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:
  
  gcd#(s(X), s(Y)) -> if#(le(Y, X), s(X), s(Y))
  if#(true, s(X), s(Y)) -> gcd#(minus(X, Y), s(Y))
  if#(false, s(X), s(Y)) -> gcd#(minus(Y, X), s(X))
  rules:
  
  gcd(0, Y) -> 0
  gcd(s(X), 0) -> s(X)
  gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y))
  if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y))
  if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X))
  le(s(X), s(Y)) -> le(X, Y)
  le(s(X), 0) -> false
  le(0, Y) -> true
  minus(X, s(Y)) -> pred(minus(X, Y))
  minus(X, 0) -> X
  pred(s(X)) -> X
  
   the pairs 
  gcd#(s(X), s(Y)) -> if#(le(Y, X), s(X), s(Y))
  if#(true, s(X), s(Y)) -> gcd#(minus(X, Y), s(Y))
  if#(false, s(X), s(Y)) -> gcd#(minus(Y, X), s(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(if#) = [(epsilon,0),(3,0)]
  pi(gcd#) = [(epsilon,0),(1,1)]
  Argument Filter: 
  pi(if#/3) = 2
  pi(true/0) = []
  pi(s/1) = [1]
  pi(gcd#/2) = 2
  pi(minus/2) = [1]
  pi(le/2) = [2]
  pi(false/0) = []
  pi(pred/1) = 1
  pi(0/0) = []
  
  RPO with the following precedence
  precedence(true[0]) = 0
  precedence(s[1]) = 1
  precedence(minus[2]) = 0
  precedence(le[2]) = 2
  precedence(false[0]) = 3
  precedence(0[0]) = 3
  
  precedence(_) = 0
  and the following status
  status(true[0]) = lex
  status(s[1]) = lex
  status(minus[2]) = lex
  status(le[2]) = lex
  status(false[0]) = lex
  status(0[0]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair gcd#(s(X), s(Y)) -> if#(le(Y, X), s(X), s(Y)) strictly:
  [(gcd#(s(X), s(Y)),0),(s(X),1)] >mu [(if#(le(Y, X), s(X), s(Y)),0),(s(Y),0)] could not be ensured