/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

analyze_all(g,a)

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

(0) Prolog
(1) CutEliminatorProof [SOUND, 0 ms]
(2) Prolog
    (3) FailTransformerProof [EQUIVALENT, 0 ms]
    (4) Prolog
    (5) UnifyTransformerProof [EQUIVALENT, 0 ms]
    (6) Prolog
    (7) OrTransformerProof [EQUIVALENT, 0 ms]
    (8) Prolog
    (9) UndefinedPredicateHandlerProof [SOUND, 0 ms]
    (10) Prolog
(11) IntegerArithmeticTransformerProof [SOUND, 0 ms]
(12) Prolog
    (13) CutEliminatorProof [SOUND, 0 ms]
    (14) Prolog
    (15) FailTransformerProof [EQUIVALENT, 0 ms]
    (16) Prolog
    (17) UnifyTransformerProof [EQUIVALENT, 0 ms]
    (18) Prolog
    (19) OrTransformerProof [EQUIVALENT, 0 ms]
    (20) Prolog
    (21) UndefinedPredicateHandlerProof [SOUND, 0 ms]
    (22) Prolog


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

(0)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), ','(!, =(NewSource, Source))), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), ','(un_number_vars(New_Source, NewSource, others), !)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, 0), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, 0, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), ','(add_annotations(Info, P, I, G), !))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(!, ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd))).
add_annotations(Info, Phrase, I, G) :- ','(!, ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), ','(!, =(Phrase, PCode))), ','(=(Vars, []), ','(!, =(Phrase, Code)))), =(Phrase, ','(PCode, Code)))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(!, ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M))).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(!, ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), ','(!, =(CInfo, sequential)))), ','(\==(NewVars, []), ','(!, =(CInfo, suspect)))), true), !)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(!, ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(!, ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), ','(!, =(Conjuncts, ','(Xcode, CGE)))), ','(=(YVars, []), ','(!, =(Conjuncts, ','(Xcode, Ycode))))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential)))))), ','(=(Ytype, sequential), ','(!, ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype)))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype))))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(!, ','(=(Type, T), ','(=(Vars, []), =(This_term, Term))))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9) :- !.
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- ','(get_phrase(VarList, NewCode, I, G), !).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(>(L, 1), ','(!, ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem)))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(!, ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(!, ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, []))))), =(ParCode, .(This_goal, .(Last_goal, [])))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(!, ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, []))))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(','(find_var(Next_calls, H), !), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(','(member(V, NextCall), !), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- ','(var(Others), !).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others) :- !.
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), ','(!, =(Pcode, Parallel)))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), ','(!, =(Code, Pcode))), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(!, ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset))))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(!, ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples)))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(!, ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples)))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(!, ','(;(','(@<(E, L), ','(!, =(Pair, .(.(E, .(L, [])), [])))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples)))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T) :- !.
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T) :- !.
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- ','(!, intersect(S1, S2, IS)).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(is(NewVars, -(Cout, Cin)), ','(length(Vars, NewVars), ','(numbervars_2(Vars, Cin, _N), !)))).
collect_vars(X, .(X, [])) :- ','(var(X), !).
collect_vars('$VAR'(X), .('$VAR'(X), [])) :- !.
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])) :- !.
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(0, X25, []) :- !.
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), ','(!, =(Bag, .(ARG, C)))), ','(atomic(ARG), ','(!, =(Bag, C)))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag)))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)) :- !.
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), ','(!, subtract(Residue, Set, Difference))).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D) :- !.
merge(D, [], D) :- !.
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), ','(!, merge(As, .(D, Ds), Bs))).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), ','(!, merge(As, Ds, Bs))).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []) :- !.
intersect(X33, [], []) :- !.
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), ','(!, intersect(As, .(D, Ds), Out))).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), ','(!, intersect(As, Ds, Out))).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(is(N1, +(N, 1)), ','(!, =(X, '$VAR'(N, _L))))).
numbervars_2(A, N, N) :- ','(atomic(A), !).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(0, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), ','(!, numbervars_2(I1, F, N0, N1))))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), ','(un_number_vars_2(Body, B, X), !)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others) :- !.
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge) :- !.
un_number_vars_2(X, X, X41) :- ','(atomic(X), !).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(0, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), ','(!, un_number_vars_2(I1, F, Tail, Y))))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, 0), =(Result, 0)), ','(check_if_cge(Y, ResultY), is(Result, *(ResultX, ResultY))))).
check_if_cge('=>'(X45, X46), 0).
check_if_cge('&'(X47, X48), 0).
check_if_cge(X49, 1).
builtin(/(fail, 0)).
builtin(/(false, 0)).
builtin(/(otherwise, 0)).
builtin(/(repeat, 0)).
builtin(/(true, 0)).
builtin(/(version, 0)).
builtin(/(version, 1)).
builtin(/(!, 0)).
builtin(/(abolish, 1)).
builtin(/(abolish, 2)).
builtin(/(abort, 0)).
builtin(/(assert, 1)).
builtin(/(assert, 2)).
builtin(/(asserta, 1)).
builtin(/(asserta, 2)).
builtin(/(assertz, 1)).
builtin(/(assertz, 2)).
builtin(/(bagof, 3)).
builtin(/(break, 0)).
builtin(/(call, 1)).
builtin(/(close, 1)).
builtin(/(compile, 1)).
builtin(/(consult, 1)).
builtin(/(debug, 0)).
builtin(/(debugging, 0)).
builtin(/(ensure_loaded, 1)).
builtin(/(erase, 1)).
builtin(/(fileerrors, 0)).
builtin(/(flush_output, 1)).
builtin(/(foreign, 2)).
builtin(/(foreign, 3)).
builtin(/(foreign_file, 2)).
builtin(/(get, 1)).
builtin(/(get, 2)).
builtin(/(get0, 1)).
builtin(/(get0, 2)).
builtin(/(halt, 0)).
builtin(/(incore, 1)).
builtin(/(load_foreign_files, 2)).
builtin(/(module, 1)).
builtin(/(nofileerrors, 0)).
builtin(/(no_style_check, 1)).
builtin(/(open, 3)).
builtin(/(open_null_stream, 1)).
builtin(/(read, 1)).
builtin(/(read, 2)).
builtin(/(recorda, 3)).
builtin(/(recorded, 3)).
builtin(/(recordz, 3)).
builtin(/(reinitialise, 0)).
builtin(/(restore, 1)).
builtin(/(restore, 2)).
builtin(/(retract, 1)).
builtin(/(retractall, 1)).
builtin(/(save, 1)).
builtin(/(save, 2)).
builtin(/(save_program, 1)).
builtin(/(see, 1)).
builtin(/(seeing, 1)).
builtin(/(seen, 0)).
builtin(/(set_input, 1)).
builtin(/(set_output, 1)).
builtin(/(setof, 3)).
builtin(/(skip, 1)).
builtin(/(skip, 2)).
builtin(/(style_check, 1)).
builtin(/(ttyget, 1)).
builtin(/(ttyget0, 1)).
builtin(/(ttyskip, 1)).
builtin(/(unknown, 2)).
builtin(/(use_module, 1)).
builtin(/(use_module, 2)).
builtin(/('^', 2)).
builtin(/(\+, 1)).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(0, _1, []).
mlist(X, SList, LList) :- ','(is(Y, -(X, 1)), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList)))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).


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

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

(2)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), =(NewSource, Source)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, 0), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, 0, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), =(Phrase, PCode)), ','(=(Vars, []), =(Phrase, Code))), =(Phrase, ','(PCode, Code))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential))), ','(\==(NewVars, []), =(CInfo, suspect))), true)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode)))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential))))), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype)))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(>(L, 1), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, [])))), =(ParCode, .(This_goal, .(Last_goal, []))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(find_var(Next_calls, H), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(member(V, NextCall), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), =(Code, Pcode)), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(;(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(is(NewVars, -(Cout, Cin)), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N)))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(0, X25, []).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), =(Bag, .(ARG, C))), ','(atomic(ARG), =(Bag, C))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag)))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(is(N1, +(N, 1)), =(X, '$VAR'(N, _L)))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(0, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1)))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(0, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y)))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, 0), =(Result, 0)), ','(check_if_cge(Y, ResultY), is(Result, *(ResultX, ResultY))))).
check_if_cge('=>'(X45, X46), 0).
check_if_cge('&'(X47, X48), 0).
check_if_cge(X49, 1).
builtin(/(fail, 0)).
builtin(/(false, 0)).
builtin(/(otherwise, 0)).
builtin(/(repeat, 0)).
builtin(/(true, 0)).
builtin(/(version, 0)).
builtin(/(version, 1)).
builtin(/(!, 0)).
builtin(/(abolish, 1)).
builtin(/(abolish, 2)).
builtin(/(abort, 0)).
builtin(/(assert, 1)).
builtin(/(assert, 2)).
builtin(/(asserta, 1)).
builtin(/(asserta, 2)).
builtin(/(assertz, 1)).
builtin(/(assertz, 2)).
builtin(/(bagof, 3)).
builtin(/(break, 0)).
builtin(/(call, 1)).
builtin(/(close, 1)).
builtin(/(compile, 1)).
builtin(/(consult, 1)).
builtin(/(debug, 0)).
builtin(/(debugging, 0)).
builtin(/(ensure_loaded, 1)).
builtin(/(erase, 1)).
builtin(/(fileerrors, 0)).
builtin(/(flush_output, 1)).
builtin(/(foreign, 2)).
builtin(/(foreign, 3)).
builtin(/(foreign_file, 2)).
builtin(/(get, 1)).
builtin(/(get, 2)).
builtin(/(get0, 1)).
builtin(/(get0, 2)).
builtin(/(halt, 0)).
builtin(/(incore, 1)).
builtin(/(load_foreign_files, 2)).
builtin(/(module, 1)).
builtin(/(nofileerrors, 0)).
builtin(/(no_style_check, 1)).
builtin(/(open, 3)).
builtin(/(open_null_stream, 1)).
builtin(/(read, 1)).
builtin(/(read, 2)).
builtin(/(recorda, 3)).
builtin(/(recorded, 3)).
builtin(/(recordz, 3)).
builtin(/(reinitialise, 0)).
builtin(/(restore, 1)).
builtin(/(restore, 2)).
builtin(/(retract, 1)).
builtin(/(retractall, 1)).
builtin(/(save, 1)).
builtin(/(save, 2)).
builtin(/(save_program, 1)).
builtin(/(see, 1)).
builtin(/(seeing, 1)).
builtin(/(seen, 0)).
builtin(/(set_input, 1)).
builtin(/(set_output, 1)).
builtin(/(setof, 3)).
builtin(/(skip, 1)).
builtin(/(skip, 2)).
builtin(/(style_check, 1)).
builtin(/(ttyget, 1)).
builtin(/(ttyget0, 1)).
builtin(/(ttyskip, 1)).
builtin(/(unknown, 2)).
builtin(/(use_module, 1)).
builtin(/(use_module, 2)).
builtin(/('^', 2)).
builtin(/(\+, 1)).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(0, _1, []).
mlist(X, SList, LList) :- ','(is(Y, -(X, 1)), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList)))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).


