NO

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  a(x1) -> c(b(b(x1)))
  b(a(c(x1))) -> a(c(a(x1)))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    b#(a(c(x1))) -> a#(x1)
    b#(a(c(x1))) -> a#(c(a(x1)))
   TRS:
    a(x1) -> b(x1)
    a(x1) -> c(b(b(x1)))
    b(a(c(x1))) -> a(c(a(x1)))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     b#(a(c(x1))) -> a#(x1)
     b#(a(c(x1))) -> a#(c(a(x1)))
    TRS:
     a(x1) -> b(x1)
     a(x1) -> c(b(b(x1)))
     b(a(c(x1))) -> a(c(a(x1)))
    graph:
     b#(a(c(x1))) -> a#(c(a(x1))) -> a#(x1) -> b#(b(x1))
     b#(a(c(x1))) -> a#(c(a(x1))) -> a#(x1) -> b#(x1)
     b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1))
     b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1)) -> b#(a(c(x1))) -> a#(c(a(x1)))
     a#(x1) -> b#(b(x1)) -> b#(a(c(x1))) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(c(a(x1)))
     a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      a(x1) -> c(b(b(x1)))
      b(a(c(x1))) -> a(c(a(x1)))
     interpretation:
      [b#](x0) = [0 2]x0,
      
      [a#](x0) = [0 2]x0,
      
                [0  0 ]  
      [c](x0) = [-& -&]x0,
      
                  
      [b](x0) = x0,
      
                [0 0]  
      [a](x0) = [0 0]x0
     orientation:
      a#(x1) = [0 2]x1 >= [0 2]x1 = b#(x1)
      
      a#(x1) = [0 2]x1 >= [0 2]x1 = b#(b(x1))
      
      b#(a(c(x1))) = [2 2]x1 >= [0 2]x1 = a#(x1)
      
      b#(a(c(x1))) = [2 2]x1 >= [0 0]x1 = a#(c(a(x1)))
      
              [0 0]                
      a(x1) = [0 0]x1 >= x1 = b(x1)
      
              [0 0]      [0  0 ]                
      a(x1) = [0 0]x1 >= [-& -&]x1 = c(b(b(x1)))
      
                    [0 0]      [0 0]                
      b(a(c(x1))) = [0 0]x1 >= [0 0]x1 = a(c(a(x1)))
     problem:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(x1))
       b#(a(c(x1))) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       a(x1) -> c(b(b(x1)))
       b(a(c(x1))) -> a(c(a(x1)))
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(x1))
       b#(a(c(x1))) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       a(x1) -> c(b(b(x1)))
       b(a(c(x1))) -> a(c(a(x1)))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        a#(x1) -> b#(b(x1))
        b#(a(c(x1))) -> a#(x1)
       TRS:
        a(x1) -> b(x1)
        a(x1) -> c(b(b(x1)))
        b(a(c(x1))) -> a(c(a(x1)))
       graph:
        b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
        b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1))
        a#(x1) -> b#(b(x1)) -> b#(a(c(x1))) -> a#(x1)
        a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(x1)
       Loop Processor:
        loop length: 14
        terms:
         b(b(a(c(b(b(a(c(a(b(b(x1)))))))))))
         b(b(a(c(b(a(c(a(a(b(b(x1)))))))))))
         b(b(a(c(a(c(a(a(a(b(b(x1)))))))))))
         b(b(a(c(a(c(b(a(a(b(b(x1)))))))))))
         b(a(c(a(a(c(b(a(a(b(b(x1)))))))))))
         b(a(c(b(a(c(b(a(a(b(b(x1)))))))))))
         b(a(c(b(a(c(b(a(c(b(b(b(b(x1)))))))))))))
         b(a(c(a(c(a(b(a(c(b(b(b(b(x1)))))))))))))
         b(a(c(a(c(a(a(c(a(b(b(b(b(x1)))))))))))))
         b(a(c(a(c(c(b(b(a(c(a(b(b(b(b(x1)))))))))))))))
         a(c(a(a(c(c(b(b(a(c(a(b(b(b(b(x1)))))))))))))))
         a(c(c(b(b(a(c(c(b(b(a(c(a(b(b(b(b(x1)))))))))))))))))
         a(c(c(b(a(c(a(c(b(b(a(c(a(b(b(b(b(x1)))))))))))))))))
         a(c(c(a(c(a(a(c(b(b(a(c(a(b(b(b(b(x1)))))))))))))))))
        context: a(c(c(a(c(c([]))))))
        substitution:
         x1 -> b(b(x1))
        Qed