/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 
  U11 : [o] --> o 
  U21 : [o] --> o 
  U31 : [o] --> o 
  U41 : [o * o] --> o 
  U42 : [o] --> o 
  U51 : [o * o] --> o 
  U52 : [o] --> o 
  U61 : [o * o] --> o 
  U62 : [o] --> o 
  U71 : [o * o * o] --> o 
  U72 : [o * o] --> o 
  U81 : [o] --> o 
  U91 : [o * o * o * o] --> o 
  U92 : [o * o * o * o] --> o 
  U93 : [o * o * o * o] --> o 
  activate : [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 
  zeros : [] --> o 

  zeros => cons(0, n!6220!6220zeros) 
  U11(tt) => tt 
  U21(tt) => tt 
  U31(tt) => tt 
  U41(tt, X) => U42(isNatIList(activate(X))) 
  U42(tt) => tt 
  U51(tt, X) => U52(isNatList(activate(X))) 
  U52(tt) => tt 
  U61(tt, X) => U62(isNatIList(activate(X))) 
  U62(tt) => tt 
  U71(tt, X, Y) => U72(isNat(activate(Y)), activate(X)) 
  U72(tt, X) => s(length(activate(X))) 
  U81(tt) => nil 
  U91(tt, X, Y, Z) => U92(isNat(activate(Y)), activate(X), activate(Y), activate(Z)) 
  U92(tt, X, Y, Z) => U93(isNat(activate(Z)), activate(X), activate(Y), activate(Z)) 
  U93(tt, X, Y, Z) => cons(activate(Z), n!6220!6220take(activate(Y), activate(X))) 
  isNat(n!6220!62200) => tt 
  isNat(n!6220!6220length(X)) => U11(isNatList(activate(X))) 
  isNat(n!6220!6220s(X)) => U21(isNat(activate(X))) 
  isNatIList(X) => U31(isNatList(activate(X))) 
  isNatIList(n!6220!6220zeros) => tt 
  isNatIList(n!6220!6220cons(X, Y)) => U41(isNat(activate(X)), activate(Y)) 
  isNatList(n!6220!6220nil) => tt 
  isNatList(n!6220!6220cons(X, Y)) => U51(isNat(activate(X)), activate(Y)) 
  isNatList(n!6220!6220take(X, Y)) => U61(isNat(activate(X)), activate(Y)) 
  length(nil) => 0 
  length(cons(X, Y)) => U71(isNatList(activate(Y)), activate(Y), X) 
  take(0, X) => U81(isNatIList(X)) 
  take(s(X), cons(Y, Z)) => U91(isNatIList(activate(Z)), activate(Z), X, Y) 
  zeros => n!6220!6220zeros 
  take(X, Y) => n!6220!6220take(X, Y) 
  0 => n!6220!62200 
  length(X) => n!6220!6220length(X) 
  s(X) => n!6220!6220s(X) 
  cons(X, Y) => n!6220!6220cons(X, Y) 
  nil => n!6220!6220nil 
  activate(n!6220!6220zeros) => zeros 
  activate(n!6220!6220take(X, Y)) => take(activate(X), activate(Y)) 
  activate(n!6220!62200) => 0 
  activate(n!6220!6220length(X)) => length(activate(X)) 
  activate(n!6220!6220s(X)) => s(activate(X)) 
  activate(n!6220!6220cons(X, Y)) => cons(activate(X), Y) 
  activate(n!6220!6220nil) => nil 
  activate(X) => X