YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> c#(x1)
   a#(b(b(x1))) -> a#(x1)
   a#(b(b(x1))) -> a#(a(x1))
  TRS:
   a(x1) -> b(c(x1))
   a(b(b(x1))) -> b(b(a(a(x1))))
   c(b(x1)) -> x1
  TDG Processor:
   DPs:
    a#(x1) -> c#(x1)
    a#(b(b(x1))) -> a#(x1)
    a#(b(b(x1))) -> a#(a(x1))
   TRS:
    a(x1) -> b(c(x1))
    a(b(b(x1))) -> b(b(a(a(x1))))
    c(b(x1)) -> x1
   graph:
    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(a(x1))
    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(x1)
    a#(b(b(x1))) -> a#(a(x1)) -> a#(x1) -> c#(x1)
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(a(x1))
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
    a#(b(b(x1))) -> a#(x1) -> a#(x1) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     a#(b(b(x1))) -> a#(a(x1))
     a#(b(b(x1))) -> a#(x1)
    TRS:
     a(x1) -> b(c(x1))
     a(b(b(x1))) -> b(b(a(a(x1))))
     c(b(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(c(x1))
      a(b(b(x1))) -> b(b(a(a(x1))))
      c(b(x1)) -> x1
     interpretation:
      [a#](x0) = [0 3]x0,
      
                [0 0]  
      [b](x0) = [1 0]x0,
      
                [0  -&]  
      [c](x0) = [0  -&]x0,
      
                [0  -&]  
      [a](x0) = [1  0 ]x0
     orientation:
      a#(b(b(x1))) = [4 4]x1 >= [4 3]x1 = a#(a(x1))
      
      a#(b(b(x1))) = [4 4]x1 >= [0 3]x1 = a#(x1)
      
              [0  -&]      [0  -&]             
      a(x1) = [1  0 ]x1 >= [1  -&]x1 = b(c(x1))
      
                    [1 0]      [1 0]                   
      a(b(b(x1))) = [2 1]x1 >= [2 1]x1 = b(b(a(a(x1))))
      
                 [0 0]             
      c(b(x1)) = [0 0]x1 >= x1 = x1
     problem:
      DPs:
       a#(b(b(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> b(c(x1))
       a(b(b(x1))) -> b(b(a(a(x1))))
       c(b(x1)) -> x1
     Restore Modifier:
      DPs:
       a#(b(b(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> b(c(x1))
       a(b(b(x1))) -> b(b(a(a(x1))))
       c(b(x1)) -> x1
      EDG Processor:
       DPs:
        a#(b(b(x1))) -> a#(a(x1))
       TRS:
        a(x1) -> b(c(x1))
        a(b(b(x1))) -> b(b(a(a(x1))))
        c(b(x1)) -> x1
       graph:
        a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(a(x1))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> b(c(x1))
         a(b(b(x1))) -> b(b(a(a(x1))))
         c(b(x1)) -> x1
        interpretation:
         [a#](x0) = [1 0]x0 + [0],
         
                   [0 0]     [-&]
         [b](x0) = [2 0]x0 + [0 ],
         
                   [0  -&]  
         [c](x0) = [0  -&]x0,
         
                   [0  -&]     [-&]
         [a](x0) = [2  -&]x0 + [0 ]
        orientation:
         a#(b(b(x1))) = [3 2]x1 + [1] >= [2  -&]x1 + [0] = a#(a(x1))
         
                 [0  -&]     [-&]    [0  -&]     [-&]           
         a(x1) = [2  -&]x1 + [0 ] >= [2  -&]x1 + [0 ] = b(c(x1))
         
                       [2 0]     [0]    [2  -&]     [0]                 
         a(b(b(x1))) = [4 2]x1 + [2] >= [4  -&]x1 + [2] = b(b(a(a(x1))))
         
                    [0 0]             
         c(b(x1)) = [0 0]x1 >= x1 = x1
        problem:
         DPs:
          
         TRS:
          a(x1) -> b(c(x1))
          a(b(b(x1))) -> b(b(a(a(x1))))
          c(b(x1)) -> x1
        Qed