MAYBE

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

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