ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.3: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  a__U31#(tt, V2) -> a__isNatKind#(V2)
  a__isNatKind#(plus(V1, V2)) -> a__U31#(a__isNatKind(V1), V2)
  a__isNatKind#(plus(V1, V2)) -> a__isNatKind#(V1)
  a__isNatKind#(s(V1)) -> a__isNatKind#(V1)
  rules:
  
  a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
  a__U11(X1, X2, X3) -> U11(X1, X2, X3)
  a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
  a__U12(X1, X2, X3) -> U12(X1, X2, X3)
  a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
  a__U13(X1, X2, X3) -> U13(X1, X2, X3)
  a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2)
  a__U14(X1, X2, X3) -> U14(X1, X2, X3)
  a__U15(tt, V2) -> a__U16(a__isNat(V2))
  a__U15(X1, X2) -> U15(X1, X2)
  a__U16(tt) -> tt
  a__U16(X) -> U16(X)
  a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1)
  a__U21(X1, X2) -> U21(X1, X2)
  a__U22(tt, V1) -> a__U23(a__isNat(V1))
  a__U22(X1, X2) -> U22(X1, X2)
  a__U23(tt) -> tt
  a__U23(X) -> U23(X)
  a__U31(tt, V2) -> a__U32(a__isNatKind(V2))
  a__U31(X1, X2) -> U31(X1, X2)
  a__U32(tt) -> tt
  a__U32(X) -> U32(X)
  a__U41(tt) -> tt
  a__U41(X) -> U41(X)
  a__U51(tt, N) -> a__U52(a__isNatKind(N), N)
  a__U51(X1, X2) -> U51(X1, X2)
  a__U52(tt, N) -> mark(N)
  a__U52(X1, X2) -> U52(X1, X2)
  a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N)
  a__U61(X1, X2, X3) -> U61(X1, X2, X3)
  a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N)
  a__U62(X1, X2, X3) -> U62(X1, X2, X3)
  a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N)
  a__U63(X1, X2, X3) -> U63(X1, X2, X3)
  a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M)))
  a__U64(X1, X2, X3) -> U64(X1, X2, X3)
  a__isNat(0) -> tt
  a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
  a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
  a__isNat(X) -> isNat(X)
  a__isNatKind(0) -> tt
  a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2)
  a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
  a__isNatKind(X) -> isNatKind(X)
  a__plus(N, 0) -> a__U51(a__isNat(N), N)
  a__plus(N, s(M)) -> a__U61(a__isNat(M), 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(isNatKind(X)) -> a__isNatKind(X)
  mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
  mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
  mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
  mark(isNat(X)) -> a__isNat(X)
  mark(U16(X)) -> a__U16(mark(X))
  mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
  mark(U23(X)) -> a__U23(mark(X))
  mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  mark(U32(X)) -> a__U32(mark(X))
  mark(U41(X)) -> a__U41(mark(X))
  mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
  mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
  mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
  mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3)
  mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3)
  mark(U64(X1, X2, X3)) -> a__U64(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__U31#(tt, V2) -> a__isNatKind#(V2)
  a__isNatKind#(plus(V1, V2)) -> a__U31#(a__isNatKind(V1), V2)
  a__isNatKind#(plus(V1, V2)) -> a__isNatKind#(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__U31#) = [(epsilon,0),(1,7),(2,0)]
  pi(a__isNatKind#) = [(epsilon,0),(1,0)]
  polynomial interpretration over naturals with negative constants
  Pol(a__U31#(x_1, x_2)) = 1
  Pol(tt) = 0
  Pol(a__isNatKind#(x_1)) = 1
  Pol(plus(x_1, x_2)) = 1 + x_2 + x_1
  Pol(a__isNatKind(x_1)) = x_1
  Pol(s(x_1)) = x_1
  Pol(0) = 0
  Pol(a__U31(x_1, x_2)) = 1 + x_2
  Pol(a__U41(x_1)) = x_1
  Pol(isNatKind(x_1)) = x_1
  Pol(a__U32(x_1)) = x_1
  Pol(U31(x_1, x_2)) = 1 + x_2
  Pol(U41(x_1)) = x_1
  Pol(U32(x_1)) = x_1
  problem when orienting DPs
  cannot orient pair a__isNatKind#(s(V1)) -> a__isNatKind#(V1) weakly:
  [(a__isNatKind#(s(V1)),0),(s(V1),0)] >=mu [(a__isNatKind#(V1),0),(V1,0)] could not be ensured