/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 
  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 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  take : [o * o] --> o 
  top : [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))) 
  active(and(X, Y)) => and(active(X), Y) 
  active(and(X, Y)) => and(X, active(Y)) 
  active(s(X)) => s(active(X)) 
  active(length(X)) => length(active(X)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(take(X, Y)) => take(active(X), Y) 
  active(take(X, Y)) => take(X, active(Y)) 
  active(uTake1(X)) => uTake1(active(X)) 
  active(uTake2(X, Y, Z, U)) => uTake2(active(X), Y, Z, U) 
  active(uLength(X, Y)) => uLength(active(X), Y) 
  and(mark(X), Y) => mark(and(X, Y)) 
  and(X, mark(Y)) => mark(and(X, Y)) 
  s(mark(X)) => mark(s(X)) 
  length(mark(X)) => mark(length(X)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  take(mark(X), Y) => mark(take(X, Y)) 
  take(X, mark(Y)) => mark(take(X, Y)) 
  uTake1(mark(X)) => mark(uTake1(X)) 
  uTake2(mark(X), Y, Z, U) => mark(uTake2(X, Y, Z, U)) 
  uLength(mark(X), Y) => mark(uLength(X, Y)) 
  proper(and(X, Y)) => and(proper(X), proper(Y)) 
  proper(tt) => ok(tt) 
  proper(isNatIList(X)) => isNatIList(proper(X)) 
  proper(isNatList(X)) => isNatList(proper(X)) 
  proper(isNat(X)) => isNat(proper(X)) 
  proper(0) => ok(0) 
  proper(s(X)) => s(proper(X)) 
  proper(length(X)) => length(proper(X)) 
  proper(zeros) => ok(zeros) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(nil) => ok(nil) 
  proper(take(X, Y)) => take(proper(X), proper(Y)) 
  proper(uTake1(X)) => uTake1(proper(X)) 
  proper(uTake2(X, Y, Z, U)) => uTake2(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(uLength(X, Y)) => uLength(proper(X), proper(Y)) 
  and(ok(X), ok(Y)) => ok(and(X, Y)) 
  isNatIList(ok(X)) => ok(isNatIList(X)) 
  isNatList(ok(X)) => ok(isNatList(X)) 
  isNat(ok(X)) => ok(isNat(X)) 
  s(ok(X)) => ok(s(X)) 
  length(ok(X)) => ok(length(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  take(ok(X), ok(Y)) => ok(take(X, Y)) 
  uTake1(ok(X)) => ok(uTake1(X)) 
  uTake2(ok(X), ok(Y), ok(Z), ok(U)) => ok(uTake2(X, Y, Z, U)) 
  uLength(ok(X), ok(Y)) => ok(uLength(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))