YES

Problem:
 cond(true(),x) -> cond(odd(x),p(p(p(x))))
 odd(0()) -> false()
 odd(s(0())) -> true()
 odd(s(s(x))) -> odd(x)
 p(0()) -> 0()
 p(s(x)) -> x

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