YES

Problem:
 cond(true(),x,y) -> cond(gr(x,y),p(x),y)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y)) -> gr(x,y)
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond#(true(),x,y) -> p#(x)
   cond#(true(),x,y) -> gr#(x,y)
   cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond(true(),x,y) -> cond(gr(x,y),p(x),y)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    cond#(true(),x,y) -> p#(x)
    cond#(true(),x,y) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond(true(),x,y) -> cond(gr(x,y),p(x),y)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    gr#(s(x),s(y)) -> gr#(x,y) -> gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> gr#(x,y) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y) ->
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y) ->
    cond#(true(),x,y) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y) -> cond#(true(),x,y) -> p#(x)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 5/16
    DPs:
     cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
    TRS:
     cond(true(),x,y) -> cond(gr(x,y),p(x),y)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [cond#](x0, x1, x2) = 1x0 + -1x1 + 2,
      
      [s](x0) = 10x0 + 9,
      
      [false] = 0,
      
      [0] = 5,
      
      [p](x0) = -6x0 + 5,
      
      [gr](x0, x1) = -5x0 + 0,
      
      [cond](x0, x1, x2) = 2x0 + 1x1 + 4x2 + 8,
      
      [true] = 4
     orientation:
      cond#(true(),x,y) = -1x + 5 >= -4x + 4 = cond#(gr(x,y),p(x),y)
      
      cond(true(),x,y) = 1x + 4y + 8 >= -3x + 4y + 8 = cond(gr(x,y),p(x),y)
      
      gr(0(),x) = 0 >= 0 = false()
      
      gr(s(x),0()) = 5x + 4 >= 4 = true()
      
      gr(s(x),s(y)) = 5x + 4 >= -5x + 0 = gr(x,y)
      
      p(0()) = 5 >= 5 = 0()
      
      p(s(x)) = 4x + 5 >= x = x
     problem:
      DPs:
       
      TRS:
       cond(true(),x,y) -> cond(gr(x,y),p(x),y)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed
    
    DPs:
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond(true(),x,y) -> cond(gr(x,y),p(x),y)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(gr#) = 1
     problem:
      DPs:
       
      TRS:
       cond(true(),x,y) -> cond(gr(x,y),p(x),y)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed