/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 
  activate : [o] --> o 
  and : [o * o] --> o 
  cons : [o * o] --> o 
  isNat : [o] --> o 
  isNatIList : [o] --> o 
  isNatList : [o] --> o 
  length : [o] --> o 
  n!6220!62200 : [] --> o 
  n!6220!6220cons : [o * o] --> o 
  n!6220!6220length : [o] --> o 
  n!6220!6220nil : [] --> o 
  n!6220!6220s : [o] --> o 
  n!6220!6220take : [o * o] --> o 
  n!6220!6220zeros : [] --> 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 

  and(tt, X) => X 
  isNatIList(X) => isNatList(activate(X)) 
  isNat(n!6220!62200) => tt 
  isNat(n!6220!6220s(X)) => isNat(activate(X)) 
  isNat(n!6220!6220length(X)) => isNatList(activate(X)) 
  isNatIList(n!6220!6220zeros) => tt 
  isNatIList(n!6220!6220cons(X, Y)) => and(isNat(activate(X)), isNatIList(activate(Y))) 
  isNatList(n!6220!6220nil) => tt 
  isNatList(n!6220!6220cons(X, Y)) => and(isNat(activate(X)), isNatList(activate(Y))) 
  isNatList(n!6220!6220take(X, Y)) => and(isNat(activate(X)), isNatIList(activate(Y))) 
  zeros => cons(0, n!6220!6220zeros) 
  take(0, X) => uTake1(isNatIList(X)) 
  uTake1(tt) => nil 
  take(s(X), cons(Y, Z)) => uTake2(and(isNat(X), and(isNat(Y), isNatIList(activate(Z)))), X, Y, activate(Z)) 
  uTake2(tt, X, Y, Z) => cons(activate(Y), n!6220!6220take(activate(X), activate(Z))) 
  length(cons(X, Y)) => uLength(and(isNat(X), isNatList(activate(Y))), activate(Y)) 
  uLength(tt, X) => s(length(activate(X))) 
  0 => n!6220!62200 
  s(X) => n!6220!6220s(X) 
  length(X) => n!6220!6220length(X) 
  zeros => n!6220!6220zeros 
  cons(X, Y) => n!6220!6220cons(X, Y) 
  nil => n!6220!6220nil 
  take(X, Y) => n!6220!6220take(X, Y) 
  activate(n!6220!62200) => 0 
  activate(n!6220!6220s(X)) => s(activate(X)) 
  activate(n!6220!6220length(X)) => length(activate(X)) 
  activate(n!6220!6220zeros) => zeros 
  activate(n!6220!6220cons(X, Y)) => cons(activate(X), Y) 
  activate(n!6220!6220nil) => nil 
  activate(n!6220!6220take(X, Y)) => take(activate(X), activate(Y)) 
  activate(X) => X