Atrivial oz code for returning the number of elements of a list can be given by: declare fun {length l} case l of nil then 0 [] h|t then 1+{length t} end end for example, the call {browse {length [1 f 2 3 s 5]}} will display 6. explain why this function is not tail recursive. write an equivalent tail recursive function. write also an invariant for this tail recursive function. using the invariant, prove the correctness for this program.

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj