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:
  
  mark#(f(X)) -> mark#(X)
  mark#(p(X)) -> mark#(X)
  mark#(cons(X1, X2)) -> mark#(X1)
  mark#(s(X)) -> mark#(X)
  rules:
  
  a__f(0) -> cons(0, f(s(0)))
  a__f(s(0)) -> a__f(a__p(s(0)))
  a__f(X) -> f(X)
  a__p(s(0)) -> 0
  a__p(X) -> p(X)
  mark(f(X)) -> a__f(mark(X))
  mark(p(X)) -> a__p(mark(X))
  mark(0) -> 0
  mark(cons(X1, X2)) -> cons(mark(X1), X2)
  mark(s(X)) -> s(mark(X))
  
   the pairs 
  mark#(p(X)) -> mark#(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(mark#) = [(epsilon,0),(1,0)]
  Argument Filter: 
  pi(mark#/1) = []
  pi(p/1) = [1]
  pi(f/1) = 1
  pi(cons/2) = 1
  pi(s/1) = 1
  
  RPO with the following precedence
  precedence(mark#[1]) = 0
  precedence(p[1]) = 0
  
  precedence(_) = 0
  and the following status
  status(mark#[1]) = lex
  status(p[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair mark#(f(X)) -> mark#(X) weakly:
  [(mark#(f(X)),0),(f(X),0)] >=mu [(mark#(X),0),(X,0)] could not be ensured