ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.2: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  a__U11#(tt, V2) -> a__isNat#(V2)
  a__isNat#(plus(V1, V2)) -> a__U11#(a__isNat(V1), V2)
  a__isNat#(plus(V1, V2)) -> a__isNat#(V1)
  a__isNat#(s(V1)) -> a__isNat#(V1)
  rules:
  
  a__U11(tt, V2) -> a__U12(a__isNat(V2))
  a__U11(X1, X2) -> U11(X1, X2)
  a__U12(tt) -> tt
  a__U12(X) -> U12(X)
  a__U21(tt) -> tt
  a__U21(X) -> U21(X)
  a__U31(tt, N) -> mark(N)
  a__U31(X1, X2) -> U31(X1, X2)
  a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N)
  a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M)))
  a__U42(X1, X2, X3) -> U42(X1, X2, X3)
  a__isNat(0) -> tt
  a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
  a__isNat(s(V1)) -> a__U21(a__isNat(V1))
  a__isNat(X) -> isNat(X)
  a__plus(N, 0) -> a__U31(a__isNat(N), N)
  a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N)
  a__plus(X1, X2) -> plus(X1, X2)
  mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  mark(U12(X)) -> a__U12(mark(X))
  mark(isNat(X)) -> a__isNat(X)
  mark(U21(X)) -> a__U21(mark(X))
  mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  mark(U42(X1, X2, X3)) -> a__U42(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 
  a__U11#(tt, V2) -> a__isNat#(V2)
  a__isNat#(plus(V1, V2)) -> a__U11#(a__isNat(V1), V2)
  a__isNat#(plus(V1, V2)) -> a__isNat#(V1)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(a__U11#) = [(epsilon,0),(1,7),(2,0)]
  pi(a__isNat#) = [(epsilon,0),(1,0)]
  polynomial interpretration over naturals with negative constants
  Pol(a__U11#(x_1, x_2)) = 1
  Pol(tt) = 0
  Pol(a__isNat#(x_1)) = 1
  Pol(plus(x_1, x_2)) = 1 + x_2 + x_1
  Pol(a__isNat(x_1)) = x_1
  Pol(s(x_1)) = x_1
  Pol(0) = 0
  Pol(a__U11(x_1, x_2)) = 1 + x_2
  Pol(a__U21(x_1)) = x_1
  Pol(isNat(x_1)) = x_1
  Pol(a__U12(x_1)) = x_1
  Pol(U11(x_1, x_2)) = 1 + x_2
  Pol(U21(x_1)) = x_1
  Pol(U12(x_1)) = x_1
  problem when orienting DPs
  cannot orient pair a__isNat#(s(V1)) -> a__isNat#(V1) weakly:
  [(a__isNat#(s(V1)),0),(s(V1),0)] >=mu [(a__isNat#(V1),0),(V1,0)] could not be ensured