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:
  
  sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z))
  rules:
  
  activate(n__from(X)) -> from(activate(X))
  activate(n__s(X)) -> s(activate(X))
  activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
  activate(X) -> X
  first(0, Z) -> nil
  first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
  first(X1, X2) -> n__first(X1, X2)
  from(X) -> cons(X, n__from(n__s(X)))
  from(X) -> n__from(X)
  s(X) -> n__s(X)
  sel(0, cons(X, Z)) -> X
  sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
  
   the pairs 
  sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z))
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MIN and the level mapping defined by 
  pi(sel#) = [(epsilon,0),(1,1)]
  Argument Filter: 
  pi(sel#/2) = [1,2]
  pi(s/1) = [1]
  pi(cons/2) = []
  pi(activate/1) = [1]
  pi(n__from/1) = [1]
  pi(from/1) = [1]
  pi(n__s/1) = [1]
  pi(n__first/2) = [1,2]
  pi(first/2) = [1,2]
  pi(0/0) = []
  pi(nil/0) = []
  
  RPO with the following precedence
  precedence(sel#[2]) = 3
  precedence(s[1]) = 3
  precedence(cons[2]) = 3
  precedence(activate[1]) = 3
  precedence(n__from[1]) = 3
  precedence(from[1]) = 3
  precedence(n__s[1]) = 3
  precedence(n__first[2]) = 0
  precedence(first[2]) = 2
  precedence(0[0]) = 4
  precedence(nil[0]) = 1
  
  precedence(_) = 0
  and the following status
  status(sel#[2]) = mul
  status(s[1]) = mul
  status(cons[2]) = mul
  status(activate[1]) = mul
  status(n__from[1]) = mul
  status(from[1]) = mul
  status(n__s[1]) = mul
  status(n__first[2]) = mul
  status(first[2]) = mul
  status(0[0]) = mul
  status(nil[0]) = mul
  
  status(_) = lex
  
  problem when orienting (usable) rules
  could not orient activate(n__from(X)) >= from(activate(X))
  pi( activate(n__from(X)) ) = activate(n__from(X))
  pi( from(activate(X)) ) = from(activate(X))
  could not orient activate(n__from(X)) >=RPO from(activate(X))