Given a problem by the following specification. Prove that program S solves the problem. A=(x:N,y:N)B=(x:N)Q=(x=xx1)R=(Qy=f(x)) where function f:NN is defined as follows: Auxiliary variables: a:N and i:N. Q=(Qi=2y=1a=0) is the intermediate condition of the sequence. P=(Qy=f(i1)a=f(i2)i[2x+1]) is the loop invariant. t=x+1i is the variant function. Q=(Qy=f(i)a=f(i1)i+1[2x+1]x+1i=t0) is the intermediate condition of the loop body (where t0Z )