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

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

(4)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), =(NewSource, Source)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, 0), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, 0, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), =(Phrase, PCode)), ','(=(Vars, []), =(Phrase, Code))), =(Phrase, ','(PCode, Code))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential))), ','(\==(NewVars, []), =(CInfo, suspect))), true)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode)))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential))))), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype)))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(>(L, 1), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, [])))), =(ParCode, .(This_goal, .(Last_goal, []))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(find_var(Next_calls, H), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(member(V, NextCall), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), =(Code, Pcode)), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(;(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(is(NewVars, -(Cout, Cin)), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N)))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(0, X25, []).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), =(Bag, .(ARG, C))), ','(atomic(ARG), =(Bag, C))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag)))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(is(N1, +(N, 1)), =(X, '$VAR'(N, _L)))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(0, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1)))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(0, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y)))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, 0), =(Result, 0)), ','(check_if_cge(Y, ResultY), is(Result, *(ResultX, ResultY))))).
check_if_cge('=>'(X45, X46), 0).
check_if_cge('&'(X47, X48), 0).
check_if_cge(X49, 1).
builtin(/(fail, 0)).
builtin(/(false, 0)).
builtin(/(otherwise, 0)).
builtin(/(repeat, 0)).
builtin(/(true, 0)).
builtin(/(version, 0)).
builtin(/(version, 1)).
builtin(/(!, 0)).
builtin(/(abolish, 1)).
builtin(/(abolish, 2)).
builtin(/(abort, 0)).
builtin(/(assert, 1)).
builtin(/(assert, 2)).
builtin(/(asserta, 1)).
builtin(/(asserta, 2)).
builtin(/(assertz, 1)).
builtin(/(assertz, 2)).
builtin(/(bagof, 3)).
builtin(/(break, 0)).
builtin(/(call, 1)).
builtin(/(close, 1)).
builtin(/(compile, 1)).
builtin(/(consult, 1)).
builtin(/(debug, 0)).
builtin(/(debugging, 0)).
builtin(/(ensure_loaded, 1)).
builtin(/(erase, 1)).
builtin(/(fileerrors, 0)).
builtin(/(flush_output, 1)).
builtin(/(foreign, 2)).
builtin(/(foreign, 3)).
builtin(/(foreign_file, 2)).
builtin(/(get, 1)).
builtin(/(get, 2)).
builtin(/(get0, 1)).
builtin(/(get0, 2)).
builtin(/(halt, 0)).
builtin(/(incore, 1)).
builtin(/(load_foreign_files, 2)).
builtin(/(module, 1)).
builtin(/(nofileerrors, 0)).
builtin(/(no_style_check, 1)).
builtin(/(open, 3)).
builtin(/(open_null_stream, 1)).
builtin(/(read, 1)).
builtin(/(read, 2)).
builtin(/(recorda, 3)).
builtin(/(recorded, 3)).
builtin(/(recordz, 3)).
builtin(/(reinitialise, 0)).
builtin(/(restore, 1)).
builtin(/(restore, 2)).
builtin(/(retract, 1)).
builtin(/(retractall, 1)).
builtin(/(save, 1)).
builtin(/(save, 2)).
builtin(/(save_program, 1)).
builtin(/(see, 1)).
builtin(/(seeing, 1)).
builtin(/(seen, 0)).
builtin(/(set_input, 1)).
builtin(/(set_output, 1)).
builtin(/(setof, 3)).
builtin(/(skip, 1)).
builtin(/(skip, 2)).
builtin(/(style_check, 1)).
builtin(/(ttyget, 1)).
builtin(/(ttyget0, 1)).
builtin(/(ttyskip, 1)).
builtin(/(unknown, 2)).
builtin(/(use_module, 1)).
builtin(/(use_module, 2)).
builtin(/('^', 2)).
builtin(/(\+, 1)).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(0, _1, []).
mlist(X, SList, LList) :- ','(is(Y, -(X, 1)), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList)))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
fail :- failure(a).
failure(b).


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

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

(6)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), =(NewSource, Source)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, 0), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, 0, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), =(Phrase, PCode)), ','(=(Vars, []), =(Phrase, Code))), =(Phrase, ','(PCode, Code))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential))), ','(\==(NewVars, []), =(CInfo, suspect))), true)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode)))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential))))), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype)))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(>(L, 1), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, [])))), =(ParCode, .(This_goal, .(Last_goal, []))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(find_var(Next_calls, H), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(member(V, NextCall), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), =(Code, Pcode)), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(;(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(is(NewVars, -(Cout, Cin)), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N)))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(0, X25, []).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), =(Bag, .(ARG, C))), ','(atomic(ARG), =(Bag, C))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag)))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(is(N1, +(N, 1)), =(X, '$VAR'(N, _L)))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(0, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1)))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(0, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y)))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, 0), =(Result, 0)), ','(check_if_cge(Y, ResultY), is(Result, *(ResultX, ResultY))))).
check_if_cge('=>'(X45, X46), 0).
check_if_cge('&'(X47, X48), 0).
check_if_cge(X49, 1).
builtin(/(fail, 0)).
builtin(/(false, 0)).
builtin(/(otherwise, 0)).
builtin(/(repeat, 0)).
builtin(/(true, 0)).
builtin(/(version, 0)).
builtin(/(version, 1)).
builtin(/(!, 0)).
builtin(/(abolish, 1)).
builtin(/(abolish, 2)).
builtin(/(abort, 0)).
builtin(/(assert, 1)).
builtin(/(assert, 2)).
builtin(/(asserta, 1)).
builtin(/(asserta, 2)).
builtin(/(assertz, 1)).
builtin(/(assertz, 2)).
builtin(/(bagof, 3)).
builtin(/(break, 0)).
builtin(/(call, 1)).
builtin(/(close, 1)).
builtin(/(compile, 1)).
builtin(/(consult, 1)).
builtin(/(debug, 0)).
builtin(/(debugging, 0)).
builtin(/(ensure_loaded, 1)).
builtin(/(erase, 1)).
builtin(/(fileerrors, 0)).
builtin(/(flush_output, 1)).
builtin(/(foreign, 2)).
builtin(/(foreign, 3)).
builtin(/(foreign_file, 2)).
builtin(/(get, 1)).
builtin(/(get, 2)).
builtin(/(get0, 1)).
builtin(/(get0, 2)).
builtin(/(halt, 0)).
builtin(/(incore, 1)).
builtin(/(load_foreign_files, 2)).
builtin(/(module, 1)).
builtin(/(nofileerrors, 0)).
builtin(/(no_style_check, 1)).
builtin(/(open, 3)).
builtin(/(open_null_stream, 1)).
builtin(/(read, 1)).
builtin(/(read, 2)).
builtin(/(recorda, 3)).
builtin(/(recorded, 3)).
builtin(/(recordz, 3)).
builtin(/(reinitialise, 0)).
builtin(/(restore, 1)).
builtin(/(restore, 2)).
builtin(/(retract, 1)).
builtin(/(retractall, 1)).
builtin(/(save, 1)).
builtin(/(save, 2)).
builtin(/(save_program, 1)).
builtin(/(see, 1)).
builtin(/(seeing, 1)).
builtin(/(seen, 0)).
builtin(/(set_input, 1)).
builtin(/(set_output, 1)).
builtin(/(setof, 3)).
builtin(/(skip, 1)).
builtin(/(skip, 2)).
builtin(/(style_check, 1)).
builtin(/(ttyget, 1)).
builtin(/(ttyget0, 1)).
builtin(/(ttyskip, 1)).
builtin(/(unknown, 2)).
builtin(/(use_module, 1)).
builtin(/(use_module, 2)).
builtin(/('^', 2)).
builtin(/(\+, 1)).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(0, _1, []).
mlist(X, SList, LList) :- ','(is(Y, -(X, 1)), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList)))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
fail :- failure(a).
failure(b).
=(X, X).


