/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 * o * o] --> o 
  U12 : [o * o] --> o 
  a!6220!6220U11 : [o * o * o * o] --> o 
  a!6220!6220U12 : [o * o] --> o 
  a!6220!6220afterNth : [o * o] --> o 
  a!6220!6220and : [o * o] --> o 
  a!6220!6220fst : [o] --> o 
  a!6220!6220head : [o] --> o 
  a!6220!6220natsFrom : [o] --> o 
  a!6220!6220sel : [o * o] --> o 
  a!6220!6220snd : [o] --> o 
  a!6220!6220splitAt : [o * o] --> o 
  a!6220!6220tail : [o] --> o 
  a!6220!6220take : [o * o] --> o 
  afterNth : [o * o] --> o 
  and : [o * o] --> o 
  cons : [o * o] --> o 
  fst : [o] --> o 
  head : [o] --> o 
  mark : [o] --> o 
  natsFrom : [o] --> o 
  nil : [] --> o 
  pair : [o * o] --> o 
  s : [o] --> o 
  sel : [o * o] --> o 
  snd : [o] --> o 
  splitAt : [o * o] --> o 
  tail : [o] --> o 
  take : [o * o] --> o 
  tt : [] --> o 

  a!6220!6220U11(tt, X, Y, Z) => a!6220!6220U12(a!6220!6220splitAt(mark(X), mark(Z)), Y) 
  a!6220!6220U12(pair(X, Y), Z) => pair(cons(mark(Z), X), mark(Y)) 
  a!6220!6220afterNth(X, Y) => a!6220!6220snd(a!6220!6220splitAt(mark(X), mark(Y))) 
  a!6220!6220and(tt, X) => mark(X) 
  a!6220!6220fst(pair(X, Y)) => mark(X) 
  a!6220!6220head(cons(X, Y)) => mark(X) 
  a!6220!6220natsFrom(X) => cons(mark(X), natsFrom(s(X))) 
  a!6220!6220sel(X, Y) => a!6220!6220head(a!6220!6220afterNth(mark(X), mark(Y))) 
  a!6220!6220snd(pair(X, Y)) => mark(Y) 
  a!6220!6220splitAt(0, X) => pair(nil, mark(X)) 
  a!6220!6220splitAt(s(X), cons(Y, Z)) => a!6220!6220U11(tt, X, Y, Z) 
  a!6220!6220tail(cons(X, Y)) => mark(Y) 
  a!6220!6220take(X, Y) => a!6220!6220fst(a!6220!6220splitAt(mark(X), mark(Y))) 
  mark(U11(X, Y, Z, U)) => a!6220!6220U11(mark(X), Y, Z, U) 
  mark(U12(X, Y)) => a!6220!6220U12(mark(X), Y) 
  mark(splitAt(X, Y)) => a!6220!6220splitAt(mark(X), mark(Y)) 
  mark(afterNth(X, Y)) => a!6220!6220afterNth(mark(X), mark(Y)) 
  mark(snd(X)) => a!6220!6220snd(mark(X)) 
  mark(and(X, Y)) => a!6220!6220and(mark(X), Y) 
  mark(fst(X)) => a!6220!6220fst(mark(X)) 
  mark(head(X)) => a!6220!6220head(mark(X)) 
  mark(natsFrom(X)) => a!6220!6220natsFrom(mark(X)) 
  mark(sel(X, Y)) => a!6220!6220sel(mark(X), mark(Y)) 
  mark(tail(X)) => a!6220!6220tail(mark(X)) 
  mark(take(X, Y)) => a!6220!6220take(mark(X), mark(Y)) 
  mark(tt) => tt 
  mark(pair(X, Y)) => pair(mark(X), mark(Y)) 
  mark(cons(X, Y)) => cons(mark(X), Y) 
  mark(s(X)) => s(mark(X)) 
  mark(0) => 0 
  mark(nil) => nil 
  a!6220!6220U11(X, Y, Z, U) => U11(X, Y, Z, U) 
  a!6220!6220U12(X, Y) => U12(X, Y) 
  a!6220!6220splitAt(X, Y) => splitAt(X, Y) 
  a!6220!6220afterNth(X, Y) => afterNth(X, Y) 
  a!6220!6220snd(X) => snd(X) 
  a!6220!6220and(X, Y) => and(X, Y) 
  a!6220!6220fst(X) => fst(X) 
  a!6220!6220head(X) => head(X) 
  a!6220!6220natsFrom(X) => natsFrom(X) 
  a!6220!6220sel(X, Y) => sel(X, Y) 
  a!6220!6220tail(X) => tail(X) 
  a!6220!6220take(X, Y) => take(X, Y)