MAYBE

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:
 Complexity Transformation Processor:
  strict:
   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))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [5](x0) = x0,
     
     [6](x0) = x0,
     
     [2](x0) = x0 + 1,
     
     [4](x0) = x0 + 1,
     
     [3](x0) = x0 + 1,
     
     [1](x0) = x0
    orientation:
     1(1(x1)) = x1 >= x1 + 2 = 4(3(x1))
     
     1(2(x1)) = x1 + 1 >= x1 + 1 = 2(1(x1))
     
     2(2(x1)) = x1 + 2 >= x1 = 1(1(1(x1)))
     
     3(3(x1)) = x1 + 2 >= x1 = 5(6(x1))
     
     3(4(x1)) = x1 + 2 >= x1 = 1(1(x1))
     
     4(4(x1)) = x1 + 2 >= x1 + 1 = 3(x1)
     
     5(5(x1)) = x1 >= x1 + 1 = 6(2(x1))
     
     5(6(x1)) = x1 >= x1 + 1 = 1(2(x1))
     
     6(6(x1)) = x1 >= x1 + 1 = 2(1(x1))
    problem:
     strict:
      1(1(x1)) -> 4(3(x1))
      1(2(x1)) -> 2(1(x1))
      5(5(x1)) -> 6(2(x1))
      5(6(x1)) -> 1(2(x1))
      6(6(x1)) -> 2(1(x1))
     weak:
      2(2(x1)) -> 1(1(1(x1)))
      3(3(x1)) -> 5(6(x1))
      3(4(x1)) -> 1(1(x1))
      4(4(x1)) -> 3(x1)
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [5](x0) = x0 + 1,
       
       [6](x0) = x0,
       
       [2](x0) = x0,
       
       [4](x0) = x0 + 1,
       
       [3](x0) = x0 + 1,
       
       [1](x0) = x0
      orientation:
       1(1(x1)) = x1 >= x1 + 2 = 4(3(x1))
       
       1(2(x1)) = x1 >= x1 = 2(1(x1))
       
       5(5(x1)) = x1 + 2 >= x1 = 6(2(x1))
       
       5(6(x1)) = x1 + 1 >= x1 = 1(2(x1))
       
       6(6(x1)) = x1 >= x1 = 2(1(x1))
       
       2(2(x1)) = x1 >= x1 = 1(1(1(x1)))
       
       3(3(x1)) = x1 + 2 >= x1 + 1 = 5(6(x1))
       
       3(4(x1)) = x1 + 2 >= x1 = 1(1(x1))
       
       4(4(x1)) = x1 + 2 >= x1 + 1 = 3(x1)
      problem:
       strict:
        1(1(x1)) -> 4(3(x1))
        1(2(x1)) -> 2(1(x1))
        6(6(x1)) -> 2(1(x1))
       weak:
        5(5(x1)) -> 6(2(x1))
        5(6(x1)) -> 1(2(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)
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [5](x0) = x0 + 1,
         
         [6](x0) = x0 + 1,
         
         [2](x0) = x0 + 1,
         
         [4](x0) = x0 + 1,
         
         [3](x0) = x0 + 1,
         
         [1](x0) = x0
        orientation:
         1(1(x1)) = x1 >= x1 + 2 = 4(3(x1))
         
         1(2(x1)) = x1 + 1 >= x1 + 1 = 2(1(x1))
         
         6(6(x1)) = x1 + 2 >= x1 + 1 = 2(1(x1))
         
         5(5(x1)) = x1 + 2 >= x1 + 2 = 6(2(x1))
         
         5(6(x1)) = x1 + 2 >= x1 + 1 = 1(2(x1))
         
         2(2(x1)) = x1 + 2 >= x1 = 1(1(1(x1)))
         
         3(3(x1)) = x1 + 2 >= x1 + 2 = 5(6(x1))
         
         3(4(x1)) = x1 + 2 >= x1 = 1(1(x1))
         
         4(4(x1)) = x1 + 2 >= x1 + 1 = 3(x1)
        problem:
         strict:
          1(1(x1)) -> 4(3(x1))
          1(2(x1)) -> 2(1(x1))
         weak:
          6(6(x1)) -> 2(1(x1))
          5(5(x1)) -> 6(2(x1))
          5(6(x1)) -> 1(2(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)
        Open