ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the reduction pair processor
 1.1.1: error below the reduction pair processor
  1.1.1.1: error below the dependency graph processor
   1.1.1.1.1: error when applying the reduction pair processor to remove from the DP problem
    pairs:
    
    a__sieve#(cons(s(N), Y)) -> mark#(N)
    a__nats#(N) -> mark#(N)
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(sieve(X)) -> mark#(X)
    mark#(nats(X)) -> a__nats#(mark(X))
    mark#(nats(X)) -> mark#(X)
    mark#(cons(X1, X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
    rules:
    
    a__filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M))
    a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M))
    a__filter(X1, X2, X3) -> filter(X1, X2, X3)
    a__nats(N) -> cons(mark(N), nats(s(N)))
    a__nats(X) -> nats(X)
    a__sieve(cons(0, Y)) -> cons(0, sieve(Y))
    a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N)))
    a__sieve(X) -> sieve(X)
    a__zprimes -> a__sieve(a__nats(s(s(0))))
    a__zprimes -> zprimes
    mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3))
    mark(sieve(X)) -> a__sieve(mark(X))
    mark(nats(X)) -> a__nats(mark(X))
    mark(zprimes) -> a__zprimes
    mark(cons(X1, X2)) -> cons(mark(X1), X2)
    mark(0) -> 0
    mark(s(X)) -> s(mark(X))
    
     the pairs 
    mark#(sieve(X)) -> mark#(X)
    mark#(nats(X)) -> mark#(X)
    
    could not apply the generic root reduction pair processor with the following
    SCNP-version with mu = MAX and the level mapping defined by 
    pi(mark#) = [(epsilon,0)]
    pi(a__sieve#) = [(1,0)]
    pi(a__nats#) = [(epsilon,0),(1,0)]
    Argument Filter: 
    pi(mark#/1) = 1
    pi(sieve/1) = [1]
    pi(a__sieve#/1) = []
    pi(mark/1) = [1]
    pi(cons/2) = 1
    pi(s/1) = 1
    pi(nats/1) = [1]
    pi(a__nats#/1) = []
    pi(filter/3) = [1,2,3]
    pi(a__filter/3) = [1,2,3]
    pi(a__sieve/1) = [1]
    pi(a__nats/1) = [1]
    pi(zprimes/0) = []
    pi(a__zprimes/0) = []
    pi(0/0) = []
    
    RPO with the following precedence
    precedence(sieve[1]) = 1
    precedence(a__sieve#[1]) = 1
    precedence(mark[1]) = 1
    precedence(nats[1]) = 1
    precedence(a__nats#[1]) = 1
    precedence(filter[3]) = 1
    precedence(a__filter[3]) = 1
    precedence(a__sieve[1]) = 1
    precedence(a__nats[1]) = 1
    precedence(zprimes[0]) = 2
    precedence(a__zprimes[0]) = 2
    precedence(0[0]) = 0
    
    precedence(_) = 0
    and the following status
    status(sieve[1]) = mul
    status(a__sieve#[1]) = mul
    status(mark[1]) = mul
    status(nats[1]) = mul
    status(a__nats#[1]) = mul
    status(filter[3]) = mul
    status(a__filter[3]) = mul
    status(a__sieve[1]) = mul
    status(a__nats[1]) = mul
    status(zprimes[0]) = mul
    status(a__zprimes[0]) = mul
    status(0[0]) = mul
    
    status(_) = lex
    
    problem when orienting (usable) rules
    could not orient mark(sieve(X)) >= a__sieve(mark(X))
    pi( mark(sieve(X)) ) = mark(sieve(X))
    pi( a__sieve(mark(X)) ) = a__sieve(mark(X))
    could not orient mark(sieve(X)) >=RPO a__sieve(mark(X))