/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 
  active : [o] --> o 
  and : [o * o] --> o 
  cons : [o * o] --> o 
  isNat : [o] --> o 
  isNatIList : [o] --> o 
  isNatList : [o] --> o 
  length : [o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  s : [o] --> o 
  take : [o * o] --> o 
  tt : [] --> o 
  uLength : [o * o] --> o 
  uTake1 : [o] --> o 
  uTake2 : [o * o * o * o] --> o 
  zeros : [] --> o 

  active(and(tt, X)) => mark(X) 
  active(isNatIList(X)) => mark(isNatList(X)) 
  active(isNat(0)) => mark(tt) 
  active(isNat(s(X))) => mark(isNat(X)) 
  active(isNat(length(X))) => mark(isNatList(X)) 
  active(isNatIList(zeros)) => mark(tt) 
  active(isNatIList(cons(X, Y))) => mark(and(isNat(X), isNatIList(Y))) 
  active(isNatList(nil)) => mark(tt) 
  active(isNatList(cons(X, Y))) => mark(and(isNat(X), isNatList(Y))) 
  active(isNatList(take(X, Y))) => mark(and(isNat(X), isNatIList(Y))) 
  active(zeros) => mark(cons(0, zeros)) 
  active(take(0, X)) => mark(uTake1(isNatIList(X))) 
  active(uTake1(tt)) => mark(nil) 
  active(take(s(X), cons(Y, Z))) => mark(uTake2(and(isNat(X), and(isNat(Y), isNatIList(Z))), X, Y, Z)) 
  active(uTake2(tt, X, Y, Z)) => mark(cons(Y, take(X, Z))) 
  active(length(cons(X, Y))) => mark(uLength(and(isNat(X), isNatList(Y)), Y)) 
  active(uLength(tt, X)) => mark(s(length(X))) 
  mark(and(X, Y)) => active(and(mark(X), mark(Y))) 
  mark(tt) => active(tt) 
  mark(isNatIList(X)) => active(isNatIList(X)) 
  mark(isNatList(X)) => active(isNatList(X)) 
  mark(isNat(X)) => active(isNat(X)) 
  mark(0) => active(0) 
  mark(s(X)) => active(s(mark(X))) 
  mark(length(X)) => active(length(mark(X))) 
  mark(zeros) => active(zeros) 
  mark(cons(X, Y)) => active(cons(mark(X), Y)) 
  mark(nil) => active(nil) 
  mark(take(X, Y)) => active(take(mark(X), mark(Y))) 
  mark(uTake1(X)) => active(uTake1(mark(X))) 
  mark(uTake2(X, Y, Z, U)) => active(uTake2(mark(X), Y, Z, U)) 
  mark(uLength(X, Y)) => active(uLength(mark(X), Y)) 
  and(mark(X), Y) => and(X, Y) 
  and(X, mark(Y)) => and(X, Y) 
  and(active(X), Y) => and(X, Y) 
  and(X, active(Y)) => and(X, Y) 
  isNatIList(mark(X)) => isNatIList(X) 
  isNatIList(active(X)) => isNatIList(X) 
  isNatList(mark(X)) => isNatList(X) 
  isNatList(active(X)) => isNatList(X) 
  isNat(mark(X)) => isNat(X) 
  isNat(active(X)) => isNat(X) 
  s(mark(X)) => s(X) 
  s(active(X)) => s(X) 
  length(mark(X)) => length(X) 
  length(active(X)) => length(X) 
  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) 
  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) 
  uTake1(mark(X)) => uTake1(X) 
  uTake1(active(X)) => uTake1(X) 
  uTake2(mark(X), Y, Z, U) => uTake2(X, Y, Z, U) 
  uTake2(X, mark(Y), Z, U) => uTake2(X, Y, Z, U) 
  uTake2(X, Y, mark(Z), U) => uTake2(X, Y, Z, U) 
  uTake2(X, Y, Z, mark(U)) => uTake2(X, Y, Z, U) 
  uTake2(active(X), Y, Z, U) => uTake2(X, Y, Z, U) 
  uTake2(X, active(Y), Z, U) => uTake2(X, Y, Z, U) 
  uTake2(X, Y, active(Z), U) => uTake2(X, Y, Z, U) 
  uTake2(X, Y, Z, active(U)) => uTake2(X, Y, Z, U) 
  uLength(mark(X), Y) => uLength(X, Y) 
  uLength(X, mark(Y)) => uLength(X, Y) 
  uLength(active(X), Y) => uLength(X, Y) 
  uLength(X, active(Y)) => uLength(X, Y)