/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files


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Graph construction failed
Graph construction failed
Graph construction failed
MAYBE
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

peephole_opt(g,a)

w.r.t. the given Prolog program could not be shown:

(0) Prolog
(1) NotTransformerProof [EQUIVALENT, 0 ms]
(2) Prolog
    (3) CallTransformerProof [EQUIVALENT, 0 ms]
    (4) Prolog
    (5) CutEliminatorProof [SOUND, 0 ms]
    (6) Prolog
    (7) IfThenElseTransformerProof [EQUIVALENT, 0 ms]
    (8) Prolog
    (9) CallTransformerProof [EQUIVALENT, 0 ms]
    (10) Prolog
    (11) CutEliminatorProof [SOUND, 0 ms]
    (12) Prolog
    (13) FailTransformerProof [EQUIVALENT, 0 ms]
    (14) Prolog
    (15) UnifyTransformerProof [EQUIVALENT, 0 ms]
    (16) Prolog
    (17) OrTransformerProof [EQUIVALENT, 0 ms]
    (18) Prolog
    (19) UndefinedPredicateHandlerProof [SOUND, 0 ms]
    (20) Prolog
(21) IntegerArithmeticTransformerProof [SOUND, 0 ms]
(22) Prolog
    (23) NotTransformerProof [EQUIVALENT, 0 ms]
    (24) Prolog
    (25) CallTransformerProof [EQUIVALENT, 0 ms]
    (26) Prolog
    (27) CutEliminatorProof [SOUND, 0 ms]
    (28) Prolog
    (29) IfThenElseTransformerProof [EQUIVALENT, 0 ms]
    (30) Prolog
    (31) CallTransformerProof [EQUIVALENT, 0 ms]
    (32) Prolog
    (33) CutEliminatorProof [SOUND, 0 ms]
    (34) Prolog
    (35) FailTransformerProof [EQUIVALENT, 0 ms]
    (36) Prolog
    (37) UnifyTransformerProof [EQUIVALENT, 0 ms]
    (38) Prolog
    (39) OrTransformerProof [EQUIVALENT, 0 ms]
    (40) Prolog
    (41) UndefinedPredicateHandlerProof [SOUND, 0 ms]
    (42) Prolog


----------------------------------------

(0)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(!, ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest))).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(!, ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest))).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, 1)), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- ','(peep_term(Inst, R), !).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- \+(P).


Query: peephole_opt(g,a)
----------------------------------------

(1) NotTransformerProof (EQUIVALENT)
Transformed all not-constructs [PROLOG].
----------------------------------------

(2)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(!, ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest))).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(!, ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest))).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, 1)), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- ','(peep_term(Inst, R), !).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call(P), ','(!, fail)).
not1(P).


Query: peephole_opt(g,a)
----------------------------------------

(3) CallTransformerProof (EQUIVALENT)
Transformed all call-constructs [PROLOG].
----------------------------------------

(4)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(!, ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest))).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(!, ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest))).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, 1)), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- ','(peep_term(Inst, R), !).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), ','(!, fail)).
not1(P).
call1(P) :- P.


Query: peephole_opt(g,a)
----------------------------------------

(5) CutEliminatorProof (SOUND)
Eliminated all cuts by simply ignoring them[PROLOG].
----------------------------------------

(6)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, 1)), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.


Query: peephole_opt(g,a)
----------------------------------------

(7) IfThenElseTransformerProof (EQUIVALENT)
Transformed all if-then-else-constructs [PROLOG].
----------------------------------------

(8)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.
if(P, P1, Flag, L1) :- ','(call(=(P, P1)), ','(!, =(Flag, 1))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).


Query: peephole_opt(g,a)
----------------------------------------

(9) CallTransformerProof (EQUIVALENT)
Transformed all call-constructs [PROLOG].
----------------------------------------

(10)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.
if(P, P1, Flag, L1) :- ','(call2(P, P1), ','(!, =(Flag, 1))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call2(P, P1) :- =(P, P1).


Query: peephole_opt(g,a)
----------------------------------------

(11) CutEliminatorProof (SOUND)
Eliminated all cuts by simply ignoring them[PROLOG].
----------------------------------------

(12)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.
if(P, P1, Flag, L1) :- ','(call2(P, P1), =(Flag, 1)).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call2(P, P1) :- =(P, P1).


