YES

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

Proof:
 String Reversal Processor:
  b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
  a(c(b(x1))) -> x1
  DP Processor:
   DPs:
    b#(a(a(x1))) -> b#(x1)
    b#(a(a(x1))) -> b#(b(x1))
    b#(a(a(x1))) -> a#(c(b(b(x1))))
    b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
    b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
   TRS:
    b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
    a(c(b(x1))) -> x1
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> b#(b(x1))
     b#(a(a(x1))) -> a#(c(b(b(x1))))
     b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
     b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
    TRS:
     b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
     a(c(b(x1))) -> x1
    graph:
     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(c(b(b(x1))))
     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1))
     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(c(b(b(x1))))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 10/25
     DPs:
      b#(a(a(x1))) -> b#(b(x1))
      b#(a(a(x1))) -> b#(x1)
     TRS:
      b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
      a(c(b(x1))) -> x1
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = x0 + 0,
       
       [c](x0) = -3x0 + 1,
       
       [a](x0) = 1x0 + 1,
       
       [b](x0) = 2x0 + 2
      orientation:
       b#(a(a(x1))) = 2x1 + 2 >= 2x1 + 2 = b#(b(x1))
       
       b#(a(a(x1))) = 2x1 + 2 >= x1 + 0 = b#(x1)
       
       b(a(a(x1))) = 4x1 + 4 >= 4x1 + 4 = a(a(a(c(b(b(x1))))))
       
       a(c(b(x1))) = x1 + 2 >= x1 = x1
      problem:
       DPs:
        b#(a(a(x1))) -> b#(b(x1))
       TRS:
        b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
        a(c(b(x1))) -> x1
      EDG Processor:
       DPs:
        b#(a(a(x1))) -> b#(b(x1))
       TRS:
        b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
        a(c(b(x1))) -> x1
       graph:
        b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1))
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [b#](x0) = -2x0 + 0,
         
         [c](x0) = -2x0 + 4,
         
         [a](x0) = 1x0 + 8,
         
         [b](x0) = 1x0
        orientation:
         b#(a(a(x1))) = x1 + 7 >= -1x1 + 0 = b#(b(x1))
         
         b(a(a(x1))) = 3x1 + 10 >= 3x1 + 10 = a(a(a(c(b(b(x1))))))
         
         a(c(b(x1))) = x1 + 8 >= x1 = x1
        problem:
         DPs:
          
         TRS:
          b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
          a(c(b(x1))) -> x1
        Qed