YES

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

Proof:
 DP Processor:
  DPs:
   c#(a(a(b(c(a(x1)))))) -> c#(x1)
   c#(a(a(b(c(a(x1)))))) -> c#(a(a(b(c(x1)))))
   c#(a(a(b(c(a(x1)))))) -> c#(c(a(a(b(c(x1))))))
  TRS:
   c(a(a(b(c(a(x1)))))) -> a(a(b(c(c(a(a(b(c(x1)))))))))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [c#](x0) = x0 + 0,
    
    [b](x0) = -16x0 + 1,
    
    [c](x0) = x0 + 6,
    
    [a](x0) = 8x0 + 0
   orientation:
    c#(a(a(b(c(a(x1)))))) = 8x1 + 17 >= x1 + 0 = c#(x1)
    
    c#(a(a(b(c(a(x1)))))) = 8x1 + 17 >= x1 + 17 = c#(a(a(b(c(x1)))))
    
    c#(a(a(b(c(a(x1)))))) = 8x1 + 17 >= x1 + 17 = c#(c(a(a(b(c(x1))))))
    
    c(a(a(b(c(a(x1)))))) = 8x1 + 17 >= x1 + 17 = a(a(b(c(c(a(a(b(c(x1)))))))))
   problem:
    DPs:
     c#(a(a(b(c(a(x1)))))) -> c#(a(a(b(c(x1)))))
     c#(a(a(b(c(a(x1)))))) -> c#(c(a(a(b(c(x1))))))
    TRS:
     c(a(a(b(c(a(x1)))))) -> a(a(b(c(c(a(a(b(c(x1)))))))))
   Matrix Interpretation Processor: dim=4
    
    interpretation:
     [c#](x0) = [0 0 1 0]x0,
     
               [0 0 0 0]  
               [0 1 0 0]  
     [b](x0) = [1 0 0 1]x0
               [0 0 0 0]  ,
     
               [1 0 0 0]  
               [0 0 1 0]  
     [c](x0) = [0 0 1 0]x0
               [0 1 0 0]  ,
     
               [0 1 0 0]     [1]
               [1 0 0 0]     [0]
     [a](x0) = [0 0 1 0]x0 + [0]
               [0 0 0 0]     [0]
    orientation:
     c#(a(a(b(c(a(x1)))))) = [1 1 0 0]x1 + [1] >= [1 1 0 0]x1 = c#(a(a(b(c(x1)))))
     
     c#(a(a(b(c(a(x1)))))) = [1 1 0 0]x1 + [1] >= [1 1 0 0]x1 = c#(c(a(a(b(c(x1))))))
     
                            [0 0 0 0]     [1]    [0 0 0 0]     [1]                                
                            [1 1 0 0]     [1]    [1 1 0 0]     [1]                                
     c(a(a(b(c(a(x1)))))) = [1 1 0 0]x1 + [1] >= [1 1 0 0]x1 + [1] = a(a(b(c(c(a(a(b(c(x1)))))))))
                            [0 0 1 0]     [1]    [0 0 0 0]     [0]                                
    problem:
     DPs:
      
     TRS:
      c(a(a(b(c(a(x1)))))) -> a(a(b(c(c(a(a(b(c(x1)))))))))
    Qed