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:
  
  implies#(not(x), not(y)) -> implies#(y, and(x, y))
  rules:
  
  and(x, false) -> false
  and(x, not(false)) -> x
  implies(false, y) -> not(false)
  implies(x, false) -> not(x)
  implies(not(x), not(y)) -> implies(y, and(x, y))
  not(not(x)) -> x
  
   the pairs 
  implies#(not(x), not(y)) -> implies#(y, and(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(implies#) = [(1,0),(2,0)]
  polynomial interpretration over naturals with negative constants
  Pol(implies#(x_1, x_2)) = 1 + x_1
  Pol(not(x_1)) = 1 + x_1
  Pol(and(x_1, x_2)) = 1 + x_1
  Pol(false) = 1
  problem when orienting DPs
  cannot orient pair implies#(not(x), not(y)) -> implies#(y, and(x, y)) strictly:
  [(not(x),0),(not(y),0)] >mu [(y,0),(and(x, y),0)] could not be ensured