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 below the reduction pair processor
   1.1.1.1.1: error below the reduction pair processor
    1.1.1.1.1.1: error below the reduction pair processor
     1.1.1.1.1.1.1: error below the dependency graph processor
      1.1.1.1.1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
       pairs:
       
       mark#(first(X1, X2)) -> mark#(X1)
       mark#(first(X1, X2)) -> mark#(X2)
       rules:
       
       active(first(0, X)) -> mark(nil)
       active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
       active(from(X)) -> mark(cons(X, from(s(X))))
       cons(mark(X1), X2) -> cons(X1, X2)
       cons(X1, mark(X2)) -> cons(X1, X2)
       cons(active(X1), X2) -> cons(X1, X2)
       cons(X1, active(X2)) -> cons(X1, X2)
       first(mark(X1), X2) -> first(X1, X2)
       first(X1, mark(X2)) -> first(X1, X2)
       first(active(X1), X2) -> first(X1, X2)
       first(X1, active(X2)) -> first(X1, X2)
       from(mark(X)) -> from(X)
       from(active(X)) -> from(X)
       mark(first(X1, X2)) -> active(first(mark(X1), mark(X2)))
       mark(0) -> active(0)
       mark(nil) -> active(nil)
       mark(s(X)) -> active(s(mark(X)))
       mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
       mark(from(X)) -> active(from(mark(X)))
       s(mark(X)) -> s(X)
       s(active(X)) -> s(X)
       
        the pairs 
       mark#(first(X1, X2)) -> mark#(X1)
       mark#(first(X1, X2)) -> mark#(X2)
       
       could not apply the generic root reduction pair processor with the following
       SCNP-version with mu = MS and the level mapping defined by 
       pi(mark#) = [(epsilon,0),(1,0)]
       polynomial interpretration over naturals with negative constants
       Pol(mark#(x_1)) = 1
       Pol(first(x_1, x_2)) = 1 + x_2 + x_1
       problem when orienting DPs
       cannot orient pair mark#(first(X1, X2)) -> mark#(X1) strictly:
       [(mark#(first(X1, X2)),0),(first(X1, X2),0)] >mu [(mark#(X1),0),(X1,0)] could not be ensured