Query: peephole_opt(g,a)
----------------------------------------

(13) FailTransformerProof (EQUIVALENT)
Added clauses for the built-in fail predicate [PROLOG].
----------------------------------------

(14)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.
if(P, P1, Flag, L1) :- ','(call2(P, P1), =(Flag, 1)).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call2(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).


Query: peephole_opt(g,a)
----------------------------------------

(15) UnifyTransformerProof (EQUIVALENT)
Added a fact for the built-in = predicate [PROLOG].
----------------------------------------

(16)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(>=(N, 0), member1(','(P, N), Seen)), <(N, 0)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.
if(P, P1, Flag, L1) :- ','(call2(P, P1), =(Flag, 1)).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call2(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).
=(X, X).


Query: peephole_opt(g,a)
----------------------------------------

(17) OrTransformerProof (EQUIVALENT)
Transformed all or-constructs[PROLOG].
----------------------------------------

(18)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(>=(N, 0), member1(','(P, N), Seen)), popt4(Rest, Seen, ORest)).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(<(N, 0), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))).
popt_chkmember(P, L, Flag) :- ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.
if(P, P1, Flag, L1) :- ','(call2(P, P1), =(Flag, 1)).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call2(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).
=(X, X).


Query: peephole_opt(g,a)
----------------------------------------

(19) UndefinedPredicateHandlerProof (SOUND)
Added facts for all undefined predicates [PROLOG].
----------------------------------------

(20)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', 2))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', 2), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', 2), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(>=(N, 0), member1(','(P, N), Seen)), popt4(Rest, Seen, ORest)).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(<(N, 0), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(=:=(SFlag, 1), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(>=(N, 0), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(=\=(SFlag, 1), =(OList, .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(<(N, 0), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ','(var(L), ','(=(L, .(P, _N)), =(Flag, 0))).
popt_chkmember(P, L, Flag) :- ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
not1(P) :- ','(call1(P), fail).
not1(P).
call1(P) :- P.
if(P, P1, Flag, L1) :- ','(call2(P, P1), =(Flag, 1)).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call2(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).
=(X, X).
>=(X0, X1).
<(X0, X1).
=:=(X0, X1).
=\=(X0, X1).
var(X0).
nonvar(X0).


Query: peephole_opt(g,a)
----------------------------------------

(21) IntegerArithmeticTransformerProof (SOUND)
Added definitions of predefined predicates [PROLOG].
----------------------------------------

(22)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(!, ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest))).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(!, ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest))).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, succ(zero))), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- ','(peep_term(Inst, R), !).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- \+(P).
nounify(X, Y) :- \+(=(X, Y)).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).


Query: peephole_opt(g,a)
----------------------------------------

(23) NotTransformerProof (EQUIVALENT)
Transformed all not-constructs [PROLOG].
----------------------------------------

(24)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(!, ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest))).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(!, ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest))).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, succ(zero))), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- ','(peep_term(Inst, R), !).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call(P), ','(!, fail)).
not1(P).
not2(X, Y) :- ','(call(=(X, Y)), ','(!, fail)).
not2(X, Y).


Query: peephole_opt(g,a)
----------------------------------------

(25) CallTransformerProof (EQUIVALENT)
Transformed all call-constructs [PROLOG].
----------------------------------------

(26)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(!, ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest))).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(!, ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest))).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, succ(zero))), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- ','(peep_term(Inst, R), !).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), ','(!, fail)).
not1(P).
not2(X, Y) :- ','(call2(X, Y), ','(!, fail)).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).


Query: peephole_opt(g,a)
----------------------------------------

(27) CutEliminatorProof (SOUND)
Eliminated all cuts by simply ignoring them[PROLOG].
----------------------------------------

(28)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), ;(->(=(P, P1), =(Flag, succ(zero))), popt_chkmember(P, L1, Flag))))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).


Query: peephole_opt(g,a)
----------------------------------------

(29) IfThenElseTransformerProof (EQUIVALENT)
Transformed all if-then-else-constructs [PROLOG].
----------------------------------------

(30)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).
if(P, P1, Flag, L1) :- ','(call(=(P, P1)), ','(!, =(Flag, succ(zero)))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).


