%!PS-Adobe-2.0 %%Creator: dvipsk 5.66a Copyright 1986-97 Radical Eye Software (www.radicaleye.com) %%Title: talp.dvi %%Pages: 4 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSCommandLine: dvips -o talp.ps talp.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2000.03.16:1526 %%BeginProcSet: texc.pro %! /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B 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b(and)i(a)f(bac)n(k-end,)g(the)h(C)p Fo(i)8 b Fv(ME)21 b(system)g([CiM],)g(for)f(pro)n(ving)f(termination) 523 3823 y(of)28 b(the)g(generated)f(TRS.)h(Exp)r(erimen)n(ts)f(sho)n (w)f(that)j(our)d(to)r(ol)i(can)f(comp)r(ete)h(with)h(other)523 3922 y(to)r(ols)e([DSV99])h(based)f(on)g(sophisticated)g(norm-based)f (approac)n(hes.)523 4214 y Fp(2)112 b(The)38 b(F)-9 b(ron)m(t-End)523 4439 y Fv(T)i(ALP)27 b(tak)n(es)f(a)h(Prolog)d(program)h(and)i(a)g (query)f(as)g(input)i(and)f(pro)r(ceeds)f(in)h(four)g(steps:)558 4625 y(1.)41 b(The)33 b(Prolog)e(program)h(is)h(translated)f(in)n(to)h (a)g(logic)f(program)f Fn(P)7 b Fv(.)33 b(In)h(this)f(pro)r(cess,)664 4725 y(clauses)f(with)h Fm(if-then)p Fv(-structures,)28 b(disjunctions,)33 b(or)f(negated)g(atoms)g(are)f(trans-)664 4825 y(lated)26 b(in)n(to)f(new)h(clauses.)f(F)-7 b(or)25 b(instance,)h(the)g(clause)f Fl(A)e Fn( )g Fl(B)t(;)14 b Fm(not)22 b Fl(C)q(;)14 b(D)28 b Fv(is)e(replaced)664 4924 y(with)i(the)g(clauses)f Fl(A)c Fn( )g Fl(B)t(;)14 b(C)q(;)g Fm(fail)27 b Fv(and)g Fl(A)d Fn( )f Fl(B)t(;)14 b(D)r Fv(.)28 b(Cuts)f(are)g(ignored.)p eop %%Page: 2 2 2 1 bop 558 448 a Fv(2.)41 b(The)f(query)f(determines)h(whic)n(h)f(of)h (the)g(argumen)n(ts)e(in)i(its)g(predicates)f(are)g(used)664 548 y(as)c(input)h(and)f(output,)h(resp)r(ectiv)n(ely)-7 b(.)35 b(According)f(to)h(this)h(information,)f(the)g(to)r(ol)664 648 y(tries)d(to)h(generate)e(a)h Fo(mo)l(ding)41 b Fv(for)32 b(the)h(logic)e(program)g(suc)n(h)h(that)h(the)g(program)d(is)664 747 y Fo(wel)t(l-mo)l(de)l(d)p Fv(.)h(If)e(this)h(step)f(is)g (successfully)g(completed,)g(the)g(logic)f(program)f(will)j(b)r(e)664 847 y(transformed)d(in)n(to)g(a)g(TRS)h(as)f(follo)n(ws.)558 946 y(3.)41 b(Ev)n(ery)e(atom)g Fl(A)45 b Fv(=)e Fl(p)p Fv(\()p Fl(t)1459 958 y Fu(1)1497 946 y Fl(;)14 b(:)g(:)g(:)f(;)h(t) 1711 958 y Fk(n)1756 946 y Fv(\))41 b(with)g(input)g(p)r(ositions)e Fl(i)2655 958 y Fu(1)2692 946 y Fl(;)14 b(:)g(:)g(:)g(;)g(i)2906 958 y Fk(k)2986 946 y Fv(and)40 b(output)664 1045 y(p)r(ositions)27 b Fl(i)1042 1057 y Fk(k)q Fu(+1)1167 1045 y Fl(;)14 b(:)g(:)g(:)f(;)h (i)1380 1057 y Fk(n)1453 1045 y Fv(asso)r(ciates)26 b(with)i(a)f (rewrite)g(rule)1230 1224 y Fl(\032)p Fv(\()p Fl(A)p Fv(\))d(=)f Fl(p)1553 1236 y Fk(in)1621 1224 y Fv(\()p Fl(t)1683 1236 y Fk(i)1706 1244 y Fj(1)1744 1224 y Fl(;)14 b(:)g(:)g(:)f(;)h(t)1958 1236 y Fk(i)1981 1245 y Fi(k)2022 1224 y Fv(\))23 b Fn(!)g Fl(p)2225 1236 y Fk(out)2326 1224 y Fv(\()p Fl(t)2388 1236 y Fk(i)2411 1245 y Fi(k)q Fj(+1)2524 1224 y Fl(;)14 b(:)g(:)g(:)f(;)h(t)2738 1236 y Fk(i)2761 1244 y Fi(n)2806 1224 y Fv(\))664 1402 y(and)30 b(ev)n(ery)f(program)f(clause)h Fl(C)34 b Fv(=)27 b Fl(A)g Fn( )g Fl(B)2079 1414 y Fu(1)2117 1402 y Fl(;)14 b(:)g(:)g(:)f(;)h(B) 2364 1414 y Fk(m)2457 1402 y Fv(is)30 b(transformed)f(in)n(to)h(a)g (con-)664 1502 y(ditional)k(rewrite)f(rule)g Fl(\032)p Fv(\()p Fl(C)6 b Fv(\))35 b(=)e Fl(\032)p Fv(\()p Fl(A)p Fv(\))h Fn(\()g Fl(\032)p Fv(\()p Fl(B)2198 1514 y Fu(1)2235 1502 y Fv(\))p Fl(;)14 b(:)g(:)g(:)g(;)g(\032)p Fv(\()p Fl(B)2590 1514 y Fk(m)2653 1502 y Fv(\).)34 b(The)g(CTRS)g Fn(R)3250 1514 y Fh(P)3340 1502 y Fv(=)664 1602 y Fn(f)14 b Fl(\032)p Fv(\()p Fl(C)6 b Fv(\))42 b Fn(j)g Fl(C)48 b Fn(2)42 b(P)7 b(g)38 b Fv(obtained)h(in)g(this)g(w)n(a)n(y)e(is)i (deterministic)g(b)r(ecause)g(the)g(logic)664 1701 y(program)26 b Fn(P)34 b Fv(is)27 b(w)n(ell-mo)r(ded.)558 1800 y(4.)41 b(Ev)n(ery)27 b(rule)h Fl(l)d Fn(!)f Fl(r)j Fn(\()d Fl(c)g Fn(2)h(R)1609 1812 y Fh(P)1693 1800 y Fv(with)k Fl(n)f Fv(conditions)g(in)h Fl(c)f Fv(is)g(transformed)f(in)n(to)h Fl(n)5 b Fv(+)g(1)664 1900 y(unconditional)27 b(rewrite)g(rules)g (\(cf.)h(Sect.)g(4\):)759 2227 y Fl(U)9 b Fv(\()p Fl(l)24 b Fn(!)f Fl(r)j Fn(\()d Fl(c)p Fv(\))g(=)1360 2007 y Fg(8)1360 2082 y(>)1360 2107 y(>)1360 2132 y(<)1360 2281 y(>)1360 2306 y(>)1360 2331 y(:)1445 2077 y Fn(f)p Fl(l)h Fn(!)g Fl(r)r Fn(g)p Fl(;)1025 b Fv(if)28 b Fl(c)g Fv(is)f(empt)n(y) 1445 2177 y Fn(f)p Fl(l)d Fn(!)g Fl(u)p Fv(\()p Fl(s;)13 b(~)-41 b(x)p Fv(\))p Fn(g)18 b([)h Fl(U)9 b Fv(\()p Fl(u)p Fv(\()p Fl(t;)k(~)-41 b(x)p Fv(\))23 b Fn(!)g Fl(r)j Fn(\()d Fl(c)2670 2147 y Fh(0)2693 2177 y Fv(\))p Fl(;)h Fv(if)k Fl(c)23 b Fv(=)g Fl(s)g Fn(!)g Fl(t;)14 b(c)3266 2147 y Fh(0)1528 2276 y Fv(where)39 b Fl(u)27 b Fv(is)h(a)f(fresh)g(function)i(sym)n(b)r(ol)e(and)1779 2376 y Fl(~)-41 b(x)24 b Fv(=)e Fn(V)7 b Fv(ar)o(\()p Fl(l)r Fv(\))18 b Fn(\\)h Fv(\()p Fn(V)7 b Fv(ar)o(\()p Fl(t)p Fv(\))19 b Fn([)g(V)7 b Fv(ar)o(\()p Fl(c)2804 2346 y Fh(0)2827 2376 y Fv(\))19 b Fn([)g(V)7 b Fv(ar)o(\()p Fl(r)r Fv(\)\))523 2630 y Fp(3)112 b(The)38 b(Bac)m(k-End)g(C)p Ff(i)11 b Fp(ME)523 2826 y Fv(The)37 b(bac)n(k-end)f(tries)h(to)g(pro)n (v)n(e)e(termination)i(of)g(the)g(rewrite)g(systems)f(generated)g(b)n (y)523 2925 y(the)j(fron)n(t-end.)g(This)f(bac)n(k-end)g(is)h(a)f (pre-release)f(of)i(v)n(ersion)e(2)h(of)h(the)g(rewrite)f(to)r(ol)523 3025 y(C)p Fo(i)8 b Fv(ME)40 b([CM96)o(])f(whic)n(h)g(is)g(a)n(v)-5 b(ailable)38 b(as)h(an)g(alpha)f(v)n(ersion)g([CiM].)i(T)-7 b(ALP)39 b(uses)f(one)523 3124 y(sp)r(eci\014c)24 b(metho)r(d)g(a)n(v) -5 b(ailable)22 b(in)h(C)p Fo(i)8 b Fv(ME)24 b(for)f(pro)n(ving)f (termination:)h(the)h(dep)r(endency)g(pair)523 3224 y(metho)r(d)32 b([A)n(G00)o(])g(in)g(com)n(bination)f(with)h(p)r(olynomial)f(in)n (terpretations)f([Gie95].)h(T)-7 b(o)32 b(b)r(e)523 3324 y(precise,)27 b(C)p Fo(i)8 b Fv(ME)28 b(p)r(erforms)f(the)h(follo)n (wing)e(steps:)558 3486 y(1.)41 b(It)28 b(computes)g(the)g Fo(estimate)l(d)i(dep)l(endency)h(gr)l(aph)k Fv(of)28 b(the)g(rewrite)f(system.)558 3584 y(2.)41 b(F)-7 b(rom)30 b(the)g(cycles)f(in)h(that)g(graph,)f(it)h(computes)g(a)f(set)h(of)g (constrain)n(ts)e(of)i(the)g(form)664 3684 y Fl(t)694 3696 y Fu(1)754 3684 y Fl(>)23 b(t)872 3696 y Fu(2)934 3684 y Fv(or)h Fl(t)1063 3696 y Fu(1)1124 3684 y Fn(\025)e Fl(t)1241 3696 y Fu(2)1278 3684 y Fv(,)j(that)h(ha)n(v)n(e)d(to)i(b)r (e)g(satis\014ed)g(b)n(y)f(a)h Fo(we)l(akly)33 b Fv(monotonic)24 b(reduction)664 3784 y(ordering.)523 3946 y(The)k(next)f(goal)g(is)g (to)h(\014nd)g(suc)n(h)f(an)g(ordering,)f(whic)n(h)i(is)f(done)h(as)f (follo)n(ws)f([CMT99)o(]:)558 4108 y(3.)41 b(With)21 b(eac)n(h)e(sym)n(b)r(ol)g Fl(f)29 b Fv(in)20 b(the)g(signature,)f(sa)n (y)f(of)i(arit)n(y)f Fl(n)p Fv(,)h(it)g(asso)r(ciates)e(a)h(parametric) 664 4208 y(p)r(olynomial)k(in)n(terpretation)g(of)g(the)h(simple)g (linear)f(form)g Fl(P)2570 4220 y Fk(f)2613 4208 y Fv(\()p Fl(x)2692 4220 y Fu(1)2730 4208 y Fl(;)14 b(:)g(:)g(:)28 b(;)14 b(x)2976 4220 y Fk(n)3021 4208 y Fv(\))24 b(=)e Fl(a)3208 4220 y Fu(1)3245 4208 y Fl(x)3292 4220 y Fu(1)3340 4208 y Fv(+)664 4307 y Fn(\001)14 b(\001)g(\001)k Fv(+)h Fl(a)907 4319 y Fk(n)952 4307 y Fl(x)999 4319 y Fk(n)1063 4307 y Fv(+)f Fl(c)p Fv(.)558 4406 y(4.)41 b(Ev)n(ery)21 b(constrain)n(t)h(is)h(translated)f(in)n(to)g(constrain)n(ts)g(on)g(p)r (olynomials,)g(and)h(then)g(in)n(to)664 4506 y(non-linear)29 b(Diophan)n(tine)h(constrain)n(ts)f(o)n(v)n(er)g(the)i Fl(a)2330 4518 y Fk(i)2357 4506 y Fv('s)f(and)g Fl(c)p Fv('s,)h(b)n(y)f(means)f(of)i(some)664 4606 y(\(incomplete\))d(p)r (ositiv)n(eness)f(criteria)g([HJ98)o(].)558 4704 y(5.)41 b(The)34 b(Diophan)n(tine)g(constrain)n(ts)e(are)h(solv)n(ed)f(for)i(v) -5 