YES

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

Proof:
 String Reversal Processor:
  a(x1) -> c(b(b(x1)))
  b(a(x1)) -> x1
  b(c(a(x1))) -> a(a(a(x1)))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    b#(c(a(x1))) -> a#(a(x1))
    b#(c(a(x1))) -> a#(a(a(x1)))
   TRS:
    a(x1) -> c(b(b(x1)))
    b(a(x1)) -> x1
    b(c(a(x1))) -> a(a(a(x1)))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     b#(c(a(x1))) -> a#(a(x1))
     b#(c(a(x1))) -> a#(a(a(x1)))
    TRS:
     a(x1) -> c(b(b(x1)))
     b(a(x1)) -> x1
     b(c(a(x1))) -> a(a(a(x1)))
    graph:
     b#(c(a(x1))) -> a#(a(a(x1))) -> a#(x1) -> b#(b(x1))
     b#(c(a(x1))) -> a#(a(a(x1))) -> a#(x1) -> b#(x1)
     b#(c(a(x1))) -> a#(a(x1)) -> a#(x1) -> b#(b(x1))
     b#(c(a(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(a(a(x1)))
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(a(x1))
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(a(a(x1)))
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(a(x1))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0) = -4x0 + 0,
      
      [a#](x0) = -4x0 + 1,
      
      [b](x0) = -1x0 + 0,
      
      [c](x0) = 3x0 + 0,
      
      [a](x0) = 1x0 + 3
     orientation:
      a#(x1) = -4x1 + 1 >= -4x1 + 0 = b#(x1)
      
      a#(x1) = -4x1 + 1 >= -5x1 + 0 = b#(b(x1))
      
      b#(c(a(x1))) = x1 + 2 >= -3x1 + 1 = a#(a(x1))
      
      b#(c(a(x1))) = x1 + 2 >= -2x1 + 1 = a#(a(a(x1)))
      
      a(x1) = 1x1 + 3 >= 1x1 + 3 = c(b(b(x1)))
      
      b(a(x1)) = x1 + 2 >= x1 = x1
      
      b(c(a(x1))) = 3x1 + 5 >= 3x1 + 5 = a(a(a(x1)))
     problem:
      DPs:
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> c(b(b(x1)))
       b(a(x1)) -> x1
       b(c(a(x1))) -> a(a(a(x1)))
     EDG Processor:
      DPs:
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> c(b(b(x1)))
       b(a(x1)) -> x1
       b(c(a(x1))) -> a(a(a(x1)))
      graph:
       
      Qed