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:
  
  mod#(s(x), s(y)) -> if_mod#(le(y, x), s(x), s(y))
  if_mod#(true, s(x), s(y)) -> mod#(minus(x, y), s(y))
  rules:
  
  if_minus(true, s(x), y) -> 0
  if_minus(false, s(x), y) -> s(minus(x, y))
  if_mod(true, s(x), s(y)) -> mod(minus(x, y), s(y))
  if_mod(false, s(x), s(y)) -> s(x)
  le(0, y) -> true
  le(s(x), 0) -> false
  le(s(x), s(y)) -> le(x, y)
  minus(0, y) -> 0
  minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
  mod(0, y) -> 0
  mod(s(x), 0) -> 0
  mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
  
   the pairs 
  mod#(s(x), s(y)) -> if_mod#(le(y, x), s(x), s(y))
  if_mod#(true, s(x), s(y)) -> mod#(minus(x, y), s(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(if_mod#) = [(epsilon,0),(2,0),(3,0)]
  pi(mod#) = [(epsilon,0),(1,3)]
  Argument Filter: 
  pi(if_mod#/3) = 1
  pi(true/0) = []
  pi(s/1) = [1]
  pi(mod#/2) = 2
  pi(minus/2) = 1
  pi(le/2) = [2]
  pi(0/0) = []
  pi(if_minus/3) = 2
  pi(false/0) = []
  
  RPO with the following precedence
  precedence(true[0]) = 1
  precedence(s[1]) = 2
  precedence(le[2]) = 2
  precedence(0[0]) = 0
  precedence(false[0]) = 2
  
  precedence(_) = 0
  and the following status
  status(true[0]) = lex
  status(s[1]) = lex
  status(le[2]) = lex
  status(0[0]) = lex
  status(false[0]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair mod#(s(x), s(y)) -> if_mod#(le(y, x), s(x), s(y)) strictly:
  [(mod#(s(x), s(y)),0),(s(x),3)] >mu [(if_mod#(le(y, x), s(x), s(y)),0),(s(x),0),(s(y),0)] could not be ensured