YES

Problem:
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 pred(s(x)) -> x
 minus(x,0()) -> x
 minus(x,s(y)) -> pred(minus(x,y))
 gcd(0(),y) -> y
 gcd(s(x),0()) -> s(x)
 gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
 if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
 if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))

Proof:
 DP Processor:
  DPs:
   le#(s(x),s(y)) -> le#(x,y)
   minus#(x,s(y)) -> minus#(x,y)
   minus#(x,s(y)) -> pred#(minus(x,y))
   gcd#(s(x),s(y)) -> le#(y,x)
   gcd#(s(x),s(y)) -> if_gcd#(le(y,x),s(x),s(y))
   if_gcd#(true(),s(x),s(y)) -> minus#(x,y)
   if_gcd#(true(),s(x),s(y)) -> gcd#(minus(x,y),s(y))
   if_gcd#(false(),s(x),s(y)) -> minus#(y,x)
   if_gcd#(false(),s(x),s(y)) -> gcd#(minus(y,x),s(x))
  TRS:
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   pred(s(x)) -> x
   minus(x,0()) -> x
   minus(x,s(y)) -> pred(minus(x,y))
   gcd(0(),y) -> y
   gcd(s(x),0()) -> s(x)
   gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
   if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
   if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))
  Usable Rule Processor:
   DPs:
    le#(s(x),s(y)) -> le#(x,y)
    minus#(x,s(y)) -> minus#(x,y)
    minus#(x,s(y)) -> pred#(minus(x,y))
    gcd#(s(x),s(y)) -> le#(y,x)
    gcd#(s(x),s(y)) -> if_gcd#(le(y,x),s(x),s(y))
    if_gcd#(true(),s(x),s(y)) -> minus#(x,y)
    if_gcd#(true(),s(x),s(y)) -> gcd#(minus(x,y),s(y))
    if_gcd#(false(),s(x),s(y)) -> minus#(y,x)
    if_gcd#(false(),s(x),s(y)) -> gcd#(minus(y,x),s(x))
   TRS:
    minus(x,0()) -> x
    minus(x,s(y)) -> pred(minus(x,y))
    pred(s(x)) -> x
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     minus(x,0()) -> x
     minus(x,s(y)) -> pred(minus(x,y))
     pred(s(x)) -> x
    interpretation:
     [if_gcd#](x0, x1, x2) = 2x1 + 2x2 + 6,
     
     [gcd#](x0, x1) = 2x0 + 2x1 + 7,
     
     [minus#](x0, x1) = x1,
     
     [pred#](x0) = 4,
     
     [le#](x0, x1) = x0,
     
     [minus](x0, x1) = x0,
     
     [pred](x0) = x0,
     
     [false] = 0,
     
     [s](x0) = x0 + 5,
     
     [true] = 0,
     
     [le](x0, x1) = 4x0,
     
     [0] = 0
    orientation:
     le#(s(x),s(y)) = x + 5 >= x = le#(x,y)
     
     minus#(x,s(y)) = y + 5 >= y = minus#(x,y)
     
     minus#(x,s(y)) = y + 5 >= 4 = pred#(minus(x,y))
     
     gcd#(s(x),s(y)) = 2x + 2y + 27 >= y = le#(y,x)
     
     gcd#(s(x),s(y)) = 2x + 2y + 27 >= 2x + 2y + 26 = if_gcd#(le(y,x),s(x),s(y))
     
     if_gcd#(true(),s(x),s(y)) = 2x + 2y + 26 >= y = minus#(x,y)
     
     if_gcd#(true(),s(x),s(y)) = 2x + 2y + 26 >= 2x + 2y + 17 = gcd#(minus(x,y),s(y))
     
     if_gcd#(false(),s(x),s(y)) = 2x + 2y + 26 >= x = minus#(y,x)
     
     if_gcd#(false(),s(x),s(y)) = 2x + 2y + 26 >= 2x + 2y + 17 = gcd#(minus(y,x),s(x))
     
     minus(x,0()) = x >= x = x
     
     minus(x,s(y)) = x >= x = pred(minus(x,y))
     
     pred(s(x)) = x + 5 >= x = x
     
     le(0(),y) = 0 >= 0 = true()
     
     le(s(x),0()) = 4x + 20 >= 0 = false()
     
     le(s(x),s(y)) = 4x + 20 >= 4x = le(x,y)
    problem:
     DPs:
      
     TRS:
      minus(x,0()) -> x
      minus(x,s(y)) -> pred(minus(x,y))
      pred(s(x)) -> x
      le(0(),y) -> true()
      le(s(x),0()) -> false()
      le(s(x),s(y)) -> le(x,y)
    Qed