YES

Problem:
 strict:
  f(0()) -> s(0())
  f(s(0())) -> s(0())
  f(s(s(x))) -> f(f(s(x)))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [f](x0) = x0,
   
   [rand](x0) = 1x0,
   
   [0] = 13,
   
   [s](x0) = x0
  orientation:
   f(0()) = 13 >= 13 = s(0())
   
   f(s(0())) = 13 >= 13 = s(0())
   
   f(s(s(x))) = x >= x = f(f(s(x)))
   
   rand(x) = 1x >= x = x
   
   rand(x) = 1x >= 1x = rand(s(x))
  problem:
   strict:
    f(0()) -> s(0())
    f(s(0())) -> s(0())
    f(s(s(x))) -> f(f(s(x)))
   weak:
    rand(x) -> rand(s(x))
  Bounds Processor:
   bound: 1
   enrichment: match-rt
   automaton:
    final states: {5}
    transitions:
     s0(5) -> 5*
     s1(33) -> 34*
     s1(8) -> 9*
     s1(56) -> 57*
     rand0(5) -> 5*
     00() -> 5*
     f0(5) -> 5*
     01() -> 8*
     rand1(34) -> 35*
     f1(28) -> 29*
     f1(27) -> 28*
     35 -> 5*
     34 -> 56*
     5 -> 33*
     9 -> 29,28,27,5
     57 -> 34*
     29 -> 5*
   problem:
    strict:
     f(s(0())) -> s(0())
     f(s(s(x))) -> f(f(s(x)))
    weak:
     rand(x) -> rand(s(x))
   Bounds Processor:
    bound: 2
    enrichment: match-rt
    automaton:
     final states: {5}
     transitions:
      s0(5) -> 5*
      s1(41) -> 42*
      s1(8) -> 9*
      s1(48) -> 49*
      rand0(5) -> 5*
      02() -> 28*
      s2(65) -> 66*
      s2(28) -> 29*
      s2(54) -> 55*
      00() -> 5*
      f0(5) -> 5*
      01() -> 8*
      rand1(42) -> 43*
      f1(20) -> 21*
      f1(21) -> 22*
      rand2(55) -> 56*
      56 -> 43*
      43 -> 5*
      42 -> 54*
      66 -> 55*
      28 -> 48*
      22 -> 5*
      49 -> 20*
      55 -> 65*
      5 -> 41*
      9 -> 20,5
      29 -> 22,21
    problem:
     strict:
      f(s(s(x))) -> f(f(s(x)))
     weak:
      rand(x) -> rand(s(x))
    String Reversal Processor:
     strict:
      s(s(f(x))) -> s(f(f(x)))
     weak:
      rand(x) -> s(rand(x))
     Bounds Processor:
      bound: 1
      enrichment: match-rt
      automaton:
       final states: {3,1,2}
       transitions:
        s0(3) -> 1*
        s0(2) -> 1*
        s0(1) -> 1*
        s1(7) -> 8*
        s1(24) -> 25*
        rand0(1) -> 3*
        rand0(2) -> 3*
        rand0(3) -> 3*
        f0(2) -> 2*
        f0(1) -> 2*
        f0(3) -> 2*
        rand1(23) -> 24*
        rand1(34) -> 35*
        rand1(32) -> 33*
        f1(17) -> 18*
        f1(5) -> 6*
        f1(15) -> 16*
        f1(6) -> 7*
        f1(21) -> 22*
        35 -> 24*
        7 -> 21*
        16 -> 6*
        2 -> 32,5
        22 -> 7*
        8 -> 1*
        1 -> 34,15
        3 -> 23,17
        18 -> 6*
        25 -> 33,35,3
        33 -> 24*
      problem:
       strict:
        
       weak:
        rand(x) -> s(rand(x))
      Qed