b(ariables)32 b(in)i(the)g(in)n(terv)-5 b(al)33 b([0;)14 b Fl(B)t Fv(],)664 4804 y(where)24 b Fl(B)30 b Fv(is)24 b(a)h(b)r(ound)g(for)f(co)r(e\016cien)n(ts)h(giv)n(en)f(b)n(y)g(the)i (user,)e(b)n(y)g(using)h Fo(\014nite)i(domain)664 4904 y Fv(constrain)n(t)g(solving)f(tec)n(hniques)h([BC93)o(].)p eop %%Page: 3 3 3 2 bop 523 448 a Fp(4)112 b(Example)523 624 y Fv(If)28 b(T)-7 b(ALP)27 b(gets)h(the)g(follo)n(wing)e(Prolog)f(program)h(with)i (query)g Fm(flat\()p Fo(in)6 b Fm(,)p Fo(out)i Fm(\))25 b Fv(as)i(input)523 767 y Fq(flat\(niltree,)42 b(nil\).)523 858 y(flat\(tree\(X,)g(niltree,)f(T\),)f(cons\(X,)h(L\)\))f(:-)f (flat\(T,)i(L\).)523 950 y(flat\(tree\(X,)h(tree\(Y,)f(T1,)f(T2\),)g (T3\),)g(L\))g(:-)601 1041 y(flat\(tree\(Y,)i(T1,)e(tree\(X,)h(T2,)f (T3\)\),)g(L\).)523 1192 y Fv(then)28 b(the)g(\014rst)f(transformation) f(yields)i(the)g(CTRS)1273 1350 y Fe(\015at)1388 1362 y Fd(in)1438 1350 y Fv(\()p Fe(niltree)p Fv(\))10 b Fn(!)f Fe(\015at)1934 1362 y Fd(out)2023 1350 y Fv(\()p Fe(nil)o Fv(\))925 1450 y Fe(\015at)1040 1462 y Fd(in)1090 1450 y Fv(\()p Fe(tree)p Fv(\()p Fl(x;)14 b Fe(niltree)q Fl(;)g(t)p Fv(\)\))c Fn(!)f Fe(\015at)1934 1462 y Fd(out)2023 1450 y Fv(\()p Fe(cons)o Fv(\()p Fl(x;)14 b(l)r Fv(\)\))47 b Fn(\()f Fe(\015at)2706 1462 y Fd(in)2756 1450 y Fv(\()p Fl(t)p Fv(\))24 b Fn(!)f Fe(\015at)3095 1462 y Fd(out)3183 1450 y Fv(\()p Fl(l)r Fv(\))654 1550 y Fe(\015at)769 1562 y Fd(in)819 1550 y Fv(\()p Fe(tree)p Fv(\()p Fl(x;)14 b Fe(tree)q Fv(\()p Fl(y)s(;)g(t)1375 1562 y Fu(1)1412 1550 y Fl(;)g(t)1479 1562 y Fu(2)1516 1550 y Fv(\))p Fl(;)g(t)1615 1562 y Fu(3)1653 1550 y Fv(\)\))c Fn(!)f Fe(\015at)1934 1562 y Fd(out)2023 1550 y Fv(\()p Fl(l)r Fv(\))46 b Fn(\()1787 1649 y Fe(\015at)1902 1661 y Fd(in)1952 1649 y Fv(\()p Fe(tree)q Fv(\()p Fl(y)s(;)14 b(t)2260 1661 y Fu(1)2297 1649 y Fl(;)g Fe(tree)p Fv(\()p Fl(x;)g(t)2612 1661 y Fu(2)2650 1649 y Fl(;)g(t)2717 1661 y Fu(3)2754 1649 y Fv(\)\)\))24 b Fn(!)f Fe(\015at)3095 1661 y Fd(out)3183 1649 y Fv(\()p Fl(l)r Fv(\))523 1809 y(and)k(the)h(second)f (transformation)f(yields)i(the)g(unconditional)f(TRS)1397 1968 y Fe(\015at)1512 1980 y Fd(in)1563 1968 y Fv(\()p Fe(niltree)p Fv(\))9 b Fn(!)h Fe(\015at)2059 1980 y Fd(out)2147 1968 y Fv(\()p Fe(nil)p Fv(\))1049 2067 y Fe(\015at)1164 2079 y Fd(in)1215 2067 y Fv(\()p Fe(tree)p Fv(\()p Fl(x;)k Fe(niltree)p Fl(;)g(t)p Fv(\)\))c Fn(!)g Fe(u)1987 2079 y Fd(1)2022 2067 y Fv(\()p Fe(\015at)2169 2079 y Fd(in)2219 2067 y Fv(\()p Fl(t)p Fv(\))p Fl(;)k(x)p Fv(\))1320 2167 y Fe(u)1363 2179 y