YES

Problem:
 1(1(x1)) -> 4(3(x1))
 1(2(x1)) -> 2(1(x1))
 2(2(x1)) -> 1(1(1(x1)))
 3(3(x1)) -> 5(6(x1))
 3(4(x1)) -> 1(1(x1))
 4(4(x1)) -> 3(x1)
 5(5(x1)) -> 6(2(x1))
 5(6(x1)) -> 1(2(x1))
 6(6(x1)) -> 2(1(x1))

Proof:
 String Reversal Processor:
  1(1(x1)) -> 3(4(x1))
  2(1(x1)) -> 1(2(x1))
  2(2(x1)) -> 1(1(1(x1)))
  3(3(x1)) -> 6(5(x1))
  4(3(x1)) -> 1(1(x1))
  4(4(x1)) -> 3(x1)
  5(5(x1)) -> 2(6(x1))
  6(5(x1)) -> 2(1(x1))
  6(6(x1)) -> 1(2(x1))
  DP Processor:
   DPs:
    1#(1(x1)) -> 4#(x1)
    1#(1(x1)) -> 3#(4(x1))
    2#(1(x1)) -> 2#(x1)
    2#(1(x1)) -> 1#(2(x1))
    2#(2(x1)) -> 1#(x1)
    2#(2(x1)) -> 1#(1(x1))
    2#(2(x1)) -> 1#(1(1(x1)))
    3#(3(x1)) -> 5#(x1)
    3#(3(x1)) -> 6#(5(x1))
    4#(3(x1)) -> 1#(x1)
    4#(3(x1)) -> 1#(1(x1))
    4#(4(x1)) -> 3#(x1)
    5#(5(x1)) -> 6#(x1)
    5#(5(x1)) -> 2#(6(x1))
    6#(5(x1)) -> 1#(x1)
    6#(5(x1)) -> 2#(1(x1))
    6#(6(x1)) -> 2#(x1)
    6#(6(x1)) -> 1#(2(x1))
   TRS:
    1(1(x1)) -> 3(4(x1))
    2(1(x1)) -> 1(2(x1))
    2(2(x1)) -> 1(1(1(x1)))
    3(3(x1)) -> 6(5(x1))
    4(3(x1)) -> 1(1(x1))
    4(4(x1)) -> 3(x1)
    5(5(x1)) -> 2(6(x1))
    6(5(x1)) -> 2(1(x1))
    6(6(x1)) -> 1(2(x1))
   TDG Processor:
    DPs:
     1#(1(x1)) -> 4#(x1)
     1#(1(x1)) -> 3#(4(x1))
     2#(1(x1)) -> 2#(x1)
     2#(1(x1)) -> 1#(2(x1))
     2#(2(x1)) -> 1#(x1)
     2#(2(x1)) -> 1#(1(x1))
     2#(2(x1)) -> 1#(1(1(x1)))
     3#(3(x1)) -> 5#(x1)
     3#(3(x1)) -> 6#(5(x1))
     4#(3(x1)) -> 1#(x1)
     4#(3(x1)) -> 1#(1(x1))
     4#(4(x1)) -> 3#(x1)
     5#(5(x1)) -> 6#(x1)
     5#(5(x1)) -> 2#(6(x1))
     6#(5(x1)) -> 1#(x1)
     6#(5(x1)) -> 2#(1(x1))
     6#(6(x1)) -> 2#(x1)
     6#(6(x1)) -> 1#(2(x1))
    TRS:
     1(1(x1)) -> 3(4(x1))
     2(1(x1)) -> 1(2(x1))
     2(2(x1)) -> 1(1(1(x1)))
     3(3(x1)) -> 6(5(x1))
     4(3(x1)) -> 1(1(x1))
     4(4(x1)) -> 3(x1)
     5(5(x1)) -> 2(6(x1))
     6(5(x1)) -> 2(1(x1))
     6(6(x1)) -> 1(2(x1))
    graph:
     6#(5(x1)) -> 2#(1(x1)) -> 2#(2(x1)) -> 1#(1(1(x1)))
     6#(5(x1)) -> 2#(1(x1)) -> 2#(2(x1)) -> 1#(1(x1))
     6#(5(x1)) -> 2#(1(x1)) -> 2#(2(x1)) -> 1#(x1)
     6#(5(x1)) -> 2#(1(x1)) -> 2#(1(x1)) -> 1#(2(x1))
     6#(5(x1)) -> 2#(1(x1)) -> 2#(1(x1)) -> 2#(x1)
     6#(5(x1)) -> 1#(x1) -> 1#(1(x1)) -> 3#(4(x1))
     6#(5(x1)) -> 1#(x1) -> 1#(1(x1)) -> 4#(x1)
     6#(6(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(1(x1)))
     6#(6(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(x1))
     6#(6(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(x1)