Query: peephole_opt(g,a)
----------------------------------------

(31) CallTransformerProof (EQUIVALENT)
Transformed all call-constructs [PROLOG].
----------------------------------------

(32)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).
if(P, P1, Flag, L1) :- ','(call3(P, P1), ','(!, =(Flag, succ(zero)))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call3(P, P1) :- =(P, P1).


Query: peephole_opt(g,a)
----------------------------------------

(33) CutEliminatorProof (SOUND)
Eliminated all cuts by simply ignoring them[PROLOG].
----------------------------------------

(34)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).
if(P, P1, Flag, L1) :- ','(call3(P, P1), =(Flag, succ(zero))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call3(P, P1) :- =(P, P1).


Query: peephole_opt(g,a)
----------------------------------------

(35) FailTransformerProof (EQUIVALENT)
Added clauses for the built-in fail predicate [PROLOG].
----------------------------------------

(36)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).
if(P, P1, Flag, L1) :- ','(call3(P, P1), =(Flag, succ(zero))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call3(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).


Query: peephole_opt(g,a)
----------------------------------------

(37) UnifyTransformerProof (EQUIVALENT)
Added a fact for the built-in = predicate [PROLOG].
----------------------------------------

(38)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(;(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), ','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(;(','(','(','(=(X, N), =(X1, zero)), ;(isGreater(X, X1), =(X, X1))), member1(','(P, N), Seen)), ','(','(=(X2, N), =(X3, zero)), isLess(X2, X3))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(;(','(','(','(=(X4, N), =(X5, zero)), ;(isGreater(X4, X5), =(X4, X5))), ','(popt_chkmember(','(P, N), Seen, SFlag), ;(','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest)))))), ','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ;(','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))), ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1)))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).
if(P, P1, Flag, L1) :- ','(call3(P, P1), =(Flag, succ(zero))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call3(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).
=(X, X).


Query: peephole_opt(g,a)
----------------------------------------

(39) OrTransformerProof (EQUIVALENT)
Transformed all or-constructs[PROLOG].
----------------------------------------

(40)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(','(','(=(X, N), =(X1, zero)), isGreater(X, X1)), member1(','(P, N), Seen)), popt4(Rest, Seen, ORest)).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(','(','(=(X, N), =(X1, zero)), =(X, X1)), member1(','(P, N), Seen)), popt4(Rest, Seen, ORest)).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(','(=(X2, N), =(X3, zero)), isLess(X2, X3)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), isGreater(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), isGreater(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), =(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), =(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))).
popt_chkmember(P, L, Flag) :- ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).
if(P, P1, Flag, L1) :- ','(call3(P, P1), =(Flag, succ(zero))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call3(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).
=(X, X).


Query: peephole_opt(g,a)
----------------------------------------

(41) UndefinedPredicateHandlerProof (SOUND)
Added facts for all undefined predicates [PROLOG].
----------------------------------------

(42)
Obligation:
Clauses:

