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
     usable rules:
      a(x1) -> c(b(b(x1)))
      b(a(x1)) -> x1
      b(c(a(x1))) -> a(a(a(x1)))
     interpretation:
      [b#](x0) = 2x0 + 8,
      
      [c](x0) = 3x0 + 0,
      
      [a#](x0) = 4x0 + 8,
      
      [a](x0) = 1x0 + 11,
      
      [b](x0) = -1x0 + 6
     orientation:
      a#(x1) = 4x1 + 8 >= 2x1 + 8 = b#(x1)
      
      a#(x1) = 4x1 + 8 >= 1x1 + 8 = b#(b(x1))
      
      b#(c(a(x1))) = 6x1 + 16 >= 5x1 + 15 = a#(a(x1))
      
      b#(c(a(x1))) = 6x1 + 16 >= 6x1 + 16 = a#(a(a(x1)))
      
      a(x1) = 1x1 + 11 >= 1x1 + 9 = c(b(b(x1)))
      
      b(a(x1)) = x1 + 10 >= x1 = x1
      
      b(c(a(x1))) = 3x1 + 13 >= 3x1 + 13 = a(a(a(x1)))
     problem:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(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)))
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(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)))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        a#(x1) -> b#(b(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#(x1)
        b#(c(a(x1))) -> a#(a(a(x1))) -> a#(x1) -> b#(b(x1))
        a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(a(a(x1)))
        a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(a(a(x1)))
       Arctic Interpretation Processor:
        dimension: 1
        usable rules:
         a(x1) -> c(b(b(x1)))
         b(a(x1)) -> x1
         b(c(a(x1))) -> a(a(a(x1)))
        interpretation:
         [b#](x0) = x0 + 0,
         
         [c](x0) = 6x0 + 8,
         
         [a#](x0) = x0 + 12,
         
         [a](x0) = 2x0 + 8,
         
         [b](x0) = -2x0 + 0
        orientation:
         a#(x1) = x1 + 12 >= x1 + 0 = b#(x1)
         
         a#(x1) = x1 + 12 >= -2x1 + 0 = b#(b(x1))
         
         b#(c(a(x1))) = 8x1 + 14 >= 4x1 + 12 = a#(a(a(x1)))
         
         a(x1) = 2x1 + 8 >= 2x1 + 8 = c(b(b(x1)))
         
         b(a(x1)) = x1 + 6 >= x1 = x1
         
         b(c(a(x1))) = 6x1 + 12 >= 6x1 + 12 = 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)))
        Restore Modifier:
         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:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1