MAYBE

Problem:
 C(C(x1)) -> c(c(x1))
 c(c(c(c(x1)))) -> x1
 b(b(b(b(x1)))) -> B(B(x1))
 B(B(B(B(x1)))) -> b(b(x1))
 c(c(B(B(c(c(b(b(c(c(x1)))))))))) -> B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
 b(b(B(B(x1)))) -> x1
 B(B(b(b(x1)))) -> x1
 c(c(C(C(x1)))) -> x1
 C(C(c(c(x1)))) -> x1

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