YES

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

Proof:
 String Reversal Processor:
  a(x1) -> c(b(x1))
  b(a(b(x1))) -> a(a(a(x1)))
  c(c(x1)) -> a(x1)
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> c#(b(x1))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> a#(a(x1))
    b#(a(b(x1))) -> a#(a(a(x1)))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> c(b(x1))
    b(a(b(x1))) -> a(a(a(x1)))
    c(c(x1)) -> a(x1)
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(x1)
     b#(a(b(x1))) -> a#(a(x1))
     b#(a(b(x1))) -> a#(a(a(x1)))
     c#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> c(b(x1))
     b(a(b(x1))) -> a(a(a(x1)))
     c(c(x1)) -> a(x1)
    graph:
     c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1))
     c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(a(a(x1))) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(a(a(x1))) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(a(x1)) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(x1) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(a(a(x1)))
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1))
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> c(b(x1))
      b(a(b(x1))) -> a(a(a(x1)))
      c(c(x1)) -> a(x1)
     interpretation:
      [b#](x0) = [1  -&]x0 + [0],
      
                [-& 0 ]     [0]
      [c](x0) = [0  1 ]x0 + [2],
      
      [a#](x0) = [2 0]x0 + [3],
      
      [c#](x0) = [0 2]x0 + [3],
      
                [0  -&]     [0]
      [a](x0) = [1  0 ]x0 + [2],
      
                [1  0 ]     [2]
      [b](x0) = [0  -&]x0 + [0]
     orientation:
      a#(x1) = [2 0]x1 + [3] >= [1  -&]x1 + [0] = b#(x1)
      
      a#(x1) = [2 0]x1 + [3] >= [2 0]x1 + [3] = c#(b(x1))
      
      b#(a(b(x1))) = [2 1]x1 + [3] >= [2 0]x1 + [3] = a#(x1)
      
      b#(a(b(x1))) = [2 1]x1 + [3] >= [2 0]x1 + [3] = a#(a(x1))
      
      b#(a(b(x1))) = [2 1]x1 + [3] >= [2 0]x1 + [3] = a#(a(a(x1)))
      
      c#(c(x1)) = [2 3]x1 + [4] >= [2 0]x1 + [3] = a#(x1)
      
              [0  -&]     [0]    [0  -&]     [0]           
      a(x1) = [1  0 ]x1 + [2] >= [1  0 ]x1 + [2] = c(b(x1))
      
                    [2 1]     [3]    [0  -&]     [0]              
      b(a(b(x1))) = [1 0]x1 + [2] >= [1  0 ]x1 + [2] = a(a(a(x1)))
      
                 [0 1]     [2]    [0  -&]     [0]        
      c(c(x1)) = [1 2]x1 + [3] >= [1  0 ]x1 + [2] = a(x1)
     problem:
      DPs:
       a#(x1) -> c#(b(x1))
       b#(a(b(x1))) -> a#(x1)
       b#(a(b(x1))) -> a#(a(x1))
       b#(a(b(x1))) -> a#(a(a(x1)))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> c(b(x1))
       b(a(b(x1))) -> a(a(a(x1)))
       c(c(x1)) -> a(x1)
     Restore Modifier:
      DPs:
       a#(x1) -> c#(b(x1))
       b#(a(b(x1))) -> a#(x1)
       b#(a(b(x1))) -> a#(a(x1))
       b#(a(b(x1))) -> a#(a(a(x1)))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> c(b(x1))
       b(a(b(x1))) -> a(a(a(x1)))
       c(c(x1)) -> a(x1)
      EDG Processor:
       DPs:
        a#(x1) -> c#(b(x1))
        b#(a(b(x1))) -> a#(x1)
        b#(a(b(x1))) -> a#(a(x1))
        b#(a(b(x1))) -> a#(a(a(x1)))
        c#(c(x1)) -> a#(x1)
       TRS:
        a(x1) -> c(b(x1))
        b(a(b(x1))) -> a(a(a(x1)))
        c(c(x1)) -> a(x1)
       graph:
        c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1))
        b#(a(b(x1))) -> a#(a(a(x1))) -> a#(x1) -> c#(b(x1))
        b#(a(b(x1))) -> a#(a(x1)) -> a#(x1) -> c#(b(x1))
        b#(a(b(x1))) -> a#(x1) -> a#(x1) -> c#(b(x1))
        a#(x1) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
       SCC Processor:
        #sccs: 1
        #rules: 2
        #arcs: 5/25
        DPs:
         c#(c(x1)) -> a#(x1)
         a#(x1) -> c#(b(x1))
        TRS:
         a(x1) -> c(b(x1))
         b(a(b(x1))) -> a(a(a(x1)))
         c(c(x1)) -> a(x1)
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> c(b(x1))
          b(a(b(x1))) -> a(a(a(x1)))
          c(c(x1)) -> a(x1)
         interpretation:
                    [2  -1]     [1 ]
          [c](x0) = [-& -&]x0 + [-4],
          
          [a#](x0) = [0  -&]x0 + [1],
          
          [c#](x0) = [1  -&]x0 + [0],
          
                    [0  1 ]     [2 ]
          [a](x0) = [-& -&]x0 + [-4],
          
                    [-2 -&]     [0]
          [b](x0) = [1  2 ]x0 + [3]
         orientation:
          c#(c(x1)) = [3 0]x1 + [2] >= [0  -&]x1 + [1] = a#(x1)
          
          a#(x1) = [0  -&]x1 + [1] >= [-1 -&]x1 + [1] = c#(b(x1))
          
                  [0  1 ]     [2 ]    [0  1 ]     [2 ]           
          a(x1) = [-& -&]x1 + [-4] >= [-& -&]x1 + [-4] = c(b(x1))
          
                        [0 1]     [2]    [0  1 ]     [2 ]              
          b(a(b(x1))) = [3 4]x1 + [5] >= [-& -&]x1 + [-4] = a(a(a(x1)))
          
                     [4  1 ]     [3 ]    [0  1 ]     [2 ]        
          c(c(x1)) = [-& -&]x1 + [-4] >= [-& -&]x1 + [-4] = a(x1)
         problem:
          DPs:
           a#(x1) -> c#(b(x1))
          TRS:
           a(x1) -> c(b(x1))
           b(a(b(x1))) -> a(a(a(x1)))
           c(c(x1)) -> a(x1)
         Restore Modifier:
          DPs:
           a#(x1) -> c#(b(x1))
          TRS:
           a(x1) -> c(b(x1))
           b(a(b(x1))) -> a(a(a(x1)))
           c(c(x1)) -> a(x1)
          EDG Processor:
           DPs:
            a#(x1) -> c#(b(x1))
           TRS:
            a(x1) -> c(b(x1))
            b(a(b(x1))) -> a(a(a(x1)))
            c(c(x1)) -> a(x1)
           graph:
            
           SCC Processor:
            #sccs: 0
            #rules: 0
            #arcs: 0/1