YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b](x0) = x0 + 9,
   
   [d](x0) = x0 + 4,
   
   [a](x0) = x0 + 14,
   
   [c](x0) = x0 + 6
  orientation:
   a(a(x1)) = x1 + 28 >= x1 + 27 = b(b(b(x1)))
   
   b(b(x1)) = x1 + 18 >= x1 + 18 = c(c(c(x1)))
   
   c(c(x1)) = x1 + 12 >= x1 + 12 = d(d(d(x1)))
   
   b(x1) = x1 + 9 >= x1 + 8 = d(d(x1))
   
   c(d(d(x1))) = x1 + 14 >= x1 + 14 = a(x1)
  problem:
   b(b(x1)) -> c(c(c(x1)))
   c(c(x1)) -> d(d(d(x1)))
   c(d(d(x1))) -> a(x1)
  String Reversal Processor:
   b(b(x1)) -> c(c(c(x1)))
   c(c(x1)) -> d(d(d(x1)))
   d(d(c(x1))) -> a(x1)
   Bounds Processor:
    bound: 2
    enrichment: match
    automaton:
     final states: {5}
     transitions:
      d0(5) -> 5*
      a1(22) -> 23*
      a1(52) -> 53*
      a0(5) -> 5*
      d2(45) -> 46*
      d2(24) -> 25*
      d2(40) -> 41*
      d2(41) -> 42*
      d2(26) -> 27*
      d2(44) -> 45*
      d2(46) -> 47*
      d2(42) -> 43*
      d2(25) -> 26*
      c0(5) -> 5*
      b0(5) -> 5*
      d1(16) -> 17*
      d1(15) -> 16*
      d1(34) -> 35*
      d1(14) -> 15*
      a2(68) -> 69*
      a2(80) -> 81*
      a2(74) -> 75*
      c1(12) -> 13*
      c1(10) -> 11*
      c1(11) -> 12*
      27 -> 11*
      43 -> 13,5
      47 -> 12*
      17 -> 11,5
      35 -> 15*
      69 -> 46,16
      12 -> 68,52,34,24
      11 -> 80,40
      53 -> 45,5,14,10,22,15
      75 -> 42*
      13 -> 5*
      5 -> 22,14,10
      10 -> 74,44
      81 -> 16,26
      23 -> 46,45,16,15,5
    problem:
     
    Qed