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),(2,0),(3,0)]
  pi(gcd#) = [(epsilon,0),(2,0)]
  polynomial interpretration over naturals with negative constants
  Pol(if#(x_1, x_2, x_3)) = x_1
  Pol(true) = 0
  Pol(s(x_1)) = 1 + x_1
  Pol(gcd#(x_1, x_2)) = 1 + x_1
  Pol(minus(x_1, x_2)) = x_1
  Pol(le(x_1, x_2)) = 1 + x_2
  Pol(false) = 0
  Pol(pred(x_1)) = x_1
  Pol(0) = 0
  problem when orienting DPs
  cannot orient pair if#(true, s(X), s(Y)) -> gcd#(minus(X, Y), s(Y)) strictly:
  [(if#(true, s(X), s(Y)),0),(s(X),0),(s(Y),0)] >mu [(gcd#(minus(X, Y), s(Y)),0),(s(Y),0)] could not be ensured