/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 
  a!6220!6220filter : [o * o] --> o 
  a!6220!6220from : [o] --> o 
  a!6220!6220head : [o] --> o 
  a!6220!6220if : [o * o * o] --> o 
  a!6220!6220primes : [] --> o 
  a!6220!6220sieve : [o] --> o 
  a!6220!6220tail : [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 

  a!6220!6220primes => a!6220!6220sieve(a!6220!6220from(s(s(0)))) 
  a!6220!6220from(X) => cons(mark(X), from(s(X))) 
  a!6220!6220head(cons(X, Y)) => mark(X) 
  a!6220!6220tail(cons(X, Y)) => mark(Y) 
  a!6220!6220if(true, X, Y) => mark(X) 
  a!6220!6220if(false, X, Y) => mark(Y) 
  a!6220!6220filter(s(s(X)), cons(Y, Z)) => a!6220!6220if(divides(s(s(mark(X))), mark(Y)), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) 
  a!6220!6220sieve(cons(X, Y)) => cons(mark(X), filter(X, sieve(Y))) 
  mark(primes) => a!6220!6220primes 
  mark(sieve(X)) => a!6220!6220sieve(mark(X)) 
  mark(from(X)) => a!6220!6220from(mark(X)) 
  mark(head(X)) => a!6220!6220head(mark(X)) 
  mark(tail(X)) => a!6220!6220tail(mark(X)) 
  mark(if(X, Y, Z)) => a!6220!6220if(mark(X), Y, Z) 
  mark(filter(X, Y)) => a!6220!6220filter(mark(X), mark(Y)) 
  mark(s(X)) => s(mark(X)) 
  mark(0) => 0 
  mark(cons(X, Y)) => cons(mark(X), Y) 
  mark(true) => true 
  mark(false) => false 
  mark(divides(X, Y)) => divides(mark(X), mark(Y)) 
  a!6220!6220primes => primes 
  a!6220!6220sieve(X) => sieve(X) 
  a!6220!6220from(X) => from(X) 
  a!6220!6220head(X) => head(X) 
  a!6220!6220tail(X) => tail(X) 
  a!6220!6220if(X, Y, Z) => if(X, Y, Z) 
  a!6220!6220filter(X, Y) => filter(X, Y)