YES

TRS:

  -(x,0()) -> x
  -(s(x),s(y)) -> -(x,y)
  *(x,0()) -> 0()
  *(x,s(y)) -> +(*(x,y),x)
  if(true(),x,y) -> x
  if(false(),x,y) -> y
  odd(0()) -> false()
  odd(s(0())) -> true()
  odd(s(s(x))) -> odd(x)
  half(0()) -> 0()
  half(s(0())) -> 0()
  half(s(s(x))) -> s(half(x))
  if(true(),x,y) -> true()
  if(false(),x,y) -> false()
  pow(x,y) -> f(x,y,s(0()))
  f(x,0(),z) -> z
  f(x,s(y),z) -> if(odd(s(y)),f(x,y,*(x,z)),f(*(x,x),half(s(y)),z))

max/plus interpretations on N:

  -_A(x1,x2) = max{0, x1, 0}
  -#_A(x1,x2) = max{0, -1, 1}
  0_A = 0
  0#_A = 13
  s_A(x1) = max{9, 12 + x1}
  s#_A(x1) = max{1, -2 + x1}
  *_A(x1,x2) = max{3, 2, 2}
  *#_A(x1,x2) = max{1, -1, 1}
  +_A(x1,x2) = max{3, 3, 3}
  +#_A(x1,x2) = max{1, 0, -2}
  if_A(x1,x2,x3) = max{3, 4, x2, x3}
  if#_A(x1,x2,x3) = max{11, 1, -1, -1}
  true_A = 4
  true#_A = 0
  false_A = 4
  false#_A = 12
  odd_A(x1) = max{4, 3}
  odd#_A(x1) = max{6, -1}
  half_A(x1) = max{1, -10 + x1}
  half#_A(x1) = max{1, -11}
  pow_A(x1,x2) = max{13, 4, 4}
  pow#_A(x1,x2) = max{14, -3, 3 + x2}
  f_A(x1,x2,x3) = max{2, 4, 4, 1 + x3}
  f#_A(x1,x2,x3) = max{5, 2, 1 + x2, 4}

precedence:

  pow > f > * > - = 0 = + > s = false = half > if = odd > true