YES

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

Proof:
 String Reversal Processor:
  b(a(a(x1))) -> c(x1)
  c(a(x1)) -> a(a(c(b(x1))))
  c(b(x1)) -> x1
  DP Processor:
   DPs:
    b#(a(a(x1))) -> c#(x1)
    c#(a(x1)) -> b#(x1)
    c#(a(x1)) -> c#(b(x1))
   TRS:
    b(a(a(x1))) -> c(x1)
    c(a(x1)) -> a(a(c(b(x1))))
    c(b(x1)) -> x1
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> c#(x1)
     c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> c#(b(x1))
    TRS:
     b(a(a(x1))) -> c(x1)
     c(a(x1)) -> a(a(c(b(x1))))
     c(b(x1)) -> x1
    graph:
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(b(x1))
     b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      b(a(a(x1))) -> c(x1)
      c(a(x1)) -> a(a(c(b(x1))))
      c(b(x1)) -> x1
     interpretation:
      [c#](x0) = -4x0 + 2,
      
      [a](x0) = 1x0 + 5,
      
      [b#](x0) = -4x0 + 0,
      
      [b](x0) = -1x0 + 3,
      
      [c](x0) = 1x0 + 0
     orientation:
      b#(a(a(x1))) = -2x1 + 2 >= -4x1 + 2 = c#(x1)
      
      c#(a(x1)) = -3x1 + 2 >= -4x1 + 0 = b#(x1)
      
      c#(a(x1)) = -3x1 + 2 >= -5x1 + 2 = c#(b(x1))
      
      b(a(a(x1))) = 1x1 + 5 >= 1x1 + 0 = c(x1)
      
      c(a(x1)) = 2x1 + 6 >= 2x1 + 6 = a(a(c(b(x1))))
      
      c(b(x1)) = x1 + 4 >= x1 = x1
     problem:
      DPs:
       b#(a(a(x1))) -> c#(x1)
       c#(a(x1)) -> c#(b(x1))
      TRS:
       b(a(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(c(b(x1))))
       c(b(x1)) -> x1
     Restore Modifier:
      DPs:
       b#(a(a(x1))) -> c#(x1)
       c#(a(x1)) -> c#(b(x1))
      TRS:
       b(a(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(c(b(x1))))
       c(b(x1)) -> x1
      EDG Processor:
       DPs:
        b#(a(a(x1))) -> c#(x1)
        c#(a(x1)) -> c#(b(x1))
       TRS:
        b(a(a(x1))) -> c(x1)
        c(a(x1)) -> a(a(c(b(x1))))
        c(b(x1)) -> x1
       graph:
        c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
        b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(b(x1))
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 2/4
        DPs:
         c#(a(x1)) -> c#(b(x1))
        TRS:
         b(a(a(x1))) -> c(x1)
         c(a(x1)) -> a(a(c(b(x1))))
         c(b(x1)) -> x1
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          b(a(a(x1))) -> c(x1)
          c(a(x1)) -> a(a(c(b(x1))))
          c(b(x1)) -> x1
         interpretation:
          [c#](x0) = x0 + 0,
          
          [a](x0) = 2x0 + 5,
          
          [b](x0) = -2x0 + 0,
          
          [c](x0) = 2x0 + 0
         orientation:
          c#(a(x1)) = 2x1 + 5 >= -2x1 + 0 = c#(b(x1))
          
          b(a(a(x1))) = 2x1 + 5 >= 2x1 + 0 = c(x1)
          
          c(a(x1)) = 4x1 + 7 >= 4x1 + 7 = a(a(c(b(x1))))
          
          c(b(x1)) = x1 + 2 >= x1 = x1
         problem:
          DPs:
           
          TRS:
           b(a(a(x1))) -> c(x1)
           c(a(x1)) -> a(a(c(b(x1))))
           c(b(x1)) -> x1
         Qed