YES

Problem:
 cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
 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,z) -> p#(y)
   cond#(true(),x,y,z) -> p#(x)
   cond#(true(),x,y,z) -> gr#(y,z)
   cond#(true(),x,y,z) -> gr#(x,z)
   cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
   cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
   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,z) -> p#(y)
    cond#(true(),x,y,z) -> p#(x)
    cond#(true(),x,y,z) -> gr#(y,z)
    cond#(true(),x,y,z) -> gr#(x,z)
    cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    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
    and(true(),true()) -> true()
    and(x,false()) -> false()
    and(false(),x) -> false()
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     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
     and(true(),true()) -> true()
     and(x,false()) -> false()
     and(false(),x) -> false()
    interpretation:
     [and#](x0, x1) = 1/2,
     
     [gr#](x0, x1) = 1/2x0,
     
     [p#](x0) = 0,
     
     [cond#](x0, x1, x2, x3) = 1/2x0 + x1 + 2x2,
     
     [s](x0) = 2x0 + 2,
     
     [0] = 0,
     
     [false] = 0,
     
     [p](x0) = 1/2x0,
     
     [and](x0, x1) = 2x1,
     
     [gr](x0, x1) = x0,
     
     [true] = 2
    orientation:
     cond#(true(),x,y,z) = x + 2y + 1 >= 0 = p#(y)
     
     cond#(true(),x,y,z) = x + 2y + 1 >= 0 = p#(x)
     
     cond#(true(),x,y,z) = x + 2y + 1 >= 1/2y = gr#(y,z)
     
     cond#(true(),x,y,z) = x + 2y + 1 >= 1/2x = gr#(x,z)
     
     cond#(true(),x,y,z) = x + 2y + 1 >= 1/2 = and#(gr(x,z),gr(y,z))
     
     cond#(true(),x,y,z) = x + 2y + 1 >= 1/2x + 2y = cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
     
     gr#(s(x),s(y)) = x + 1 >= 1/2x = gr#(x,y)
     
     gr(0(),0()) = 0 >= 0 = false()
     
     gr(0(),x) = 0 >= 0 = false()
     
     gr(s(x),0()) = 2x + 2 >= 2 = true()
     
     gr(s(x),s(y)) = 2x + 2 >= x = gr(x,y)
     
     p(0()) = 0 >= 0 = 0()
     
     p(s(x)) = x + 1 >= x = x
     
     and(true(),true()) = 4 >= 2 = true()
     
     and(x,false()) = 0 >= 0 = false()
     
     and(false(),x) = 2x >= 0 = false()
    problem:
     DPs:
      
     TRS:
      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
      and(true(),true()) -> true()
      and(x,false()) -> false()
      and(false(),x) -> false()
    Qed