MAYBE

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

Proof:
 Complexity Transformation Processor:
  strict:
   b(c(a(x1))) -> a(b(x1))
   b(b(b(x1))) -> c(a(c(x1)))
   c(d(x1)) -> d(c(x1))
   c(d(b(x1))) -> d(c(c(x1)))
   d(c(x1)) -> b(b(b(x1)))
   c(b(x1)) -> d(a(x1))
   d(b(c(x1))) -> a(a(x1))
   d(a(x1)) -> b(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [d](x0) = x0 + 1,
     
     [b](x0) = x0,
     
     [c](x0) = x0,
     
     [a](x0) = x0 + 1
    orientation:
     b(c(a(x1))) = x1 + 1 >= x1 + 1 = a(b(x1))
     
     b(b(b(x1))) = x1 >= x1 + 1 = c(a(c(x1)))
     
     c(d(x1)) = x1 + 1 >= x1 + 1 = d(c(x1))
     
     c(d(b(x1))) = x1 + 1 >= x1 + 1 = d(c(c(x1)))
     
     d(c(x1)) = x1 + 1 >= x1 = b(b(b(x1)))
     
     c(b(x1)) = x1 >= x1 + 2 = d(a(x1))
     
     d(b(c(x1))) = x1 + 1 >= x1 + 2 = a(a(x1))
     
     d(a(x1)) = x1 + 2 >= x1 = b(x1)
    problem:
     strict:
      b(c(a(x1))) -> a(b(x1))
      b(b(b(x1))) -> c(a(c(x1)))
      c(d(x1)) -> d(c(x1))
      c(d(b(x1))) -> d(c(c(x1)))
      c(b(x1)) -> d(a(x1))
      d(b(c(x1))) -> a(a(x1))
     weak:
      d(c(x1)) -> b(b(b(x1)))
      d(a(x1)) -> b(x1)
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [d](x0) = x0 + 1,
       
       [b](x0) = x0,
       
       [c](x0) = x0,
       
       [a](x0) = x0
      orientation:
       b(c(a(x1))) = x1 >= x1 = a(b(x1))
       
       b(b(b(x1))) = x1 >= x1 = c(a(c(x1)))
       
       c(d(x1)) = x1 + 1 >= x1 + 1 = d(c(x1))
       
       c(d(b(x1))) = x1 + 1 >= x1 + 1 = d(c(c(x1)))
       
       c(b(x1)) = x1 >= x1 + 1 = d(a(x1))
       
       d(b(c(x1))) = x1 + 1 >= x1 = a(a(x1))
       
       d(c(x1)) = x1 + 1 >= x1 = b(b(b(x1)))
       
       d(a(x1)) = x1 + 1 >= x1 = b(x1)
      problem:
       strict:
        b(c(a(x1))) -> a(b(x1))
        b(b(b(x1))) -> c(a(c(x1)))
        c(d(x1)) -> d(c(x1))
        c(d(b(x1))) -> d(c(c(x1)))
        c(b(x1)) -> d(a(x1))
       weak:
        d(b(c(x1))) -> a(a(x1))
        d(c(x1)) -> b(b(b(x1)))
        d(a(x1)) -> b(x1)
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [d](x0) = x0,
         
         [b](x0) = x0,
         
         [c](x0) = x0 + 1,
         
         [a](x0) = x0
        orientation:
         b(c(a(x1))) = x1 + 1 >= x1 = a(b(x1))
         
         b(b(b(x1))) = x1 >= x1 + 2 = c(a(c(x1)))
         
         c(d(x1)) = x1 + 1 >= x1 + 1 = d(c(x1))
         
         c(d(b(x1))) = x1 + 1 >= x1 + 2 = d(c(c(x1)))
         
         c(b(x1)) = x1 + 1 >= x1 = d(a(x1))
         
         d(b(c(x1))) = x1 + 1 >= x1 = a(a(x1))
         
         d(c(x1)) = x1 + 1 >= x1 = b(b(b(x1)))
         
         d(a(x1)) = x1 >= x1 = b(x1)
        problem:
         strict:
          b(b(b(x1))) -> c(a(c(x1)))
          c(d(x1)) -> d(c(x1))
          c(d(b(x1))) -> d(c(c(x1)))
         weak:
          b(c(a(x1))) -> a(b(x1))
          c(b(x1)) -> d(a(x1))
          d(b(c(x1))) -> a(a(x1))
          d(c(x1)) -> b(b(b(x1)))
          d(a(x1)) -> b(x1)
        Matrix Interpretation Processor:
         dimension: 2
         max_matrix:
          [1 1]
          [0 0]
          interpretation:
                     [1 1]     [1]
           [d](x0) = [0 0]x0 + [1],
           
                     [1 1]     [0]
           [b](x0) = [0 0]x0 + [1],
           
                     [1 1]     [0]
           [c](x0) = [0 0]x0 + [1],
           
                     [1 1]  
           [a](x0) = [0 0]x0
          orientation:
                         [1 1]     [2]    [1 1]     [1]              
           b(b(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(a(c(x1)))
           
                      [1 1]     [2]    [1 1]     [2]           
           c(d(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(c(x1))
           
                         [1 1]     [3]    [1 1]     [3]              
           c(d(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(c(c(x1)))
           
                         [1 1]     [1]    [1 1]     [1]           
           b(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a(b(x1))
           
                      [1 1]     [1]    [1 1]     [1]           
           c(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(a(x1))
           
                         [1 1]     [3]    [1 1]             
           d(b(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 = a(a(x1))
           
                      [1 1]     [2]    [1 1]     [2]              
           d(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(b(b(x1)))
           
                      [1 1]     [1]    [1 1]     [0]        
           d(a(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(x1)
          problem:
           strict:
            c(d(x1)) -> d(c(x1))
            c(d(b(x1))) -> d(c(c(x1)))
           weak:
            b(b(b(x1))) -> c(a(c(x1)))
            b(c(a(x1))) -> a(b(x1))
            c(b(x1)) -> d(a(x1))
            d(b(c(x1))) -> a(a(x1))
            d(c(x1)) -> b(b(b(x1)))
            d(a(x1)) -> b(x1)
          Open