YES

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