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

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

(8)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(Body, true), =(NewSource, Source))).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ','(=(Result, 0), =(P, B))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), rewrite(clause(H, B), clause(H, P), I, G, Info)).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, 0, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(var(Code), =(Phrase, PCode)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(=(Vars, []), =(Phrase, Code)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), =(Phrase, ','(PCode, Code)))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential)))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(\==(NewVars, []), =(CInfo, suspect))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), true).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(=(Conjuncts, ','(Xcode, ','(CGE, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype)))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), [])))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ','(>(L, 1), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem)))).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), []))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, []))))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), =(ParCode, .(This_goal, .(Last_goal, [])))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode)))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- find_var(Next_calls, H).
found(.(H, T), Next_calls) :- found(T, Next_calls).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- member(V, NextCall).
find_var(.(','(_R, NextCall), Others), V) :- find_var(Others, V).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =(Code, ','(Pcode, C))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), =(Code, ','(Pcode, C))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), merge(Pair, T1, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(=(Pair, .(.(L, .(E, [])), [])), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(is(NewVars, -(Cout, Cin)), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N)))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(0, X25, []).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(var(ARG), =(Bag, .(ARG, C)))))).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(atomic(ARG), =(Bag, C))))).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(collect_vars(ARG, Cs), append(Cs, C, Bag))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(is(N1, +(N, 1)), =(X, '$VAR'(N, _L)))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(0, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1)))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(0, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y)))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(=(ResultX, 0), =(Result, 0))).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(check_if_cge(Y, ResultY), is(Result, *(ResultX, ResultY)))).
check_if_cge('=>'(X45, X46), 0).
check_if_cge('&'(X47, X48), 0).
check_if_cge(X49, 1).
builtin(/(fail, 0)).
builtin(/(false, 0)).
builtin(/(otherwise, 0)).
builtin(/(repeat, 0)).
builtin(/(true, 0)).
builtin(/(version, 0)).
builtin(/(version, 1)).
builtin(/(!, 0)).
builtin(/(abolish, 1)).
builtin(/(abolish, 2)).
builtin(/(abort, 0)).
builtin(/(assert, 1)).
builtin(/(assert, 2)).
builtin(/(asserta, 1)).
builtin(/(asserta, 2)).
builtin(/(assertz, 1)).
builtin(/(assertz, 2)).
builtin(/(bagof, 3)).
builtin(/(break, 0)).
builtin(/(call, 1)).
builtin(/(close, 1)).
builtin(/(compile, 1)).
builtin(/(consult, 1)).
builtin(/(debug, 0)).
builtin(/(debugging, 0)).
builtin(/(ensure_loaded, 1)).
builtin(/(erase, 1)).
builtin(/(fileerrors, 0)).
builtin(/(flush_output, 1)).
builtin(/(foreign, 2)).
builtin(/(foreign, 3)).
builtin(/(foreign_file, 2)).
builtin(/(get, 1)).
builtin(/(get, 2)).
builtin(/(get0, 1)).
builtin(/(get0, 2)).
builtin(/(halt, 0)).
builtin(/(incore, 1)).
builtin(/(load_foreign_files, 2)).
builtin(/(module, 1)).
builtin(/(nofileerrors, 0)).
builtin(/(no_style_check, 1)).
builtin(/(open, 3)).
builtin(/(open_null_stream, 1)).
builtin(/(read, 1)).
builtin(/(read, 2)).
builtin(/(recorda, 3)).
builtin(/(recorded, 3)).
builtin(/(recordz, 3)).
builtin(/(reinitialise, 0)).
builtin(/(restore, 1)).
builtin(/(restore, 2)).
builtin(/(retract, 1)).
builtin(/(retractall, 1)).
builtin(/(save, 1)).
builtin(/(save, 2)).
builtin(/(save_program, 1)).
builtin(/(see, 1)).
builtin(/(seeing, 1)).
builtin(/(seen, 0)).
builtin(/(set_input, 1)).
builtin(/(set_output, 1)).
builtin(/(setof, 3)).
builtin(/(skip, 1)).
builtin(/(skip, 2)).
builtin(/(style_check, 1)).
builtin(/(ttyget, 1)).
builtin(/(ttyget0, 1)).
builtin(/(ttyskip, 1)).
builtin(/(unknown, 2)).
builtin(/(use_module, 1)).
builtin(/(use_module, 2)).
builtin(/('^', 2)).
builtin(/(\+, 1)).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(0, _1, []).
mlist(X, SList, LList) :- ','(is(Y, -(X, 1)), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList)))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
fail :- failure(a).
failure(b).
=(X, X).


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

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

(10)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(Body, true), =(NewSource, Source))).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ','(=(Result, 0), =(P, B))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), rewrite(clause(H, B), clause(H, P), I, G, Info)).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, 0, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(var(Code), =(Phrase, PCode)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(=(Vars, []), =(Phrase, Code)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), =(Phrase, ','(PCode, Code)))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential)))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(\==(NewVars, []), =(CInfo, suspect))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), true).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(=(Conjuncts, ','(Xcode, ','(CGE, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype)))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), [])))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ','(>(L, 1), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem)))).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), []))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, []))))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), =(ParCode, .(This_goal, .(Last_goal, [])))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode)))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- find_var(Next_calls, H).
found(.(H, T), Next_calls) :- found(T, Next_calls).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- member(V, NextCall).
find_var(.(','(_R, NextCall), Others), V) :- find_var(Others, V).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =(Code, ','(Pcode, C))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), =(Code, ','(Pcode, C))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), merge(Pair, T1, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(=(Pair, .(.(L, .(E, [])), [])), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(is(NewVars, -(Cout, Cin)), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N)))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(0, X25, []).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(var(ARG), =(Bag, .(ARG, C)))))).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(atomic(ARG), =(Bag, C))))).
go_inside(N, T, Bag) :- ','(is(Nth, -(N, 1)), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(collect_vars(ARG, Cs), append(Cs, C, Bag))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(is(N1, +(N, 1)), =(X, '$VAR'(N, _L)))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(0, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1)))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(0, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(is(I1, +(I, 1)), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y)))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(=(ResultX, 0), =(Result, 0))).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(check_if_cge(Y, ResultY), is(Result, *(ResultX, ResultY)))).
check_if_cge('=>'(X45, X46), 0).
check_if_cge('&'(X47, X48), 0).
check_if_cge(X49, 1).
builtin(/(fail, 0)).
builtin(/(false, 0)).
builtin(/(otherwise, 0)).
builtin(/(repeat, 0)).
builtin(/(true, 0)).
builtin(/(version, 0)).
builtin(/(version, 1)).
builtin(/(!, 0)).
builtin(/(abolish, 1)).
builtin(/(abolish, 2)).
builtin(/(abort, 0)).
builtin(/(assert, 1)).
builtin(/(assert, 2)).
builtin(/(asserta, 1)).
builtin(/(asserta, 2)).
builtin(/(assertz, 1)).
builtin(/(assertz, 2)).
builtin(/(bagof, 3)).
builtin(/(break, 0)).
builtin(/(call, 1)).
builtin(/(close, 1)).
builtin(/(compile, 1)).
builtin(/(consult, 1)).
builtin(/(debug, 0)).
builtin(/(debugging, 0)).
builtin(/(ensure_loaded, 1)).
builtin(/(erase, 1)).
builtin(/(fileerrors, 0)).
builtin(/(flush_output, 1)).
builtin(/(foreign, 2)).
builtin(/(foreign, 3)).
builtin(/(foreign_file, 2)).
builtin(/(get, 1)).
builtin(/(get, 2)).
builtin(/(get0, 1)).
builtin(/(get0, 2)).
builtin(/(halt, 0)).
builtin(/(incore, 1)).
builtin(/(load_foreign_files, 2)).
builtin(/(module, 1)).
builtin(/(nofileerrors, 0)).
builtin(/(no_style_check, 1)).
builtin(/(open, 3)).
builtin(/(open_null_stream, 1)).
builtin(/(read, 1)).
builtin(/(read, 2)).
builtin(/(recorda, 3)).
builtin(/(recorded, 3)).
builtin(/(recordz, 3)).
builtin(/(reinitialise, 0)).
builtin(/(restore, 1)).
builtin(/(restore, 2)).
builtin(/(retract, 1)).
builtin(/(retractall, 1)).
builtin(/(save, 1)).
builtin(/(save, 2)).
builtin(/(save_program, 1)).
builtin(/(see, 1)).
builtin(/(seeing, 1)).
builtin(/(seen, 0)).
builtin(/(set_input, 1)).
builtin(/(set_output, 1)).
builtin(/(setof, 3)).
builtin(/(skip, 1)).
builtin(/(skip, 2)).
builtin(/(style_check, 1)).
builtin(/(ttyget, 1)).
builtin(/(ttyget0, 1)).
builtin(/(ttyskip, 1)).
builtin(/(unknown, 2)).
builtin(/(use_module, 1)).
builtin(/(use_module, 2)).
builtin(/('^', 2)).
builtin(/(\+, 1)).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(0, _1, []).
mlist(X, SList, LList) :- ','(is(Y, -(X, 1)), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList)))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
fail :- failure(a).
failure(b).
=(X, X).
var(X0).
functor(X0, X1, X2).
\==(X0, X1).
true.
==(X0, X1).
length(X0, X1).
>(X0, X1).
=..(X0, X1).
@<(X0, X1).
is(X0, X1).
sort(X0, X1).
arg(X0, X1, X2).
atomic(X0).
statistics(X0, X1).
write(X0).
nl.
copy_term(X0, X1).


