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 below the reduction pair processor
   1.1.2.1.1: error below the reduction pair processor
    1.1.2.1.1.1: error below the reduction pair processor
     1.1.2.1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
      pairs:
      
      active#(U22(X)) -> active#(X)
      active#(s(X)) -> active#(X)
      active#(U61(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, X3) -> mark(U31(X1, X2, X3))
      U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3))
      U32(mark(X1), X2) -> mark(U32(X1, X2))
      U32(ok(X1), ok(X2)) -> ok(U32(X1, X2))
      U33(mark(X)) -> mark(U33(X))
      U33(ok(X)) -> ok(U33(X))
      U41(mark(X1), X2) -> mark(U41(X1, X2))
      U41(ok(X1), ok(X2)) -> ok(U41(X1, X2))
      U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3))
      U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3))
      U61(mark(X)) -> mark(U61(X))
      U61(ok(X)) -> ok(U61(X))
      U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3))
      U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(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, V1, V2)) -> mark(U32(isNat(V1), V2))
      active(U32(tt, V2)) -> mark(U33(isNat(V2)))
      active(U33(tt)) -> mark(tt)
      active(U41(tt, N)) -> mark(N)
      active(U51(tt, M, N)) -> mark(s(plus(N, M)))
      active(U61(tt)) -> mark(0)
      active(U71(tt, M, N)) -> mark(plus(x(N, M), N))
      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(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2))
      active(isNatKind(0)) -> mark(tt)
      active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
      active(isNatKind(s(V1))) -> mark(isNatKind(V1))
      active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
      active(plus(N, 0)) -> mark(U41(and(isNat(N), isNatKind(N)), N))
      active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
      active(x(N, 0)) -> mark(U61(and(isNat(N), isNatKind(N))))
      active(x(N, s(M))) -> mark(U71(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, X3)) -> U31(active(X1), X2, X3)
      active(U32(X1, X2)) -> U32(active(X1), X2)
      active(U33(X)) -> U33(active(X))
      active(U41(X1, X2)) -> U41(active(X1), X2)
      active(U51(X1, X2, X3)) -> U51(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(U61(X)) -> U61(active(X))
      active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3)
      active(x(X1, X2)) -> x(active(X1), X2)
      active(x(X1, X2)) -> x(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, X3)) -> U31(proper(X1), proper(X2), proper(X3))
      proper(U32(X1, X2)) -> U32(proper(X1), proper(X2))
      proper(U33(X)) -> U33(proper(X))
      proper(U41(X1, X2)) -> U41(proper(X1), proper(X2))
      proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3))
      proper(s(X)) -> s(proper(X))
      proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
      proper(U61(X)) -> U61(proper(X))
      proper(0) -> ok(0)
      proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3))
      proper(x(X1, X2)) -> x(proper(X1), proper(X2))
      proper(and(X1, X2)) -> and(proper(X1), proper(X2))
      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))
      x(mark(X1), X2) -> mark(x(X1, X2))
      x(X1, mark(X2)) -> mark(x(X1, X2))
      x(ok(X1), ok(X2)) -> ok(x(X1, X2))
      
       the pairs 
      active#(s(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(U22/1) = 1
      pi(s/1) = [1]
      pi(U61/1) = 1
      
      RPO with the following precedence
      precedence(active#[1]) = 0
      precedence(s[1]) = 1
      
      precedence(_) = 0
      and the following status
      status(active#[1]) = lex
      status(s[1]) = lex
      
      status(_) = lex
      
      problem when orienting DPs
      cannot orient pair active#(U22(X)) -> active#(X) weakly:
      [(active#(U22(X)),0),(U22(X),0)] >=mu [(active#(X),0),(X,0)] could not be ensured