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