YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1)))
   a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1))))))
   a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1)))))))))
   a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(b(c(a(b(c(a(b(c(x1))))))))))
   a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(b(c(a(b(c(a(b(c(x1)))))))))))
   a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(a(b(c(a(b(c(a(b(c(x1))))))))))))
  TRS:
   a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1))))))))))))
  Matrix Interpretation Processor: dim=4
   
   interpretation:
    [a#](x0) = [1 0 0 0]x0,
    
              [0 0 0 1]  
              [0 1 0 0]  
    [b](x0) = [1 0 0 0]x0
              [0 0 0 0]  ,
    
              [0 1 0 0]  
              [1 0 0 0]  
    [c](x0) = [0 0 0 0]x0
              [0 1 0 0]  ,
    
              [0 0 1 0]     [0]
              [1 0 0 1]     [0]
    [a](x0) = [0 1 0 0]x0 + [0]
              [0 0 0 0]     [1]
   orientation:
    a#(b(c(a(b(c(a(a(a(x1))))))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(b(c(x1)))
    
    a#(b(c(a(b(c(a(a(a(x1))))))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(b(c(a(b(c(x1))))))
    
    a#(b(c(a(b(c(a(a(a(x1))))))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(b(c(a(b(c(a(b(c(x1)))))))))
    
    a#(b(c(a(b(c(a(a(a(x1))))))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(a(b(c(a(b(c(a(b(c(x1))))))))))
    
    a#(b(c(a(b(c(a(a(a(x1))))))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(a(a(b(c(a(b(c(a(b(c(x1)))))))))))
    
    a#(b(c(a(b(c(a(a(a(x1))))))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(a(a(a(b(c(a(b(c(a(b(c(x1))))))))))))
    
                                    [0 1 0 0]     [1]    [0 1 0 0]     [1]                                         
                                    [0 1 0 0]     [1]    [0 1 0 0]     [1]                                         
    a(b(c(a(b(c(a(a(a(x1))))))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 + [1] = a(a(a(a(b(c(a(b(c(a(b(c(x1))))))))))))
                                    [0 0 0 0]     [1]    [0 0 0 0]     [1]                                         
   problem:
    DPs:
     
    TRS:
     a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1))))))))))))
   Qed