NO

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> b#(x1)
   b#(a(a(c(x1)))) -> a#(x1)
   b#(a(a(c(x1)))) -> a#(a(x1))
   b#(a(a(c(x1)))) -> a#(a(a(x1)))
   b#(a(a(c(x1)))) -> a#(c(c(a(a(a(x1))))))
  TRS:
   a(x1) -> b(x1)
   b(a(a(c(x1)))) -> a(c(c(a(a(a(x1))))))
  TDG Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(a(a(c(x1)))) -> a#(x1)
    b#(a(a(c(x1)))) -> a#(a(x1))
    b#(a(a(c(x1)))) -> a#(a(a(x1)))
    b#(a(a(c(x1)))) -> a#(c(c(a(a(a(x1))))))
   TRS:
    a(x1) -> b(x1)
    b(a(a(c(x1)))) -> a(c(c(a(a(a(x1))))))
   graph:
    b#(a(a(c(x1)))) -> a#(c(c(a(a(a(x1)))))) -> a#(x1) -> b#(x1)
    b#(a(a(c(x1)))) -> a#(a(a(x1))) -> a#(x1) -> b#(x1)
    b#(a(a(c(x1)))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
    b#(a(a(c(x1)))) -> a#(x1) -> a#(x1) -> b#(x1)
    a#(x1) -> b#(x1) -> b#(a(a(c(x1)))) -> a#(c(c(a(a(a(x1))))))
    a#(x1) -> b#(x1) -> b#(a(a(c(x1)))) -> a#(a(a(x1)))
    a#(x1) -> b#(x1) -> b#(a(a(c(x1)))) -> a#(a(x1))
    a#(x1) -> b#(x1) -> b#(a(a(c(x1)))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    usable rules:
     a(x1) -> b(x1)
     b(a(a(c(x1)))) -> a(c(c(a(a(a(x1))))))
    interpretation:
     [b#](x0) = [0  -&]x0,
     
     [a#](x0) = [0  -&]x0 + [0],
     
               [-& -&]     [0]
     [c](x0) = [0  0 ]x0 + [1],
     
               [0 0]  
     [b](x0) = [0 0]x0,
     
               [0 0]     [-&]
     [a](x0) = [0 0]x0 + [1 ]
    orientation:
     a#(x1) = [0  -&]x1 + [0] >= [0  -&]x1 = b#(x1)
     
     b#(a(a(c(x1)))) = [0 0]x1 + [1] >= [0  -&]x1 + [0] = a#(x1)
     
     b#(a(a(c(x1)))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a#(a(x1))
     
     b#(a(a(c(x1)))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a#(a(a(x1)))
     
     b#(a(a(c(x1)))) = [0 0]x1 + [1] >= [0] = a#(c(c(a(a(a(x1))))))
     
             [0 0]     [-&]    [0 0]          
     a(x1) = [0 0]x1 + [1 ] >= [0 0]x1 = b(x1)
     
                      [0 0]     [1]    [0 0]     [1]                       
     b(a(a(c(x1)))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(c(c(a(a(a(x1))))))
    problem:
     DPs:
      a#(x1) -> b#(x1)
      b#(a(a(c(x1)))) -> a#(x1)
      b#(a(a(c(x1)))) -> a#(a(x1))
      b#(a(a(c(x1)))) -> a#(a(a(x1)))
     TRS:
      a(x1) -> b(x1)
      b(a(a(c(x1)))) -> a(c(c(a(a(a(x1))))))
    Restore Modifier:
     DPs:
      a#(x1) -> b#(x1)
      b#(a(a(c(x1)))) -> a#(x1)
      b#(a(a(c(x1)))) -> a#(a(x1))
      b#(a(a(c(x1)))) -> a#(a(a(x1)))
     TRS:
      a(x1) -> b(x1)
      b(a(a(c(x1)))) -> a(c(c(a(a(a(x1))))))
     EDG Processor:
      DPs:
       a#(x1) -> b#(x1)
       b#(a(a(c(x1)))) -> a#(x1)
       b#(a(a(c(x1)))) -> a#(a(x1))
       b#(a(a(c(x1)))) -> a#(a(a(x1)))
      TRS:
       a(x1) -> b(x1)
       b(a(a(c(x1)))) -> a(c(c(a(a(a(x1))))))
      graph:
       b#(a(a(c(x1)))) -> a#(a(a(x1))) -> a#(x1) -> b#(x1)
       b#(a(a(c(x1)))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
       b#(a(a(c(x1)))) -> a#(x1) -> a#(x1) -> b#(x1)
       a#(x1) -> b#(x1) -> b#(a(a(c(x1)))) -> a#(x1)
       a#(x1) -> b#(x1) -> b#(a(a(c(x1)))) -> a#(a(x1))
       a#(x1) -> b#(x1) -> b#(a(a(c(x1)))) -> a#(a(a(x1)))
      Loop Processor:
       loop length: 19
       terms:
        b(a(a(a(b(a(b(a(a(c(b(x1)))))))))))
        b(a(b(a(b(a(b(a(a(c(b(x1)))))))))))
        b(a(b(a(b(a(a(c(c(a(a(a(b(x1)))))))))))))
        b(a(b(a(b(a(a(c(c(b(a(a(b(x1)))))))))))))
        b(a(b(a(b(a(a(c(c(b(a(b(b(x1)))))))))))))
        b(a(b(a(b(a(a(c(c(b(b(b(b(x1)))))))))))))
        b(a(b(a(a(c(c(a(a(a(c(b(b(b(b(x1)))))))))))))))
        b(a(a(c(c(a(a(a(c(a(a(a(c(b(b(b(b(x1)))))))))))))))))
        a(c(c(a(a(a(c(a(a(a(c(a(a(a(c(b(b(b(b(x1)))))))))))))))))))
        a(c(c(a(a(a(c(b(a(a(c(a(a(a(c(b(b(b(b(x1)))))))))))))))))))
        a(c(c(b(a(a(c(b(a(a(c(a(a(a(c(b(b(b(b(x1)))))))))))))))))))
        a(c(c(b(a(a(c(a(c(c(a(a(a(a(a(a(c(b(b(b(b(x1)))))))))))))))))))))
        a(c(c(b(a(a(c(a(c(c(a(b(a(a(a(a(c(b(b(b(b(x1)))))))))))))))))))))
        a(c(c(b(a(a(c(a(c(c(a(b(a(b(a(a(c(b(b(b(b(x1)))))))))))))))))))))
        a(c(c(a(c(c(a(a(a(a(c(c(a(b(a(b(a(a(c(b(b(b(b(x1)))))))))))))))))))))))
        a(c(c(a(c(c(a(b(a(a(c(c(a(b(a(b(a(a(c(b(b(b(b(x1)))))))))))))))))))))))
        a(c(c(a(c(c(a(a(c(c(a(a(a(c(a(b(a(b(a(a(c(b(b(b(b(x1)))))))))))))))))))))))))
        a(c(c(a(c(c(a(a(c(c(b(a(a(c(a(b(a(b(a(a(c(b(b(b(b(x1)))))))))))))))))))))))))
        a(c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(a(b(a(b(a(a(c(b(b(b(b(x1)))))))))))))))))))))))))))
       context: a(c(c(a(c(c(a(a(c(c(a(c(c([])))))))))))))
       substitution:
        x1 -> b(b(b(x1)))
       Qed