     6#(6(x1)) -> 2#(x1) -> 2#(1(x1)) -> 1#(2(x1))
     6#(6(x1)) -> 2#(x1) -> 2#(1(x1)) -> 2#(x1)
     6#(6(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 3#(4(x1))
     6#(6(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 4#(x1)
     5#(5(x1)) -> 6#(x1) -> 6#(6(x1)) -> 1#(2(x1))
     5#(5(x1)) -> 6#(x1) -> 6#(6(x1)) -> 2#(x1)
     5#(5(x1)) -> 6#(x1) -> 6#(5(x1)) -> 2#(1(x1))
     5#(5(x1)) -> 6#(x1) -> 6#(5(x1)) -> 1#(x1)
     5#(5(x1)) -> 2#(6(x1)) -> 2#(2(x1)) -> 1#(1(1(x1)))
     5#(5(x1)) -> 2#(6(x1)) -> 2#(2(x1)) -> 1#(1(x1))
     5#(5(x1)) -> 2#(6(x1)) -> 2#(2(x1)) -> 1#(x1)
     5#(5(x1)) -> 2#(6(x1)) -> 2#(1(x1)) -> 1#(2(x1))
     5#(5(x1)) -> 2#(6(x1)) -> 2#(1(x1)) -> 2#(x1)
     2#(2(x1)) -> 1#(1(1(x1))) -> 1#(1(x1)) -> 3#(4(x1))
     2#(2(x1)) -> 1#(1(1(x1))) -> 1#(1(x1)) -> 4#(x1)
     2#(2(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 3#(4(x1))
     2#(2(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 4#(x1)
     2#(2(x1)) -> 1#(x1) -> 1#(1(x1)) -> 3#(4(x1))
     2#(2(x1)) -> 1#(x1) -> 1#(1(x1)) -> 4#(x1)
     2#(1(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(1(x1)))
     2#(1(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(x1))
     2#(1(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(x1)
     2#(1(x1)) -> 2#(x1) -> 2#(1(x1)) -> 1#(2(x1))
     2#(1(x1)) -> 2#(x1) -> 2#(1(x1)) -> 2#(x1)
     2#(1(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 3#(4(x1))
     2#(1(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 4#(x1)
     3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 1#(2(x1))
     3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 2#(x1)
     3#(3(x1)) -> 6#(5(x1)) -> 6#(5(x1)) -> 2#(1(x1))
     3#(3(x1)) -> 6#(5(x1)) -> 6#(5(x1)) -> 1#(x1)
     3#(3(x1)) -> 5#(x1) -> 5#(5(x1)) -> 2#(6(x1))
     3#(3(x1)) -> 5#(x1) -> 5#(5(x1)) -> 6#(x1)
     4#(4(x1)) -> 3#(x1) -> 3#(3(x1)) -> 6#(5(x1))
     4#(4(x1)) -> 3#(x1) -> 3#(3(x1)) -> 5#(x1)
     4#(3(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 3#(4(x1))
     4#(3(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 4#(x1)
     4#(3(x1)) -> 1#(x1) -> 1#(1(x1)) -> 3#(4(x1))
     4#(3(x1)) -> 1#(x1) -> 1#(1(x1)) -> 4#(x1)
     1#(1(x1)) -> 3#(4(x1)) -> 3#(3(x1)) -> 6#(5(x1))
     1#(1(x1)) -> 3#(4(x1)) -> 3#(3(x1)) -> 5#(x1)
     1#(1(x1)) -> 4#(x1) -> 4#(4(x1)) -> 3#(x1)
     1#(1(x1)) -> 4#(x1) -> 4#(3(x1)) -> 1#(1(x1))
     1#(1(x1)) -> 4#(x1) -> 4#(3(x1)) -> 1#(x1)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [6#](x0) = 2x0 + 16,
      
