MAYBE

Problem:
 r1(a(x1)) -> a(a(a(r1(x1))))
 r2(a(x1)) -> a(a(a(r2(x1))))
 a(l1(x1)) -> l1(a(a(a(x1))))
 a(a(l2(x1))) -> l2(a(a(x1)))
 r1(b(x1)) -> l1(b(x1))
 r2(b(x1)) -> l2(a(b(x1)))
 b(l1(x1)) -> b(r2(x1))
 b(l2(x1)) -> b(r1(x1))
 a(a(x1)) -> x1

Proof:
 Complexity Transformation Processor:
  strict:
   r1(a(x1)) -> a(a(a(r1(x1))))
   r2(a(x1)) -> a(a(a(r2(x1))))
   a(l1(x1)) -> l1(a(a(a(x1))))
   a(a(l2(x1))) -> l2(a(a(x1)))
   r1(b(x1)) -> l1(b(x1))
   r2(b(x1)) -> l2(a(b(x1)))
   b(l1(x1)) -> b(r2(x1))
   b(l2(x1)) -> b(r1(x1))
   a(a(x1)) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [b](x0) = x0,
     
     [l2](x0) = x0 + 1,
     
     [l1](x0) = x0,
     
     [r2](x0) = x0,
     
     [r1](x0) = x0,
     
     [a](x0) = x0
    orientation:
     r1(a(x1)) = x1 >= x1 = a(a(a(r1(x1))))
     
     r2(a(x1)) = x1 >= x1 = a(a(a(r2(x1))))
     
     a(l1(x1)) = x1 >= x1 = l1(a(a(a(x1))))
     
     a(a(l2(x1))) = x1 + 1 >= x1 + 1 = l2(a(a(x1)))
     
     r1(b(x1)) = x1 >= x1 = l1(b(x1))
     
     r2(b(x1)) = x1 >= x1 + 1 = l2(a(b(x1)))
     
     b(l1(x1)) = x1 >= x1 = b(r2(x1))
     
     b(l2(x1)) = x1 + 1 >= x1 = b(r1(x1))
     
     a(a(x1)) = x1 >= x1 = x1
    problem:
     strict:
      r1(a(x1)) -> a(a(a(r1(x1))))
      r2(a(x1)) -> a(a(a(r2(x1))))
      a(l1(x1)) -> l1(a(a(a(x1))))
      a(a(l2(x1))) -> l2(a(a(x1)))
      r1(b(x1)) -> l1(b(x1))
      r2(b(x1)) -> l2(a(b(x1)))
      b(l1(x1)) -> b(r2(x1))
      a(a(x1)) -> x1
     weak:
      b(l2(x1)) -> b(r1(x1))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [b](x0) = x0,
       
       [l2](x0) = x0,
       
       [l1](x0) = x0 + 1,
       
       [r2](x0) = x0,
       
       [r1](x0) = x0,
       
       [a](x0) = x0
      orientation:
       r1(a(x1)) = x1 >= x1 = a(a(a(r1(x1))))
       
       r2(a(x1)) = x1 >= x1 = a(a(a(r2(x1))))
       
       a(l1(x1)) = x1 + 1 >= x1 + 1 = l1(a(a(a(x1))))
       
       a(a(l2(x1))) = x1 >= x1 = l2(a(a(x1)))
       
       r1(b(x1)) = x1 >= x1 + 1 = l1(b(x1))
       
       r2(b(x1)) = x1 >= x1 = l2(a(b(x1)))
       
       b(l1(x1)) = x1 + 1 >= x1 = b(r2(x1))
       
       a(a(x1)) = x1 >= x1 = x1
       
       b(l2(x1)) = x1 >= x1 = b(r1(x1))
      problem:
       strict:
        r1(a(x1)) -> a(a(a(r1(x1))))
        r2(a(x1)) -> a(a(a(r2(x1))))
        a(l1(x1)) -> l1(a(a(a(x1))))
        a(a(l2(x1))) -> l2(a(a(x1)))
        r1(b(x1)) -> l1(b(x1))
        r2(b(x1)) -> l2(a(b(x1)))
        a(a(x1)) -> x1
       weak:
        b(l1(x1)) -> b(r2(x1))
        b(l2(x1)) -> b(r1(x1))
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [b](x0) = x0,
         
         [l2](x0) = x0,
         
         [l1](x0) = x0,
         
         [r2](x0) = x0,
         
         [r1](x0) = x0,
         
         [a](x0) = x0 + 1
        orientation:
         r1(a(x1)) = x1 + 1 >= x1 + 3 = a(a(a(r1(x1))))
         
         r2(a(x1)) = x1 + 1 >= x1 + 3 = a(a(a(r2(x1))))
         
         a(l1(x1)) = x1 + 1 >= x1 + 3 = l1(a(a(a(x1))))
         
         a(a(l2(x1))) = x1 + 2 >= x1 + 2 = l2(a(a(x1)))
         
         r1(b(x1)) = x1 >= x1 = l1(b(x1))
         
         r2(b(x1)) = x1 >= x1 + 1 = l2(a(b(x1)))
         
         a(a(x1)) = x1 + 2 >= x1 = x1
         
         b(l1(x1)) = x1 >= x1 = b(r2(x1))
         
         b(l2(x1)) = x1 >= x1 = b(r1(x1))
        problem:
         strict:
          r1(a(x1)) -> a(a(a(r1(x1))))
          r2(a(x1)) -> a(a(a(r2(x1))))
          a(l1(x1)) -> l1(a(a(a(x1))))
          a(a(l2(x1))) -> l2(a(a(x1)))
          r1(b(x1)) -> l1(b(x1))
          r2(b(x1)) -> l2(a(b(x1)))
         weak:
          a(a(x1)) -> x1
          b(l1(x1)) -> b(r2(x1))
          b(l2(x1)) -> b(r1(x1))
        Matrix Interpretation Processor:
         dimension: 1
         max_matrix:
          1
          interpretation:
           [b](x0) = x0,
           
           [l2](x0) = x0,
           
           [l1](x0) = x0 + 1,
           
           [r2](x0) = x0 + 1,
           
           [r1](x0) = x0,
           
           [a](x0) = x0
          orientation:
           r1(a(x1)) = x1 >= x1 = a(a(a(r1(x1))))
           
           r2(a(x1)) = x1 + 1 >= x1 + 1 = a(a(a(r2(x1))))
           
           a(l1(x1)) = x1 + 1 >= x1 + 1 = l1(a(a(a(x1))))
           
           a(a(l2(x1))) = x1 >= x1 = l2(a(a(x1)))
           
           r1(b(x1)) = x1 >= x1 + 1 = l1(b(x1))
           
           r2(b(x1)) = x1 + 1 >= x1 = l2(a(b(x1)))
           
           a(a(x1)) = x1 >= x1 = x1
           
           b(l1(x1)) = x1 + 1 >= x1 + 1 = b(r2(x1))
           
           b(l2(x1)) = x1 >= x1 = b(r1(x1))
          problem:
           strict:
            r1(a(x1)) -> a(a(a(r1(x1))))
            r2(a(x1)) -> a(a(a(r2(x1))))
            a(l1(x1)) -> l1(a(a(a(x1))))
            a(a(l2(x1))) -> l2(a(a(x1)))
            r1(b(x1)) -> l1(b(x1))
           weak:
            r2(b(x1)) -> l2(a(b(x1)))
            a(a(x1)) -> x1
            b(l1(x1)) -> b(r2(x1))
            b(l2(x1)) -> b(r1(x1))
          Open