YES

Problem:
 a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
 a(c(b(x1))) -> a(a(b(c(b(a(x1))))))

Proof:
 String Reversal Processor:
  a(a(b(a(x1)))) -> a(b(a(b(c(x1)))))
  b(c(a(x1))) -> a(b(c(b(a(a(x1))))))
  Bounds Processor:
   bound: 4
   enrichment: match
   automaton:
    final states: {3,2,1}
    transitions:
     b3(107) -> 108*
     b3(109) -> 110*
     b3(121) -> 122*
     b3(123) -> 124*
     c3(108) -> 109*
     c3(120) -> 121*
     a4(131) -> 132*
     a4(135) -> 136*
     a4(130) -> 131*
     b4(132) -> 133*
     b4(134) -> 135*
     a0(2) -> 1*
     a0(1) -> 1*
     a0(3) -> 1*
     c4(133) -> 134*
     b0(2) -> 2*
     b0(1) -> 2*
     b0(3) -> 2*
     c0(2) -> 3*
     c0(1) -> 3*
     c0(3) -> 3*
     a1(42) -> 43*
     a1(32) -> 33*
     a1(7) -> 8*
     a1(9) -> 10*
     a1(36) -> 37*
     a1(31) -> 32*
     a1(38) -> 39*
     b1(35) -> 36*
     b1(6) -> 7*
     b1(73) -> 74*
     b1(33) -> 34*
     b1(8) -> 9*
     c1(50) -> 51*
     c1(5) -> 6*
     c1(52) -> 53*
     c1(22) -> 23*
     c1(34) -> 35*
     c1(24) -> 25*
     c1(90) -> 91*
     a2(75) -> 76*
     a2(96) -> 97*
     a2(86) -> 87*
     a2(76) -> 77*
     a2(46) -> 47*
     a2(48) -> 49*
     a2(80) -> 81*
     b2(45) -> 46*
     b2(77) -> 78*
     b2(47) -> 48*
     b2(79) -> 80*
     c2(44) -> 45*
     c2(88) -> 89*
     c2(78) -> 79*
     a3(122) -> 123*
     a3(124) -> 125*
     a3(106) -> 107*
     a3(128) -> 129*
     a3(110) -> 111*
     a3(105) -> 106*
     1 -> 38,22
     2 -> 31,5
     3 -> 42,24
     7 -> 44*
     9 -> 86,52
     10 -> 33,39,1
     23 -> 6*
     25 -> 6*
     32 -> 73*
     36 -> 75,50
     37 -> 7,2
     39 -> 32*
     43 -> 32*
     46 -> 120,88
     48 -> 90*
     49 -> 96,77,33,1,39
     51 -> 45*
     53 -> 45*
     74 -> 34*
     80 -> 105*
     81 -> 46,7
     87 -> 76*
     89 -> 45*
     91 -> 6*
     97 -> 77*
     110 -> 130*
     111 -> 122,128,46
     125 -> 97,77
     129 -> 107*
     136 -> 122*
   problem:
    
   Qed