      [5#](x0) = 2x0 + 25,
      
      [2#](x0) = 2x0 + 26,
      
      [3#](x0) = 2x0 + 18,
      
      [4#](x0) = 2x0 + 2,
      
      [1#](x0) = 2x0 + 10,
      
      [5](x0) = x0 + 17,
      
      [6](x0) = x0 + 15,
      
      [2](x0) = x0 + 18,
      
      [4](x0) = x0 + 8,
      
      [3](x0) = x0 + 16,
      
      [1](x0) = x0 + 12
     orientation:
      1#(1(x1)) = 2x1 + 34 >= 2x1 + 2 = 4#(x1)
      
      1#(1(x1)) = 2x1 + 34 >= 2x1 + 34 = 3#(4(x1))
      
      2#(1(x1)) = 2x1 + 50 >= 2x1 + 26 = 2#(x1)
      
      2#(1(x1)) = 2x1 + 50 >= 2x1 + 46 = 1#(2(x1))
      
      2#(2(x1)) = 2x1 + 62 >= 2x1 + 10 = 1#(x1)
      
      2#(2(x1)) = 2x1 + 62 >= 2x1 + 34 = 1#(1(x1))
      
      2#(2(x1)) = 2x1 + 62 >= 2x1 + 58 = 1#(1(1(x1)))
      
      3#(3(x1)) = 2x1 + 50 >= 2x1 + 25 = 5#(x1)
      
      3#(3(x1)) = 2x1 + 50 >= 2x1 + 50 = 6#(5(x1))
      
      4#(3(x1)) = 2x1 + 34 >= 2x1 + 10 = 1#(x1)
      
      4#(3(x1)) = 2x1 + 34 >= 2x1 + 34 = 1#(1(x1))
      
      4#(4(x1)) = 2x1 + 18 >= 2x1 + 18 = 3#(x1)
      
      5#(5(x1)) = 2x1 + 59 >= 2x1 + 16 = 6#(x1)
      
      5#(5(x1)) = 2x1 + 59 >= 2x1 + 56 = 2#(6(x1))
      
      6#(5(x1)) = 2x1 + 50 >= 2x1 + 10 = 1#(x1)
      
      6#(5(x1)) = 2x1 + 50 >= 2x1 + 50 = 2#(1(x1))
      
      6#(6(x1)) = 2x1 + 46 >= 2x1 + 26 = 2#(x1)
      
      6#(6(x1)) = 2x1 + 46 >= 2x1 + 46 = 1#(2(x1))
      
      1(1(x1)) = x1 + 24 >= x1 + 24 = 3(4(x1))
      
      2(1(x1)) = x1 + 30 >= x1 + 30 = 1(2(x1))
      
      2(2(x1)) = x1 + 36 >= x1 + 36 = 1(1(1(x1)))
      
      3(3(x1)) = x1 + 32 >= x1 + 32 = 6(5(x1))
      
      4(3(x1)) = x1 + 24 >= x1 + 24 = 1(1(x1))
      
      4(4(x1)) = x1 + 16 >= x1 + 16 = 3(x1)
      
      5(5(x1)) = x1 + 34 >= x1 + 33 = 2(6(x1))
      
      6(5(x1)) = x1 + 32 >= x1 + 30 = 2(1(x1))
      
