YES

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

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