YES

Problem:
 F(H(x),y) -> F(H(x),I(I(y)))
 F(x,G(y)) -> F(I(x),G(y))
 I(x) -> x

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.11):
  I(H(x31)) -> H(x31)
  F(H(x33),G(x32)) -> F(H(x33),I(I(G(x32))))
  critical peaks: joinable
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 1]     [0]
    [G](x0) = [0 0]x0 + [2],
    
              [1 0]  
    [I](x0) = [0 0]x0,
    
                  [2 0]     [2 1]     [0]
    [F](x0, x1) = [0 0]x0 + [0 0]x1 + [2],
    
              [2 0]  
    [H](x0) = [0 0]x0
   orientation:
                [2 0]       [2 0]            
    I(H(x31)) = [0 0]x31 >= [0 0]x31 = H(x31)
    
                       [2 2]      [4 0]      [2]    [2 2]      [4 0]      [0]                         
    F(H(x33),G(x32)) = [0 0]x32 + [0 0]x33 + [2] >= [0 0]x32 + [0 0]x33 + [2] = F(H(x33),I(I(G(x32))))
   problem:
    I(H(x31)) -> H(x31)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [I](x0) = x0 + 1,
     
     [H](x0) = x0 + 4
    orientation:
     I(H(x31)) = x31 + 5 >= x31 + 4 = H(x31)
    problem:
     
    Qed