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 when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  sum#(cons(s(n), x), cons(m, y)) -> sum#(cons(n, x), cons(s(m), y))
  sum#(cons(0, x), y) -> sum#(x, y)
  rules:
  
  sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
  sum(cons(0, x), y) -> sum(x, y)
  sum(nil, y) -> y
  weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0, x)))
  weight(cons(n, nil)) -> n
  
   the pairs 
  sum#(cons(0, x), y) -> sum#(x, y)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(sum#) = [(1,0),(2,3)]
  Argument Filter: 
  pi(sum#/2) = []
  pi(cons/2) = [1,2]
  pi(0/0) = []
  pi(s/1) = 1
  
  RPO with the following precedence
  precedence(cons[2]) = 0
  precedence(sum#[2]) = 1
  precedence(0[0]) = 2
  
  precedence(_) = 0
  and the following status
  status(cons[2]) = lex
  status(sum#[2]) = lex
  status(0[0]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair sum#(cons(s(n), x), cons(m, y)) -> sum#(cons(n, x), cons(s(m), y)) weakly:
  [(cons(s(n), x),0),(cons(m, y),3)] >=mu [(cons(n, x),0),(cons(s(m), y),3)] could not be ensured