YES

Problem:
 cond(true(),x) -> cond(odd(x),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) -> odd#(x)
   cond#(true(),x) -> cond#(odd(x),p(x))
   odd#(s(s(x))) -> odd#(x)
  TRS:
   cond(true(),x) -> cond(odd(x),p(x))
   odd(0()) -> false()
   odd(s(0())) -> true()
   odd(s(s(x))) -> odd(x)
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    cond#(true(),x) -> p#(x)
    cond#(true(),x) -> odd#(x)
    cond#(true(),x) -> cond#(odd(x),p(x))
    odd#(s(s(x))) -> odd#(x)
   TRS:
    cond(true(),x) -> cond(odd(x),p(x))
    odd(0()) -> false()
    odd(s(0())) -> true()
    odd(s(s(x))) -> odd(x)
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    odd#(s(s(x))) -> odd#(x) -> odd#(s(s(x))) -> odd#(x)
    cond#(true(),x) -> odd#(x) -> odd#(s(s(x))) -> odd#(x)
    cond#(true(),x) -> cond#(odd(x),p(x)) ->
    cond#(true(),x) -> cond#(odd(x),p(x))
    cond#(true(),x) -> cond#(odd(x),p(x)) ->
    cond#(true(),x) -> odd#(x)
    cond#(true(),x) -> cond#(odd(x),p(x)) -> cond#(true(),x) -> p#(x)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 5/16
    DPs:
     cond#(true(),x) -> cond#(odd(x),p(x))
    TRS:
     cond(true(),x) -> cond(odd(x),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:
      [cond#](x0, x1) = -2x0 + x1 + 0,
      
      [s](x0) = 2x0 + 4,
      
      [false] = 0,
      
      [0] = 0,
      
      [p](x0) = -1x0 + 1,
      
      [odd](x0) = 1x0,
      
      [cond](x0, x1) = -3x0 + -1x1 + 0,
      
      [true] = 4
     orientation:
      cond#(true(),x) = x + 2 >= -1x + 1 = cond#(odd(x),p(x))
      
      cond(true(),x) = -1x + 1 >= -2x + 0 = cond(odd(x),p(x))
      
      odd(0()) = 1 >= 0 = false()
      
      odd(s(0())) = 5 >= 4 = true()
      
      odd(s(s(x))) = 5x + 7 >= 1x = odd(x)
      
      p(0()) = 1 >= 0 = 0()
      
      p(s(x)) = 1x + 3 >= x = x
     problem:
      DPs:
       
      TRS:
       cond(true(),x) -> cond(odd(x),p(x))
       odd(0()) -> false()
       odd(s(0())) -> true()
       odd(s(s(x))) -> odd(x)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed
    
    DPs:
     odd#(s(s(x))) -> odd#(x)
    TRS:
     cond(true(),x) -> cond(odd(x),p(x))
     odd(0()) -> false()
     odd(s(0())) -> true()
     odd(s(s(x))) -> odd(x)
     p(0()) -> 0()
     p(s(x)) -> x
    KBO Processor:
     argument filtering:
      pi(true) = []
      pi(cond) = []
      pi(odd) = []
      pi(p) = 0
      pi(0) = []
      pi(false) = []
      pi(s) = [0]
      pi(odd#) = 0
     weight function:
      w0 = 1
      w(odd#) = w(false) = w(0) = w(p) = w(odd) = w(cond) = w(true) = 1
      w(s) = 0
     precedence:
      odd# > s ~ 0 ~ odd ~ cond > false ~ p ~ true
     problem:
      DPs:
       
      TRS:
       cond(true(),x) -> cond(odd(x),p(x))
       odd(0()) -> false()
       odd(s(0())) -> true()
       odd(s(s(x))) -> odd(x)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed