YES(?,O(n^2))

Problem:
 g(f(x,y),z) -> f(x,g(y,z))
 g(h(x,y),z) -> g(x,f(y,z))
 g(x,h(y,z)) -> h(g(x,y),z)

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
                      [1 4]     [1 ]
   [h](x0, x1) = x0 + [0 0]x1 + [14],
   
                 [1 1]     [1 2]  
   [g](x0, x1) = [0 1]x0 + [0 1]x1,
   
                 [1 2]          [8]
   [f](x0, x1) = [0 0]x0 + x1 + [1]
  orientation:
                 [1 2]    [1 1]    [1 2]    [9]    [1 2]    [1 1]    [1 2]    [8]              
   g(f(x,y),z) = [0 0]x + [0 1]y + [0 1]z + [1] >= [0 0]x + [0 1]y + [0 1]z + [1] = f(x,g(y,z))
   
                 [1 1]    [1 4]    [1 2]    [15]    [1 1]    [1 2]    [1 2]    [10]              
   g(h(x,y),z) = [0 1]x + [0 0]y + [0 1]z + [14] >= [0 1]x + [0 0]y + [0 1]z + [1 ] = g(x,f(y,z))
   
                 [1 1]    [1 2]    [1 4]    [29]    [1 1]    [1 2]    [1 4]    [1 ]              
   g(x,h(y,z)) = [0 1]x + [0 1]y + [0 0]z + [14] >= [0 1]x + [0 1]y + [0 0]z + [14] = h(g(x,y),z)
  problem:
   
  Qed