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

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

(12)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), ','(!, =(NewSource, Source))), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), ','(un_number_vars(New_Source, NewSource, others), !)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, zero), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, zero, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), ','(add_annotations(Info, P, I, G), !))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(!, ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd))).
add_annotations(Info, Phrase, I, G) :- ','(!, ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), ','(!, =(Phrase, PCode))), ','(=(Vars, []), ','(!, =(Phrase, Code)))), =(Phrase, ','(PCode, Code)))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(!, ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M))).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(!, ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), ','(!, =(CInfo, sequential)))), ','(\==(NewVars, []), ','(!, =(CInfo, suspect)))), true), !)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(!, ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(!, ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), ','(!, =(Conjuncts, ','(Xcode, CGE)))), ','(=(YVars, []), ','(!, =(Conjuncts, ','(Xcode, Ycode))))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential)))))), ','(=(Ytype, sequential), ','(!, ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype)))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype))))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(!, ','(=(Type, T), ','(=(Vars, []), =(This_term, Term))))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9) :- !.
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- ','(get_phrase(VarList, NewCode, I, G), !).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(','(','(=(X, L), =(X1, succ(zero))), isGreater(X, X1)), ','(!, ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem)))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(!, ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(!, ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, []))))), =(ParCode, .(This_goal, .(Last_goal, [])))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(!, ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, []))))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(','(find_var(Next_calls, H), !), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(','(member(V, NextCall), !), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- ','(var(Others), !).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others) :- !.
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), ','(!, =(Pcode, Parallel)))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), ','(!, =(Code, Pcode))), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(!, ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset))))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(!, ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples)))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(!, ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples)))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(!, ','(;(','(@<(E, L), ','(!, =(Pair, .(.(E, .(L, [])), [])))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples)))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T) :- !.
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T) :- !.
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- ','(!, intersect(S1, S2, IS)).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(isMinus(Cout, Cin, U), ','(=(NewVars, U), ','(length(Vars, NewVars), ','(numbervars_2(Vars, Cin, _N), !))))).
collect_vars(X, .(X, [])) :- ','(var(X), !).
collect_vars('$VAR'(X), .('$VAR'(X), [])) :- !.
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])) :- !.
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(zero, X25, []) :- !.
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), ','(!, =(Bag, .(ARG, C)))), ','(atomic(ARG), ','(!, =(Bag, C)))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag))))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)) :- !.
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), ','(!, subtract(Residue, Set, Difference))).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D) :- !.
merge(D, [], D) :- !.
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), ','(!, merge(As, .(D, Ds), Bs))).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), ','(!, merge(As, Ds, Bs))).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []) :- !.
intersect(X33, [], []) :- !.
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), ','(!, intersect(As, .(D, Ds), Out))).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), ','(!, intersect(As, Ds, Out))).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(isPlus(N, succ(zero), U), ','(=(N1, U), ','(!, =(X, '$VAR'(N, _L)))))).
numbervars_2(A, N, N) :- ','(atomic(A), !).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(zero, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), ','(!, numbervars_2(I1, F, N0, N1)))))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), ','(un_number_vars_2(Body, B, X), !)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others) :- !.
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge) :- !.
un_number_vars_2(X, X, X41) :- ','(atomic(X), !).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(zero, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), ','(!, un_number_vars_2(I1, F, Tail, Y)))))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, zero), =(Result, zero)), ','(check_if_cge(Y, ResultY), ','(isTimes(ResultX, ResultY, U), =(Result, U))))).
check_if_cge('=>'(X45, X46), zero).
check_if_cge('&'(X47, X48), zero).
check_if_cge(X49, succ(zero)).
builtin(/(fail, zero)).
builtin(/(false, zero)).
builtin(/(otherwise, zero)).
builtin(/(repeat, zero)).
builtin(/(true, zero)).
builtin(/(version, zero)).
builtin(/(version, succ(zero))).
builtin(/(!, zero)).
builtin(/(abolish, succ(zero))).
builtin(/(abolish, succ(succ(zero)))).
builtin(/(abort, zero)).
builtin(/(assert, succ(zero))).
builtin(/(assert, succ(succ(zero)))).
builtin(/(asserta, succ(zero))).
builtin(/(asserta, succ(succ(zero)))).
builtin(/(assertz, succ(zero))).
builtin(/(assertz, succ(succ(zero)))).
builtin(/(bagof, succ(succ(succ(zero))))).
builtin(/(break, zero)).
builtin(/(call, succ(zero))).
builtin(/(close, succ(zero))).
builtin(/(compile, succ(zero))).
builtin(/(consult, succ(zero))).
builtin(/(debug, zero)).
builtin(/(debugging, zero)).
builtin(/(ensure_loaded, succ(zero))).
builtin(/(erase, succ(zero))).
builtin(/(fileerrors, zero)).
builtin(/(flush_output, succ(zero))).
builtin(/(foreign, succ(succ(zero)))).
builtin(/(foreign, succ(succ(succ(zero))))).
builtin(/(foreign_file, succ(succ(zero)))).
builtin(/(get, succ(zero))).
builtin(/(get, succ(succ(zero)))).
builtin(/(get0, succ(zero))).
builtin(/(get0, succ(succ(zero)))).
builtin(/(halt, zero)).
builtin(/(incore, succ(zero))).
builtin(/(load_foreign_files, succ(succ(zero)))).
builtin(/(module, succ(zero))).
builtin(/(nofileerrors, zero)).
builtin(/(no_style_check, succ(zero))).
builtin(/(open, succ(succ(succ(zero))))).
builtin(/(open_null_stream, succ(zero))).
builtin(/(read, succ(zero))).
builtin(/(read, succ(succ(zero)))).
builtin(/(recorda, succ(succ(succ(zero))))).
builtin(/(recorded, succ(succ(succ(zero))))).
builtin(/(recordz, succ(succ(succ(zero))))).
builtin(/(reinitialise, zero)).
builtin(/(restore, succ(zero))).
builtin(/(restore, succ(succ(zero)))).
builtin(/(retract, succ(zero))).
builtin(/(retractall, succ(zero))).
builtin(/(save, succ(zero))).
builtin(/(save, succ(succ(zero)))).
builtin(/(save_program, succ(zero))).
builtin(/(see, succ(zero))).
builtin(/(seeing, succ(zero))).
builtin(/(seen, zero)).
builtin(/(set_input, succ(zero))).
builtin(/(set_output, succ(zero))).
builtin(/(setof, succ(succ(succ(zero))))).
builtin(/(skip, succ(zero))).
builtin(/(skip, succ(succ(zero)))).
builtin(/(style_check, succ(zero))).
builtin(/(ttyget, succ(zero))).
builtin(/(ttyget0, succ(zero))).
builtin(/(ttyskip, succ(zero))).
builtin(/(unknown, succ(succ(zero)))).
builtin(/(use_module, succ(zero))).
builtin(/(use_module, succ(succ(zero)))).
builtin(/('^', succ(succ(zero)))).
builtin(/(\+, succ(zero))).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(zero, _1, []).
mlist(X, SList, LList) :- ','(isMinus(X, succ(zero), U), ','(=(Y, U), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList))))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
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).