      6(6(x1)) = x1 + 30 >= x1 + 30 = 1(2(x1))
     problem:
      DPs:
       1#(1(x1)) -> 3#(4(x1))
       3#(3(x1)) -> 6#(5(x1))
       4#(3(x1)) -> 1#(1(x1))
       4#(4(x1)) -> 3#(x1)
       6#(5(x1)) -> 2#(1(x1))
       6#(6(x1)) -> 1#(2(x1))
      TRS:
       1(1(x1)) -> 3(4(x1))
       2(1(x1)) -> 1(2(x1))
       2(2(x1)) -> 1(1(1(x1)))
       3(3(x1)) -> 6(5(x1))
       4(3(x1)) -> 1(1(x1))
       4(4(x1)) -> 3(x1)
       5(5(x1)) -> 2(6(x1))
       6(5(x1)) -> 2(1(x1))
       6(6(x1)) -> 1(2(x1))
     Restore Modifier:
      DPs:
       1#(1(x1)) -> 3#(4(x1))
       3#(3(x1)) -> 6#(5(x1))
       4#(3(x1)) -> 1#(1(x1))
       4#(4(x1)) -> 3#(x1)
       6#(5(x1)) -> 2#(1(x1))
       6#(6(x1)) -> 1#(2(x1))
      TRS:
       1(1(x1)) -> 3(4(x1))
       2(1(x1)) -> 1(2(x1))
       2(2(x1)) -> 1(1(1(x1)))
       3(3(x1)) -> 6(5(x1))
       4(3(x1)) -> 1(1(x1))
       4(4(x1)) -> 3(x1)
       5(5(x1)) -> 2(6(x1))
       6(5(x1)) -> 2(1(x1))
       6(6(x1)) -> 1(2(x1))
      EDG Processor:
       DPs:
        1#(1(x1)) -> 3#(4(x1))
        3#(3(x1)) -> 6#(5(x1))
        4#(3(x1)) -> 1#(1(x1))
        4#(4(x1)) -> 3#(x1)
        6#(5(x1)) -> 2#(1(x1))
        6#(6(x1)) -> 1#(2(x1))
       TRS:
        1(1(x1)) -> 3(4(x1))
        2(1(x1)) -> 1(2(x1))
        2(2(x1)) -> 1(1(1(x1)))
        3(3(x1)) -> 6(5(x1))
        4(3(x1)) -> 1(1(x1))
        4(4(x1)) -> 3(x1)
        5(5(x1)) -> 2(6(x1))
        6(5(x1)) -> 2(1(x1))
        6(6(x1)) -> 1(2(x1))
       graph:
        6#(6(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 3#(4(x1))
        3#(3(x1)) -> 6#(5(x1)) -> 6#(5(x1)) -> 2#(1(x1))
        3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 1#(2(x1))
        4#(4(x1)) -> 3#(x1) -> 3#(3(x1)) -> 6#(5(x1))
        4#(3(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 3#(4(x1))
        1#(1(x1)) -> 3#(4(x1)) -> 3#(3(x1)) -> 6#(5(x1))
       SCC Processor:
        #sccs: 1
        #rules: 3
        #arcs: 6/36
        DPs:
         6#(6(x1)) -> 1#(2(x1))
         1#(1(x1)) -> 3#(4(x1))
         3#(3(x1)) -> 6#(5(x1))
        TRS:
         1(1(x1)) -> 3(4(x1))
         2(1(x1)) -> 1(2(x1))
         2(2(x1)) -> 1(1(1(x1)))
         3(3(x1)) -> 6(5(x1))
         4(3(x1)) -> 1(1(x1))
         4(4(x1)) -> 3(x1)
         5(5(x1)) -> 2(6(x1))
         6(5(x1)) -> 2(1(x1))
         6(6(x1)) -> 1(2(x1))
        Matrix Interpretation Processor: dim=4
         
         interpretation:
          [6#](x0) = [0 0 1 0]x0,
          
          [3#](x0) = [0 0 0 1]x0,
          
          [1#](x0) = [0 1 1 0]x0,
          
                    [0 0 0 0]     [1]
                    [0 0 0 0]     [1]
          [5](x0) = [1 0 0 0]x0 + [0]
                    [0 1 0 0]     [0],
          
                    [0]
                    [0]
          [6](x0) = [1]
                    [0],
          
                    [0]
                    [0]
          [2](x0) = [1]
                    [0],
          
                    [0 0 0 0]     [0]
                    [0 0 0 0]     [0]
          [4](x0) = [0 0 0 1]x0 + [1]
                    [1 0 0 1]     [0],
          
                    [0 0 0 0]     [0]
                    [0 0 0 0]     [0]
          [3](x0) = [0 0 0 0]x0 + [1]
                    [1 0 0 0]     [0],
          