Fd(1)1398 2167 y Fv(\()p Fe(\015at)1545 2179 y Fd(out)1634 2167 y Fv(\()p Fl(l)r Fv(\))p Fl(;)g(x)p Fv(\))c Fn(!)g Fe(\015at)2059 2179 y Fd(out)2147 2167 y Fv(\()p Fe(cons)p Fv(\()p Fl(x;)k(l)r Fv(\)\))778 2267 y Fe(\015at)893 2279 y Fd(in)943 2267 y Fv(\()p Fe(tree)q Fv(\()p Fl(x;)g Fe(tree)q Fv(\()p Fl(y)s(;)g(t)1500 2279 y Fu(1)1537 2267 y Fl(;)g(t)1604 2279 y Fu(2)1641 2267 y Fv(\))p Fl(;)g(t)1740 2279 y Fu(3)1777 2267 y Fv(\)\))c Fn(!)g Fe(u)1987 2279 y Fd(2)2022 2267 y Fv(\()p Fe(\015at)2169 2279 y Fd(in)2219 2267 y Fv(\()p Fe(tree)p Fv(\()p Fl(y)s(;)k(t)2526 2279 y Fu(1)2564 2267 y Fl(;)g Fe(tree)p Fv(\()p Fl(x;)g(t)2879 2279 y Fu(2)2916 2267 y Fl(;)g(t)2983 2279 y Fu(3)3021 2267 y Fv(\)\)\)\))1405 2366 y Fe(u)1448 2378 y Fd(2)1483 2366 y Fv(\()p Fe(\015at)1630 2378 y Fd(out)1719 2366 y Fv(\()p Fl(l)r Fv(\)\))9 b Fn(!)h Fe(\015at)2059 2378 y Fd(out)2147 2366 y Fv(\()p Fl(l)r Fv(\))523 2526 y(Subsequen)n(tly)41 b(C)p Fo(i)8 b Fv(ME)41 b(is)f(ask)n(ed)f(to)h(\014nd)g(a)g(linear)f(p) r(olynomial)g(in)n(terpretation)g(with)523 2626 y(co)r(e\016cien)n(ts) 27 b(in)h(the)g(in)n(terv)-5 b(al)27 b([0;)14 b(2].)27 b(It)h(generates)e(the)i(follo)n(wing)e(in)n(terpretation)677 2816 y([)-14 b([)p Fe(nil)p Fv(])g(])255 b(=)23 b(0)677 2916 y([)-14 b([)p Fe(niltree)p Fv(])g(])123 b(=)23 b(0)677 3015 y([)-14 b([)p Fe(\015at)824 3027 y Fd(in)875 3015 y Fv(])g(]\()p Fl(x)986 3027 y Fu(0)1024 3015 y Fv(\))23 b(=)g(0)1319 2816 y([)-14 b([)p Fe(\015at)1466 2828 y Fd(out)1555 2816 y Fv(])g(]\()p Fl(x)1666 2828 y Fu(0)1704 2816 y Fv(\))95 b(=)23 b(0)1319 2916 y([)-14 b([)p Fe(u)1394 2928 y Fd(2)1430 2916 y Fv(])g(]\()p Fl(x)1541 2928 y Fu(0)1579 2916 y Fv(\))220 b(=)23 b(0)1319 3015 y([)-14 b([)p Fe(cons)p Fv(])g(]\()p Fl(x)1616 3027 y Fu(0)1654 3015 y Fl(;)14 b(x)1738 3027 y Fu(1)1776 3015 y Fv(\))23 b(=)g(0)2053 2816 y([)-14 b([)p Fe(u)2128 2828 y Fd(1)2163 2816 y Fv(])g(]\()p Fl(x)2274 2828 y Fu(0)2312 2816 y Fl(;)14 b(x)2396 2828 y Fu(1)2434 2816 y Fv(\))199 b(=)23 b(0)2053 2916 y([)-14 b([)p Fe(tree)p Fv(])g(]\()p Fl(x)2328 2928 y Fu(0)2367 2916 y Fl(;)14 b(x)2451 2928 y Fu(1)2488 2916 y Fl(;)g(x)2572 2928 y Fu(2)2610 2916 y Fv(\))23 b(=)g Fl(x)2800 2928 y Fu(2)2856 2916 y Fv(+)18 b(2)p Fl(x)3028 2928 y Fu(1)3084 2916 y Fv(+)g(1)2053 3015 y([)-14 b([)p Fe(FLA)-7 b(T)2282 3027 y Fd(in)2333 3015 y Fv(])-14 b(]\()p Fl(x)2444 3027 y Fu(0)2482 3015 y Fv(\))151 b(=)23 b Fl(x)2800 3027 y Fu(0)523 3194 y Fv(and)29 b(the)g(induced)h(p)r(olynomial)e(ordering)g(satis\014es)g(all)h (constrain)n(ts)e(obtained)i(from)g(the)523 3294 y(cycles)e(in)h(the)g (estimated)g(dep)r(endency)g(graph.)523 3545 y Fp(5)112 b(Exp)s(erimen)m(tal)36 b(Results)523 3729 y Fv(As)30 b(in)h([DSV99],)f(w)n(e)g(ha)n(v)n(e)f(tested)h(the)g(T)-7 b(ALP)30 b(system)g(on)g(w)n(ell-kno)n(wn)f(examples)g(\(the)523 3828 y(b)r(enc)n(hmarks)h(are)g(collected)h(in)h([LS97)o(]\).)f(A)h(W) -7 b(eb)31 b(in)n(terface)g(for)f(T)-7 b(ALP)31 b(is)g(a)n(v)-5 b(ailable)30 b(at)523 3928 y Fm(http://bibiserv.)o(tec)o(hf)o(ak.)o(un) o(i-)o(bie)o(le)o(fel)o(d.)o(de)o(/ta)o(lp)o(/)p Fv(.)19 b(Ov)n(erall,)k(our)i(results)f(are)523 4028 y(comparable)19 b(to)h(those)f(rep)r(orted)h(in)g([DSV99])g(but)h(there)f(are)f (examples)h(for)f(whic)n(h)h(T)-7 b(ALP)523 4127 y(succeeds)24 b(and)g(other)g(to)r(ols)g(don't)h(\(e.g.)g(the)f(example)h(in)f(Sect.) h(4)f(and)h(Example)e(2.3.1)h(in)523 4227 y([Pl)r(\177)-44 b(u90)o(]\))33 b(and)f(vice)g(v)n(ersa.)f(During)i(our)e(exp)r(erimen)n (ts)i(w)n(e)f(made)g(the)h(follo)n(wing)e(obser-)523 4327 y(v)-5 b(ations.)29 b(F)-7 b(or)28 b(all)h(those)g(examples)g(for) f(whic)n(h)h(C)p Fo(i)8 b Fv(ME)30 b(w)n(as)e(able)h(to)g(\014nd)h(a)e (termination)523 4426 y(pro)r(of,)18 b(it)i(w)n(as)e(also)f(able)i(to)g (generate)e(a)i(suitable)f(linear)g(p)r(olynomial)h(in)n(terpretation)e (with)523 4526 y(co)r(e\016cien)n(ts)26 b(in)h(the)g(in)n(terv)-5 b(al)26 b([0;)14 b(2].)26 b(The)h(restriction)e(to)i(linear)e(p)r (olynomial)h(in)n(terpreta-)523 4625 y(tions)i(seems)f(to)h(b)r(e)g(a)f (v)n(ery)g(go)r(o)r(d)g(heuristic)g(b)r(ecause)h(whenev)n(er)e(searc)n (hing)g(for)h(a)h(linear)523 4725 y(in)n(terpretation)35 b(fails,)h(then)h(searc)n(hing)e(for)g(a)h(more)f(general)g(one,)h(lik) n(e)g(simple-mixed,)523 4825 y(do)r(es)d(not)g(succeed)g(either.)h(T)-7 b(able)33 b(1)f(con)n(tains)h(the)h(execution)f(times)g(of)g(the)h(bac) n(k-end)523 4924 y(for)27 b(\014nding)h(a)f(termination)g(pro)r(of)g (on)h(a)f(Sun)h(SP)-7 b(AR)n(Cstation)27 b(10.)p eop %%Page: 4 4 4 3 bop 1045 369 1838 4 v 1045 460 a Fs(Program)172 b(Query)404 b(Time)130 b(Ref.)p 1045 506 V 1045 597 a(p)r(erm)n(utation)48 b Fq(perm\(i,o\))261 b Fs(0.64)27 b(sec.)d([Pl)r(\177)-41 b(u90)r(])26 b(1.2)1045 689 y(transitivit)n(y)89 b Fq(p\(i,o\))378 b Fs(0.19)27 b(sec.)d([Pl)r(\177)-41 b(u90)r(])26 b(2.3.1)1045 780 y(quic)n(ksort)157 b Fq(qsort\(i,o\))222 b Fs(1.73)27 b(sec.)d([Pl)r(\177)-41 b(u90)r(])26 b(6.1.1)1045 871 y(m)n(ult)306 b Fq(mult\(i,i,o\))183 b Fs(0.22)27 b(sec.)d([Pl)r(\177) -41 b(u90)r(])26 b(7.2.9)1045 963 y(mergesort)134 b Fq (mergesort\(i,o\))66 b Fs(3.03)27 b(sec.)d([Pl)r(\177)-41 b(u90)r(])26 b(8.2.1a)1045 1054 y(\015at)352 b Fq(flat\(i,o\))261 b Fs(2.19)27 b(sec.)d([AZ96)q(])p 1045 1112 V 1592 1255 a Fc(T)-7 b(able)29 b(1.)c Fs(Benc)n(hmarks)523 1430 y Fp(References)523 1583 y Fs([A)n(G00])87 b(T.)25 b(Arts)f(and)g(J.)i (Giesl.)33 b(T)-6 b(ermination)25 b(of)g(term)e(rewriting)j(using)f (dep)r(endency)e(pairs.)844 1675 y Fb(The)l(or)l(etic)l(al)29 b(Computer)g(Scienc)l(e)p Fs(,)e(2000.)36 b(T)-6 b(o)26 b(app)r(ear.)523 1758 y([AZ96])98 b(T.)39 b(Arts)e(and)h(H.)g(Zan)n (tema.)71 b(T)-6 b(ermination)37 b(of)i(logic)h(programs)e(using)g (seman)n(tic)844 1850 y(uni\014cation.)70 b(In)37 b Fb(Pr)l(o)l(c.)i (5th)g(Int.)f(Workshop)i(on)f(L)l(o)l(gic)g(Pr)l(o)l(gr)l(am)g (Synthesis)h(and)844 1941 y(T)-6 b(r)l(ansformation)p Fs(,)36 b(v)n(olume)c(1048)k(of)e Fb(L)l(e)l(ctur)l(e)j(Notes)f(in)f (Computer)h(Scienc)l(e)f Fs(pages)844 2032 y(219{233,)29 b(1996.)e(Springer-V)-6 b(erlag.)523 2116 y([BC93])94 b(F.)32 b(Benhamou)f(and)g(A.)g(Colmerauer,)i(editors.)52 b Fb(Constr)l(aint)35 b(L)l(o)l(gic)e(Pr)l(o)l(gr)l(amming:)844 2207 y(sele)l(cte)l(d)c(r)l(ese)l(ar)l(ch)p Fs(.)37 b(MIT)26 b(Press,)h(1993.)523 2291 y([CiM])133 b(CiME)18 b(2.)j(Prerelease)e(a)n (v)l(ailable)g(at)e Fq(http://www.lri.fr/)p Fr(\030)p Fq(demons/cime-2)q(.0.h)q(tml)p Fs(.)523 2375 y([CM96])78 b(E.)28 b(Con)n(tejean)h(and)f(C.)g(Marc)n(h)n(\023)-36 b(e.)41 b(CiME:)30 b(Completion)e(Mo)r(dulo)h Fa(E)t Fs(.)40 b Fb(Pr)l(o)l(c.)30 b(7th)g(Int.)844 2466 y(Confer)l(enc)l(e)j (on)e(R)l(ewriting)h(T)-6 b(e)l(chniques)33 b(and)f(Applic)l(ations)p Fs(,)f(v)n(olume)e(1103)i(of)g Fb(L)l(e)l(c-)844 2558 y(tur)l(e)e(Notes)g(in)f(Computer)h(Scienc)l(e)p Fs(,)e(pages)g (416{419,)j(July)c(1996.)i(Springer-V)-6 b(erlag.)844 2649 y(System)24 b(description)i(a)n(v)l(ailable)h(at)f Fq(http://www.lri.fr/)p Fr(\030)p Fq(demons/cime.h)q(tml)p Fs(.)523 2733 y([CMT99])44 b(E.)26 b(Con)n(tejean,)g(C.)f(Marc)n(h)n (\023)-36 b(e,)26 b(A.-P)-6 b(.)24 b(T)-6 b(om\023)-38 b(as,)25 b(and)f(X.)h(Urbain.)32 b(Solving)25 b(termination)844 2824 y(constrain)n(ts)h(via)g(\014nite)g(domain)f(p)r(olynomial)g(in)n (terpretations.)35 b(Draft,)27 b(1999.)523 2908 y([CR93])91 b(M.)39 b(Ch)n(tourou)g(and)f(M.)h(Rusino)n(witc)n(h.)73 b(M)n(\023)-36 b(etho)r(de)39 b(transformationnelle)h(p)r(our)e(la)844 2999 y(preuv)n(e)31 b(de)h(terminaison)h(des)f(programmes)g(logiques.) 