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 
  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#) = [(2,0),(3,1)]
  pi(mod#) = [(epsilon,0),(2,1)]
  polynomial interpretration over naturals with negative constants
  Pol(if_mod#(x_1, x_2, x_3)) = x_1
  Pol(true) = 0
  Pol(s(x_1)) = 1 + x_1
  Pol(mod#(x_1, x_2)) = x_1
  Pol(minus(x_1, x_2)) = x_1
  Pol(le(x_1, x_2)) = 1 + x_2
  Pol(0) = 0
  Pol(if_minus(x_1, x_2, x_3)) = x_2
  Pol(false) = 0
  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),1)] >=mu [(s(x),0),(s(y),1)] could not be ensured