YES

Problem:
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 p(s(x)) -> x
 f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
 f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))

Proof:
 DP Processor:
  DPs:
   -#(s(x),s(y)) -> -#(x,y)
   f#(s(x),y) -> -#(y,s(x))
   f#(s(x),y) -> p#(-(y,s(x)))
   f#(s(x),y) -> -#(s(x),y)
   f#(s(x),y) -> p#(-(s(x),y))
   f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x))))
   f#(x,s(y)) -> -#(s(y),x)
   f#(x,s(y)) -> p#(-(s(y),x))
   f#(x,s(y)) -> -#(x,s(y))
   f#(x,s(y)) -> p#(-(x,s(y)))
   f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x)))
  TRS:
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   p(s(x)) -> x
   f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
   f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))
  Usable Rule Processor:
   DPs:
    -#(s(x),s(y)) -> -#(x,y)
    f#(s(x),y) -> -#(y,s(x))
    f#(s(x),y) -> p#(-(y,s(x)))
    f#(s(x),y) -> -#(s(x),y)
    f#(s(x),y) -> p#(-(s(x),y))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x))))
    f#(x,s(y)) -> -#(s(y),x)
    f#(x,s(y)) -> p#(-(s(y),x))
    f#(x,s(y)) -> -#(x,s(y))
    f#(x,s(y)) -> p#(-(x,s(y)))
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x)))
   TRS:
    -(s(x),s(y)) -> -(x,y)
    -(x,0()) -> x
    p(s(x)) -> x
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     -(s(x),s(y)) -> -(x,y)
     -(x,0()) -> x
     p(s(x)) -> x
    interpretation:
     [f#](x0, x1) = x0 + x1 + 0,
     
     [p#](x0) = -4x0 + 0,
     
     [-#](x0, x1) = -2x1 + 0,
     
     [p](x0) = -5x0 + 4,
     
     [s](x0) = 6x0 + 6,
     
     [-](x0, x1) = 1x0 + 1x1 + 0,
     
     [0] = 0
    orientation:
     -#(s(x),s(y)) = 4y + 4 >= -2y + 0 = -#(x,y)
     
     f#(s(x),y) = 6x + y + 6 >= 4x + 4 = -#(y,s(x))
     
     f#(s(x),y) = 6x + y + 6 >= 3x + -3y + 3 = p#(-(y,s(x)))
     
     f#(s(x),y) = 6x + y + 6 >= -2y + 0 = -#(s(x),y)
     
     f#(s(x),y) = 6x + y + 6 >= 3x + -3y + 3 = p#(-(s(x),y))
     
     f#(s(x),y) = 6x + y + 6 >= 2x + -4y + 4 = f#(p(-(s(x),y)),p(-(y,s(x))))
     
     f#(x,s(y)) = x + 6y + 6 >= -2x + 0 = -#(s(y),x)
     
     f#(x,s(y)) = x + 6y + 6 >= -3x + 3y + 3 = p#(-(s(y),x))
     
     f#(x,s(y)) = x + 6y + 6 >= 4y + 4 = -#(x,s(y))
     
     f#(x,s(y)) = x + 6y + 6 >= -3x + 3y + 3 = p#(-(x,s(y)))
     
     f#(x,s(y)) = x + 6y + 6 >= -4x + 2y + 4 = f#(p(-(x,s(y))),p(-(s(y),x)))
     
     -(s(x),s(y)) = 7x + 7y + 7 >= 1x + 1y + 0 = -(x,y)
     
     -(x,0()) = 1x + 1 >= x = x
     
     p(s(x)) = 1x + 4 >= x = x
    problem:
     DPs:
      
     TRS:
      -(s(x),s(y)) -> -(x,y)
      -(x,0()) -> x
      p(s(x)) -> x
    Qed