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))
  Usable Rule Processor:
   DPs:
    f#(s(x),y,y) -> f#(y,x,s(x))
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [f#](x0, x1, x2) = 1x0 + 2x1 + x2 + -16,
     
     [s](x0) = 2x0 + 4
    orientation:
     f#(s(x),y,y) = 3x + 2y + 5 >= 2x + 1y + 4 = f#(y,x,s(x))
    problem:
     DPs:
      
     TRS:
      
    Qed