/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 
  2nd : [o] --> o 
  active : [o] --> o 
  cons : [o * o] --> o 
  from : [o] --> o 
  head : [o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  sel : [o * o] --> o 
  take : [o * o] --> o 
  top : [o] --> o 

  active(from(X)) => mark(cons(X, from(s(X)))) 
  active(head(cons(X, Y))) => mark(X) 
  active(2nd(cons(X, Y))) => mark(head(Y)) 
  active(take(0, X)) => mark(nil) 
  active(take(s(X), cons(Y, Z))) => mark(cons(Y, take(X, Z))) 
  active(sel(0, cons(X, Y))) => mark(X) 
  active(sel(s(X), cons(Y, Z))) => mark(sel(X, Z)) 
  active(from(X)) => from(active(X)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(s(X)) => s(active(X)) 
  active(head(X)) => head(active(X)) 
  active(2nd(X)) => 2nd(active(X)) 
  active(take(X, Y)) => take(active(X), Y) 
  active(take(X, Y)) => take(X, active(Y)) 
  active(sel(X, Y)) => sel(active(X), Y) 
  active(sel(X, Y)) => sel(X, active(Y)) 
  from(mark(X)) => mark(from(X)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  s(mark(X)) => mark(s(X)) 
  head(mark(X)) => mark(head(X)) 
  2nd(mark(X)) => mark(2nd(X)) 
  take(mark(X), Y) => mark(take(X, Y)) 
  take(X, mark(Y)) => mark(take(X, Y)) 
  sel(mark(X), Y) => mark(sel(X, Y)) 
  sel(X, mark(Y)) => mark(sel(X, Y)) 
  proper(from(X)) => from(proper(X)) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(s(X)) => s(proper(X)) 
  proper(head(X)) => head(proper(X)) 
  proper(2nd(X)) => 2nd(proper(X)) 
  proper(take(X, Y)) => take(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(nil) => ok(nil) 
  proper(sel(X, Y)) => sel(proper(X), proper(Y)) 
  from(ok(X)) => ok(from(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  s(ok(X)) => ok(s(X)) 
  head(ok(X)) => ok(head(X)) 
  2nd(ok(X)) => ok(2nd(X)) 
  take(ok(X), ok(Y)) => ok(take(X, Y)) 
  sel(ok(X), ok(Y)) => ok(sel(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))