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) = x0 + 1x1,
    
    [f](x0, x1, x2) = 4x0 + 5x1 + 3x2 + 0,
    
    [s](x0) = 2x0 + 1,
    
    [g](x0, x1) = 8x0 + 1x1 + 0
   orientation:
    f#(s(x),y,y) = 2x + 1y + 1 >= 1x + y = f#(y,x,s(x))
    
    g(x,y) = 8x + 1y + 0 >= x = x
    
    g(x,y) = 8x + 1y + 0 >= y = y
    
    f(s(x),y,y) = 6x + 5y + 5 >= 5x + 4y + 4 = 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