ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  top#(mark(X)) -> top#(proper(X))
  top#(ok(X)) -> top#(active(X))
  rules:
  
  active(and(tt, X)) -> mark(X)
  active(plus(N, 0)) -> mark(N)
  active(plus(N, s(M))) -> mark(s(plus(N, M)))
  active(x(N, 0)) -> mark(0)
  active(x(N, s(M))) -> mark(plus(x(N, M), N))
  active(and(X1, X2)) -> and(active(X1), X2)
  active(plus(X1, X2)) -> plus(active(X1), X2)
  active(plus(X1, X2)) -> plus(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(x(X1, X2)) -> x(active(X1), X2)
  active(x(X1, X2)) -> x(X1, active(X2))
  and(mark(X1), X2) -> mark(and(X1, X2))
  and(ok(X1), ok(X2)) -> ok(and(X1, X2))
  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(and(X1, X2)) -> and(proper(X1), proper(X2))
  proper(tt) -> ok(tt)
  proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(s(X)) -> s(proper(X))
  proper(x(X1, X2)) -> x(proper(X1), proper(X2))
  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 
  top#(mark(X)) -> top#(proper(X))
  
  could not apply the generic reduction pair processor with the following
  Argument Filter: 
  pi(top#/1) = [1]
  pi(ok/1) = 1
  pi(active/1) = 1
  pi(mark/1) = [1]
  pi(proper/1) = 1
  pi(and/2) = [2,1]
  pi(tt/0) = []
  pi(plus/2) = [2,1]
  pi(0/0) = []
  pi(s/1) = [1]
  pi(x/2) = [1,2]
  
  RPO with the following precedence
  precedence(top#[1]) = 0
  precedence(mark[1]) = 1
  precedence(and[2]) = 2
  precedence(tt[0]) = 3
  precedence(plus[2]) = 4
  precedence(0[0]) = 1
  precedence(s[1]) = 1
  precedence(x[2]) = 5
  
  precedence(_) = 0
  and the following status
  status(top#[1]) = mul
  status(mark[1]) = mul
  status(and[2]) = lex
  status(tt[0]) = mul
  status(plus[2]) = lex
  status(0[0]) = mul
  status(s[1]) = mul
  status(x[2]) = mul
  
  status(_) = lex
  
  problem when orienting (usable) rules
  could not orient s(mark(X)) >= mark(s(X))
  pi( s(mark(X)) ) = s(mark(X))
  pi( mark(s(X)) ) = mark(s(X))
  could not orient s(mark(X)) >=RPO mark(s(X))