peephole_opt(Pil, OptPil) :- ','(popt1(Pil, Pil1), ','(popt2(Pil1, Pil2), ','(popt3(Pil2, Pil3), popt4(Pil3, _N, OptPil)))).
popt1([], []).
popt1(.(Inst, Rest), Pil1) :- popt11(Inst, Rest, Pil1).
popt1(.(Inst, Rest), Pil1) :- ','(not(popt11(Inst, Rest, Pil)), ','(=(Pil1, .(Inst, Pil)), popt1(Rest, Pil))).
popt11(puttvar(T, R), .(getstr(S, R), PilRest), .(putstr(S, T), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(getstr(S, T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(getstr(S, R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(getstr(S, R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(puttbreg(T), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(puttbreg(R), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(puttbreg(R), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(addreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(addreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(addreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(subreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(subreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(subreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(mulreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(mulreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(mulreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(peep_chk(PilRest, R), =(OptInstList, .(divreg(T, S), OptPilRest))), popt1(PilRest, OptPilRest)).
popt11(movreg(T, R), .(divreg(R, S), PilRest), OptInstList) :- ','(','(not(peep_chk(PilRest, R)), =(OptInstList, .(movreg(T, R), .(divreg(R, S), OptPilRest)))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getpval(V, R), PilRest), .(putpvar(V, R), OptPilRest)) :- popt1(PilRest, OptPilRest).
popt11(putpval(V, R), .(getstr(Str, R), PilRest), .(getstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1(PilRest, OptPilRest)).
popt11(putpvar(V, R), .(getstr(Str, R), PilRest), .(putstrv(Str, V), OptPilRest)) :- ','(not(=(Str, ','('.', succ(succ(zero))))), popt1a(PilRest, OptPilRest)).
popt11(gettval(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(movreg(R, R), PRest, OptPRest) :- popt1(PRest, OptPRest).
popt11(jump(L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt11(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1(PRest, OptPRest).
popt1a([], []).
popt1a(.(Inst, PilRest), Pil1) :- popt1a1(Inst, PilRest, Pil1).
popt1a(.(Inst, PilRest), Pil1) :- ','(not(popt1a1(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt1a(PilRest, Pil1Rest))).
popt1a1(unipvar(X), PilRest, .(bldpvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unipval(X), PilRest, .(bldpval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitvar(X), PilRest, .(bldtvar(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unitval(X), PilRest, .(bldtval(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unicon(X), PilRest, .(bldcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(uninumcon(X), PilRest, .(bldnumcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(unifloatcon(X), PilRest, .(bldfloatcon(X), OptPilRest)) :- popt1a(PilRest, OptPilRest).
popt1a1(gettval(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(movreg(R, R), PRest, OptPRest) :- popt1a(PRest, OptPRest).
popt1a1(jump(L), .(label(L), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jump(Addr), .(jump(_N), PRest), .(jump(Addr), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpnz(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumplt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumple(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpgt(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt1a1(jumpge(_N, L), .(label(L), PRest), .(label(L), OptPRest)) :- popt1a(PRest, OptPRest).
popt2([], []).
popt2(.(Inst, PilRest), Pil1) :- popt21(Inst, PilRest, Pil1).
popt2(.(Inst, PilRest), Pil1) :- ','(not(popt21(Inst, PilRest, Pil1)), ','(=(Pil1, .(Inst, Pil1Rest)), popt2(PilRest, Pil1Rest))).
popt21(getstr(','('.', succ(succ(zero))), R), PilRest, .(getlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putstr(','('.', succ(succ(zero))), R), PilRest, .(putlist(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(getcon('[]', R), PilRest, .(getnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(putcon('[]', R), PilRest, .(putnil(R), OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(unicon('[]'), PilRest, .(uninil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt21(bldcon('[]'), PilRest, .(bldnil, OptPilRest)) :- popt2(PilRest, OptPilRest).
popt3([], []).
popt3(.(Inst, Rest), Pil) :- popt31(Inst, Rest, Pil).
