/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 
  a!6220!6220and : [o * o] --> o 
  a!6220!6220isNat : [o] --> o 
  a!6220!6220isNatIList : [o] --> o 
  a!6220!6220isNatList : [o] --> o 
  a!6220!6220length : [o] --> o 
  a!6220!6220take : [o * o] --> o 
  a!6220!6220uLength : [o * o] --> o 
  a!6220!6220uTake1 : [o] --> o 
  a!6220!6220uTake2 : [o * o * o * o] --> o 
  a!6220!6220zeros : [] --> 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 

  a!6220!6220and(tt, X) => mark(X) 
  a!6220!6220isNatIList(X) => a!6220!6220isNatList(X) 
  a!6220!6220isNat(0) => tt 
  a!6220!6220isNat(s(X)) => a!6220!6220isNat(X) 
  a!6220!6220isNat(length(X)) => a!6220!6220isNatList(X) 
  a!6220!6220isNatIList(zeros) => tt 
  a!6220!6220isNatIList(cons(X, Y)) => a!6220!6220and(a!6220!6220isNat(X), a!6220!6220isNatIList(Y)) 
  a!6220!6220isNatList(nil) => tt 
  a!6220!6220isNatList(cons(X, Y)) => a!6220!6220and(a!6220!6220isNat(X), a!6220!6220isNatList(Y)) 
  a!6220!6220isNatList(take(X, Y)) => a!6220!6220and(a!6220!6220isNat(X), a!6220!6220isNatIList(Y)) 
  a!6220!6220zeros => cons(0, zeros) 
  a!6220!6220take(0, X) => a!6220!6220uTake1(a!6220!6220isNatIList(X)) 
  a!6220!6220uTake1(tt) => nil 
  a!6220!6220take(s(X), cons(Y, Z)) => a!6220!6220uTake2(a!6220!6220and(a!6220!6220isNat(X), a!6220!6220and(a!6220!6220isNat(Y), a!6220!6220isNatIList(Z))), X, Y, Z) 
  a!6220!6220uTake2(tt, X, Y, Z) => cons(mark(Y), take(X, Z)) 
  a!6220!6220length(cons(X, Y)) => a!6220!6220uLength(a!6220!6220and(a!6220!6220isNat(X), a!6220!6220isNatList(Y)), Y) 
  a!6220!6220uLength(tt, X) => s(a!6220!6220length(mark(X))) 
  mark(and(X, Y)) => a!6220!6220and(mark(X), mark(Y)) 
  mark(isNatIList(X)) => a!6220!6220isNatIList(X) 
  mark(isNatList(X)) => a!6220!6220isNatList(X) 
  mark(isNat(X)) => a!6220!6220isNat(X) 
  mark(length(X)) => a!6220!6220length(mark(X)) 
  mark(zeros) => a!6220!6220zeros 
  mark(take(X, Y)) => a!6220!6220take(mark(X), mark(Y)) 
  mark(uTake1(X)) => a!6220!6220uTake1(mark(X)) 
  mark(uTake2(X, Y, Z, U)) => a!6220!6220uTake2(mark(X), Y, Z, U) 
  mark(uLength(X, Y)) => a!6220!6220uLength(mark(X), Y) 
  mark(tt) => tt 
  mark(0) => 0 
  mark(s(X)) => s(mark(X)) 
  mark(cons(X, Y)) => cons(mark(X), Y) 
  mark(nil) => nil 
  a!6220!6220and(X, Y) => and(X, Y) 
  a!6220!6220isNatIList(X) => isNatIList(X) 
  a!6220!6220isNatList(X) => isNatList(X) 
  a!6220!6220isNat(X) => isNat(X) 
  a!6220!6220length(X) => length(X) 
  a!6220!6220zeros => zeros 
  a!6220!6220take(X, Y) => take(X, Y) 
  a!6220!6220uTake1(X) => uTake1(X) 
  a!6220!6220uTake2(X, Y, Z, U) => uTake2(X, Y, Z, U) 
  a!6220!6220uLength(X, Y) => uLength(X, Y)