ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the reduction pair processor
 1.1.1: error below the reduction pair processor
  1.1.1.1: error below the dependency graph processor
   1.1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
    pairs:
    
    mark#(plus(X1, X2)) -> mark#(X1)
    mark#(plus(X1, X2)) -> mark#(X2)
    rules:
    
    a__U11(tt, M, N) -> a__U12(tt, M, N)
    a__U11(X1, X2, X3) -> U11(X1, X2, X3)
    a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M)))
    a__U12(X1, X2, X3) -> U12(X1, X2, X3)
    a__plus(N, 0) -> mark(N)
    a__plus(N, s(M)) -> a__U11(tt, M, N)
    a__plus(X1, X2) -> plus(X1, X2)
    mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
    mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
    mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
    mark(tt) -> tt
    mark(s(X)) -> s(mark(X))
    mark(0) -> 0
    
     the pairs 
    mark#(plus(X1, X2)) -> mark#(X1)
    mark#(plus(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(plus(x_1, x_2)) = 1 + x_2 + x_1
    problem when orienting DPs
    cannot orient pair mark#(plus(X1, X2)) -> mark#(X1) strictly:
    [(mark#(plus(X1, X2)),0),(plus(X1, X2),0)] >mu [(mark#(X1),0),(X1,0)] could not be ensured