/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 
  a : [o * o] --> o 
  cons : [] --> o 
  div2 : [] --> o 
  divides : [] --> o 
  false : [] --> o 
  filter : [] --> o 
  if : [] --> o 
  nil : [] --> o 
  not : [] --> o 
  not2 : [] --> o 
  s : [] --> o 
  sieve : [] --> o 
  true : [] --> o 

  a(a(divides, 0), a(s, X)) => true 
  a(a(divides, a(s, X)), a(s, Y)) => a(a(a(div2, X), a(s, Y)), Y) 
  a(a(a(div2, X), Y), 0) => a(a(divides, X), Y) 
  a(a(a(div2, 0), X), a(s, Y)) => false 
  a(a(a(div2, a(s, X)), Y), a(s, Z)) => a(a(a(div2, X), Y), Z) 
  a(a(filter, X), nil) => nil 
  a(a(filter, X), a(a(cons, Y), Z)) => a(a(a(if, a(X, Y)), Y), a(a(filter, X), Z)) 
  a(a(a(if, true), X), Y) => a(a(cons, X), Y) 
  a(a(a(if, false), X), Y) => Y 
  a(a(not, X), Y) => a(not2, a(X, Y)) 
  a(not2, true) => false 
  a(not2, false) => true 
  a(sieve, nil) => nil 
  a(sieve, a(a(cons, X), Y)) => a(a(cons, X), a(sieve, a(a(filter, a(not, a(divides, X))), Y)))