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

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

(14)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), =(NewSource, Source)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, zero), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, zero, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), =(Phrase, PCode)), ','(=(Vars, []), =(Phrase, Code))), =(Phrase, ','(PCode, Code))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential))), ','(\==(NewVars, []), =(CInfo, suspect))), true)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode)))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential))))), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype)))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(','(','(=(X, L), =(X1, succ(zero))), isGreater(X, X1)), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, [])))), =(ParCode, .(This_goal, .(Last_goal, []))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(find_var(Next_calls, H), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(member(V, NextCall), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), =(Code, Pcode)), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(;(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(isMinus(Cout, Cin, U), ','(=(NewVars, U), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N))))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(zero, X25, []).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), =(Bag, .(ARG, C))), ','(atomic(ARG), =(Bag, C))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag))))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(isPlus(N, succ(zero), U), ','(=(N1, U), =(X, '$VAR'(N, _L))))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(zero, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1))))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(zero, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y))))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, zero), =(Result, zero)), ','(check_if_cge(Y, ResultY), ','(isTimes(ResultX, ResultY, U), =(Result, U))))).
check_if_cge('=>'(X45, X46), zero).
check_if_cge('&'(X47, X48), zero).
check_if_cge(X49, succ(zero)).
builtin(/(fail, zero)).
builtin(/(false, zero)).
builtin(/(otherwise, zero)).
builtin(/(repeat, zero)).
builtin(/(true, zero)).
builtin(/(version, zero)).
builtin(/(version, succ(zero))).
builtin(/(!, zero)).
builtin(/(abolish, succ(zero))).
builtin(/(abolish, succ(succ(zero)))).
builtin(/(abort, zero)).
builtin(/(assert, succ(zero))).
builtin(/(assert, succ(succ(zero)))).
builtin(/(asserta, succ(zero))).
builtin(/(asserta, succ(succ(zero)))).
builtin(/(assertz, succ(zero))).
builtin(/(assertz, succ(succ(zero)))).
builtin(/(bagof, succ(succ(succ(zero))))).
builtin(/(break, zero)).
builtin(/(call, succ(zero))).
builtin(/(close, succ(zero))).
builtin(/(compile, succ(zero))).
builtin(/(consult, succ(zero))).
builtin(/(debug, zero)).
builtin(/(debugging, zero)).
builtin(/(ensure_loaded, succ(zero))).
builtin(/(erase, succ(zero))).
builtin(/(fileerrors, zero)).
builtin(/(flush_output, succ(zero))).
builtin(/(foreign, succ(succ(zero)))).
builtin(/(foreign, succ(succ(succ(zero))))).
builtin(/(foreign_file, succ(succ(zero)))).
builtin(/(get, succ(zero))).
builtin(/(get, succ(succ(zero)))).
builtin(/(get0, succ(zero))).
builtin(/(get0, succ(succ(zero)))).
builtin(/(halt, zero)).
builtin(/(incore, succ(zero))).
builtin(/(load_foreign_files, succ(succ(zero)))).
builtin(/(module, succ(zero))).
builtin(/(nofileerrors, zero)).
builtin(/(no_style_check, succ(zero))).
builtin(/(open, succ(succ(succ(zero))))).
builtin(/(open_null_stream, succ(zero))).
builtin(/(read, succ(zero))).
builtin(/(read, succ(succ(zero)))).
builtin(/(recorda, succ(succ(succ(zero))))).
builtin(/(recorded, succ(succ(succ(zero))))).
builtin(/(recordz, succ(succ(succ(zero))))).
builtin(/(reinitialise, zero)).
builtin(/(restore, succ(zero))).
builtin(/(restore, succ(succ(zero)))).
builtin(/(retract, succ(zero))).
builtin(/(retractall, succ(zero))).
builtin(/(save, succ(zero))).
builtin(/(save, succ(succ(zero)))).
builtin(/(save_program, succ(zero))).
builtin(/(see, succ(zero))).
builtin(/(seeing, succ(zero))).
builtin(/(seen, zero)).
builtin(/(set_input, succ(zero))).
builtin(/(set_output, succ(zero))).
builtin(/(setof, succ(succ(succ(zero))))).
builtin(/(skip, succ(zero))).
builtin(/(skip, succ(succ(zero)))).
builtin(/(style_check, succ(zero))).
builtin(/(ttyget, succ(zero))).
builtin(/(ttyget0, succ(zero))).
builtin(/(ttyskip, succ(zero))).
builtin(/(unknown, succ(succ(zero)))).
builtin(/(use_module, succ(zero))).
builtin(/(use_module, succ(succ(zero)))).
builtin(/('^', succ(succ(zero)))).
builtin(/(\+, succ(zero))).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(zero, _1, []).
mlist(X, SList, LList) :- ','(isMinus(X, succ(zero), U), ','(=(Y, U), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList))))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
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).


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

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

(16)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), =(NewSource, Source)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, zero), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, zero, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), =(Phrase, PCode)), ','(=(Vars, []), =(Phrase, Code))), =(Phrase, ','(PCode, Code))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential))), ','(\==(NewVars, []), =(CInfo, suspect))), true)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode)))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential))))), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype)))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(','(','(=(X, L), =(X1, succ(zero))), isGreater(X, X1)), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, [])))), =(ParCode, .(This_goal, .(Last_goal, []))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(find_var(Next_calls, H), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(member(V, NextCall), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), =(Code, Pcode)), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(;(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(isMinus(Cout, Cin, U), ','(=(NewVars, U), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N))))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(zero, X25, []).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), =(Bag, .(ARG, C))), ','(atomic(ARG), =(Bag, C))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag))))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(isPlus(N, succ(zero), U), ','(=(N1, U), =(X, '$VAR'(N, _L))))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(zero, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1))))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(zero, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y))))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, zero), =(Result, zero)), ','(check_if_cge(Y, ResultY), ','(isTimes(ResultX, ResultY, U), =(Result, U))))).
check_if_cge('=>'(X45, X46), zero).
check_if_cge('&'(X47, X48), zero).
check_if_cge(X49, succ(zero)).
builtin(/(fail, zero)).
builtin(/(false, zero)).
builtin(/(otherwise, zero)).
builtin(/(repeat, zero)).
builtin(/(true, zero)).
builtin(/(version, zero)).
builtin(/(version, succ(zero))).
builtin(/(!, zero)).
builtin(/(abolish, succ(zero))).
builtin(/(abolish, succ(succ(zero)))).
builtin(/(abort, zero)).
builtin(/(assert, succ(zero))).
builtin(/(assert, succ(succ(zero)))).
builtin(/(asserta, succ(zero))).
builtin(/(asserta, succ(succ(zero)))).
builtin(/(assertz, succ(zero))).
builtin(/(assertz, succ(succ(zero)))).
builtin(/(bagof, succ(succ(succ(zero))))).
builtin(/(break, zero)).
builtin(/(call, succ(zero))).
builtin(/(close, succ(zero))).
builtin(/(compile, succ(zero))).
builtin(/(consult, succ(zero))).
builtin(/(debug, zero)).
builtin(/(debugging, zero)).
builtin(/(ensure_loaded, succ(zero))).
builtin(/(erase, succ(zero))).
builtin(/(fileerrors, zero)).
builtin(/(flush_output, succ(zero))).
builtin(/(foreign, succ(succ(zero)))).
builtin(/(foreign, succ(succ(succ(zero))))).
builtin(/(foreign_file, succ(succ(zero)))).
builtin(/(get, succ(zero))).
builtin(/(get, succ(succ(zero)))).
builtin(/(get0, succ(zero))).
builtin(/(get0, succ(succ(zero)))).
builtin(/(halt, zero)).
builtin(/(incore, succ(zero))).
builtin(/(load_foreign_files, succ(succ(zero)))).
builtin(/(module, succ(zero))).
builtin(/(nofileerrors, zero)).
builtin(/(no_style_check, succ(zero))).
builtin(/(open, succ(succ(succ(zero))))).
builtin(/(open_null_stream, succ(zero))).
builtin(/(read, succ(zero))).
builtin(/(read, succ(succ(zero)))).
builtin(/(recorda, succ(succ(succ(zero))))).
builtin(/(recorded, succ(succ(succ(zero))))).
builtin(/(recordz, succ(succ(succ(zero))))).
builtin(/(reinitialise, zero)).
builtin(/(restore, succ(zero))).
builtin(/(restore, succ(succ(zero)))).
builtin(/(retract, succ(zero))).
builtin(/(retractall, succ(zero))).
builtin(/(save, succ(zero))).
builtin(/(save, succ(succ(zero)))).
builtin(/(save_program, succ(zero))).
builtin(/(see, succ(zero))).
builtin(/(seeing, succ(zero))).
builtin(/(seen, zero)).
builtin(/(set_input, succ(zero))).
builtin(/(set_output, succ(zero))).
builtin(/(setof, succ(succ(succ(zero))))).
builtin(/(skip, succ(zero))).
builtin(/(skip, succ(succ(zero)))).
builtin(/(style_check, succ(zero))).
builtin(/(ttyget, succ(zero))).
builtin(/(ttyget0, succ(zero))).
builtin(/(ttyskip, succ(zero))).
builtin(/(unknown, succ(succ(zero)))).
builtin(/(use_module, succ(zero))).
builtin(/(use_module, succ(succ(zero)))).
builtin(/('^', succ(succ(zero)))).
builtin(/(\+, succ(zero))).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(zero, _1, []).
mlist(X, SList, LList) :- ','(isMinus(X, succ(zero), U), ','(=(Y, U), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList))))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
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).
fail :- failure(a).
failure(b).


