ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.7: error below the reduction pair processor
  1.1.7.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
   pairs:
   
   U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3)
   U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3)
   U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3)
   U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)
   U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3)
   rules:
   
   U11(mark(X1), X2) -> U11(X1, X2)
   U11(X1, mark(X2)) -> U11(X1, X2)
   U11(active(X1), X2) -> U11(X1, X2)
   U11(X1, active(X2)) -> U11(X1, X2)
   U12(mark(X)) -> U12(X)
   U12(active(X)) -> U12(X)
   U21(mark(X)) -> U21(X)
   U21(active(X)) -> U21(X)
   U31(mark(X1), X2) -> U31(X1, X2)
   U31(X1, mark(X2)) -> U31(X1, X2)
   U31(active(X1), X2) -> U31(X1, X2)
   U31(X1, active(X2)) -> U31(X1, X2)
   U41(mark(X1), X2, X3) -> U41(X1, X2, X3)
   U41(X1, mark(X2), X3) -> U41(X1, X2, X3)
   U41(X1, X2, mark(X3)) -> U41(X1, X2, X3)
   U41(active(X1), X2, X3) -> U41(X1, X2, X3)
   U41(X1, active(X2), X3) -> U41(X1, X2, X3)
   U41(X1, X2, active(X3)) -> U41(X1, X2, X3)
   U42(mark(X1), X2, X3) -> U42(X1, X2, X3)
   U42(X1, mark(X2), X3) -> U42(X1, X2, X3)
   U42(X1, X2, mark(X3)) -> U42(X1, X2, X3)
   U42(active(X1), X2, X3) -> U42(X1, X2, X3)
   U42(X1, active(X2), X3) -> U42(X1, X2, X3)
   U42(X1, X2, active(X3)) -> U42(X1, X2, X3)
   active(U11(tt, V2)) -> mark(U12(isNat(V2)))
   active(U12(tt)) -> mark(tt)
   active(U21(tt)) -> mark(tt)
   active(U31(tt, N)) -> mark(N)
   active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N))
   active(U42(tt, M, N)) -> mark(s(plus(N, M)))
   active(isNat(0)) -> mark(tt)
   active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2))
   active(isNat(s(V1))) -> mark(U21(isNat(V1)))
   active(plus(N, 0)) -> mark(U31(isNat(N), N))
   active(plus(N, s(M))) -> mark(U41(isNat(M), M, N))
   isNat(mark(X)) -> isNat(X)
   isNat(active(X)) -> isNat(X)
   mark(U11(X1, X2)) -> active(U11(mark(X1), X2))
   mark(tt) -> active(tt)
   mark(U12(X)) -> active(U12(mark(X)))
   mark(isNat(X)) -> active(isNat(X))
   mark(U21(X)) -> active(U21(mark(X)))
   mark(U31(X1, X2)) -> active(U31(mark(X1), X2))
   mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3))
   mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3))
   mark(s(X)) -> active(s(mark(X)))
   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
   mark(0) -> active(0)
   plus(mark(X1), X2) -> plus(X1, X2)
   plus(X1, mark(X2)) -> plus(X1, X2)
   plus(active(X1), X2) -> plus(X1, X2)
   plus(X1, active(X2)) -> plus(X1, X2)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   
    the pairs 
   U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)
   U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3)
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = MS and the level mapping defined by 
   pi(U41#) = [(2,2),(3,3)]
   polynomial interpretration over naturals with negative constants
   Pol(U41#(x_1, x_2, x_3)) = 0
   Pol(mark(x_1)) = x_1
   Pol(active(x_1)) = 1 + x_1
   problem when orienting DPs
   cannot orient pair U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3) weakly:
   [(mark(X2),2),(X3,3)] >=mu [(X2,2),(X3,3)] could not be ensured