/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 
  U11 : [o * o] --> o 
  U12 : [o] --> o 
  U21 : [o * o] --> o 
  U22 : [o] --> o 
  U31 : [o * o] --> o 
  U32 : [o] --> o 
  U41 : [o * o * o] --> o 
  U42 : [o * o] --> o 
  U43 : [o] --> o 
  U51 : [o * o * o] --> o 
  U52 : [o * o] --> o 
  U53 : [o] --> o 
  U61 : [o * o] --> o 
  activate : [o] --> o 
  and : [o * o] --> o 
  cons : [o * o] --> o 
  isNat : [o] --> o 
  isNatIList : [o] --> o 
  isNatIListKind : [o] --> o 
  isNatKind : [o] --> o 
  isNatList : [o] --> o 
  length : [o] --> o 
  n!6220!62200 : [] --> o 
  n!6220!6220and : [o * o] --> o 
  n!6220!6220cons : [o * o] --> o 
  n!6220!6220isNatIListKind : [o] --> o 
  n!6220!6220isNatKind : [o] --> o 
  n!6220!6220length : [o] --> o 
  n!6220!6220nil : [] --> o 
  n!6220!6220s : [o] --> o 
  n!6220!6220zeros : [] --> o 
  nil : [] --> o 
  s : [o] --> o 
  tt : [] --> o 
  zeros : [] --> o 

  zeros => cons(0, n!6220!6220zeros) 
  U11(tt, X) => U12(isNatList(activate(X))) 
  U12(tt) => tt 
  U21(tt, X) => U22(isNat(activate(X))) 
  U22(tt) => tt 
  U31(tt, X) => U32(isNatList(activate(X))) 
  U32(tt) => tt 
  U41(tt, X, Y) => U42(isNat(activate(X)), activate(Y)) 
  U42(tt, X) => U43(isNatIList(activate(X))) 
  U43(tt) => tt 
  U51(tt, X, Y) => U52(isNat(activate(X)), activate(Y)) 
  U52(tt, X) => U53(isNatList(activate(X))) 
  U53(tt) => tt 
  U61(tt, X) => s(length(activate(X))) 
  and(tt, X) => activate(X) 
  isNat(n!6220!62200) => tt 
  isNat(n!6220!6220length(X)) => U11(isNatIListKind(activate(X)), activate(X)) 
  isNat(n!6220!6220s(X)) => U21(isNatKind(activate(X)), activate(X)) 
  isNatIList(X) => U31(isNatIListKind(activate(X)), activate(X)) 
  isNatIList(n!6220!6220zeros) => tt 
  isNatIList(n!6220!6220cons(X, Y)) => U41(and(isNatKind(activate(X)), n!6220!6220isNatIListKind(activate(Y))), activate(X), activate(Y)) 
  isNatIListKind(n!6220!6220nil) => tt 
  isNatIListKind(n!6220!6220zeros) => tt 
  isNatIListKind(n!6220!6220cons(X, Y)) => and(isNatKind(activate(X)), n!6220!6220isNatIListKind(activate(Y))) 
  isNatKind(n!6220!62200) => tt 
  isNatKind(n!6220!6220length(X)) => isNatIListKind(activate(X)) 
  isNatKind(n!6220!6220s(X)) => isNatKind(activate(X)) 
  isNatList(n!6220!6220nil) => tt 
  isNatList(n!6220!6220cons(X, Y)) => U51(and(isNatKind(activate(X)), n!6220!6220isNatIListKind(activate(Y))), activate(X), activate(Y)) 
  length(nil) => 0 
  length(cons(X, Y)) => U61(and(and(isNatList(activate(Y)), n!6220!6220isNatIListKind(activate(Y))), n!6220!6220and(isNat(X), n!6220!6220isNatKind(X))), activate(Y)) 
  zeros => n!6220!6220zeros 
  0 => n!6220!62200 
  length(X) => n!6220!6220length(X) 
  s(X) => n!6220!6220s(X) 
  cons(X, Y) => n!6220!6220cons(X, Y) 
  isNatIListKind(X) => n!6220!6220isNatIListKind(X) 
  nil => n!6220!6220nil 
  and(X, Y) => n!6220!6220and(X, Y) 
  isNatKind(X) => n!6220!6220isNatKind(X) 
  activate(n!6220!6220zeros) => zeros 
  activate(n!6220!62200) => 0 
  activate(n!6220!6220length(X)) => length(X) 
  activate(n!6220!6220s(X)) => s(X) 
  activate(n!6220!6220cons(X, Y)) => cons(X, Y) 
  activate(n!6220!6220isNatIListKind(X)) => isNatIListKind(X) 
  activate(n!6220!6220nil) => nil 
  activate(n!6220!6220and(X, Y)) => and(X, Y) 
  activate(n!6220!6220isNatKind(X)) => isNatKind(X) 
  activate(X) => X