YES

Problem:
 g(x,y) -> x
 g(x,y) -> y
 f(s(x),y,y) -> f(y,x,s(x))

Proof:
 DP Processor:
  DPs:
   f#(s(x),y,y) -> f#(y,x,s(x))
  TRS:
   g(x,y) -> x
   g(x,y) -> y
   f(s(x),y,y) -> f(y,x,s(x))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [f#](x0, x1, x2) = -6x0 + -4x1 + -12x2 + 0,
    
    [f](x0, x1, x2) = -8x0 + x1 + -16x2 + -16,
    
    [s](x0) = 9x0 + 8,
    
    [g](x0, x1) = 9x0 + 10x1 + 15
   orientation:
    f#(s(x),y,y) = 3x + -4y + 2 >= -3x + -6y + 0 = f#(y,x,s(x))
    
    g(x,y) = 9x + 10y + 15 >= x = x
    
    g(x,y) = 9x + 10y + 15 >= y = y
    
    f(s(x),y,y) = 1x + y + 0 >= x + -8y + -8 = f(y,x,s(x))
   problem:
    DPs:
     
    TRS:
     g(x,y) -> x
     g(x,y) -> y
     f(s(x),y,y) -> f(y,x,s(x))
   Qed