M1 >(defun g (n a)
         (if (zp n)
             a
           (g (- n 1) (* n a))))

The admission of G is trivial, using the relation O< (which is known
to be well-founded on the domain recognized by O-P) and the measure
(ACL2-COUNT N).  We observe that the type of G is described by the
theorem (OR (ACL2-NUMBERP (G N A)) (EQUAL (G N A) A)).  We used primitive
type reasoning.

Summary
Form:  ( DEFUN G ...)
Rules: ((:FAKE-RUNE-FOR-TYPE-SET NIL))
Warnings:  None
Time:  0.01 seconds (prove: 0.00, print: 0.00, other: 0.00)
 G
M1 >(defconst *g*
       '((PUSH 1)
         (STORE 1)
         (LOAD 0)
         (IFLE 10)
         (LOAD 0)
         (LOAD 1)
         (MUL)
         (STORE 1)
         (LOAD 0)
         (PUSH 1)
         (SUB)
         (STORE 0)
         (GOTO -10)
         (LOAD 1)
         (HALT)))

Summary
Form:  ( DEFCONST *G* ...)
Rules: NIL
Warnings:  None
Time:  0.00 seconds (prove: 0.00, print: 0.00, other: 0.00)
 *G*
M1 >(defun g-sched-loop (n)
         (if (zp n)
             (repeat 0 4)
           (append (repeat 0 11)
                   (g-sched-loop (- n 1)))))

The admission of G-SCHED-LOOP is trivial, using the relation O< (which
is known to be well-founded on the domain recognized by O-P) and the
measure (ACL2-COUNT N).  We observe that the type of G-SCHED-LOOP is
described by the theorem (TRUE-LISTP (G-SCHED-LOOP N)).  We used the
:type-prescription rules ACL2::APPEND-TRUE-LISTP-TYPE-PRESCRIPTION,
BINARY-APPEND and REPEAT.

Summary
Form:  ( DEFUN G-SCHED-LOOP ...)
Rules: ((:TYPE-PRESCRIPTION ACL2::APPEND-TRUE-LISTP-TYPE-PRESCRIPTION)
        (:TYPE-PRESCRIPTION BINARY-APPEND)
        (:TYPE-PRESCRIPTION REPEAT))
Warnings:  None
Time:  0.00 seconds (prove: 0.00, print: 0.00, other: 0.00)
 G-SCHED-LOOP
M1 >(defun g-sched (n)
         (append (repeat 0 2)
                 (g-sched-loop n)))

Since G-SCHED is non-recursive, its admission is trivial.  We observe
that the type of G-SCHED is described by the theorem 
(TRUE-LISTP (G-SCHED N)).  We used the :type-prescription rules ACL2::-
APPEND-TRUE-LISTP-TYPE-PRESCRIPTION and G-SCHED-LOOP.

Summary
Form:  ( DEFUN G-SCHED ...)
Rules: ((:TYPE-PRESCRIPTION ACL2::APPEND-TRUE-LISTP-TYPE-PRESCRIPTION)
        (:TYPE-PRESCRIPTION G-SCHED-LOOP))
Warnings:  None
Time:  0.00 seconds (prove: 0.00, print: 0.00, other: 0.00)
 G-SCHED
M1 >(defun run-g (n)
         (top
          (stack
           (run (g-sched n)
                (make-state 0
                            (list n 0)
                            nil
                            *g*)))))

Since RUN-G is non-recursive, its admission is trivial.  We could deduce
no constraints on the type of RUN-G.

Summary
Form:  ( DEFUN RUN-G ...)
Rules: NIL
Warnings:  None
Time:  0.00 seconds (prove: 0.00, print: 0.00, other: 0.00)
 RUN-G
M1 >(run-g 5)
120
M1 >(run-g 1000)
402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
M1 >(len (g-sched 1000))
11006
M1 >(quote (End of Demo 1))
(END OF DEMO 1)
M1 >(include-book "compile")

Summary
Form:  ( INCLUDE-BOOK "compile" ...)
Rules: NIL
Warnings:  None
Time:  0.06 seconds (prove: 0.00, print: 0.00, other: 0.06)
 "/v/filer4b/v11q001/text/marktoberdorf-08/scripts/compile.lisp"
M1 >(compile '(n)               ; Factorial
             '((a = 1)
               (while (n > 0)
                 (a = (n * a))
                 (n = (n - 1)))
               (return a)))
((PUSH 1)
 (STORE 1)
 (LOAD 0)
 (IFLE 10)
 (LOAD 0)
 (LOAD 1)
 (MUL)
 (STORE 1)
 (LOAD 0)
 (PUSH 1)
 (SUB)
 (STORE 0)
 (GOTO -10)
 (LOAD 1)
 (RETURN))
M1 >(quote (End of Demo 2))
(END OF DEMO 2)
M1 >