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

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

(18)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ;(','(=(Body, true), =(NewSource, Source)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others)))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ;(','(=(Result, zero), =(P, B)), rewrite(clause(H, B), clause(H, P), I, G, Info))).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, zero, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ;(;(','(var(Code), =(Phrase, PCode)), ','(=(Vars, []), =(Phrase, Code))), =(Phrase, ','(PCode, Code))))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ;(;(','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential))), ','(\==(NewVars, []), =(CInfo, suspect))), true)).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ;(;(','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(;(;(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode)))), =(Conjuncts, ','(Xcode, ','(CGE, Ycode)))), ','(=(BagofVars, []), =(Type, sequential))))), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype))))), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype)))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ;(','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))), ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), []))))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ;(','(','(','(=(X, L), =(X1, succ(zero))), isGreater(X, X1)), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem))), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), [])))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ;(','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, [])))), =(ParCode, .(This_goal, .(Last_goal, []))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ;(','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode))))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- ;(find_var(Next_calls, H), found(T, Next_calls)).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- ;(member(V, NextCall), find_var(Others, V)).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(;(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =..(Pcode, .('=>', .(Conds, .(Parallel, []))))), ;(','(var(C), =(Code, Pcode)), =(Code, ','(Pcode, C)))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(;(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), =(Pair, .(.(L, .(E, [])), []))), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(isMinus(Cout, Cin, U), ','(=(NewVars, U), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N))))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(zero, X25, []).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ;(;(','(var(ARG), =(Bag, .(ARG, C))), ','(atomic(ARG), =(Bag, C))), ','(collect_vars(ARG, Cs), append(Cs, C, Bag))))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(isPlus(N, succ(zero), U), ','(=(N1, U), =(X, '$VAR'(N, _L))))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(zero, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1))))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(zero, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y))))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ;(','(=(ResultX, zero), =(Result, zero)), ','(check_if_cge(Y, ResultY), ','(isTimes(ResultX, ResultY, U), =(Result, U))))).
check_if_cge('=>'(X45, X46), zero).
check_if_cge('&'(X47, X48), zero).
check_if_cge(X49, succ(zero)).
builtin(/(fail, zero)).
builtin(/(false, zero)).
builtin(/(otherwise, zero)).
builtin(/(repeat, zero)).
builtin(/(true, zero)).
builtin(/(version, zero)).
builtin(/(version, succ(zero))).
builtin(/(!, zero)).
builtin(/(abolish, succ(zero))).
builtin(/(abolish, succ(succ(zero)))).
builtin(/(abort, zero)).
builtin(/(assert, succ(zero))).
builtin(/(assert, succ(succ(zero)))).
builtin(/(asserta, succ(zero))).
builtin(/(asserta, succ(succ(zero)))).
builtin(/(assertz, succ(zero))).
builtin(/(assertz, succ(succ(zero)))).
builtin(/(bagof, succ(succ(succ(zero))))).
builtin(/(break, zero)).
builtin(/(call, succ(zero))).
builtin(/(close, succ(zero))).
builtin(/(compile, succ(zero))).
builtin(/(consult, succ(zero))).
builtin(/(debug, zero)).
builtin(/(debugging, zero)).
builtin(/(ensure_loaded, succ(zero))).
builtin(/(erase, succ(zero))).
builtin(/(fileerrors, zero)).
builtin(/(flush_output, succ(zero))).
builtin(/(foreign, succ(succ(zero)))).
builtin(/(foreign, succ(succ(succ(zero))))).
builtin(/(foreign_file, succ(succ(zero)))).
builtin(/(get, succ(zero))).
builtin(/(get, succ(succ(zero)))).
builtin(/(get0, succ(zero))).
builtin(/(get0, succ(succ(zero)))).
builtin(/(halt, zero)).
builtin(/(incore, succ(zero))).
builtin(/(load_foreign_files, succ(succ(zero)))).
builtin(/(module, succ(zero))).
builtin(/(nofileerrors, zero)).
builtin(/(no_style_check, succ(zero))).
builtin(/(open, succ(succ(succ(zero))))).
builtin(/(open_null_stream, succ(zero))).
builtin(/(read, succ(zero))).
builtin(/(read, succ(succ(zero)))).
builtin(/(recorda, succ(succ(succ(zero))))).
builtin(/(recorded, succ(succ(succ(zero))))).
builtin(/(recordz, succ(succ(succ(zero))))).
builtin(/(reinitialise, zero)).
builtin(/(restore, succ(zero))).
builtin(/(restore, succ(succ(zero)))).
builtin(/(retract, succ(zero))).
builtin(/(retractall, succ(zero))).
builtin(/(save, succ(zero))).
builtin(/(save, succ(succ(zero)))).
builtin(/(save_program, succ(zero))).
builtin(/(see, succ(zero))).
builtin(/(seeing, succ(zero))).
builtin(/(seen, zero)).
builtin(/(set_input, succ(zero))).
builtin(/(set_output, succ(zero))).
builtin(/(setof, succ(succ(succ(zero))))).
builtin(/(skip, succ(zero))).
builtin(/(skip, succ(succ(zero)))).
builtin(/(style_check, succ(zero))).
builtin(/(ttyget, succ(zero))).
builtin(/(ttyget0, succ(zero))).
builtin(/(ttyskip, succ(zero))).
builtin(/(unknown, succ(succ(zero)))).
builtin(/(use_module, succ(zero))).
builtin(/(use_module, succ(succ(zero)))).
builtin(/('^', succ(succ(zero)))).
builtin(/(\+, succ(zero))).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(zero, _1, []).
mlist(X, SList, LList) :- ','(isMinus(X, succ(zero), U), ','(=(Y, U), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList))))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
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).
fail :- failure(a).
failure(b).
=(X, X).


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

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

(20)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(Body, true), =(NewSource, Source))).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ','(=(Result, zero), =(P, B))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), rewrite(clause(H, B), clause(H, P), I, G, Info)).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, zero, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(var(Code), =(Phrase, PCode)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(=(Vars, []), =(Phrase, Code)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), =(Phrase, ','(PCode, Code)))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential)))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(\==(NewVars, []), =(CInfo, suspect))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), true).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(=(Conjuncts, ','(Xcode, ','(CGE, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype)))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), [])))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ','(','(','(=(X, L), =(X1, succ(zero))), isGreater(X, X1)), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem)))).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), []))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, []))))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), =(ParCode, .(This_goal, .(Last_goal, [])))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode)))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- find_var(Next_calls, H).
found(.(H, T), Next_calls) :- found(T, Next_calls).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- member(V, NextCall).
find_var(.(','(_R, NextCall), Others), V) :- find_var(Others, V).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =(Code, ','(Pcode, C))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), =(Code, ','(Pcode, C))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), merge(Pair, T1, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(=(Pair, .(.(L, .(E, [])), [])), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(isMinus(Cout, Cin, U), ','(=(NewVars, U), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N))))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(zero, X25, []).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(var(ARG), =(Bag, .(ARG, C))))))).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(atomic(ARG), =(Bag, C)))))).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(collect_vars(ARG, Cs), append(Cs, C, Bag)))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(isPlus(N, succ(zero), U), ','(=(N1, U), =(X, '$VAR'(N, _L))))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(zero, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1))))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(zero, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y))))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(=(ResultX, zero), =(Result, zero))).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(check_if_cge(Y, ResultY), ','(isTimes(ResultX, ResultY, U), =(Result, U)))).
check_if_cge('=>'(X45, X46), zero).
check_if_cge('&'(X47, X48), zero).
check_if_cge(X49, succ(zero)).
builtin(/(fail, zero)).
builtin(/(false, zero)).
builtin(/(otherwise, zero)).
builtin(/(repeat, zero)).
builtin(/(true, zero)).
builtin(/(version, zero)).
builtin(/(version, succ(zero))).
builtin(/(!, zero)).
builtin(/(abolish, succ(zero))).
builtin(/(abolish, succ(succ(zero)))).
builtin(/(abort, zero)).
builtin(/(assert, succ(zero))).
builtin(/(assert, succ(succ(zero)))).
builtin(/(asserta, succ(zero))).
builtin(/(asserta, succ(succ(zero)))).
builtin(/(assertz, succ(zero))).
builtin(/(assertz, succ(succ(zero)))).
builtin(/(bagof, succ(succ(succ(zero))))).
builtin(/(break, zero)).
builtin(/(call, succ(zero))).
builtin(/(close, succ(zero))).
builtin(/(compile, succ(zero))).
builtin(/(consult, succ(zero))).
builtin(/(debug, zero)).
builtin(/(debugging, zero)).
builtin(/(ensure_loaded, succ(zero))).
builtin(/(erase, succ(zero))).
builtin(/(fileerrors, zero)).
builtin(/(flush_output, succ(zero))).
builtin(/(foreign, succ(succ(zero)))).
builtin(/(foreign, succ(succ(succ(zero))))).
builtin(/(foreign_file, succ(succ(zero)))).
builtin(/(get, succ(zero))).
builtin(/(get, succ(succ(zero)))).
builtin(/(get0, succ(zero))).
builtin(/(get0, succ(succ(zero)))).
builtin(/(halt, zero)).
builtin(/(incore, succ(zero))).
builtin(/(load_foreign_files, succ(succ(zero)))).
builtin(/(module, succ(zero))).
builtin(/(nofileerrors, zero)).
builtin(/(no_style_check, succ(zero))).
builtin(/(open, succ(succ(succ(zero))))).
builtin(/(open_null_stream, succ(zero))).
builtin(/(read, succ(zero))).
builtin(/(read, succ(succ(zero)))).
builtin(/(recorda, succ(succ(succ(zero))))).
builtin(/(recorded, succ(succ(succ(zero))))).
builtin(/(recordz, succ(succ(succ(zero))))).
builtin(/(reinitialise, zero)).
builtin(/(restore, succ(zero))).
builtin(/(restore, succ(succ(zero)))).
builtin(/(retract, succ(zero))).
builtin(/(retractall, succ(zero))).
builtin(/(save, succ(zero))).
builtin(/(save, succ(succ(zero)))).
builtin(/(save_program, succ(zero))).
builtin(/(see, succ(zero))).
builtin(/(seeing, succ(zero))).
builtin(/(seen, zero)).
builtin(/(set_input, succ(zero))).
builtin(/(set_output, succ(zero))).
builtin(/(setof, succ(succ(succ(zero))))).
builtin(/(skip, succ(zero))).
builtin(/(skip, succ(succ(zero)))).
builtin(/(style_check, succ(zero))).
builtin(/(ttyget, succ(zero))).
builtin(/(ttyget0, succ(zero))).
builtin(/(ttyskip, succ(zero))).
builtin(/(unknown, succ(succ(zero)))).
builtin(/(use_module, succ(zero))).
builtin(/(use_module, succ(succ(zero)))).
builtin(/('^', succ(succ(zero)))).
builtin(/(\+, succ(zero))).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(zero, _1, []).
mlist(X, SList, LList) :- ','(isMinus(X, succ(zero), U), ','(=(Y, U), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList))))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
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).
fail :- failure(a).
failure(b).
=(X, X).


