MAYBE

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

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