/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 
  app : [o * o] --> o 
  cons : [] --> o 
  d : [] --> o 
  false : [] --> o 
  filter : [] --> o 
  gtr : [] --> o 
  if : [] --> o 
  len : [] --> o 
  nil : [] --> o 
  s : [] --> o 
  sub : [] --> o 
  true : [] --> o 

  app(app(app(if, true), X), Y) => X 
  app(app(app(if, false), X), Y) => Y 
  app(app(sub, X), 0) => X 
  app(app(sub, app(s, X)), app(s, Y)) => app(app(sub, X), Y) 
  app(app(gtr, 0), X) => false 
  app(app(gtr, app(s, X)), 0) => true 
  app(app(gtr, app(s, X)), app(s, Y)) => app(app(gtr, X), Y) 
  app(app(d, X), 0) => true 
  app(app(d, app(s, X)), app(s, Y)) => app(app(app(if, app(app(gtr, X), Y)), false), app(app(d, app(s, X)), app(app(sub, Y), X))) 
  app(len, nil) => 0 
  app(len, app(app(cons, X), Y)) => app(s, app(len, Y)) 
  app(app(filter, X), nil) => nil 
  app(app(filter, X), app(app(cons, Y), Z)) => app(app(app(if, app(X, Y)), app(app(cons, Y), app(app(filter, X), Z))), app(app(filter, X), Z))