/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 
  U12 : [o * o] --> o 
  U21 : [o * o * o * o] --> o 
  U22 : [o * o * o * o] --> o 
  U23 : [o * o * o * o] --> o 
  active : [o] --> o 
  cons : [o * o] --> o 
  length : [o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  take : [o * o] --> o 
  top : [o] --> o 
  tt : [] --> o 
  zeros : [] --> o 

  active(zeros) => mark(cons(0, zeros)) 
  active(U11(tt, X)) => mark(U12(tt, X)) 
  active(U12(tt, X)) => mark(s(length(X))) 
  active(U21(tt, X, Y, Z)) => mark(U22(tt, X, Y, Z)) 
  active(U22(tt, X, Y, Z)) => mark(U23(tt, X, Y, Z)) 
  active(U23(tt, X, Y, Z)) => mark(cons(Z, take(Y, X))) 
  active(length(nil)) => mark(0) 
  active(length(cons(X, Y))) => mark(U11(tt, Y)) 
  active(take(0, X)) => mark(nil) 
  active(take(s(X), cons(Y, Z))) => mark(U21(tt, Z, X, Y)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(U11(X, Y)) => U11(active(X), Y) 
  active(U12(X, Y)) => U12(active(X), Y) 
  active(s(X)) => s(active(X)) 
  active(length(X)) => length(active(X)) 
  active(U21(X, Y, Z, U)) => U21(active(X), Y, Z, U) 
  active(U22(X, Y, Z, U)) => U22(active(X), Y, Z, U) 
  active(U23(X, Y, Z, U)) => U23(active(X), Y, Z, U) 
  active(take(X, Y)) => take(active(X), Y) 
  active(take(X, Y)) => take(X, active(Y)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  U11(mark(X), Y) => mark(U11(X, Y)) 
  U12(mark(X), Y) => mark(U12(X, Y)) 
  s(mark(X)) => mark(s(X)) 
  length(mark(X)) => mark(length(X)) 
  U21(mark(X), Y, Z, U) => mark(U21(X, Y, Z, U)) 
  U22(mark(X), Y, Z, U) => mark(U22(X, Y, Z, U)) 
  U23(mark(X), Y, Z, U) => mark(U23(X, Y, Z, U)) 
  take(mark(X), Y) => mark(take(X, Y)) 
  take(X, mark(Y)) => mark(take(X, Y)) 
  proper(zeros) => ok(zeros) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(U11(X, Y)) => U11(proper(X), proper(Y)) 
  proper(tt) => ok(tt) 
  proper(U12(X, Y)) => U12(proper(X), proper(Y)) 
  proper(s(X)) => s(proper(X)) 
  proper(length(X)) => length(proper(X)) 
  proper(U21(X, Y, Z, U)) => U21(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(U22(X, Y, Z, U)) => U22(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(U23(X, Y, Z, U)) => U23(proper(X), proper(Y), proper(Z), proper(U)) 
  proper(take(X, Y)) => take(proper(X), proper(Y)) 
  proper(nil) => ok(nil) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  U11(ok(X), ok(Y)) => ok(U11(X, Y)) 
  U12(ok(X), ok(Y)) => ok(U12(X, Y)) 
  s(ok(X)) => ok(s(X)) 
  length(ok(X)) => ok(length(X)) 
  U21(ok(X), ok(Y), ok(Z), ok(U)) => ok(U21(X, Y, Z, U)) 
  U22(ok(X), ok(Y), ok(Z), ok(U)) => ok(U22(X, Y, Z, U)) 
  U23(ok(X), ok(Y), ok(Z), ok(U)) => ok(U23(X, Y, Z, U)) 
  take(ok(X), ok(Y)) => ok(take(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))