YES

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

Proof:
 DP Processor:
  DPs:
   f#(s(x),y) -> f#(x,s(s(x)))
   f#(x,s(s(y))) -> f#(y,x)
  TRS:
   f(s(x),y) -> f(x,s(s(x)))
   f(x,s(s(y))) -> f(y,x)
  Usable Rule Processor:
   DPs:
    f#(s(x),y) -> f#(x,s(s(x)))
    f#(x,s(s(y))) -> f#(y,x)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [f#](x0, x1) = 4x0 + x1,
     
     [s](x0) = 3x0 + -7
    orientation:
     f#(s(x),y) = 7x + y + -3 >= 6x + -4 = f#(x,s(s(x)))
     
     f#(x,s(s(y))) = 4x + 6y + -4 >= x + 4y = f#(y,x)
    problem:
     DPs:
      
     TRS:
      
    Qed