ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.3: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  Sum_sub#(xi, Cons_sum(psi, k, s)) -> Sum_sub#(xi, s)
  Sum_sub#(xi, Cons_usual(y, m, s)) -> Sum_sub#(xi, s)
  rules:
  
  Concat(Concat(s, t), u) -> Concat(s, Concat(t, u))
  Concat(Cons_usual(x, m, s), t) -> Cons_usual(x, Term_sub(m, t), Concat(s, t))
  Concat(Cons_sum(xi, k, s), t) -> Cons_sum(xi, k, Concat(s, t))
  Concat(Id, s) -> s
  Frozen(m, Sum_constant(Left), n, s) -> Term_sub(m, s)
  Frozen(m, Sum_constant(Right), n, s) -> Term_sub(n, s)
  Frozen(m, Sum_term_var(xi), n, s) -> Case(Term_sub(m, s), xi, Term_sub(n, s))
  Sum_sub(xi, Id) -> Sum_term_var(xi)
  Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_constant(k)
  Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_sub(xi, s)
  Sum_sub(xi, Cons_usual(y, m, s)) -> Sum_sub(xi, s)
  Term_sub(Case(m, xi, n), s) -> Frozen(m, Sum_sub(xi, s), n, s)
  Term_sub(Term_app(m, n), s) -> Term_app(Term_sub(m, s), Term_sub(n, s))
  Term_sub(Term_pair(m, n), s) -> Term_pair(Term_sub(m, s), Term_sub(n, s))
  Term_sub(Term_inl(m), s) -> Term_inl(Term_sub(m, s))
  Term_sub(Term_inr(m), s) -> Term_inr(Term_sub(m, s))
  Term_sub(Term_var(x), Id) -> Term_var(x)
  Term_sub(Term_var(x), Cons_usual(y, m, s)) -> m
  Term_sub(Term_var(x), Cons_usual(y, m, s)) -> Term_sub(Term_var(x), s)
  Term_sub(Term_var(x), Cons_sum(xi, k, s)) -> Term_sub(Term_var(x), s)
  Term_sub(Term_sub(m, s), t) -> Term_sub(m, Concat(s, t))
  
   the pairs 
  Sum_sub#(xi, Cons_usual(y, m, s)) -> Sum_sub#(xi, s)
  
  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_sub#) = [(epsilon,0),(1,1),(2,2)]
  Argument Filter: 
  pi(Sum_sub#/2) = 1
  pi(Cons_usual/3) = [1,2,3]
  pi(Cons_sum/3) = 3
  
  RPO with the following precedence
  precedence(Cons_usual[3]) = 0
  
  precedence(_) = 0
  and the following status
  status(Cons_usual[3]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair Sum_sub#(xi, Cons_sum(psi, k, s)) -> Sum_sub#(xi, s) weakly:
  [(Sum_sub#(xi, Cons_sum(psi, k, s)),0),(xi,1),(Cons_sum(psi, k, s),2)] >=mu [(Sum_sub#(xi, s),0),(xi,1),(s,2)] could not be ensured