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) = x0 + -2x1 + 0,
      
      [s](x0) = 7x0 + 12,
      
      [false] = 1,
      
      [0] = 0,
      
      [p](x0) = -6x0 + 1,
      
      [gr](x0, x1) = -8x0 + 2,
      
      [cond](x0, x1, x2) = 2x0 + 3x1 + 0,
      
      [true] = 3
     orientation:
      cond#(true(),x,y) = -2x + 3 >= -8x + 2 = cond#(gr(x,y),p(x),y)
      
      cond(true(),x,y) = 3x + 5 >= -3x + 4 = cond(gr(x,y),p(x),y)
      
      gr(0(),x) = 2 >= 1 = false()
      
      gr(s(x),0()) = -1x + 4 >= 3 = true()
      
      gr(s(x),s(y)) = -1x + 4 >= -8x + 2 = gr(x,y)
      
      p(0()) = 1 >= 0 = 0()
      
      p(s(x)) = 1x + 6 >= 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
    KBO Processor:
     argument filtering:
      pi(true) = []
      pi(cond) = 2
      pi(gr) = 0
      pi(p) = [0]
      pi(0) = []
      pi(false) = []
      pi(s) = [0]
      pi(gr#) = 1
     weight function:
      w0 = 1
      w(gr#) = w(s) = w(false) = w(0) = w(gr) = w(cond) = w(true) = 1
      w(p) = 0
     precedence:
      gr# ~ s ~ p ~ true > 0 > false ~ gr ~ cond
     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