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[(and)-16000(setting)]TJ /T13 1 Tf 222 0 TD (\016)Tj /T8 1 Tf 18 6 TD (11)Tj /T14 1 Tf 51 -6 TD [(=)-16000(1)-16000(giv)]TJ 139 0 TD [(es)-16000(the)]TJ -892.9999 55 TD [(single)-14000(constrain)]TJ 281 0 TD 14 Tc (t2)Tj /T13 1 Tf 51 0 TD 0 Tc (\013)Tj /T17 1 Tf 38 0 TD (\025)Tj /T14 1 Tf 44 0 TD (1.)Tj -372.0001 60 TD [(Because)-28000(this)-26000(is)-27000(the)-27000(only)-25000(rule)-27000(and)-26000(only)-26000(recursiv)]TJ 939.0002 0 TD (e)Tj -981.0001 54 TD [(subgoal,)-19000(termination)-17000(can)-19000(b)-1000(e)-20000(demonstrated)-19000(using)]TJ /T13 1 Tf 920.9999 0 TD (\013)Tj /T14 1 Tf 47 0 TD (=)Tj -967.9999 55 TD (1)Tj /T13 1 Tf 21 0 TD (=)Tj /T14 1 Tf 20.9999 0 TD (2.)Tj ET q 8.16 0 0 -0.48 340.056 682.524 cm BI /W 1 /H 1 /BPC 1 /IM true /F /CCF /DP <> ID P EI Q q 0.48 0 0 -8.16 340.056 682.284 cm BI /W 1 /H 1 /BPC 1 /IM true /F /CCF /DP <> ID P EI Q q 0.48 0 0 -8.16 347.736 682.284 cm BI /W 1 /H 1 /BPC 1 /IM true /F /CCF /DP <> ID P EI Q q 8.16 0 0 -0.48 340.056 674.124 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[(hange)-16000(should)-16000(not)-16000(mak)]TJ 409.9999 0 TD 14 Tc (ea)Tj -947.9999 55 TD 0 Tc (substan)Tj 137 0 TD [(tial)-16000(di\013erence.)-29000(He)-17000(had)-16000(to)-17000(mak)]TJ 569.0001 0 TD [(e)-15000(further)]TJ /T6 1 Tf 175 0 TD [(ad)-18000(ho)]TJ 100 0 TD (c)Tj /T14 1 Tf -981.0001 55 TD [(assumptions)-13000(to)-14000(handle)]TJ /T9 1 Tf 421 0 TD (parse)Tj /T14 1 Tf 110.0001 0 TD (.)Tj -489.0001 55 TD (W)Tj 40 0 TD [(e)-25000(shall)-25000(only)-26000(discuss)-27000(in)-25000(detail)-25000(the)-27000(deriv)]TJ 767 0 TD [(ation)-25000(of)]TJ -849.0001 53.9998 TD (constrain)Tj 165 0 TD [(ts)-18000(for)-17000(the)-18000(\014rst)-17000(rule)-18000(and)-17000(its)]TJ /T13 1 Tf 512 0 TD (e)Tj /T14 1 Tf 36 0 TD [(subgoal.)-27000(Recall)]TJ -713 55.0002 TD [(that)-14000(the)-15000(form)-12000(is)]TJ /T13 1 Tf 0 93 TD (x)Tj /T14 1 Tf 36 0 TD (=)Tj /T13 1 Tf 43 0 TD (a)Tj /T14 1 Tf 24 0 TD (+)Tj /T13 1 Tf 34 0 TD (A\025)Tj 139 0 TD (y)Tj /T14 1 Tf 33 0 TD (=)Tj /T13 1 Tf 44 0 TD (b)Tj /T14 1 Tf 20 0 TD (+)Tj /T13 1 Tf 34 0 TD 2 Tc (B\025)Tj /T14 1 Tf 141 0 TD 11 Tc (0=)Tj /T13 1 Tf 76 0 TD 0 Tc (c)Tj /T14 1 Tf 20 0 TD (+)Tj /T13 1 Tf 34.0001 0 TD 3 Tc (C\025)Tj 140 0 TD 0 Tc [(x;)-7000(y)-1000(;)-7000(\025)]TJ /T17 1 Tf 118 0 TD (\025)Tj /T14 1 Tf 44 0 TD (0)Tj -980.0001 93 TD [(The)-22000(\014rst)-22000(p)-1000(oin)]TJ 265 0 TD [(t)-20000(i)0(s)-21000(that)-21000(the)]TJ /T9 1 Tf 261 0 TD (t)Tj /T14 1 Tf 43 0 TD [(subgoal)-20000(precedes)-24000(the)]TJ /T9 1 Tf 409.9999 0 TD (e)Tj /T14 1 Tf -978.9999 55 TD [(subgoal,)-13000(so)-13000(should)-13000(supply)-14000(feasibilit)]TJ 630 0 TD [(y)-11000(constrain)]TJ 198.0001 0 TD [(ts)-15000(\(v)]TJ 83 0 TD (alues)Tj -911.0001 54.9998 TD (for)Tj /T13 1 Tf 60 0 TD (c)Tj /T14 1 Tf 28 0 TD (and)Tj /T13 1 Tf 77 0 TD (C)Tj /T14 1 Tf 43 0 TD [(in)-9000(Eq.)