNatIListKind(X)) => isNatIListKind(proper(X)) 
  proper(isNatKind(X)) => isNatKind(proper(X)) 
  proper(nil) => ok(nil) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  U11(ok(X), ok(Y)) => ok(U11(X, Y)) 
  U12(ok(X)) => ok(U12(X)) 
  isNatList(ok(X)) => ok(isNatList(X)) 
  U21(ok(X), ok(Y)) => ok(U21(X, Y)) 
  U22(ok(X)) => ok(U22(X)) 
  isNat(ok(X)) => ok(isNat(X)) 
  U31(ok(X), ok(Y)) => ok(U31(X, Y)) 
  U32(ok(X)) => ok(U32(X)) 
  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)) 
  isNatIList(ok(X)) => ok(isNatIList(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)) 
  s(ok(X)) => ok(s(X)) 
  length(ok(X)) => ok(length(X)) 
  and(ok(X), ok(Y)) => ok(and(X, Y)) 
  isNatIListKind(ok(X)) => ok(isNatIListKind(X)) 
  isNatKind(ok(X)) => ok(isNatKind(X)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))