MAYBE

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

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