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:
   
   filter#(mark(X1), X2, X3) -> filter#(X1, X2, X3)
   filter#(X1, X2, mark(X3)) -> filter#(X1, X2, X3)
   filter#(active(X1), X2, X3) -> filter#(X1, X2, X3)
   filter#(X1, active(X2), X3) -> filter#(X1, X2, X3)
   filter#(X1, X2, active(X3)) -> filter#(X1, X2, X3)
   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)))))
   cons(mark(X1), X2) -> cons(X1, X2)
   cons(X1, mark(X2)) -> cons(X1, X2)
   cons(active(X1), X2) -> cons(X1, X2)
   cons(X1, active(X2)) -> cons(X1, X2)
   filter(mark(X1), X2, X3) -> filter(X1, X2, X3)
   filter(X1, mark(X2), X3) -> filter(X1, X2, X3)
   filter(X1, X2, mark(X3)) -> filter(X1, X2, X3)
   filter(active(X1), X2, X3) -> filter(X1, X2, X3)
   filter(X1, active(X2), X3) -> filter(X1, X2, X3)
   filter(X1, X2, active(X3)) -> filter(X1, X2, X3)
   mark(filter(X1, X2, X3)) -> active(filter(mark(X1), mark(X2), mark(X3)))
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(0) -> active(0)
   mark(s(X)) -> active(s(mark(X)))
   mark(sieve(X)) -> active(sieve(mark(X)))
   mark(nats(X)) -> active(nats(mark(X)))
   mark(zprimes) -> active(zprimes)
   nats(mark(X)) -> nats(X)
   nats(active(X)) -> nats(X)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   sieve(mark(X)) -> sieve(X)
   sieve(active(X)) -> sieve(X)
   
    the pairs 
   filter#(mark(X1), X2, X3) -> filter#(X1, X2, X3)
   filter#(X1, X2, mark(X3)) -> filter#(X1, X2, X3)
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = MS and the level mapping defined by 
   pi(filter#) = [(epsilon,0),(1,3),(2,0),(3,0)]
   Argument Filter: 
   pi(filter#/3) = [3,1]
   pi(mark/1) = [1]
   pi(active/1) = 1
   
   RPO with the following precedence
   precedence(filter#[3]) = 0
   precedence(mark[1]) = 1
   
   precedence(_) = 0
   and the following status
   status(filter#[3]) = lex
   status(mark[1]) = lex
   
   status(_) = lex
   
   problem when orienting DPs
   cannot orient pair filter#(active(X1), X2, X3) -> filter#(X1, X2, X3) weakly:
   [(filter#(active(X1), X2, X3),0),(active(X1),3),(X2,0),(X3,0)] >=mu [(filter#(X1, X2, X3),0),(X1,3),(X2,0),(X3,0)] could not be ensured