/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 
  active : [o] --> o 
  cons : [o * o] --> o 
  f : [o] --> o 
  g : [o] --> o 
  mark : [o] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  sel : [o * o] --> o 
  top : [o] --> o 

  active(f(X)) => mark(cons(X, f(g(X)))) 
  active(g(0)) => mark(s(0)) 
  active(g(s(X))) => mark(s(s(g(X)))) 
  active(sel(0, cons(X, Y))) => mark(X) 
  active(sel(s(X), cons(Y, Z))) => mark(sel(X, Z)) 
  active(f(X)) => f(active(X)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(g(X)) => g(active(X)) 
  active(s(X)) => s(active(X)) 
  active(sel(X, Y)) => sel(active(X), Y) 
  active(sel(X, Y)) => sel(X, active(Y)) 
  f(mark(X)) => mark(f(X)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  g(mark(X)) => mark(g(X)) 
  s(mark(X)) => mark(s(X)) 
  sel(mark(X), Y) => mark(sel(X, Y)) 
  sel(X, mark(Y)) => mark(sel(X, Y)) 
  proper(f(X)) => f(proper(X)) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(g(X)) => g(proper(X)) 
  proper(0) => ok(0) 
  proper(s(X)) => s(proper(X)) 
  proper(sel(X, Y)) => sel(proper(X), proper(Y)) 
  f(ok(X)) => ok(f(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  g(ok(X)) => ok(g(X)) 
  s(ok(X)) => ok(s(X)) 
  sel(ok(X), ok(Y)) => ok(sel(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))