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:
  
  g#(x, c(y)) -> g#(x, y)
  g#(x, c(y)) -> g#(s(x), y)
  rules:
  
  f(0) -> true
  f(1) -> false
  f(s(x)) -> f(x)
  g(x, c(y)) -> c(g(x, y))
  g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y)))
  if(true, s(x), s(y)) -> s(x)
  if(false, s(x), s(y)) -> s(y)
  
   the pairs 
  g#(x, c(y)) -> g#(x, y)
  g#(x, c(y)) -> g#(s(x), y)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(g#) = [(epsilon,0),(1,0),(2,0)]
  Argument Filter: 
  pi(g#/2) = []
  pi(c/1) = [1]
  pi(s/1) = 1
  
  RPO with the following precedence
  precedence(c[1]) = 0
  precedence(g#[2]) = 1
  
  precedence(_) = 0
  and the following status
  status(c[1]) = lex
  status(g#[2]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair g#(x, c(y)) -> g#(x, y) strictly:
  [(g#(x, c(y)),0),(x,0),(c(y),0)] >mu [(g#(x, y),0),(x,0),(y,0)] could not be ensured