YES

Problem:
 strict:
  o(l(x1)) -> r(x1)
  n(l(o(x1))) -> r(o(x1))
  L(l(o(x1))) -> L(r(o(x1)))
  r(o(x1)) -> l(x1)
  o(r(n(x1))) -> o(l(x1))
  o(r(R(x1))) -> o(l(R(x1)))
 weak:
  L(x1) -> L(n(x1))
  R(x1) -> n(R(x1))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [L](x0) = 4x0,
   
   [o](x0) = 1x0,
   
   [n](x0) = x0,
   
   [R](x0) = x0,
   
   [l](x0) = x0,
   
   [r](x0) = x0
  orientation:
   o(l(x1)) = 1x1 >= x1 = r(x1)
   
   n(l(o(x1))) = 1x1 >= 1x1 = r(o(x1))
   
   L(l(o(x1))) = 5x1 >= 5x1 = L(r(o(x1)))
   
   r(o(x1)) = 1x1 >= x1 = l(x1)
   
   o(r(n(x1))) = 1x1 >= 1x1 = o(l(x1))
   
   o(r(R(x1))) = 1x1 >= 1x1 = o(l(R(x1)))
   
   L(x1) = 4x1 >= 4x1 = L(n(x1))
   
   R(x1) = x1 >= x1 = n(R(x1))
  problem:
   strict:
    n(l(o(x1))) -> r(o(x1))
    L(l(o(x1))) -> L(r(o(x1)))
    o(r(n(x1))) -> o(l(x1))
    o(r(R(x1))) -> o(l(R(x1)))
   weak:
    L(x1) -> L(n(x1))
    R(x1) -> n(R(x1))
  String Reversal Processor:
   strict:
    o(l(n(x1))) -> o(r(x1))
    o(l(L(x1))) -> o(r(L(x1)))
    n(r(o(x1))) -> l(o(x1))
    R(r(o(x1))) -> R(l(o(x1)))
   weak:
    L(x1) -> n(L(x1))
    R(x1) -> R(n(x1))
   Bounds Processor:
    bound: 1
    enrichment: match-rt
    automaton:
     final states: {7}
     transitions:
      o0(7) -> 7*
      L1(80) -> 81*
      R1(54) -> 55*
      n0(7) -> 7*
      l0(7) -> 7*
      r1(11) -> 12*
      r1(87) -> 88*
      o1(12) -> 13*
      o1(138) -> 139*
      r0(7) -> 7*
      R0(7) -> 7*
      L0(7) -> 7*
      n1(110) -> 111*
      n1(81) -> 82*
      n1(161) -> 162*
      l1(48) -> 49*
      162 -> 54*
      7 -> 138,110,80,11
      82 -> 81,7
      54 -> 161*
      88 -> 12*
      139 -> 48*
      13 -> 139,48,7
      49 -> 111,54,7
      55 -> 7*
      81 -> 87*
      111 -> 54*
    problem:
     strict:
      o(l(L(x1))) -> o(r(L(x1)))
      n(r(o(x1))) -> l(o(x1))
      R(r(o(x1))) -> R(l(o(x1)))
     weak:
      L(x1) -> n(L(x1))
      R(x1) -> R(n(x1))
    Bounds Processor:
     bound: 1
     enrichment: match-rt
     automaton:
      final states: {7}
      transitions:
       o0(7) -> 7*
       L1(35) -> 36*
       R1(61) -> 62*
       n0(7) -> 7*
       l0(7) -> 7*
       r1(36) -> 37*
       o1(19) -> 20*
       r0(7) -> 7*
       R0(7) -> 7*
       L0(7) -> 7*
       n1(60) -> 61*
       n1(50) -> 51*
       n1(90) -> 91*
       l1(20) -> 21*
       7 -> 60,35,19
       21 -> 61,7
       36 -> 50*
       91 -> 61*
       62 -> 7*
       37 -> 19*
       51 -> 36,7
       61 -> 90*
     problem:
      strict:
       o(l(L(x1))) -> o(r(L(x1)))
       R(r(o(x1))) -> R(l(o(x1)))
      weak:
       L(x1) -> n(L(x1))
       R(x1) -> R(n(x1))
     String Reversal Processor:
      strict:
       L(l(o(x1))) -> L(r(o(x1)))
       o(r(R(x1))) -> o(l(R(x1)))
      weak:
       L(x1) -> L(n(x1))
       R(x1) -> n(R(x1))
      Bounds Processor:
       bound: 1
       enrichment: match-rt
       automaton:
        final states: {7}
        transitions:
         o0(7) -> 7*
         L1(25) -> 26*
         R1(20) -> 21*
         n0(7) -> 7*
         l0(7) -> 7*
         r1(24) -> 25*
         o1(22) -> 23*
         r0(7) -> 7*
         R0(7) -> 7*
         L0(7) -> 7*
         n1(42) -> 43*
         n1(56) -> 57*
         n1(40) -> 41*
         l1(21) -> 22*
         43 -> 21,7
         7 -> 40,20
         21 -> 42*
         26 -> 7*
         57 -> 25*
         41 -> 25*
         25 -> 56*
         23 -> 24,7
       problem:
        strict:
         L(l(o(x1))) -> L(r(o(x1)))
        weak:
         L(x1) -> L(n(x1))
         R(x1) -> n(R(x1))
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [L](x0) = x0,
         
         [o](x0) = 1x0,
         
         [n](x0) = x0,
         
         [R](x0) = x0,
         
         [l](x0) = 15x0,
         
         [r](x0) = x0
        orientation:
         L(l(o(x1))) = 16x1 >= 1x1 = L(r(o(x1)))
         
         L(x1) = x1 >= x1 = L(n(x1))
         
         R(x1) = x1 >= x1 = n(R(x1))
        problem:
         strict:
          
         weak:
          L(x1) -> L(n(x1))
          R(x1) -> n(R(x1))
        Qed