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
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [gr#](x0, x1) = 1x0 + 0,
    
    [p#](x0) = x0 + 0,
    
    [cond#](x0, x1, x2) = -1x0 + 2x1 + 0,
    
    [s](x0) = 5x0 + 5,
    
    [false] = 0,
    
    [0] = 0,
    
    [p](x0) = -4x0 + 1,
    
    [gr](x0, x1) = 1x0 + 4,
    
    [cond](x0, x1, x2) = x0 + 2x1 + 0,
    
    [true] = 5
   orientation:
    cond#(true(),x,y) = 2x + 4 >= x + 0 = p#(x)
    
    cond#(true(),x,y) = 2x + 4 >= 1x + 0 = gr#(x,y)
    
    cond#(true(),x,y) = 2x + 4 >= x + 3 = cond#(gr(x,y),p(x),y)
    
    gr#(s(x),s(y)) = 6x + 6 >= 1x + 0 = gr#(x,y)
    
    cond(true(),x,y) = 2x + 5 >= 1x + 4 = cond(gr(x,y),p(x),y)
    
    gr(0(),x) = 4 >= 0 = false()
    
    gr(s(x),0()) = 6x + 6 >= 5 = true()
    
    gr(s(x),s(y)) = 6x + 6 >= 1x + 4 = gr(x,y)
    
    p(0()) = 1 >= 0 = 0()
    
    p(s(x)) = 1x + 1 >= 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