                    [0 0 0 0]     [0]
                    [1 0 0 0]     [0]
          [1](x0) = [0 1 0 1]x0 + [1]
                    [0 0 0 0]     [0]
         orientation:
          6#(6(x1)) = [1] >= [1] = 1#(2(x1))
          
          1#(1(x1)) = [1 1 0 1]x1 + [1] >= [1 0 0 1]x1 = 3#(4(x1))
          
          3#(3(x1)) = [1 0 0 0]x1 >= [1 0 0 0]x1 = 6#(5(x1))
          
                     [0 0 0 0]     [0]    [0]           
                     [0 0 0 0]     [0]    [0]           
          1(1(x1)) = [1 0 0 0]x1 + [1] >= [1] = 3(4(x1))
                     [0 0 0 0]     [0]    [0]           
          
                     [0]    [0]           
                     [0]    [0]           
          2(1(x1)) = [1] >= [1] = 1(2(x1))
                     [0]    [0]           
          
                     [0]    [0]              
                     [0]    [0]              
          2(2(x1)) = [1] >= [1] = 1(1(1(x1)))
                     [0]    [0]              
          
                     [0]    [0]           
                     [0]    [0]           
          3(3(x1)) = [1] >= [1] = 6(5(x1))
                     [0]    [0]           
          
                     [0 0 0 0]     [0]    [0 0 0 0]     [0]           
                     [0 0 0 0]     [0]    [0 0 0 0]     [0]           
          4(3(x1)) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 + [1] = 1(1(x1))
                     [1 0 0 0]     [0]    [0 0 0 0]     [0]           
          
                     [0 0 0 0]     [0]    [0 0 0 0]     [0]        
                     [0 0 0 0]     [0]    [0 0 0 0]     [0]        
          4(4(x1)) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = 3(x1)
                     [1 0 0 1]     [0]    [1 0 0 0]     [0]        
          
                     [1]    [0]           
                     [1]    [0]           
          5(5(x1)) = [1] >= [1] = 2(6(x1))
                     [1]    [0]           
          
                     [0]    [0]           
                     [0]    [0]           
          6(5(x1)) = [1] >= [1] = 2(1(x1))
                     [0]    [0]           
          
                     [0]    [0]           
                     [0]    [0]           
          6(6(x1)) = [1] >= [1] = 1(2(x1))
                     [0]    [0]           
         problem:
          DPs:
           6#(6(x1)) -> 1#(2(x1))
           3#(3(x1)) -> 6#(5(x1))
          TRS:
           1(1(x1)) -> 3(4(x1))
           2(1(x1)) -> 1(2(x1))
           2(2(x1)) -> 1(1(1(x1)))
           3(3(x1)) -> 6(5(x1))
           4(3(x1)) -> 1(1(x1))
           4(4(x1)) -> 3(x1)
           5(5(x1)) -> 2(6(x1))
           6(5(x1)) -> 2(1(x1))
           6(6(x1)) -> 1(2(x1))
         Restore Modifier:
          DPs:
           6#(6(x1)) -> 1#(2(x1))
           3#(3(x1)) -> 6#(5(x1))
          TRS:
           1(1(x1)) -> 3(4(x1))
           2(1(x1)) -> 1(2(x1))
           2(2(x1)) -> 1(1(1(x1)))
           3(3(x1)) -> 6(5(x1))
           4(3(x1)) -> 1(1(x1))
           4(4(x1)) -> 3(x1)
           5(5(x1)) -> 2(6(x1))
           6(5(x1)) -> 2(1(x1))
           6(6(x1)) -> 1(2(x1))
          EDG Processor:
           DPs:
            6#(6(x1)) -> 1#(2(x1))
            3#(3(x1)) -> 6#(5(x1))
           TRS:
            1(1(x1)) -> 3(4(x1))
            2(1(x1)) -> 1(2(x1))
            2(2(x1)) -> 1(1(1(x1)))
            3(3(x1)) -> 6(5(x1))
            4(3(x1)) -> 1(1(x1))
            4(4(x1)) -> 3(x1)
            5(5(x1)) -> 2(6(x1))
            6(5(x1)) -> 2(1(x1))
            6(6(x1)) -> 1(2(x1))
           graph:
            3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 1#(2(x1))
           SCC Processor:
            #sccs: 0
            #rules: 0
            #arcs: 1/4