YES

Problem:
 H(H(x)) -> K(x)
 H(K(x)) -> K(H(x))

Proof:
 Church Rosser Transformation Processor (kb):
  H(H(x)) -> K(x)
  H(K(x)) -> K(H(x))
  critical peaks: joinable
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [K](x0) = 4x0 + 5,
     
     [H](x0) = 4x0 + 1
    orientation:
     H(H(x)) = 16x + 5 >= 4x + 5 = K(x)
     
     H(K(x)) = 16x + 21 >= 16x + 9 = K(H(x))
    problem:
     H(H(x)) -> K(x)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [K](x0) = x0,
      
      [H](x0) = 2x0 + 1
     orientation:
      H(H(x)) = 4x + 3 >= x = K(x)
     problem:
      
     Qed