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:
  
  weight#(cons(n, cons(m, x))) -> weight#(sum(cons(n, cons(m, x)), cons(0, x)))
  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 
  weight#(cons(n, cons(m, x))) -> weight#(sum(cons(n, cons(m, x)), cons(0, x)))
  
  could not apply the generic reduction pair processor with the following
  Argument Filter: 
  pi(weight#/1) = [1]
  pi(cons/2) = [1,2]
  pi(sum/2) = [2]
  pi(0/0) = []
  pi(s/1) = []
  pi(nil/0) = []
  
  RPO with the following precedence
  precedence(weight#[1]) = 2
  precedence(cons[2]) = 2
  precedence(sum[2]) = 1
  precedence(0[0]) = 0
  precedence(s[1]) = 0
  precedence(nil[0]) = 3
  
  precedence(_) = 0
  and the following status
  status(weight#[1]) = mul
  status(cons[2]) = mul
  status(sum[2]) = mul
  status(0[0]) = mul
  status(s[1]) = mul
  status(nil[0]) = mul
  
  status(_) = lex
  
  problem when orienting (usable) rules
  could not orient sum(cons(s(n), x), cons(m, y)) >= sum(cons(n, x), cons(s(m), y))
  pi( sum(cons(s(n), x), cons(m, y)) ) = sum(cons(m, y))
  pi( sum(cons(n, x), cons(s(m), y)) ) = sum(cons(s, y))
  could not orient sum(cons(m, y)) >=RPO sum(cons(s, y))