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 below the reduction pair processor
  1.1.1.1: error below the reduction pair processor
   1.1.1.1.1: error below the reduction pair processor
    1.1.1.1.1.1: error below the dependency graph processor
     1.1.1.1.1.1.1: error below the reduction pair processor
      1.1.1.1.1.1.1.1: error below the reduction pair processor
       1.1.1.1.1.1.1.1.1: error when applying the reduction pair processor to remove from the DP problem
        pairs:
        
        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))))
        mark#(cons(X1, X2)) -> mark#(X1)
        mark#(s(X)) -> active#(s(mark(X)))
        mark#(sieve(X)) -> active#(sieve(mark(X)))
        mark#(nats(X)) -> active#(nats(mark(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)))))
        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 
        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))))
        mark#(s(X)) -> active#(s(mark(X)))
        mark#(sieve(X)) -> active#(sieve(mark(X)))
        
        could not apply the generic reduction pair processor with the following
        Argument Filter: 
        pi(active#/1) = 1
        pi(sieve/1) = []
        pi(cons/2) = 1
        pi(0/0) = []
        pi(mark#/1) = [1]
        pi(s/1) = []
        pi(filter/3) = [1,2,3]
        pi(mark/1) = [1]
        pi(nats/1) = [1]
        pi(active/1) = 1
        pi(zprimes/0) = []
        
        RPO with the following precedence
        precedence(sieve[1]) = 3
        precedence(0[0]) = 0
        precedence(mark#[1]) = 2
        precedence(s[1]) = 1
        precedence(filter[3]) = 2
        precedence(mark[1]) = 2
        precedence(nats[1]) = 2
        precedence(zprimes[0]) = 4
        
        precedence(_) = 0
        and the following status
        status(sieve[1]) = mul
        status(0[0]) = mul
        status(mark#[1]) = mul
        status(s[1]) = mul
        status(filter[3]) = mul
        status(mark[1]) = mul
        status(nats[1]) = mul
        status(zprimes[0]) = mul
        
        status(_) = lex
        
        problem when orienting (usable) rules
        could not orient mark(nats(X)) >= active(nats(mark(X)))
        pi( mark(nats(X)) ) = mark(nats(X))
        pi( active(nats(mark(X))) ) = nats(mark(X))
        could not orient mark(nats(X)) >=RPO nats(mark(X))