MAYBE

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

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