YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [d](x0) = x0,
   
   [a](x0) = x0 + 1,
   
   [b](x0) = x0 + 1,
   
   [c](x0) = x0 + 1
  orientation:
   b(b(d(d(b(b(x1)))))) = x1 + 4 >= x1 + 4 = c(c(d(d(b(b(x1))))))
   
   b(b(a(a(c(c(x1)))))) = x1 + 6 >= x1 + 4 = b(b(c(c(x1))))
   
   a(a(d(d(x1)))) = x1 + 2 >= x1 + 2 = d(d(c(c(x1))))
   
   b(b(b(b(b(b(x1)))))) = x1 + 6 >= x1 + 6 = a(a(b(b(c(c(x1))))))
   
   d(d(c(c(x1)))) = x1 + 2 >= x1 + 2 = b(b(d(d(x1))))
   
   d(d(c(c(x1)))) = x1 + 2 >= x1 + 2 = d(d(b(b(d(d(x1))))))
   
   d(d(a(a(c(c(x1)))))) = x1 + 4 >= x1 + 4 = b(b(b(b(x1))))
  problem:
   b(b(d(d(b(b(x1)))))) -> c(c(d(d(b(b(x1))))))
   a(a(d(d(x1)))) -> d(d(c(c(x1))))
   b(b(b(b(b(b(x1)))))) -> a(a(b(b(c(c(x1))))))
   d(d(c(c(x1)))) -> b(b(d(d(x1))))
   d(d(c(c(x1)))) -> d(d(b(b(d(d(x1))))))
   d(d(a(a(c(c(x1)))))) -> b(b(b(b(x1))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [d](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0],
    
              [1 1 0]  
    [a](x0) = [0 0 1]x0
              [0 1 0]  ,
    
              [1 0 0]  
    [b](x0) = [0 0 0]x0
              [0 0 0]  ,
    
              [1 0 0]  
    [c](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
                           [1 0 0]      [1 0 0]                         
    b(b(d(d(b(b(x1)))))) = [0 0 0]x1 >= [0 0 0]x1 = c(c(d(d(b(b(x1))))))
                           [0 0 0]      [0 0 0]                         
    
                     [1 0 0]     [1]    [1 0 0]     [0]                 
    a(a(d(d(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = d(d(c(c(x1))))
                     [0 0 0]     [0]    [0 0 0]     [0]                 
    
                           [1 0 0]      [1 0 0]                         
    b(b(b(b(b(b(x1)))))) = [0 0 0]x1 >= [0 0 0]x1 = a(a(b(b(c(c(x1))))))
                           [0 0 0]      [0 0 0]                         
    
                     [1 0 0]     [0]    [1 0 0]                   
    d(d(c(c(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(d(d(x1))))
                     [0 0 0]     [0]    [0 0 0]                   
    
                     [1 0 0]     [0]    [1 0 0]     [0]                       
    d(d(c(c(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = d(d(b(b(d(d(x1))))))
                     [0 0 0]     [0]    [0 0 0]     [0]                       
    
                           [1 0 0]     [0]    [1 0 0]                   
    d(d(a(a(c(c(x1)))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(b(b(x1))))
                           [0 0 0]     [0]    [0 0 0]                   
   problem:
    b(b(d(d(b(b(x1)))))) -> c(c(d(d(b(b(x1))))))
    b(b(b(b(b(b(x1)))))) -> a(a(b(b(c(c(x1))))))
    d(d(c(c(x1)))) -> b(b(d(d(x1))))
    d(d(c(c(x1)))) -> d(d(b(b(d(d(x1))))))
    d(d(a(a(c(c(x1)))))) -> b(b(b(b(x1))))
   String Reversal Processor:
    b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1))))))
    b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1))))))
    c(c(d(d(x1)))) -> d(d(b(b(x1))))
    c(c(d(d(x1)))) -> d(d(b(b(d(d(x1))))))
    c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1))))
    Bounds Processor:
     bound: 1
     enrichment: match
     automaton:
      final states: {24,18,14,8,1}
      transitions:
       b0(7) -> 1*
       b0(16) -> 25*
       b0(25) -> 24*
       b0(11) -> 12*
       b0(21) -> 22*
       b0(2) -> 15*
       b0(20) -> 21*
       b0(6) -> 7*
       b0(15) -> 16*
       b0(10) -> 11*
       c0(13) -> 8*
       c0(12) -> 13*
       c0(3) -> 4*
       c0(2) -> 3*
       d0(17) -> 14*
       d0(4) -> 5*
       d0(2) -> 19*
       d0(16) -> 17*
       d0(23) -> 18*
       d0(5) -> 6*
       d0(22) -> 23*
       d0(19) -> 20*
       c1(27) -> 28*
       c1(26) -> 27*
       f40() -> 2*
       a0(2) -> 9*
       a0(9) -> 10*
       d1(29) -> 30*
       d1(28) -> 29*
       b1(30) -> 31*
       b1(31) -> 32*
       24 -> 3,4
       14 -> 3,4
       16 -> 26*
       8 -> 15,16,25,24
       1 -> 15,16,22
       18 -> 3,4
       32 -> 1,16,22,15
     problem:
      
     Qed