/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 
  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 
  ok : [o] --> o 
  pair : [o * o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  sel : [o * o] --> o 
  snd : [o] --> o 
  splitAt : [o * o] --> o 
  tail : [o] --> o 
  take : [o * o] --> o 
  top : [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))) 
  active(U11(X, Y, Z, U)) => U11(active(X), Y, Z, U) 
  active(U12(X, Y)) => U12(active(X), Y) 
  active(splitAt(X, Y)) => splitAt(active(X), Y) 
  active(splitAt(X, Y)) => splitAt(X, active(Y)) 
  active(pair(X, Y)) => pair(active(X), Y) 
  active(pair(X, Y)) => pair(X, active(Y)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(afterNth(X, Y)) => afterNth(active(X), Y) 
  active(afterNth(X, Y)) => afterNth(X, active(Y)) 
  active(snd(X)) => snd(active(X)) 
  active(and(X, Y)) => and(active(X), Y) 
  active(fst(X)) => fst(active(X)) 
  active(head(X)) => head(active(X)) 
  active(natsFrom(X)) => natsFrom(active(X)) 
  active(s(X)) => s(active(X)) 
  active(sel(X, Y)) => sel(active(X), Y) 
  active(sel(X, Y)) => sel(X, active(Y)) 
  active(tail(X)) => tail(active(X)) 
  active(take(X, Y)) => take(active(X), Y) 
  active(take(X, Y)) => take(X, active(Y)) 
  U11(mark(X), Y, Z, U) => mark(U11(X, Y, Z, U)) 
  U12(mark(X), Y) => mark(U12(X, Y)) 
  splitAt(mark(X), Y) => mark(splitAt(X, Y)) 
  splitAt(X, mark(Y)) => mark(splitAt(X, Y)) 
  pair(mark(X), Y) => mark(pair(X, Y)) 
  pair(X, mark(Y)) => mark(pair(X, Y)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  afterNth(mark(X), Y) => mark(afterNth(X, Y)) 
  afterNth(X, mark(Y)) => mark(afterNth(X, Y)) 
  snd(mark(X)) => mark(snd(X)) 
  and(mark(X), Y) => mark(and(X, Y)) 
  fst(mark(X)) => mark(fst(X)) 
  head(mark(X)) => mark(head(X)) 
  natsFrom(mark(X)) => mark(natsFrom(X)) 
  s(mark(X)) => mark(s(X)) 
  sel(mark(X), Y) => mark(sel(X, Y)) 
  sel(X, mark(Y)) => mark(sel(X, Y)) 
  tail(mark(X)) => mark(tail(X)) 
  take(mark(X), Y) => mark(take(X, Y)) 
  take(X, mark(Y)) => mark(take(X, Y)) 
  proper(U11(X, Y, Z, U)) => U11(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(tt) => ok(tt) 
  proper(U12(X, Y)) => U12(proper(X), proper(Y)) 
  proper(splitAt(X, Y)) => splitAt(proper(X), proper(Y)) 
  proper(pair(X, Y)) => pair(proper(X), proper(Y)) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(afterNth(X, Y)) => afterNth(proper(X), proper(Y)) 
  proper(snd(X)) => snd(proper(X)) 
  proper(and(X, Y)) => and(proper(X), proper(Y)) 
  proper(fst(X)) => fst(proper(X)) 
  proper(head(X)) => head(proper(X)) 
  proper(natsFrom(X)) => natsFrom(proper(X)) 
  proper(s(X)) => s(proper(X)) 
  proper(sel(X, Y)) => sel(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(nil) => ok(nil) 
  proper(tail(X)) => tail(proper(X)) 
  proper(take(X, Y)) => take(proper(X), proper(Y)) 
  U11(ok(X), ok(Y), ok(Z), ok(U)) => ok(U11(X, Y, Z, U)) 
  U12(ok(X), ok(Y)) => ok(U12(X, Y)) 
  splitAt(ok(X), ok(Y)) => ok(splitAt(X, Y)) 
  pair(ok(X), ok(Y)) => ok(pair(X, Y)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  afterNth(ok(X), ok(Y)) => ok(afterNth(X, Y)) 
  snd(ok(X)) => ok(snd(X)) 
  and(ok(X), ok(Y)) => ok(and(X, Y)) 
  fst(ok(X)) => ok(fst(X)) 
  head(ok(X)) => ok(head(X)) 
  natsFrom(ok(X)) => ok(natsFrom(X)) 
  s(ok(X)) => ok(s(X)) 
  sel(ok(X), ok(Y)) => ok(sel(X, Y)) 
  tail(ok(X)) => ok(tail(X)) 
  take(ok(X), ok(Y)) => ok(take(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))