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:
  
  insert#(x, cons(v, w)) -> choose#(x, cons(v, w), x, v)
  choose#(x, cons(v, w), 0, s(z)) -> insert#(x, w)
  choose#(x, cons(v, w), s(y), s(z)) -> choose#(x, cons(v, w), y, z)
  rules:
  
  choose(x, cons(v, w), y, 0) -> cons(x, cons(v, w))
  choose(x, cons(v, w), 0, s(z)) -> cons(v, insert(x, w))
  choose(x, cons(v, w), s(y), s(z)) -> choose(x, cons(v, w), y, z)
  insert(x, nil) -> cons(x, nil)
  insert(x, cons(v, w)) -> choose(x, cons(v, w), x, v)
  sort(nil) -> nil
  sort(cons(x, y)) -> insert(x, sort(y))
  
   the pairs 
  insert#(x, cons(v, w)) -> choose#(x, cons(v, w), x, v)
  choose#(x, cons(v, w), 0, s(z)) -> insert#(x, w)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(choose#) = [(epsilon,0),(1,0),(2,2),(4,7)]
  pi(insert#) = [(1,0),(2,4)]
  Argument Filter: 
  pi(choose#/4) = 4
  pi(cons/2) = [1,2]
  pi(0/0) = []
  pi(s/1) = 1
  pi(insert#/2) = [1,2]
  
  RPO with the following precedence
  precedence(cons[2]) = 1
  precedence(0[0]) = 2
  precedence(insert#[2]) = 0
  
  precedence(_) = 0
  and the following status
  status(cons[2]) = mul
  status(0[0]) = mul
  status(insert#[2]) = mul
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair choose#(x, cons(v, w), s(y), s(z)) -> choose#(x, cons(v, w), y, z) weakly:
  [(choose#(x, cons(v, w), s(y), s(z)),0),(x,0),(cons(v, w),2),(s(z),7)] >=mu [(choose#(x, cons(v, w), y, z),0),(x,0),(cons(v, w),2),(z,7)] could not be ensured