ceta_equiv: 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 to remove from the DP problem
  pairs:
  
  f#(s(x), s(y), 0) -> f#(x, y, s(0))
  f#(s(x), 0, s(z)) -> f#(x, s(0), z)
  f#(s(x), s(y), s(z)) -> f#(x, y, f(s(x), s(y), z))
  f#(s(x), s(y), s(z)) -> f#(s(x), s(y), z)
  rules:
  
  f(x, 0, 0) -> s(x)
  f(0, y, 0) -> s(y)
  f(0, 0, z) -> s(z)
  f(s(0), y, z) -> f(0, s(y), s(z))
  f(s(x), s(y), 0) -> f(x, y, s(0))
  f(s(x), 0, s(z)) -> f(x, s(0), z)
  f(0, s(0), s(0)) -> s(s(0))
  f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
  f(0, s(s(y)), s(0)) -> f(0, y, s(0))
  f(0, s(0), s(s(z))) -> f(0, s(0), z)
  f(0, s(s(y)), s(s(z))) -> f(0, y, f(0, s(s(y)), s(z)))
  
   the pairs 
  f#(s(x), s(y), 0) -> f#(x, y, s(0))
  f#(s(x), 0, s(z)) -> f#(x, s(0), z)
  f#(s(x), s(y), s(z)) -> f#(x, y, f(s(x), s(y), z))
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MAX and the level mapping defined by 
  pi(f#) = [(1,3),(2,2)]
  Argument Filter: 
  pi(f#/3) = [2,3]
  pi(s/1) = [1]
  pi(0/0) = []
  pi(f/3) = [1,2,3]
  
  RPO with the following precedence
  precedence(f#[3]) = 2
  precedence(s[1]) = 0
  precedence(0[0]) = 0
  precedence(f[3]) = 1
  
  precedence(_) = 0
  and the following status
  status(f#[3]) = mul
  status(s[1]) = mul
  status(0[0]) = mul
  status(f[3]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair f#(s(x), 0, s(z)) -> f#(x, s(0), z) strictly:
  [(s(x),3),(0,2)] >mu [(x,3),(s(0),2)] could not be ensured