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
  Usable Rule 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:
    p(0()) -> 0()
    p(s(x)) -> x
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     p(0()) -> 0()
     p(s(x)) -> x
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
    interpretation:
     [gr#](x0, x1) = x0 + -5,
     
     [p#](x0) = x0 + 5,
     
     [cond#](x0, x1, x2) = x0 + 3x1 + -16,
     
     [s](x0) = 4x0 + 7,
     
     [false] = 0,
     
     [0] = 1,
     
     [p](x0) = -3x0 + 2,
     
     [gr](x0, x1) = x0 + -8,
     
     [true] = 6
    orientation:
     cond#(true(),x,y) = 3x + 6 >= x + 5 = p#(x)
     
     cond#(true(),x,y) = 3x + 6 >= x + -5 = gr#(x,y)
     
     cond#(true(),x,y) = 3x + 6 >= x + 5 = cond#(gr(x,y),p(x),y)
     
     gr#(s(x),s(y)) = 4x + 7 >= x + -5 = gr#(x,y)
     
     p(0()) = 2 >= 1 = 0()
     
     p(s(x)) = 1x + 4 >= x = x
     
     gr(0(),x) = 1 >= 0 = false()
     
     gr(s(x),0()) = 4x + 7 >= 6 = true()
     
     gr(s(x),s(y)) = 4x + 7 >= x + -8 = gr(x,y)
    problem:
     DPs:
      
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      gr(0(),x) -> false()
      gr(s(x),0()) -> true()
      gr(s(x),s(y)) -> gr(x,y)
    Qed