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)))
    Usable Rule Processor:
     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:
      -(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) = x1 + 0,
       
       [p](x0) = -7x0 + 0,
       
       [s](x0) = 7x0 + 2,
       
       [-](x0, x1) = x0 + 7,
       
       [0] = 0
      orientation:
       f#(s(x),y) = y + 0 >= -7y + 0 = f#(p(-(s(x),y)),p(-(y,s(x))))
       
       f#(x,s(y)) = 7y + 2 >= y + 0 = f#(p(-(x,s(y))),p(-(s(y),x)))
       
       -(s(x),s(y)) = 7x + 7 >= x + 7 = -(x,y)
       
       -(x,0()) = x + 7 >= x = x
       
       p(s(x)) = x + 0 >= x = x
      problem:
       DPs:
        f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(x))))
       TRS:
        -(s(x),s(y)) -> -(x,y)
        -(x,0()) -> x
        p(s(x)) -> x
      Restore Modifier:
       DPs:
        f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(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:
         f#(s(x),y) -> f#(p(-(s(x),y)),p(-(y,s(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) = -4x0 + -4x1 + 0,
          
          [p](x0) = -4x0 + 4,
          
          [s](x0) = 4x0 + 6,
          
          [-](x0, x1) = x0 + 1x1 + 8,
          
          [0] = 2
         orientation:
          f#(s(x),y) = x + -4y + 2 >= -3x + -7y + 0 = f#(p(-(s(x),y)),p(-(y,s(x))))
          
          -(s(x),s(y)) = 4x + 5y + 8 >= x + 1y + 8 = -(x,y)
          
          -(x,0()) = x + 8 >= x = x
          
          p(s(x)) = x + 4 >= x = x
         problem:
          DPs:
           
          TRS:
           -(s(x),s(y)) -> -(x,y)
           -(x,0()) -> x
           p(s(x)) -> 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)))
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 1
     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