YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [d](x0) = 7x0,
   
   [b](x0) = x0,
   
   [c](x0) = x0,
   
   [a](x0) = x0
  orientation:
   b(c(a(x1))) = x1 >= x1 = a(b(a(b(c(x1)))))
   
   b(x1) = x1 >= x1 = c(c(x1))
   
   c(d(x1)) = 7x1 >= x1 = a(b(c(a(x1))))
   
   a(a(x1)) = x1 >= x1 = a(c(b(a(x1))))
  problem:
   b(c(a(x1))) -> a(b(a(b(c(x1)))))
   b(x1) -> c(c(x1))
   a(a(x1)) -> a(c(b(a(x1))))
  String Reversal Processor:
   a(c(b(x1))) -> c(b(a(b(a(x1)))))
   b(x1) -> c(c(x1))
   a(a(x1)) -> a(b(c(a(x1))))
   Bounds Processor:
    bound: 4
    enrichment: match
    automaton:
     final states: {4}
     transitions:
      c3(80) -> 81*
      c3(87) -> 88*
      c3(84) -> 85*
      c3(96) -> 97*
      c3(86) -> 87*
      c3(81) -> 82*
      c3(83) -> 84*
      c3(105) -> 106*
      c3(95) -> 96*
      a3(107) -> 108*
      a3(104) -> 105*
      b3(106) -> 107*
      c4(117) -> 118*
      c4(116) -> 117*
      a0(4) -> 4*
      c0(4) -> 4*
      b0(4) -> 4*
      a1(25) -> 26*
      a1(11) -> 12*
      a1(13) -> 14*
      b1(12) -> 13*
      b1(24) -> 25*
      b1(14) -> 15*
      c1(15) -> 16*
      c1(17) -> 18*
      c1(23) -> 24*
      a2(62) -> 63*
      a2(27) -> 28*
      a2(89) -> 90*
      a2(59) -> 60*
      a2(29) -> 30*
      a2(78) -> 79*
      b2(30) -> 31*
      b2(91) -> 92*
      b2(61) -> 62*
      b2(28) -> 29*
      c2(60) -> 61*
      c2(50) -> 51*
      c2(57) -> 58*
      c2(54) -> 55*
      c2(56) -> 57*
      c2(51) -> 52*
      c2(31) -> 32*
      c2(53) -> 54*
      c2(90) -> 91*
      4 -> 17,11
      12 -> 56,23
      13 -> 89*
      14 -> 53,27
      16 -> 12,23,4
      18 -> 15*
      24 -> 50*
      25 -> 59*
      26 -> 12,23,4
      28 -> 83*
      29 -> 104*
      30 -> 86,78
      32 -> 12,4,11,17,23
      52 -> 25*
      55 -> 15*
      58 -> 13*
      61 -> 80*
      63 -> 12,23
      79 -> 28*
      82 -> 62*
      85 -> 29*
      88 -> 31*
      91 -> 95*
      92 -> 27*
      97 -> 92,27
      106 -> 116*
      108 -> 79,28,83
      118 -> 107*
    problem:
     
    Qed