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:
   
   active#(U13(X)) -> active#(X)
   active#(U22(X)) -> active#(X)
   active#(s(X)) -> active#(X)
   rules:
   
   U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
   U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
   U12(mark(X1), X2) -> mark(U12(X1, X2))
   U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
   U13(mark(X)) -> mark(U13(X))
   U13(ok(X)) -> ok(U13(X))
   U21(mark(X1), X2) -> mark(U21(X1, X2))
   U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
   U22(mark(X)) -> mark(U22(X))
   U22(ok(X)) -> ok(U22(X))
   U31(mark(X1), X2) -> mark(U31(X1, X2))
   U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
   U41(ok(X1), ok(X2), ok(X3)) -> ok(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))
   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
   active(U12(X1, X2)) -> U12(active(X1), X2)
   active(U13(X)) -> U13(active(X))
   active(U21(X1, X2)) -> U21(active(X1), X2)
   active(U22(X)) -> U22(active(X))
   active(U31(X1, X2)) -> U31(active(X1), X2)
   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
   active(s(X)) -> s(active(X))
   active(plus(X1, X2)) -> plus(active(X1), X2)
   active(plus(X1, X2)) -> plus(X1, active(X2))
   active(and(X1, X2)) -> and(active(X1), X2)
   and(mark(X1), X2) -> mark(and(X1, X2))
   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
   isNat(ok(X)) -> ok(isNat(X))
   isNatKind(ok(X)) -> ok(isNatKind(X))
   plus(mark(X1), X2) -> mark(plus(X1, X2))
   plus(X1, mark(X2)) -> mark(plus(X1, X2))
   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
   proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3))
   proper(tt) -> ok(tt)
   proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
   proper(isNat(X)) -> isNat(proper(X))
   proper(U13(X)) -> U13(proper(X))
   proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
   proper(U22(X)) -> U22(proper(X))
   proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
   proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
   proper(s(X)) -> s(proper(X))
   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
   proper(0) -> ok(0)
   proper(isNatKind(X)) -> isNatKind(proper(X))
   s(mark(X)) -> mark(s(X))
   s(ok(X)) -> ok(s(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
   
    the pairs 
   active#(U22(X)) -> active#(X)
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = MS and the level mapping defined by 
   pi(active#) = [(epsilon,0),(1,0)]
   Argument Filter: 
   pi(active#/1) = []
   pi(U13/1) = 1
   pi(U22/1) = [1]
   pi(s/1) = 1
   
   RPO with the following precedence
   precedence(active#[1]) = 0
   precedence(U22[1]) = 1
   
   precedence(_) = 0
   and the following status
   status(active#[1]) = lex
   status(U22[1]) = lex
   
   status(_) = lex
   
   problem when orienting DPs
   cannot orient pair active#(U13(X)) -> active#(X) weakly:
   [(active#(U13(X)),0),(U13(X),0)] >=mu [(active#(X),0),(X,0)] could not be ensured