YES

Problem:
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 minus(x,0()) -> x
 minus(s(x),s(y)) -> 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#(s(x),s(y)) -> 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)
   minus(x,0()) -> x
   minus(s(x),s(y)) -> 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#(s(x),s(y)) -> 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)
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
    interpretation:
     [if_gcd#](x0, x1, x2) = x0 + x1 + x2 + 1,
     
     [gcd#](x0, x1) = x0 + x1 + 2,
     
     [minus#](x0, x1) = x1 + 1/2,
     
     [le#](x0, x1) = x0 + 3/2,
     
     [minus](x0, x1) = x0,
     
     [false] = 1/2,
     
     [s](x0) = 3/2x0 + 2,
     
     [true] = 0,
     
     [le](x0, x1) = 1/2,
     
     [0] = 0
    orientation:
     le#(s(x),s(y)) = 3/2x + 7/2 >= x + 3/2 = le#(x,y)
     
     minus#(s(x),s(y)) = 3/2y + 5/2 >= y + 1/2 = minus#(x,y)
     
     gcd#(s(x),s(y)) = 3/2x + 3/2y + 6 >= y + 3/2 = le#(y,x)
     
     gcd#(s(x),s(y)) = 3/2x + 3/2y + 6 >= 3/2x + 3/2y + 11/2 = if_gcd#(le(y,x),s(x),s(y))
     
     if_gcd#(true(),s(x),s(y)) = 3/2x + 3/2y + 5 >= y + 1/2 = minus#(x,y)
     
     if_gcd#(true(),s(x),s(y)) = 3/2x + 3/2y + 5 >= x + 3/2y + 4 = gcd#(minus(x,y),s(y))
     
     if_gcd#(false(),s(x),s(y)) = 3/2x + 3/2y + 11/2 >= x + 1/2 = minus#(y,x)
     
     if_gcd#(false(),s(x),s(y)) = 3/2x + 3/2y + 11/2 >= 3/2x + y + 4 = gcd#(minus(y,x),s(x))
     
     le(0(),y) = 1/2 >= 0 = true()
     
     le(s(x),0()) = 1/2 >= 1/2 = false()
     
     le(s(x),s(y)) = 1/2 >= 1/2 = le(x,y)
     
     minus(x,0()) = x >= x = x
     
     minus(s(x),s(y)) = 3/2x + 2 >= x = minus(x,y)
    problem:
     DPs:
      
     TRS:
      le(0(),y) -> true()
      le(s(x),0()) -> false()
      le(s(x),s(y)) -> le(x,y)
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
    Qed