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_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(x, 0) -> x
  minus(x, s(y)) -> pred(minus(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))
  pred(s(x)) -> x
  
   the pairs 
  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(mod#) = [(epsilon,0),(2,0)]
  pi(if_mod#) = [(epsilon,0),(2,0)]
  Argument Filter: 
  pi(mod#/2) = 1
  pi(s/1) = [1]
  pi(if_mod#/3) = 3
  pi(le/2) = [1,2]
  pi(true/0) = []
  pi(minus/2) = 1
  pi(0/0) = []
  pi(false/0) = []
  pi(pred/1) = 1
  
  RPO with the following precedence
  precedence(le[2]) = 0
  precedence(true[0]) = 1
  precedence(false[0]) = 2
  precedence(s[1]) = 3
  precedence(0[0]) = 4
  
  precedence(_) = 0
  and the following status
  status(le[2]) = lex
  status(true[0]) = lex
  status(false[0]) = lex
  status(s[1]) = lex
  status(0[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)) weakly:
  [(mod#(s(x), s(y)),0),(s(y),0)] >=mu [(if_mod#(le(y, x), s(x), s(y)),0),(s(x),0)] could not be ensured