MAYBE

Problem:
 A(b(x1)) -> b(a(B(A(x1))))
 B(a(x1)) -> a(b(A(B(x1))))
 A(a(x1)) -> x1
 B(b(x1)) -> x1

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