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) = x0 + 23,
      
      [3#](x0) = x0 + 7,
      
      [3](x0) = x0 + 24,
      
      [2](x0) = x0 + 27,
      
      [5](x0) = x0 + 25,
      
      [5#](x0) = x0 + 15,
      
      [1](x0) = x0 + 18,
      
      [4#](x0) = x0,
      
      [6#](x0) = x0 + 6,
      
      [2#](x0) = x0 + 12,
      
      [1#](x0) = x0 + 2,
      
      [4](x0) = x0 + 12
     orientation:
      1#(1(x1)) = x1 + 20 >= x1 = 4#(x1)
      
      1#(1(x1)) = x1 + 20 >= x1 + 19 = 3#(4(x1))
      
      2#(1(x1)) = x1 + 30 >= x1 + 12 = 2#(x1)
      
      2#(1(x1)) = x1 + 30 >= x1 + 29 = 1#(2(x1))
      
      2#(2(x1)) = x1 + 39 >= x1 + 2 = 1#(x1)
      
      2#(2(x1)) = x1 + 39 >= x1 + 20 = 1#(1(x1))
      
      2#(2(x1)) = x1 + 39 >= x1 + 38 = 1#(1(1(x1)))
      
      3#(3(x1)) = x1 + 31 >= x1 + 15 = 5#(x1)
      
      3#(3(x1)) = x1 + 31 >= x1 + 31 = 6#(5(x1))
      
      4#(3(x1)) = x1 + 24 >= x1 + 2 = 1#(x1)
      
      4#(3(x1)) = x1 + 24 >= x1 + 20 = 1#(1(x1))
      
      4#(4(x1)) = x1 + 12 >= x1 + 7 = 3#(x1)
      
      5#(5(x1)) = x1 + 40 >= x1 + 6 = 6#(x1)
      
      5#(5(x1)) = x1 + 40 >= x1 + 35 = 2#(6(x1))
      
      6#(5(x1)) = x1 + 31 >= x1 + 2 = 1#(x1)
      
      6#(5(x1)) = x1 + 31 >= x1 + 30 = 2#(1(x1))
      
      6#(6(x1)) = x1 + 29 >= x1 + 12 = 2#(x1)
      
      6#(6(x1)) = x1 + 29 >= x1 + 29 = 1#(2(x1))
      
      1(1(x1)) = x1 + 36 >= x1 + 36 = 3(4(x1))
      
      2(1(x1)) = x1 + 45 >= x1 + 45 = 1(2(x1))
      
      2(2(x1)) = x1 + 54 >= x1 + 54 = 1(1(1(x1)))
      
      3(3(x1)) = x1 + 48 >= x1 + 48 = 6(5(x1))
      
      4(3(x1)) = x1 + 36 >= x1 + 36 = 1(1(x1))
      
      4(4(x1)) = x1 + 24 >= x1 + 24 = 3(x1)
      
      5(5(x1)) = x1 + 50 >= x1 + 50 = 2(6(x1))
      
      6(5(x1)) = x1 + 48 >= x1 + 45 = 2(1(x1))
      
      6(6(x1)) = x1 + 46 >= x1 + 45 = 1(2(x1))
     problem:
      DPs:
       3#(3(x1)) -> 6#(5(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:
       3#(3(x1)) -> 6#(5(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:
        3#(3(x1)) -> 6#(5(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:
        3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 1#(2(x1))
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 1/4