55 b(Unpublished)31 b(man)n(uscript,)844 3091 y(1993.)523 3174 y([DSV99])43 b(S.)24 b(Decorte,)g(D.)g(De)g(Sc)n(hrey)n(e,)f(and)h (H.)f(V)-6 b(andecasteele.)32 b(Constrain)n(t-based)25 b(termina-)844 3266 y(tion)h(analysis)h(of)f(logic)h(programs.)35 b Fb(A)n(CM)27 b(TOPLAS)p Fs(,)f(1999.)36 b(T)-6 b(o)26 b(app)r(ear.)523 3350 y([Gie95])88 b(J.)31 b(Giesl.)49 b(Generating)30 b(p)r(olynomial)h(orderings)g(for)f(termination)g(pro)r (ofs.)49 b(In)29 b Fb(Pr)l(o)l(c.)844 3441 y(6th)k(Int.)f(Confer)l(enc) l(e)i(on)f(R)l(ewriting)g(T)-6 b(e)l(chniques)34 b(and)f(Applic)l (ations)p Fs(,)f(v)n(olume)e(914)844 3532 y(of)c Fb(L)l(e)l(ctur)l(e)k (Notes)f(in)e(Computer)i(Scienc)l(e)p Fs(,)e(April)e(1995.)j (Springer-V)-6 b(erlag.)523 3616 y([GW93])64 b(H.)35 b(Ganzinger)h(and)e(U.)h(W)-6 b(aldmann.)61 b(T)-6 b(ermination)35 b(pro)r(ofs)h(of)g(w)n(ell-mo)r(ded)e(logic)844 3707 y(programs)h(via)f(conditional)i(rewrite)f(systems.)60 b(In)33 b Fb(Pr)l(o)l(c.)j(3r)l(d)h(Int.)e(Workshop)i(on)844 3799 y(Conditional)29 b(T)-6 b(erm)30 b(R)l(ewriting)g(Systems)p Fs(,)f(v)n(olume)e(656)h(of)h Fb(L)l(e)l(ctur)l(e)i(Notes)g(in)e(Com-) 844 3890 y(puter)g(Scienc)l(e)p Fs(,)e(pages)f(113{127,)j(Berlin,)e (1993.)g(Springer-V)-6 b(erlag.)523 3974 y([HJ98])106 b(Ho)r(on)24 b(Hong)h(and)f(Dalib)r(or)h(Jakus.)33 b(T)-6 b(esting)25 b(p)r(ositiv)n(eness)g(of)g(p)r(olynomials.)33 b Fb(Journal)844 4065 y(of)27 b(A)n(utomate)l(d)i(R)l(e)l(asoning)p Fs(,)f(21\(1\):23{38,)h(August)c(1998.)523 4149 y([LS97])112 b(N.)24 b(Lindenstrauss)h(and)e(Y.)h(Sagiv.)33 b(Automatic)23 b(termination)h(analysis)h(of)g(logic)h(pro-)844 4240 y(grams)31 b(\(with)g(detailed)h(exp)r(erimen)n(tal)e(results\).)51 b(T)-6 b(ec)n(hnical)32 b(rep)r(ort,)g(Hebrew)f(Uni-)844 4332 y(v)n(ersit)n(y)-6 b(,)25 b(Jerusalem,)h(1997.)523 4415 y([Ohl99])79 b(E.)38 b(Ohlebusc)n(h.)68 b(T)-6 b(ransforming)38 b(conditional)h(rewrite)f(systems)e(with)i(extra)f(v)l(ari-)844 4507 y(ables)29 b(in)n(to)g(unconditional)g(systems.)42 b(In)27 b Fb(Pr)l(o)l(c.)k(6th)g(Int.)e(Confer)l(enc)l(e)j(on)e(L)l(o)l (gic)h(for)844 4598 y(Pr)l(o)l(gr)l(amming)38 b(and)f(A)n(utomate)l(d)h (R)l(e)l(asoning)p Fs(,)f(v)n(olume)d(1705)j(of)g Fb(L)l(e)l(ctur)l(e)h (Notes)g(in)844 4689 y(A)n(rti\014cial)28 b(Intel)t(ligenc)l(e)p Fs(,)e(pages)g(111{130,)j(1999.)f(Springer-V)-6 b(erlag.)523 4773 y([Pl)r(\177)-41 b(u90])88 b(L.)32 b(Pl)r(\177)-41 b(umer.)52 b Fb(T)-6 b(ermination)33 b(Pr)l(o)l(ofs)h(for)f(L)l(o)l (gic)g(Pr)l(o)l(gr)l(ams)p Fs(,)h(v)n(olume)c(446)i(of)h Fb(L)l(e)l(ctur)l(e)844 4864 y(Notes)c(in)e(A)n(rti\014cial)g(Intel)t (ligenc)l(e)p Fs(.)35 b(Springer-V)-6 b(erlag,)26 b(Berlin,)h(1990.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF