YES

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

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