YES

Problem:
 gcd(x,0()) -> x
 gcd(0(),y) -> y
 gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))

Proof:
 DP Processor:
  DPs:
   gcd#(s(x),s(y)) -> gcd#(-(x,y),s(y))
   gcd#(s(x),s(y)) -> gcd#(s(x),-(y,x))
  TRS:
   gcd(x,0()) -> x
   gcd(0(),y) -> y
   gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [gcd#](x0, x1) = 3x0 + x1 + 3,
    
    [if](x0, x1, x2) = x2 + 1,
    
    [-](x0, x1) = 3,
    
    [<](x0, x1) = 0,
    
    [s](x0) = 4,
    
    [gcd](x0, x1) = x0 + x1,
    
    [0] = 0
   orientation:
    gcd#(s(x),s(y)) = 19 >= 16 = gcd#(-(x,y),s(y))
    
    gcd#(s(x),s(y)) = 19 >= 18 = gcd#(s(x),-(y,x))
    
    gcd(x,0()) = x >= x = x
    
    gcd(0(),y) = y >= y = y
    
    gcd(s(x),s(y)) = 8 >= 8 = if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
   problem:
    DPs:
     
    TRS:
     gcd(x,0()) -> x
     gcd(0(),y) -> y
     gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
   Qed