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

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

(22)
Obligation:
Clauses:

analyze_all(.(X, Y), .(X1, Y1)) :- ','(analyze(X, X1), analyze_all(Y, Y1)).
analyze_all([], []).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(Body, true), =(NewSource, Source))).
analyze(Source, NewSource) :- ','(=(Source, clause(_X, Body)), ','(=(I, []), ','(=(G, []), ','(rewrite_3(Source, New_Source, I, G, _Y), un_number_vars(New_Source, NewSource, others))))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), ','(=(Result, zero), =(P, B))).
rewrite_3(clause(H, B), clause(H, P), I, G, Info) :- ','(check_if_cge(B, Result), rewrite(clause(H, B), clause(H, P), I, G, Info)).
rewrite(clause(H, B), clause(H, P), I, G, Info) :- ','(numbervars_2(H, zero, Lhv), ','(collect_info(B, Info, Lhv, _X, _Y), add_annotations(Info, P, I, G))).
add_annotations([], [], X5, X6).
add_annotations(.(I, Is), .(P, Ps), Indep, Gnd) :- ','(add_annotations(I, P, Indep, Gnd), add_annotations(Is, Ps, Indep, Gnd)).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(var(Code), =(Phrase, PCode)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), ','(=(Vars, []), =(Phrase, Code)))).
add_annotations(Info, Phrase, I, G) :- ','(para_phrase(Info, Code, Type, Vars, I, G), ','(make_CGE_phrase(Type, Code, Vars, PCode, I, G), =(Phrase, ','(PCode, Code)))).
collect_info(;(A, B), ','([], ','(sequential, ;(A, B))), Cin, Cout, _X) :- ','(collect_info(A, _Y, Cin, C, _Z), collect_info(B, _N, C, Cout, _M)).
collect_info(','(A, B), and(Ia, Ib), Cin, Cout, _X) :- ','(collect_info(A, Ia, Cin, C, _Y), collect_info(B, Ib, C, Cout, _Z)).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(functor(A, F, Arity), ','(builtin(/(F, Arity)), =(CInfo, sequential)))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), ','(\==(NewVars, []), =(CInfo, suspect))).
collect_info(A, ','(NewVars, ','(CInfo, A)), In, Out, _R) :- ','(find_vars(A, NewVars, In, Out), true).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(var(Ycode), =(Conjuncts, ','(Xcode, CGE))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(','(=(YVars, []), =(Conjuncts, ','(Xcode, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Xtype, sequential), ','(make_CGE_phrase(Ytype, Ycode, YVars, CGE, I, G), ','(=(Conjuncts, ','(Xcode, ','(CGE, Ycode))), ','(=(BagofVars, []), =(Type, sequential))))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Ytype, sequential), ','(=(Conjuncts, Ycode), ','(=(BagofVars, XVars), =(Type, Xtype)))))).
para_phrase(and(X, Y), Conjuncts, Type, BagofVars, I, G) :- ','(para_phrase(X, Xcode, Xtype, XVars, I, G), ','(para_phrase(Y, Ycode, Ytype, YVars, I, G), ','(=(Conjuncts, Ycode), ','(append(XVars, YVars, BagofVars), =(Type, Xtype))))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(==(T, sequential), ','(=(Type, T), ','(=(Vars, []), =(This_term, Term)))).
para_phrase(','(N, ','(T, Term)), This_term, Type, Vars, _X, _Y) :- ','(collect_vars(Term, Vs), ','(=(Type, par), =(Vars, .(','(','(T, ','(N, Term)), Vs), [])))).
make_CGE_phrase(sequential, Code, X7, Code, X8, X9).
make_CGE_phrase(_X, _Y, VarList, NewCode, I, G) :- get_phrase(VarList, NewCode, I, G).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), ','(','(','(=(X, L), =(X1, succ(zero))), isGreater(X, X1)), ','(eliminate_suspect_code(VarList, Rem, Vs, I, G), get_CGE_2(Vs, I, G, Code, Rem)))).
get_phrase(VarList, Code, I, G) :- ','(length(VarList, L), =(VarList, .(','(','(_X, ','(_Y, Code)), _Z), []))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), ','(found(FVars, .(Last_goal, [])), ','(=(Last_goal, ','(','(_L, ','(_M, SeqCode)), _N)), =(ParCode, .(This_goal, []))))).
eliminate_suspect_code(.(This_goal, .(Last_goal, [])), SeqCode, ParCode, _X, _Y) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _Z)), _W)), =(ParCode, .(This_goal, .(Last_goal, [])))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(found(FVars, PCode), ','(get_CGE_2(PCode, I, G, Code, SCode), =(ParCode, .(This_goal, [])))))).
eliminate_suspect_code(.(This_goal, Subsequent_goals), Code, ParCode, I, G) :- ','(=(This_goal, ','(','(suspect, ','(FVars, _X)), _Y)), ','(eliminate_suspect_code(Subsequent_goals, SCode, PCode, I, G), ','(=(ParCode, .(This_goal, PCode)), =(Code, SCode)))).
found([], _R) :- fail.
found(.(H, T), Next_calls) :- find_var(Next_calls, H).
found(.(H, T), Next_calls) :- found(T, Next_calls).
find_var([], _R) :- fail.
find_var(.(','(_R, NextCall), Others), V) :- member(V, NextCall).
find_var(.(','(_R, NextCall), Others), V) :- find_var(Others, V).
get_CGE_2(.(','(','(_X, ','(_Y, Goal)), _Z), []), _W, _M, Goal, Others) :- var(Others).
get_CGE_2(.(','(','(X10, ','(X11, Goal)), X12), []), X13, X14, ','(Goal, Others), Others).
get_CGE_2(Vs, I, G, Code, Rem) :- ','(get_conds(Vs, Conds, I, G), ','(make_norml_2(Vs, Parallel), babel_2(Conds, Parallel, Rem, Code))).
get_conds(VARS, Y, I, G) :- ','(do_intersect(VARS, GS), ','(subtract(GS, G, Gnd), ','(singleton(VARS, VOIDS), ','(reduce_set(VARS, Gnd, VOIDS, I, RSET), ','(produce_tuples(RSET, Indep), get_text(Gnd, Indep, Y)))))).
'$simplify_unconditional_cges'(off).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(','(=(Conds, true), ','('$simplify_unconditional_cges'(on), =(Pcode, Parallel))), =(Code, ','(Pcode, C))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), ','(var(C), =(Code, Pcode))).
babel_2(Conds, Parallel, C, Code) :- ','(=..(Pcode, .('=>', .(Conds, .(Parallel, [])))), =(Code, ','(Pcode, C))).
reduce_set([], _X, _Y, _Z, []).
reduce_set(.(','(Info, V), Vs), Gnd, VOIDS, Indep, .(','(Info, Rset), Rs)) :- ','(reduce_set(Vs, Gnd, VOIDS, Indep, Rs), ','(subtract(V, Gnd, Rg), ','(subtract(Rg, VOIDS, Rv), subtract(Rv, Indep, Rset)))).
produce_tuples([], []).
produce_tuples(.(','(_N, V), Vs), Tuples) :- ','(produce_tuples(Vs, Ts), ','(pair(Vs, V, Ps), merge(Ps, Ts, Tuples))).
pair([], X15, []).
pair(.(','(_N, L), Ls), Vs, Tuples) :- ','(pair(Ls, Vs, Ps), ','(tuple(L, Vs, Ts), merge(Ts, Ps, Tuples))).
tuple([], X16, []).
tuple(X17, [], []).
tuple(List, .(L, Ls), Tuples) :- ','(tuple(List, Ls, T1), ','(tuple(List, L, T2), merge(T1, T2, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(','(@<(E, L), =(Pair, .(.(E, .(L, [])), []))), merge(Pair, T1, Tuples))).
tuple(.(E, Es), L, Tuples) :- ','(tuple(Es, L, T1), ','(=(Pair, .(.(L, .(E, [])), [])), merge(Pair, T1, Tuples))).
make_norml(.(','(','(X18, ','(X19, T)), X20), []), T).
make_norml(.(','(','(_X, ','(_Y, T)), _Z), Nxt), ','(T, Nc)) :- make_norml(Nxt, Nc).
make_norml_2(.(','(','(X21, ','(X22, T)), X23), []), T).
make_norml_2(.(','(','(_X, ','(_Y, T)), _Z), Nxt), '&'(T, Nc)) :- make_norml_2(Nxt, Nc).
do_intersect([], []).
do_intersect(.(','(_X, S1), .(','(_Y, S2), [])), IS) :- intersect(S1, S2, IS).
do_intersect(.(S1, .(S2, Ss)), IS) :- ','(do_intersect(.(S2, Ss), IS1), ','(do_intersect(.(S1, Ss), IS2), ','(do_intersect(.(S1, .(S2, [])), IS3), ','(merge(IS1, IS2, T1), merge(IS3, T1, IS))))).
get_text([], [], true).
get_text([], X, indep(X)).
get_text(X, [], ground(X)).
get_text(X, Y, ','(ground(X), indep(Y))).
