ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.7: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  plus#(mark(X1), X2) -> plus#(X1, X2)
  plus#(X1, mark(X2)) -> plus#(X1, X2)
  plus#(ok(X1), ok(X2)) -> plus#(X1, X2)
  rules:
  
  U11(mark(X1), X2) -> mark(U11(X1, X2))
  U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
  U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3))
  U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3))
  active(U11(tt, N)) -> mark(N)
  active(U21(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(and(isNat(V1), isNat(V2)))
  active(isNat(s(V1))) -> mark(isNat(V1))
  active(plus(N, 0)) -> mark(U11(isNat(N), N))
  active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N))
  active(U11(X1, X2)) -> U11(active(X1), X2)
  active(U21(X1, X2, X3)) -> U21(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))
  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)) -> U11(proper(X1), proper(X2))
  proper(tt) -> ok(tt)
  proper(U21(X1, X2, X3)) -> U21(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(isNat(X)) -> isNat(proper(X))
  proper(0) -> ok(0)
  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 
  plus#(mark(X1), X2) -> plus#(X1, X2)
  plus#(X1, mark(X2)) -> plus#(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(plus#) = [(1,0),(2,2)]
  Argument Filter: 
  pi(plus#/2) = []
  pi(mark/1) = [1]
  pi(ok/1) = 1
  
  RPO with the following precedence
  precedence(plus#[2]) = 0
  precedence(mark[1]) = 1
  
  precedence(_) = 0
  and the following status
  status(plus#[2]) = lex
  status(mark[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair plus#(ok(X1), ok(X2)) -> plus#(X1, X2) weakly:
  [(ok(X1),0),(ok(X2),2)] >=mu [(X1,0),(X2,2)] could not be ensured