popt3(.(Inst, Rest), Pil) :- ','(not(popt31(Inst, Rest, Pil)), ','(=(Pil, .(Inst, Pil1)), popt3(Pil, Pil1))).
popt31(getlist(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getlist_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt31(getcomma(R0), .(unitvar(R1), .(unitvar(R2), Rest)), .(getcomma_tvar_tvar(R0, R1, R2), OptRest)) :- popt3(Rest, OptRest).
popt4([], X1, []).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(','(','(=(X, N), =(X1, zero)), isGreater(X, X1)), member1(','(P, N), Seen)), popt4(Rest, Seen, ORest)).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(','(','(=(X, N), =(X1, zero)), =(X, X1)), member1(','(P, N), Seen)), popt4(Rest, Seen, ORest)).
popt4(.(label(','(P, ','(N, K))), Rest), Seen, .(label(','(P, ','(N, K))), ORest)) :- ','(','(','(=(X2, N), =(X3, zero)), isLess(X2, X3)), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), isGreater(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), isGreater(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), =(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X, SFlag), =(X1, succ(zero))), =(X, X1)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X4, N), =(X5, zero)), =(X4, X5)), ','(popt_chkmember(','(P, N), Seen, SFlag), ','(','(','(=(X2, SFlag), =(X3, succ(zero))), nounify(X2, X3)), =(OList, .(label(','(P, ','(N, K))), ORest))))), popt4(Rest, Seen, ORest)).
popt4(.(execute(','(P, N)), .(label(','(P, ','(N, K))), Rest)), Seen, OList) :- ','(','(','(','(=(X6, N), =(X7, zero)), isLess(X6, X7)), =(OList, .(execute(','(P, N)), .(label(','(P, ','(N, K))), ORest)))), popt4(Rest, Seen, ORest)).
popt4(.(Inst, Rest), Seen, .(Inst, ORest)) :- popt4(Rest, Seen, ORest).
popt_chkmember(P, L, Flag) :- ','(var(L), ','(=(L, .(P, _N)), =(Flag, zero))).
popt_chkmember(P, L, Flag) :- ','(nonvar(L), ','(=(L, .(P1, L1)), if(P, P1, Flag, L1))).
peep_use(getcon(X2, R), R).
peep_use(getnumcon(X3, R), R).
peep_use(getfloatcon(X4, R), R).
peep_use(getpval(X5, R), R).
peep_use(gettval(X6, R), R).
peep_use(gettval(R, X7), R).
peep_use(gettbreg(R), R).
peep_use(getpbreg(R), R).
peep_use(getstr(X8, R), R).
peep_use(getstrv(X9, R), R).
peep_use(getlist(R), R).
peep_use(getlist_tvar_tvar(R, X10, X11), R).
peep_use(getcomma(R), R).
peep_use(getcomma_tvar_tvar(R, X12, X13), R).
peep_use(unitval(R), R).
peep_use(unipval(R), R).
peep_use(bldtval(R), R).
peep_use(bldpval(R), R).
peep_use(and(R, X14), R).
peep_use(and(X15, R), R).
peep_use(negate(R), R).
peep_use(or(R, X16), R).
peep_use(or(X17, R), R).
peep_use(logshiftl(R, X18), R).
peep_use(logshiftl(X19, R), R).
peep_use(logshiftr(R, X20), R).
peep_use(logshiftr(X21, R), R).
peep_use(addreg(R, X22), R).
peep_use(addreg(X23, R), R).
peep_use(subreg(R, X24), R).
peep_use(subreg(X25, R), R).
peep_use(mulreg(R, X26), R).
peep_use(mulreg(X27, R), R).
peep_use(divreg(R, X28), R).
peep_use(divreg(X29, R), R).
peep_use(movreg(R, X30), R).
peep_use(switchonterm(R, X31, X32), R).
peep_use(switchoncon(R, X33, X34), R).
peep_use(switchonstr(R, X35, X36), R).
peep_use(switchonbound(R, X37, X38), R).
peep_use(jump(X39), X40).
peep_use(jumpeq(X41, X42), X43).
peep_use(jumpne(X44, X45), X46).
peep_use(jumplt(X47, X48), X49).
peep_use(jumple(X50, X51), X52).
peep_use(jumpgt(X53, X54), X55).
peep_use(jumpge(X56, X57), X58).
peep_chk([], X59).
peep_chk(.(Inst, Rest), R) :- ','(not(peep_use(Inst, R)), term_or_chk(.(Inst, Rest), R)).
term_or_chk(.(Inst, _N), R) :- peep_term(Inst, R).
term_or_chk(.(_N, Rest), R) :- peep_chk(Rest, R).
peep_term(call(X60, X61), X62).
peep_term(calld(X63, X64), X65).
peep_term(execute(X66), X67).
peep_term(putcon(R), R).
peep_term(putnumcon(R), R).
peep_term(putfloatcon(R), R).
peep_term(puttvar(R, X68), R).
peep_term(putpvar(X69, R), R).
peep_term(putdval(X70, R), R).
peep_term(putuval(X71, R), R).
peep_term(puttbreg(R), R).
peep_term(putpval(X72, R), R).
peep_term(putstr(X73, R), R).
peep_term(putstrv(X74, R), R).
peep_term(putlist(R), R).
peep_term(putnil(R), R).
peep_term(movreg(X75, R), R).
peep_term(bldtvar(R), R).
member1(X, .(X, Xs)).
member1(X, .(_N, Xs)) :- member1(X, Xs).
not(P) :- not1(P).
nounify(X, Y) :- not2(X, Y).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not1(P) :- ','(call1(P), fail).
not1(P).
not2(X, Y) :- ','(call2(X, Y), fail).
not2(X, Y).
call1(P) :- P.
call2(X, Y) :- =(X, Y).
if(P, P1, Flag, L1) :- ','(call3(P, P1), =(Flag, succ(zero))).
if(P, P1, Flag, L1) :- popt_chkmember(P, L1, Flag).
call3(P, P1) :- =(P, P1).
fail :- failure(a).
failure(b).
=(X, X).
var(X0).
nonvar(X0).


Query: peephole_opt(g,a)