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)))
  TDG 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)))
   graph:
    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)))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(x,s(y)) -> p#(-(x,s(y)))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(x,s(y)) -> -#(x,s(y))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(x,s(y)) -> p#(-(s(y),x))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(x,s(y)) -> -#(s(y),x)
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x))))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(s(x),y) -> p#(-(s(x),y))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(s(x),y) -> -#(s(x),y)
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) ->
    f#(s(x),y) -> p#(-(y,s(x)))
    f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x)))) -> f#(s(x),y) -> -#(y,s(x))
    f#(s(x),y) -> -#(s(x),y) -> -#(s(x),s(y)) -> -#(x,y)
    f#(s(x),y) -> -#(y,s(x)) -> -#(s(x),s(y)) -> -#(x,y)
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) ->
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x)))
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) ->
    f#(x,s(y)) -> p#(-(x,s(y)))
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) ->
    f#(x,s(y)) -> -#(x,s(y))
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) ->
    f#(x,s(y)) -> p#(-(s(y),x))
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) ->
    f#(x,s(y)) -> -#(s(y),x)
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),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))) ->
    f#(s(x),y) -> p#(-(s(x),y))
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) ->
    f#(s(x),y) -> -#(s(x),y)
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) ->
    f#(s(x),y) -> p#(-(y,s(x)))
    f#(x,s(y)) -> f#(p(-(x,s(y))),p(-(s(y),x))) -> f#(s(x),y) -> -#(y,s(x))
    f#(x,s(y)) -> -#(s(y),x) -> -#(s(x),s(y)) -> -#(x,y)
    f#(x,s(y)) -> -#(x,s(y)) -> -#(s(x),s(y)) -> -#(x,y)
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 25/121
    DPs:
     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)))
    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)))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = -3x0 + -3x1 + 0,
      
      [f](x0, x1) = -3x0 + -3x1 + 0,
      
      [p](x0) = -3x0 + 3,
      
      [s](x0) = 4x0 + 4,
      
      [-](x0, x1) = 1x0 + 2x1 + -16,
      
      [0] = 2
     orientation:
      f#(s(x),y) = 1x + -3y + 1 >= x + -4y + 0 = f#(p(-(s(x),y)),p(-(y,s(x))))
      
      f#(x,s(y)) = -3x + 1y + 1 >= -4x + y + 0 = f#(p(-(x,s(y))),p(-(s(y),x)))
      
      -(x,0()) = 1x + 4 >= x = x
      
      -(s(x),s(y)) = 5x + 6y + 6 >= 1x + 2y + -16 = -(x,y)
      
      p(s(x)) = 1x + 3 >= x = x
      
      f(s(x),y) = 1x + -3y + 1 >= x + -4y + 0 = f(p(-(s(x),y)),p(-(y,s(x))))
      
      f(x,s(y)) = -3x + 1y + 1 >= -4x + y + 0 = f(p(-(x,s(y))),p(-(s(y),x)))
     problem:
      DPs:
       
      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)))
     Qed
    
    DPs:
     -#(s(x),s(y)) -> -#(x,y)
    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)))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(-) = 0
      pi(s) = [0]
      pi(p) = 0
      pi(f) = []
      pi(-#) = 0
     weight function:
      w0 = 1
      w(-#) = w(f) = w(p) = w(s) = w(-) = w(0) = 1
     precedence:
      -# ~ f ~ p ~ s ~ - ~ 0
     problem:
      DPs:
       
      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)))
     Qed