/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 * o] --> o 
  U12 : [o * o] --> o 
  active : [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 

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