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 below the reduction pair processor
  1.1.2.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
   pairs:
   
   U11#(mark(X1), 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)
   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 
   U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3)
   U11#(X1, X2, mark(X3)) -> U11#(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(U11#) = [(epsilon,0),(1,3),(2,0),(3,0)]
   Argument Filter: 
   pi(U11#/3) = [3,1]
   pi(mark/1) = [1]
   pi(active/1) = 1
   
   RPO with the following precedence
   precedence(U11#[3]) = 0
   precedence(mark[1]) = 1
   
   precedence(_) = 0
   and the following status
   status(U11#[3]) = lex
   status(mark[1]) = lex
   
   status(_) = lex
   
   problem when orienting DPs
   cannot orient pair U11#(active(X1), X2, X3) -> U11#(X1, X2, X3) weakly:
   [(U11#(active(X1), X2, X3),0),(active(X1),3),(X2,0),(X3,0)] >=mu [(U11#(X1, X2, X3),0),(X1,3),(X2,0),(X3,0)] could not be ensured