/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 
  divides : [o * o] --> o 
  false : [] --> o 
  filter : [o * o] --> o 
  from : [o] --> o 
  head : [o] --> o 
  if : [o * o * o] --> o 
  mark : [o] --> o 
  ok : [o] --> o 
  primes : [] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  sieve : [o] --> o 
  tail : [o] --> o 
  top : [o] --> o 
  true : [] --> o 

  active(primes) => mark(sieve(from(s(s(0))))) 
  active(from(X)) => mark(cons(X, from(s(X)))) 
  active(head(cons(X, Y))) => mark(X) 
  active(tail(cons(X, Y))) => mark(Y) 
  active(if(true, X, Y)) => mark(X) 
  active(if(false, X, Y)) => mark(Y) 
  active(filter(s(s(X)), cons(Y, Z))) => mark(if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y))))) 
  active(sieve(cons(X, Y))) => mark(cons(X, filter(X, sieve(Y)))) 
  active(sieve(X)) => sieve(active(X)) 
  active(from(X)) => from(active(X)) 
  active(s(X)) => s(active(X)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(head(X)) => head(active(X)) 
  active(tail(X)) => tail(active(X)) 
  active(if(X, Y, Z)) => if(active(X), Y, Z) 
  active(filter(X, Y)) => filter(active(X), Y) 
  active(filter(X, Y)) => filter(X, active(Y)) 
  active(divides(X, Y)) => divides(active(X), Y) 
  active(divides(X, Y)) => divides(X, active(Y)) 
  sieve(mark(X)) => mark(sieve(X)) 
  from(mark(X)) => mark(from(X)) 
  s(mark(X)) => mark(s(X)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  head(mark(X)) => mark(head(X)) 
  tail(mark(X)) => mark(tail(X)) 
  if(mark(X), Y, Z) => mark(if(X, Y, Z)) 
  filter(mark(X), Y) => mark(filter(X, Y)) 
  filter(X, mark(Y)) => mark(filter(X, Y)) 
  divides(mark(X), Y) => mark(divides(X, Y)) 
  divides(X, mark(Y)) => mark(divides(X, Y)) 
  proper(primes) => ok(primes) 
  proper(sieve(X)) => sieve(proper(X)) 
  proper(from(X)) => from(proper(X)) 
  proper(s(X)) => s(proper(X)) 
  proper(0) => ok(0) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(head(X)) => head(proper(X)) 
  proper(tail(X)) => tail(proper(X)) 
  proper(if(X, Y, Z)) => if(proper(X), proper(Y), proper(Z)) 
  proper(true) => ok(true) 
  proper(false) => ok(false) 
  proper(filter(X, Y)) => filter(proper(X), proper(Y)) 
  proper(divides(X, Y)) => divides(proper(X), proper(Y)) 
  sieve(ok(X)) => ok(sieve(X)) 
  from(ok(X)) => ok(from(X)) 
  s(ok(X)) => ok(s(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  head(ok(X)) => ok(head(X)) 
  tail(ok(X)) => ok(tail(X)) 
  if(ok(X), ok(Y), ok(Z)) => ok(if(X, Y, Z)) 
  filter(ok(X), ok(Y)) => ok(filter(X, Y)) 
  divides(ok(X), ok(Y)) => ok(divides(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))