YES
We show the termination of the TRS R:

  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


-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: cond#(true(),x) -> cond#(odd(x),p(p(p(x))))
p2: cond#(true(),x) -> odd#(x)
p3: cond#(true(),x) -> p#(p(p(x)))
p4: cond#(true(),x) -> p#(p(x))
p5: cond#(true(),x) -> p#(x)
p6: odd#(s(s(x))) -> odd#(x)

and R consists of:

r1: cond(true(),x) -> cond(odd(x),p(p(p(x))))
r2: odd(|0|()) -> false()
r3: odd(s(|0|())) -> true()
r4: odd(s(s(x))) -> odd(x)
r5: p(|0|()) -> |0|()
r6: p(s(x)) -> x

The estimated dependency graph contains the following SCCs:

  {p1}
  {p6}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: cond#(true(),x) -> cond#(odd(x),p(p(p(x))))

and R consists of:

r1: cond(true(),x) -> cond(odd(x),p(p(p(x))))
r2: odd(|0|()) -> false()
r3: odd(s(|0|())) -> true()
r4: odd(s(s(x))) -> odd(x)
r5: p(|0|()) -> |0|()
r6: p(s(x)) -> x

The set of usable rules consists of

  r1, r2, r3, r4, r5, r6

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        cond#_A(x1,x2) = max{x1 - 16, x2 + 3}
        true_A = 32
        odd_A(x1) = max{15, x1 - 15}
        p_A(x1) = max{2, x1 - 6}
        cond_A(x1,x2) = max{33, x1 - 49, x2 - 6}
        |0|_A = 1
        false_A = 0
        s_A(x1) = max{48, x1 + 7}
  
    base order 2:
  
      precedence:
      
        cond# = cond > p > |0| > true = s > odd > false
      
  
    partial status:
  
      pi(cond#) = [2]
      pi(true) = []
      pi(odd) = []
      pi(p) = []
      pi(cond) = []
      pi(|0|) = []
      pi(false) = []
      pi(s) = [1]

The following rules are removed:

  p1

Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: odd#(s(s(x))) -> odd#(x)

and R consists of:

r1: cond(true(),x) -> cond(odd(x),p(p(p(x))))
r2: odd(|0|()) -> false()
r3: odd(s(|0|())) -> true()
r4: odd(s(s(x))) -> odd(x)
r5: p(|0|()) -> |0|()
r6: p(s(x)) -> x

The set of usable rules consists of

  r2, r3, r6

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        odd#_A(x1) = max{21, x1 + 19}
        s_A(x1) = max{22, x1 + 20}
        odd_A(x1) = max{16, x1 - 23}
        |0|_A = 2
        false_A = 0
        true_A = 1
        p_A(x1) = max{3, x1 - 8}
  
    base order 2:
  
      precedence:
      
        odd# > s = p > odd = |0| > false = true
      
  
    partial status:
  
      pi(odd#) = [1]
      pi(s) = [1]
      pi(odd) = []
      pi(|0|) = []
      pi(false) = []
      pi(true) = []
      pi(p) = []

The following rules are removed:

  p1

Then no dependency pair remains.