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:
  
  U12#(mark(X1), X2) -> U12#(X1, X2)
  U12#(X1, mark(X2)) -> U12#(X1, X2)
  U12#(active(X1), X2) -> U12#(X1, X2)
  U12#(X1, active(X2)) -> U12#(X1, X2)
  rules:
  
  U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
  U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
  U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
  U11(active(X1), X2, X3) -> U11(X1, X2, X3)
  U11(X1, active(X2), X3) -> U11(X1, X2, X3)
  U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
  U12(mark(X1), X2) -> U12(X1, X2)
  U12(X1, mark(X2)) -> U12(X1, X2)
  U12(active(X1), X2) -> U12(X1, X2)
  U12(X1, active(X2)) -> U12(X1, X2)
  U13(mark(X)) -> U13(X)
  U13(active(X)) -> U13(X)
  U21(mark(X1), X2) -> U21(X1, X2)
  U21(X1, mark(X2)) -> U21(X1, X2)
  U21(active(X1), X2) -> U21(X1, X2)
  U21(X1, active(X2)) -> U21(X1, X2)
  U22(mark(X)) -> U22(X)
  U22(active(X)) -> U22(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)
  active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2))
  active(U12(tt, V2)) -> mark(U13(isNat(V2)))
  active(U13(tt)) -> mark(tt)
  active(U21(tt, V1)) -> mark(U22(isNat(V1)))
  active(U22(tt)) -> mark(tt)
  active(U31(tt, N)) -> mark(N)
  active(U41(tt, M, N)) -> mark(s(plus(N, M)))
  active(and(tt, X)) -> mark(X)
  active(isNat(0)) -> mark(tt)
  active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
  active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
  active(isNatKind(0)) -> mark(tt)
  active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
  active(isNatKind(s(V1))) -> mark(isNatKind(V1))
  active(plus(N, 0)) -> mark(U31(and(isNat(N), isNatKind(N)), N))
  active(plus(N, s(M))) -> mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
  and(mark(X1), X2) -> and(X1, X2)
  and(X1, mark(X2)) -> and(X1, X2)
  and(active(X1), X2) -> and(X1, X2)
  and(X1, active(X2)) -> and(X1, X2)
  isNat(mark(X)) -> isNat(X)
  isNat(active(X)) -> isNat(X)
  isNatKind(mark(X)) -> isNatKind(X)
  isNatKind(active(X)) -> isNatKind(X)
  mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
  mark(tt) -> active(tt)
  mark(U12(X1, X2)) -> active(U12(mark(X1), X2))
  mark(isNat(X)) -> active(isNat(X))
  mark(U13(X)) -> active(U13(mark(X)))
  mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
  mark(U22(X)) -> active(U22(mark(X)))
  mark(U31(X1, X2)) -> active(U31(mark(X1), X2))
  mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3))
  mark(s(X)) -> active(s(mark(X)))
  mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
  mark(and(X1, X2)) -> active(and(mark(X1), X2))
  mark(0) -> active(0)
  mark(isNatKind(X)) -> active(isNatKind(X))
  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 
  U12#(active(X1), X2) -> U12#(X1, 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(U12#) = [(epsilon,0),(1,1)]
  Argument Filter: 
  pi(U12#/2) = []
  pi(mark/1) = 1
  pi(active/1) = [1]
  
  RPO with the following precedence
  precedence(U12#[2]) = 0
  precedence(active[1]) = 1
  
  precedence(_) = 0
  and the following status
  status(U12#[2]) = lex
  status(active[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair U12#(mark(X1), X2) -> U12#(X1, X2) weakly:
  [(U12#(mark(X1), X2),0),(mark(X1),1)] >=mu [(U12#(X1, X2),0),(X1,1)] could not be ensured