find_vars(T, Vars, Cin, Cout) :- ','(numbervars_2(T, Cin, Cout), ','(isMinus(Cout, Cin, U), ','(=(NewVars, U), ','(length(Vars, NewVars), numbervars_2(Vars, Cin, _N))))).
collect_vars(X, .(X, [])) :- var(X).
collect_vars('$VAR'(X), .('$VAR'(X), [])).
collect_vars('$VAR'(X, Y), .('$VAR'(X, Y), [])).
collect_vars(Term, Vars) :- ','(functor(Term, _N, A), ','(go_inside(A, Term, Vs), sort(Vs, Vars))).
collect_vars(X24, []).
go_inside(zero, X25, []).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(var(ARG), =(Bag, .(ARG, C))))))).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(atomic(ARG), =(Bag, C)))))).
go_inside(N, T, Bag) :- ','(isMinus(N, succ(zero), U), ','(=(Nth, U), ','(go_inside(Nth, T, C), ','(arg(N, T, ARG), ','(collect_vars(ARG, Cs), append(Cs, C, Bag)))))).
append([], L, L).
append(.(H, T), L, .(H, R)) :- append(T, L, R).
member(Element, .(Element, X26)).
member(Element, .(_N, Rest)) :- member(Element, Rest).
memberchk(Element, .(Element, X27)).
memberchk(Element, .(_N, Rest)) :- memberchk(Element, Rest).
subtract([], X28, []).
subtract(.(Element, Residue), Set, Difference) :- ','(memberchk(Element, Set), subtract(Residue, Set, Difference)).
subtract(.(Element, Residue), Set, .(Element, Difference)) :- subtract(Residue, Set, Difference).
singleton(.(','(','(X29, ','(X, X30)), X31), []), X).
singleton(.(','(','(_A, ','(V, _B)), _C), Vs), X) :- ','(singleton(Vs, Y), merge(V, Y, X)).
merge([], D, D).
merge(D, [], D).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(@<(A, D), merge(As, .(D, Ds), Bs)).
merge(.(A, As), .(D, Ds), .(A, Bs)) :- ','(==(A, D), merge(As, Ds, Bs)).
merge(As, .(D, Ds), .(D, Bs)) :- merge(As, Ds, Bs).
intersect([], X32, []).
intersect(X33, [], []).
intersect(.(A, As), .(D, Ds), Out) :- ','(@<(A, D), intersect(As, .(D, Ds), Out)).
intersect(.(A, As), .(D, Ds), .(A, Out)) :- ','(==(A, D), intersect(As, Ds, Out)).
intersect(As, .(_N, Ds), Out) :- intersect(As, Ds, Out).
numbervars_2(X, N, N1) :- ','(var(X), ','(isPlus(N, succ(zero), U), ','(=(N1, U), =(X, '$VAR'(N, _L))))).
numbervars_2(A, N, N) :- atomic(A).
numbervars_2('$VAR'(X34, X35), N, N).
numbervars_2(F, N, N1) :- numbervars_2(zero, F, N, N1).
numbervars_2(I, F, N, N1) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(numbervars_2(X, N, N0), numbervars_2(I1, F, N0, N1))))).
numbervars_2(X36, X37, N, N).
un_number_vars(clause(Head, Body), clause(H, B), X) :- ','(un_number_vars_2(Head, H, X), un_number_vars_2(Body, B, X)).
un_number_vars(directive(X), directive(X), X38).
un_number_vars_2('$VAR'(X39, X), X, others).
un_number_vars_2('$VAR'(X, X40), '$VAR'(X), cge).
un_number_vars_2(X, X, X41) :- atomic(X).
un_number_vars_2(F, F1, Y) :- ','(functor(F, Func, _N), ','(un_number_vars_2(zero, F, List, Y), =..(F1, .(Func, List)))).
un_number_vars_2(I, F, .(X1, Tail), Y) :- ','(isPlus(I, succ(zero), U), ','(=(I1, U), ','(arg(I1, F, X), ','(un_number_vars_2(X, X1, Y), un_number_vars_2(I1, F, Tail, Y))))).
un_number_vars_2(X42, X43, [], X44).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(=(ResultX, zero), =(Result, zero))).
check_if_cge(','(X, Y), Result) :- ','(check_if_cge(X, ResultX), ','(check_if_cge(Y, ResultY), ','(isTimes(ResultX, ResultY, U), =(Result, U)))).
check_if_cge('=>'(X45, X46), zero).
check_if_cge('&'(X47, X48), zero).
check_if_cge(X49, succ(zero)).
builtin(/(fail, zero)).
builtin(/(false, zero)).
builtin(/(otherwise, zero)).
builtin(/(repeat, zero)).
builtin(/(true, zero)).
builtin(/(version, zero)).
builtin(/(version, succ(zero))).
builtin(/(!, zero)).
builtin(/(abolish, succ(zero))).
builtin(/(abolish, succ(succ(zero)))).
builtin(/(abort, zero)).
builtin(/(assert, succ(zero))).
builtin(/(assert, succ(succ(zero)))).
builtin(/(asserta, succ(zero))).
builtin(/(asserta, succ(succ(zero)))).
builtin(/(assertz, succ(zero))).
builtin(/(assertz, succ(succ(zero)))).
builtin(/(bagof, succ(succ(succ(zero))))).
builtin(/(break, zero)).
builtin(/(call, succ(zero))).
builtin(/(close, succ(zero))).
builtin(/(compile, succ(zero))).
builtin(/(consult, succ(zero))).
builtin(/(debug, zero)).
builtin(/(debugging, zero)).
builtin(/(ensure_loaded, succ(zero))).
builtin(/(erase, succ(zero))).
builtin(/(fileerrors, zero)).
builtin(/(flush_output, succ(zero))).
builtin(/(foreign, succ(succ(zero)))).
builtin(/(foreign, succ(succ(succ(zero))))).
builtin(/(foreign_file, succ(succ(zero)))).
builtin(/(get, succ(zero))).
builtin(/(get, succ(succ(zero)))).
builtin(/(get0, succ(zero))).
builtin(/(get0, succ(succ(zero)))).
builtin(/(halt, zero)).
builtin(/(incore, succ(zero))).
builtin(/(load_foreign_files, succ(succ(zero)))).
builtin(/(module, succ(zero))).
builtin(/(nofileerrors, zero)).
builtin(/(no_style_check, succ(zero))).
builtin(/(open, succ(succ(succ(zero))))).
builtin(/(open_null_stream, succ(zero))).
builtin(/(read, succ(zero))).
builtin(/(read, succ(succ(zero)))).
builtin(/(recorda, succ(succ(succ(zero))))).
builtin(/(recorded, succ(succ(succ(zero))))).
builtin(/(recordz, succ(succ(succ(zero))))).
builtin(/(reinitialise, zero)).
builtin(/(restore, succ(zero))).
builtin(/(restore, succ(succ(zero)))).
builtin(/(retract, succ(zero))).
builtin(/(retractall, succ(zero))).
builtin(/(save, succ(zero))).
builtin(/(save, succ(succ(zero)))).
builtin(/(save_program, succ(zero))).
builtin(/(see, succ(zero))).
builtin(/(seeing, succ(zero))).
builtin(/(seen, zero)).
builtin(/(set_input, succ(zero))).
builtin(/(set_output, succ(zero))).
builtin(/(setof, succ(succ(succ(zero))))).
builtin(/(skip, succ(zero))).
builtin(/(skip, succ(succ(zero)))).
builtin(/(style_check, succ(zero))).
builtin(/(ttyget, succ(zero))).
builtin(/(ttyget0, succ(zero))).
builtin(/(ttyskip, succ(zero))).
builtin(/(unknown, succ(succ(zero)))).
builtin(/(use_module, succ(zero))).
builtin(/(use_module, succ(succ(zero)))).
builtin(/('^', succ(succ(zero)))).
builtin(/(\+, succ(zero))).
go(N) :- ','(prepare(N, ManyClauses), ','(analyze_all(ManyClauses, Result), conclude(Result))).
time(A) :- statistics(runtime, .(_N, .(A, []))).
prepare(N, ManyClauses) :- ','(data(Clauses), ','(mlist(N, Clauses, ManyClauses), time(_N))).
conclude(Result) :- ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(length(Result, L), ','(write('Length = '), ','(write(L), nl)))))))).
mlist(zero, _1, []).
mlist(X, SList, LList) :- ','(isMinus(X, succ(zero), U), ','(=(Y, U), ','(mlist(Y, SList, MList), ','(copy_term(SList, NewSlist), append(NewSlist, MList, LList))))).
data(.(clause(f(X, Z), ','(p(X, Y), q(Y, Z))), .(clause(f(X1, Y1, Z1), ','(p(X1, Y1), q(Y1, Z1))), .(clause(f(X2, Y2, Z2), ','(is(Y2, +(X2, Z2)), ','(p(X2, Y2), ','(r(Y2), q(Y2, Z2))))), .(clause(f(X3, Y3, Z3), ','(var(X3), ','(f(X3), ','(q(Y3), ','(r(X3, Y3, Z3), q(X3)))))), .(clause(f(X4, Y4, Z4), ','(r(X4, Y4), ','(p(X4, Y4), ','(p(W4), ','(s(X4), q(Y4, W4, Z4)))))), [])))))).
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).
fail :- failure(a).
failure(b).
=(X, X).
var(X0).
functor(X0, X1, X2).
\==(X0, X1).
true.
==(X0, X1).
length(X0, X1).
=..(X0, X1).
@<(X0, X1).
sort(X0, X1).
arg(X0, X1, X2).
atomic(X0).
statistics(X0, X1).
write(X0).
nl.
copy_term(X0, X1).


Query: analyze_all(g,a)