YES

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

Proof:
 String Reversal Processor:
  a(b(x1)) -> d(a(a(x1)))
  c(a(x1)) -> b(b(x1))
  b(a(d(x1))) -> c(d(d(b(x1))))
  d(x1) -> a(x1)
  a(c(a(b(x1)))) -> x1
  Bounds Processor:
   bound: 4
   enrichment: match
   automaton:
    final states: {2,3,7,5,1}
    transitions:
     d0(4) -> 1*
     d0(6) -> 8*
     d0(8) -> 9*
     d2(42) -> 43*
     d2(50) -> 51*
     d2(88) -> 89*
     c1(67) -> 68*
     b0(6) -> 5*
     b0(2) -> 6*
     a0(2) -> 3*
     a0(3) -> 4*
     a2(86) -> 87*
     a2(78) -> 79*
     a2(41) -> 42*
     a2(36) -> 37*
     a2(49) -> 50*
     a2(76) -> 77*
     a2(130) -> 131*
     a2(40) -> 41*
     a2(87) -> 88*
     a2(48) -> 49*
     d1(65) -> 66*
     d1(28) -> 29*
     d1(66) -> 67*
     f40() -> 2*
     c0(9) -> 7*
     b1(33) -> 34*
     b1(64) -> 65*
     b1(34) -> 35*
     b1(124) -> 125*
     a1(10) -> 11*
     a1(27) -> 28*
     a1(18) -> 19*
     a1(26) -> 27*
     a1(16) -> 17*
     b2(94) -> 95*
     b2(132) -> 133*
     b2(93) -> 94*
     a4(122) -> 123*
     a4(118) -> 119*
     d3(102) -> 103*
     d3(116) -> 117*
     a3(100) -> 101*
     a3(58) -> 59*
     a3(115) -> 116*
     a3(138) -> 139*
     a3(101) -> 102*
     a3(114) -> 115*
     a3(60) -> 61*
     a3(106) -> 107*
     94 -> 100*
     43 -> 11,8
     19 -> 1*
     131 -> 49*
     132 -> 138*
     68 -> 133,125,94,100,65,34,40
     17 -> 9*
     35 -> 7*
     64 -> 86*
     42 -> 58*
     7 -> 6,10
     77 -> 66*
     93 -> 114*
     16 -> 33*
     66 -> 78*
     28 -> 36*
     4 -> 64,18
     11 -> 8*
     2 -> 101,1,37,28,4,36,27,3,26
     117 -> 101*
     124 -> 130*
     88 -> 106*
     116 -> 122*
     6 -> 10*
     79 -> 67*
     125 -> 34*
     139 -> 101*
     8 -> 16*
     123 -> 117,101
     1 ->
     123,119,59,116,139,102,42,58,118,122,115,79,61,107,131,50,88,49,17,106,87,19,37,28,4,36,27,3
     107 -> 89*
     65 -> 76*
     34 -> 40*
     59 -> 43,11,8
     95 -> 68,65,34,76
     37 -> 29,11,8
     50 -> 60*
     18 -> 132,124
     133 -> 94*
     119 -> 103,77,41
     51 -> 41*
     103 -> 101,77,41,66
     89 -> 77,78
     29 -> 11,16
     102 -> 118*
     61 -> 51,41
     33 -> 48*
     78 -> 93*
   problem:
    
   Qed