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:
 DP Processor:
  DPs:
   b#(c(a(x1))) -> c#(x1)
   b#(c(a(x1))) -> b#(c(x1))
   b#(c(a(x1))) -> a#(b(c(x1)))
   b#(c(a(x1))) -> b#(a(b(c(x1))))
   b#(c(a(x1))) -> a#(b(a(b(c(x1)))))
   b#(x1) -> c#(x1)
   b#(x1) -> c#(c(x1))
   c#(d(x1)) -> a#(x1)
   c#(d(x1)) -> c#(a(x1))
   c#(d(x1)) -> b#(c(a(x1)))
   c#(d(x1)) -> a#(b(c(a(x1))))
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> c#(b(a(x1)))
   a#(a(x1)) -> a#(c(b(a(x1))))
  TRS:
   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))))
  Matrix Interpretation Processor: dim=5
   
   interpretation:
    [a#](x0) = [1 1 1 1 0]x0 + [1],
    
    [c#](x0) = [0 1 0 1 1]x0,
    
    [b#](x0) = [1 1 0 1 1]x0 + [1],
    
              [0 0 0 0 0]     [0]
              [0 1 1 1 1]     [1]
    [d](x0) = [0 0 0 1 0]x0 + [0]
              [1 0 0 1 0]     [1]
              [1 0 0 1 0]     [1],
    
              [0 1 0 0 1]  
              [0 0 0 0 0]  
    [b](x0) = [1 0 0 0 0]x0
              [0 0 0 0 1]  
              [0 0 0 0 0]  ,
    
              [0 0 1 1 0]  
              [0 0 0 0 1]  
    [c](x0) = [0 0 0 0 1]x0
              [0 1 0 0 0]  
              [0 0 0 0 0]  ,
    
              [0 0 0 0 1]     [0]
              [0 1 0 0 1]     [0]
    [a](x0) = [0 0 0 0 0]x0 + [1]
              [0 0 1 1 0]     [0]
              [0 0 0 0 0]     [0]
   orientation:
    b#(c(a(x1))) = [0 1 1 1 1]x1 + [2] >= [0 1 0 1 1]x1 = c#(x1)
    
    b#(c(a(x1))) = [0 1 1 1 1]x1 + [2] >= [0 1 1 1 1]x1 + [1] = b#(c(x1))
    
    b#(c(a(x1))) = [0 1 1 1 1]x1 + [2] >= [0 0 1 1 1]x1 + [1] = a#(b(c(x1)))
    
    b#(c(a(x1))) = [0 1 1 1 1]x1 + [2] >= [0 0 1 1 0]x1 + [1] = b#(a(b(c(x1))))
    
    b#(c(a(x1))) = [0 1 1 1 1]x1 + [2] >= [1] = a#(b(a(b(c(x1)))))
    
    b#(x1) = [1 1 0 1 1]x1 + [1] >= [0 1 0 1 1]x1 = c#(x1)
    
    b#(x1) = [1 1 0 1 1]x1 + [1] >= [0 1 0 0 1]x1 = c#(c(x1))
    
    c#(d(x1)) = [2 1 1 3 1]x1 + [3] >= [1 1 1 1 0]x1 + [1] = a#(x1)
    
    c#(d(x1)) = [2 1 1 3 1]x1 + [3] >= [0 1 1 1 1]x1 = c#(a(x1))
    
    c#(d(x1)) = [2 1 1 3 1]x1 + [3] >= [0 1 1 1 1]x1 + [2] = b#(c(a(x1)))
    
    c#(d(x1)) = [2 1 1 3 1]x1 + [3] >= [0 0 1 1 0]x1 + [2] = a#(b(c(a(x1))))
    
    a#(a(x1)) = [0 1 1 1 2]x1 + [2] >= [0 1 1 1 2]x1 + [1] = b#(a(x1))
    
    a#(a(x1)) = [0 1 1 1 2]x1 + [2] >= [0] = c#(b(a(x1)))
    
    a#(a(x1)) = [0 1 1 1 2]x1 + [2] >= [0 0 0 0 1]x1 + [1] = a#(c(b(a(x1))))
    
                  [0 0 0 0 0]     [0]    [0]                    
                  [0 0 0 0 0]     [0]    [0]                    
    b(c(a(x1))) = [0 0 1 1 0]x1 + [1] >= [1] = a(b(a(b(c(x1)))))
                  [0 0 0 0 0]     [0]    [0]                    
                  [0 0 0 0 0]     [0]    [0]                    
    
            [0 1 0 0 1]      [0 1 0 0 1]             
            [0 0 0 0 0]      [0 0 0 0 0]             
    b(x1) = [1 0 0 0 0]x1 >= [0 0 0 0 0]x1 = c(c(x1))
            [0 0 0 0 1]      [0 0 0 0 1]             
            [0 0 0 0 0]      [0 0 0 0 0]             
    
               [1 0 0 2 0]     [1]    [0 0 0 0 0]     [0]                 
               [1 0 0 1 0]     [1]    [0 0 0 0 0]     [0]                 
    c(d(x1)) = [1 0 0 1 0]x1 + [1] >= [0 0 0 0 0]x1 + [1] = a(b(c(a(x1))))
               [0 1 1 1 1]     [1]    [0 0 1 1 0]     [1]                 
               [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]                 
    
               [0 0 0 0 0]     [0]    [0]                 
               [0 1 0 0 1]     [0]    [0]                 
    a(a(x1)) = [0 0 0 0 0]x1 + [1] >= [1] = a(c(b(a(x1))))
               [0 0 1 1 0]     [1]    [0]                 
               [0 0 0 0 0]     [0]    [0]                 
   problem:
    DPs:
     
    TRS:
     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))))
   Qed