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 below the reduction pair processor
  1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
   pairs:
   
   b#(y, z) -> c#(y, z, z)
   c#(f(z), f(c(a, x, a)), y) -> b#(x, z)
   c#(f(z), f(c(a, x, a)), y) -> c#(z, y, a)
   rules:
   
   b(y, z) -> f(c(c(y, z, z), a, a))
   b(b(z, y), a) -> z
   c(f(z), f(c(a, x, a)), y) -> c(f(b(x, z)), c(z, y, a), a)
   
    the pairs 
   b#(y, z) -> c#(y, z, z)
   c#(f(z), f(c(a, x, a)), y) -> b#(x, z)
   c#(f(z), f(c(a, x, a)), y) -> c#(z, y, a)
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = MS and the level mapping defined by 
   pi(b#) = [(epsilon,0),(1,1),(2,1)]
   pi(c#) = [(epsilon,0),(1,1),(2,0)]
   polynomial interpretration over naturals with negative constants
   Pol(b#(x_1, x_2)) = 1
   Pol(c#(x_1, x_2, x_3)) = x_3
   Pol(f(x_1)) = x_1
   Pol(c(x_1, x_2, x_3)) = 1 + x_2 + x_1
   Pol(a) = 1
   problem when orienting DPs
   cannot orient pair c#(f(z), f(c(a, x, a)), y) -> b#(x, z) strictly:
   [(c#(f(z), f(c(a, x, a)), y),0),(f(z),1),(f(c(a, x, a)),0)] >mu [(b#(x, z),0),(x,1),(z,1)] could not be ensured