ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.2: error below the reduction pair processor
  1.1.2.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
   pairs:
   
   active#(s(X)) -> active#(X)
   active#(sieve(X)) -> active#(X)
   active#(nats(X)) -> 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 
   active#(sieve(X)) -> active#(X)
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = MS and the level mapping defined by 
   pi(active#) = [(epsilon,0),(1,0)]
   Argument Filter: 
   pi(active#/1) = []
   pi(s/1) = 1
   pi(sieve/1) = [1]
   pi(nats/1) = 1
   
   RPO with the following precedence
   precedence(active#[1]) = 0
   precedence(sieve[1]) = 1
   
   precedence(_) = 0
   and the following status
   status(active#[1]) = lex
   status(sieve[1]) = lex
   
   status(_) = lex
   
   problem when orienting DPs
   cannot orient pair active#(s(X)) -> active#(X) weakly:
   [(active#(s(X)),0),(s(X),0)] >=mu [(active#(X),0),(X,0)] could not be ensured