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