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:
  
  splitAt#(s(N), cons(X, XS)) -> splitAt#(N, activate(XS))
  rules:
  
  activate(n__natsFrom(X)) -> natsFrom(X)
  activate(X) -> X
  afterNth(N, XS) -> snd(splitAt(N, XS))
  fst(pair(XS, YS)) -> XS
  head(cons(N, XS)) -> N
  natsFrom(N) -> cons(N, n__natsFrom(s(N)))
  natsFrom(X) -> n__natsFrom(X)
  sel(N, XS) -> head(afterNth(N, XS))
  snd(pair(XS, YS)) -> YS
  splitAt(0, XS) -> pair(nil, XS)
  splitAt(s(N), cons(X, XS)) -> u(splitAt(N, activate(XS)), N, X, activate(XS))
  tail(cons(N, XS)) -> activate(XS)
  take(N, XS) -> fst(splitAt(N, XS))
  u(pair(YS, ZS), N, X, XS) -> pair(cons(activate(X), YS), ZS)
  
   the pairs 
  splitAt#(s(N), cons(X, XS)) -> splitAt#(N, activate(XS))
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(splitAt#) = [(1,2),(2,2)]
  Argument Filter: 
  pi(splitAt#/2) = []
  pi(s/1) = [1]
  pi(cons/2) = 2
  pi(activate/1) = 1
  pi(n__natsFrom/1) = []
  pi(natsFrom/1) = []
  
  RPO with the following precedence
  precedence(splitAt#[2]) = 1
  precedence(s[1]) = 0
  precedence(n__natsFrom[1]) = 2
  precedence(natsFrom[1]) = 2
  
  precedence(_) = 0
  and the following status
  status(splitAt#[2]) = lex
  status(s[1]) = lex
  status(n__natsFrom[1]) = lex
  status(natsFrom[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair splitAt#(s(N), cons(X, XS)) -> splitAt#(N, activate(XS)) strictly:
  [(s(N),2),(cons(X, XS),2)] >mu [(N,2),(activate(XS),2)] could not be ensured