/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


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 
  s : [o] --> o 
  take : [o * 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)) 
  mark(zeros) => active(zeros) 
  mark(cons(X, Y)) => active(cons(mark(X), Y)) 
  mark(0) => active(0) 
  mark(U11(X, Y)) => active(U11(mark(X), Y)) 
  mark(tt) => active(tt) 
  mark(U12(X, Y)) => active(U12(mark(X), Y)) 
  mark(s(X)) => active(s(mark(X))) 
  mark(length(X)) => active(length(mark(X))) 
  mark(U21(X, Y, Z, U)) => active(U21(mark(X), Y, Z, U)) 
  mark(U22(X, Y, Z, U)) => active(U22(mark(X), Y, Z, U)) 
  mark(U23(X, Y, Z, U)) => active(U23(mark(X), Y, Z, U)) 
  mark(take(X, Y)) => active(take(mark(X), mark(Y))) 
  mark(nil) => active(nil) 
  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) 
  U11(mark(X), Y) => U11(X, Y) 
  U11(X, mark(Y)) => U11(X, Y) 
  U11(active(X), Y) => U11(X, Y) 
  U11(X, active(Y)) => U11(X, Y) 
  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) 
  s(mark(X)) => s(X) 
  s(active(X)) => s(X) 
  length(mark(X)) => length(X) 
  length(active(X)) => length(X) 
  U21(mark(X), Y, Z, U) => U21(X, Y, Z, U) 
  U21(X, mark(Y), Z, U) => U21(X, Y, Z, U) 
  U21(X, Y, mark(Z), U) => U21(X, Y, Z, U) 
  U21(X, Y, Z, mark(U)) => U21(X, Y, Z, U) 
  U21(active(X), Y, Z, U) => U21(X, Y, Z, U) 
  U21(X, active(Y), Z, U) => U21(X, Y, Z, U) 
  U21(X, Y, active(Z), U) => U21(X, Y, Z, U) 
  U21(X, Y, Z, active(U)) => U21(X, Y, Z, U) 
  U22(mark(X), Y, Z, U) => U22(X, Y, Z, U) 
  U22(X, mark(Y), Z, U) => U22(X, Y, Z, U) 
  U22(X, Y, mark(Z), U) => U22(X, Y, Z, U) 
  U22(X, Y, Z, mark(U)) => U22(X, Y, Z, U) 
  U22(active(X), Y, Z, U) => U22(X, Y, Z, U) 
  U22(X, active(Y), Z, U) => U22(X, Y, Z, U) 
  U22(X, Y, active(Z), U) => U22(X, Y, Z, U) 
  U22(X, Y, Z, active(U)) => U22(X, Y, Z, U) 
  U23(mark(X), Y, Z, U) => U23(X, Y, Z, U) 
  U23(X, mark(Y), Z, U) => U23(X, Y, Z, U) 
  U23(X, Y, mark(Z), U) => U23(X, Y, Z, U) 
  U23(X, Y, Z, mark(U)) => U23(X, Y, Z, U) 
  U23(active(X), Y, Z, U) => U23(X, Y, Z, U) 
  U23(X, active(Y), Z, U) => U23(X, Y, Z, U) 
  U23(X, Y, active(Z), U) => U23(X, Y, Z, U) 
  U23(X, Y, Z, active(U)) => U23(X, Y, Z, U) 
  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)