YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b](x0) = x0 + 3,
   
   [d](x0) = x0 + 4,
   
   [a](x0) = x0 + 2,
   
   [c](x0) = x0 + 8
  orientation:
   a(a(a(x1))) = x1 + 6 >= x1 + 6 = b(b(x1))
   
   b(b(b(x1))) = x1 + 9 >= x1 + 8 = c(x1)
   
   c(x1) = x1 + 8 >= x1 + 8 = d(d(x1))
   
   d(x1) = x1 + 4 >= x1 + 4 = a(a(x1))
  problem:
   a(a(a(x1))) -> b(b(x1))
   c(x1) -> d(d(x1))
   d(x1) -> a(a(x1))
  Bounds Processor:
   bound: 3
   enrichment: match
   automaton:
    final states: {5}
    transitions:
     c0(5) -> 5*
     a1(20) -> 21*
     a1(19) -> 20*
     d0(5) -> 5*
     b3(112) -> 113*
     b3(78) -> 79*
     b3(111) -> 112*
     b3(71) -> 72*
     b3(91) -> 92*
     b3(79) -> 80*
     b3(72) -> 73*
     b3(90) -> 91*
     b2(23) -> 24*
     b2(45) -> 46*
     b2(95) -> 96*
     b2(22) -> 23*
     b2(93) -> 94*
     b2(44) -> 45*
     b0(5) -> 5*
     a0(5) -> 5*
     d1(13) -> 14*
     d1(12) -> 13*
     a2(67) -> 68*
     a2(66) -> 67*
     a2(60) -> 61*
     a2(59) -> 60*
     b1(103) -> 104*
     b1(85) -> 86*
     b1(10) -> 11*
     b1(9) -> 10*
     b1(86) -> 87*
     b1(37) -> 38*
     b1(30) -> 31*
     b1(31) -> 32*
     94 -> 45*
     19 -> 37,22
     24 -> 67,20
     92 -> 61,14
     68 -> 13*
     46 -> 68,13,59,21,5,12,9,19
     113 -> 60*
     104 -> 10*
     12 -> 66*
     14 -> 5*
     66 -> 111*
     11 -> 68,13,67,59,21,20,5
     67 -> 90*
     21 -> 5*
     38 -> 10*
     73 -> 68,13,59
     60 -> 93,85,71
     13 -> 59*
     20 -> 44,30
     59 -> 103,95,78
     5 -> 19,12,9
     96 -> 23*
     80 -> 67*
     87 -> 20,30,5,44,67
     32 -> 67,5,12,9,19,20
     61 -> 14,5
   problem:
    
   Qed