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(minus(0, Y)) -> mark(0)
  active(minus(s(X), s(Y))) -> mark(minus(X, Y))
  active(geq(X, 0)) -> mark(true)
  active(geq(0, s(Y))) -> mark(false)
  active(geq(s(X), s(Y))) -> mark(geq(X, Y))
  active(div(0, s(Y))) -> mark(0)
  active(div(s(X), s(Y))) -> mark(if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0))
  active(if(true, X, Y)) -> mark(X)
  active(if(false, X, Y)) -> mark(Y)
  active(s(X)) -> s(active(X))
  active(div(X1, X2)) -> div(active(X1), X2)
  active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
  div(mark(X1), X2) -> mark(div(X1, X2))
  div(ok(X1), ok(X2)) -> ok(div(X1, X2))
  geq(ok(X1), ok(X2)) -> ok(geq(X1, X2))
  if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
  if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
  minus(ok(X1), ok(X2)) -> ok(minus(X1, X2))
  proper(minus(X1, X2)) -> minus(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(s(X)) -> s(proper(X))
  proper(geq(X1, X2)) -> geq(proper(X1), proper(X2))
  proper(true) -> ok(true)
  proper(false) -> ok(false)
  proper(div(X1, X2)) -> div(proper(X1), proper(X2))
  proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
  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 
  top#(mark(X)) -> top#(proper(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(top#) = [(epsilon,0),(1,0)]
  Argument Filter: 
  pi(top#/1) = []
  pi(ok/1) = 1
  pi(active/1) = 1
  pi(mark/1) = [1]
  pi(proper/1) = 1
  pi(minus/2) = [1]
  pi(0/0) = []
  pi(s/1) = [1]
  pi(geq/2) = [2,1]
  pi(true/0) = []
  pi(false/0) = []
  pi(div/2) = [2,1]
  pi(if/3) = [2,3,1]
  
  RPO with the following precedence
  precedence(top#[1]) = 0
  precedence(mark[1]) = 1
  precedence(minus[2]) = 1
  precedence(0[0]) = 6
  precedence(s[1]) = 3
  precedence(geq[2]) = 2
  precedence(true[0]) = 6
  precedence(false[0]) = 4
  precedence(div[2]) = 6
  precedence(if[3]) = 5
  
  precedence(_) = 0
  and the following status
  status(top#[1]) = lex
  status(mark[1]) = lex
  status(minus[2]) = lex
  status(0[0]) = lex
  status(s[1]) = lex
  status(geq[2]) = lex
  status(true[0]) = lex
  status(false[0]) = lex
  status(div[2]) = lex
  status(if[3]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair top#(ok(X)) -> top#(active(X)) weakly:
  [(top#(ok(X)),0),(ok(X),0)] >=mu [(top#(active(X)),0),(active(X),0)] could not be ensured