/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 
  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 
  primes : [] --> o 
  s : [o] --> o 
  sieve : [o] --> o 
  tail : [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)))) 
  mark(primes) => active(primes) 
  mark(sieve(X)) => active(sieve(mark(X))) 
  mark(from(X)) => active(from(mark(X))) 
  mark(s(X)) => active(s(mark(X))) 
  mark(0) => active(0) 
  mark(cons(X, Y)) => active(cons(mark(X), Y)) 
  mark(head(X)) => active(head(mark(X))) 
  mark(tail(X)) => active(tail(mark(X))) 
  mark(if(X, Y, Z)) => active(if(mark(X), Y, Z)) 
  mark(true) => active(true) 
  mark(false) => active(false) 
  mark(filter(X, Y)) => active(filter(mark(X), mark(Y))) 
  mark(divides(X, Y)) => active(divides(mark(X), mark(Y))) 
  sieve(mark(X)) => sieve(X) 
  sieve(active(X)) => sieve(X) 
  from(mark(X)) => from(X) 
  from(active(X)) => from(X) 
  s(mark(X)) => s(X) 
  s(active(X)) => s(X) 
  cons(mark(X), Y) => cons(X, Y) 
  cons(X, mark(Y)) => cons(X, Y) 
  cons(active(X), Y) => cons(X, Y) 
  cons(X, active(Y)) => cons(X, Y) 
  head(mark(X)) => head(X) 
  head(active(X)) => head(X) 
  tail(mark(X)) => tail(X) 
  tail(active(X)) => tail(X) 
  if(mark(X), Y, Z) => if(X, Y, Z) 
  if(X, mark(Y), Z) => if(X, Y, Z) 
  if(X, Y, mark(Z)) => if(X, Y, Z) 
  if(active(X), Y, Z) => if(X, Y, Z) 
  if(X, active(Y), Z) => if(X, Y, Z) 
  if(X, Y, active(Z)) => if(X, Y, Z) 
  filter(mark(X), Y) => filter(X, Y) 
  filter(X, mark(Y)) => filter(X, Y) 
  filter(active(X), Y) => filter(X, Y) 
  filter(X, active(Y)) => filter(X, Y) 
  divides(mark(X), Y) => divides(X, Y) 
  divides(X, mark(Y)) => divides(X, Y) 
  divides(active(X), Y) => divides(X, Y) 
  divides(X, active(Y)) => divides(X, Y)