/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 
  active : [o] --> o 
  cons : [o * o] --> o 
  eq : [o * o] --> o 
  false : [] --> o 
  inf : [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 
  true : [] --> o 

  active(eq(0, 0)) => mark(true) 
  active(eq(s(X), s(Y))) => mark(eq(X, Y)) 
  active(eq(X, Y)) => mark(false) 
  active(inf(X)) => mark(cons(X, inf(s(X)))) 
  active(take(0, X)) => mark(nil) 
  active(take(s(X), cons(Y, Z))) => mark(cons(Y, take(X, Z))) 
  active(length(nil)) => mark(0) 
  active(length(cons(X, Y))) => mark(s(length(Y))) 
  active(inf(X)) => inf(active(X)) 
  active(take(X, Y)) => take(active(X), Y) 
  active(take(X, Y)) => take(X, active(Y)) 
  active(length(X)) => length(active(X)) 
  inf(mark(X)) => mark(inf(X)) 
  take(mark(X), Y) => mark(take(X, Y)) 
  take(X, mark(Y)) => mark(take(X, Y)) 
  length(mark(X)) => mark(length(X)) 
  proper(eq(X, Y)) => eq(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(true) => ok(true) 
  proper(s(X)) => s(proper(X)) 
  proper(false) => ok(false) 
  proper(inf(X)) => inf(proper(X)) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(take(X, Y)) => take(proper(X), proper(Y)) 
  proper(nil) => ok(nil) 
  proper(length(X)) => length(proper(X)) 
  eq(ok(X), ok(Y)) => ok(eq(X, Y)) 
  s(ok(X)) => ok(s(X)) 
  inf(ok(X)) => ok(inf(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  take(ok(X), ok(Y)) => ok(take(X, Y)) 
  length(ok(X)) => ok(length(X)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))