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:
  
  quot#(s(X), s(Y)) -> quot#(minus(X, Y), s(Y))
  rules:
  
  ifMinus(true, s(X), Y) -> 0
  ifMinus(false, s(X), Y) -> s(minus(X, Y))
  le(0, Y) -> true
  le(s(X), 0) -> false
  le(s(X), s(Y)) -> le(X, Y)
  minus(0, Y) -> 0
  minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y)
  quot(0, s(Y)) -> 0
  quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
  
   the pairs 
  quot#(s(X), s(Y)) -> quot#(minus(X, Y), s(Y))
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(quot#) = [(epsilon,0),(1,0),(2,0)]
  Argument Filter: 
  pi(quot#/2) = []
  pi(s/1) = [1]
  pi(minus/2) = 1
  pi(0/0) = []
  pi(ifMinus/3) = 2
  pi(le/2) = 2
  pi(false/0) = []
  pi(true/0) = []
  
  RPO with the following precedence
  precedence(quot#[2]) = 2
  precedence(s[1]) = 1
  precedence(0[0]) = 1
  precedence(false[0]) = 3
  precedence(true[0]) = 0
  
  precedence(_) = 0
  and the following status
  status(quot#[2]) = lex
  status(s[1]) = lex
  status(0[0]) = lex
  status(false[0]) = lex
  status(true[0]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair quot#(s(X), s(Y)) -> quot#(minus(X, Y), s(Y)) strictly:
  [(quot#(s(X), s(Y)),0),(s(X),0),(s(Y),0)] >mu [(quot#(minus(X, Y), s(Y)),0),(minus(X, Y),0),(s(Y),0)] could not be ensured