YES

Problem:
 div(X,e()) -> i(X)
 i(div(X,Y)) -> div(Y,X)
 div(div(X,Y),Z) -> div(Y,div(i(X),Z))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [i](x0) = 2x0 + 1,
   
   [div](x0, x1) = 2x0 + x1 + 4,
   
   [e] = 1
  orientation:
   div(X,e()) = 2X + 5 >= 2X + 1 = i(X)
   
   i(div(X,Y)) = 4X + 2Y + 9 >= X + 2Y + 4 = div(Y,X)
   
   div(div(X,Y),Z) = 4X + 2Y + Z + 12 >= 4X + 2Y + Z + 10 = div(Y,div(i(X),Z))
  problem:
   
  Qed