ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  top#(mark(X)) -> top#(proper(X))
  top#(ok(X)) -> top#(active(X))
  rules:
  
  active(filter(cons(X, Y), 0, M)) -> mark(cons(0, filter(Y, M, M)))
  active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M)))
  active(sieve(cons(0, Y))) -> mark(cons(0, sieve(Y)))
  active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N))))
  active(nats(N)) -> mark(cons(N, nats(s(N))))
  active(zprimes) -> mark(sieve(nats(s(s(0)))))
  active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3)
  active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3)
  active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(s(X)) -> s(active(X))
  active(sieve(X)) -> sieve(active(X))
  active(nats(X)) -> nats(active(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3))
  filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3))
  filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3))
  filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3))
  nats(mark(X)) -> mark(nats(X))
  nats(ok(X)) -> ok(nats(X))
  proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(s(X)) -> s(proper(X))
  proper(sieve(X)) -> sieve(proper(X))
  proper(nats(X)) -> nats(proper(X))
  proper(zprimes) -> ok(zprimes)
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  sieve(mark(X)) -> mark(sieve(X))
  sieve(ok(X)) -> ok(sieve(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))
  
   the pairs 
  top#(mark(X)) -> top#(proper(X))
  
  could not apply the generic reduction pair processor with the following
  Argument Filter: 
  pi(top#/1) = 1
  pi(ok/1) = 1
  pi(active/1) = 1
  pi(mark/1) = [1]
  pi(proper/1) = 1
  pi(filter/3) = [1,2,3]
  pi(cons/2) = 1
  pi(0/0) = []
  pi(s/1) = [1]
  pi(sieve/1) = [1]
  pi(nats/1) = [1]
  pi(zprimes/0) = []
  
  RPO with the following precedence
  precedence(mark[1]) = 0
  precedence(filter[3]) = 1
  precedence(0[0]) = 2
  precedence(s[1]) = 3
  precedence(sieve[1]) = 0
  precedence(nats[1]) = 4
  precedence(zprimes[0]) = 5
  
  precedence(_) = 0
  and the following status
  status(mark[1]) = mul
  status(filter[3]) = mul
  status(0[0]) = mul
  status(s[1]) = mul
  status(sieve[1]) = mul
  status(nats[1]) = mul
  status(zprimes[0]) = mul
  
  status(_) = lex
  
  problem when orienting (usable) rules
  could not orient sieve(mark(X)) >= mark(sieve(X))
  pi( sieve(mark(X)) ) = sieve(mark(X))
  pi( mark(sieve(X)) ) = mark(sieve(X))
  could not orient sieve(mark(X)) >=RPO mark(sieve(X))