-10000(1\),)]TJ /T6 1 Tf 175 0 TD [(even)-12000(though)-13000(it)-11000(is)-11000(in)-11000(the)-12000(same)-11000(SCC)]TJ /T14 1 Tf 605.9999 0 TD (.)Tj -988.9999 54 TD [(It)-10000(is)-9000(not)-9000(immediately)-6000(ob)]TJ 422.0001 0 TD [(vious)-9000(what)-9000(these)-11000(constrain)]TJ 469 0 TD [(ts)-10000(are,)]TJ -891.0001 55.0002 TD [(but)-20000(they)-20000(can)-20000(b)-1000(e)-20000(found)-19000(b)]TJ 469 0 TD [(y)-20000(the)-20000(V)]TJ 147 0 TD [(an)-19000(Gelder's)-20000(metho)-1000(ds)]TJ -616 55 TD ([V)Tj 42 0 TD (G90)Tj 74 0 TD [(],)-13000(and)-13000(are:)]TJ 207 92.9999 TD 11 Tc [(0=)-1000(2)]TJ /T17 1 Tf 106 0 TD 0 Tc (\000)Tj /T9 1 Tf 42 0 TD (t)Tj /T8 1 Tf 22 6 TD (1)Tj /T14 1 Tf 27 -6 TD (+)Tj /T9 1 Tf 42.0001 0 TD (t)Tj /T8 1 Tf 21.9999 6 TD (2)Tj /T14 1 Tf 26.9999 -6 TD (+)Tj /T13 1 Tf 41.9999 0 TD (\026)Tj /T14 1 Tf -652.9999 92.9999 TD [(that)-14000(is,)]TJ /T9 1 Tf 143 0 TD (t)Tj /T8 1 Tf 22 6 TD (1)Tj /T17 1 Tf 30 -6 TD (\025)Tj /T14 1 Tf 44 0 TD 9 Tc (2+)Tj /T9 1 Tf 72.0001 0 TD 0 Tc (t)Tj /T8 1 Tf 22 6 TD (2)Tj /T14 1 Tf 31.9999 -6 TD (\()Tj /T13 1 Tf 16 0 TD (\026)Tj /T14 1 Tf 39 0 TD [(is)-14000(a)-13000(\\slac)]TJ 163 0 TD 14 Tc (kv)Tj 55.9999 0 TD 0 Tc (ariable"\).)Tj -596.9999 55.0001 TD (Let)Tj /T13 1 Tf 71 0 TD (\025)Tj /T14 1 Tf 36 0 TD [(b)-1000(e)-12000(the)-11000(v)]TJ 143 0 TD [(ector)-12000(\()]TJ /T13 1 Tf 117 0 TD [(L;)-7000(T)-3000(;)-7000(C)-1000(;)-7000(\026)]TJ /T14 1 Tf 168 0 TD (\))Tj /T8 1 Tf 15.9999 -15.0001 TD (T)Tj /T14 1 Tf 25 15.0001 TD [(.)-17000(The)-12000(ab)-1000(o)]TJ 177.0001 0 TD (v)Tj 20.9999 0 TD [(e)-11000(equation)]TJ -815.9999 55 TD (generates)Tj /T13 1 Tf 283.0001 88 TD (c)Tj /T14 1 Tf 60 0 TD (=)Tj /T4 1 Tf 73 -33.0001 TD (\002)Tj /T14 1 Tf 38 34 TD (4)Tj /T4 1 Tf 42 -34 TD (\003)Tj /T13 1 Tf -228 89.0001 TD (C)Tj /T14 1 Tf 75 0 TD (=)Tj /T4 1 Tf 73 -34 TD (\002)Tj /T17 1 Tf 38 34.9999 TD (\000)Tj /T14 1 Tf 32.0001 0 TD (1)Tj 62.9999 0 TD (0)Tj 62 0 TD (1)Tj 63 0 TD (1)Tj /T4 1 Tf 40.9999 -34.9999 TD (\003)Tj /T14 1 Tf -714.9999 122 TD (W)Tj 40 0 TD [(e)-14000(also)-13000(ha)]TJ 158 0 TD (v)Tj 21 0 TD (e)Tj /T13 1 Tf 77 81 TD (a)Tj /T14 1 Tf 63 0 TD (=)Tj /T4 1 Tf 74 -34 TD (\002)Tj /T14 1 Tf 38 34.9999 TD (0)Tj /T4 1 Tf 42 -34.9999 TD (\003)Tj /T13 1 Tf -226 89 TD (A)Tj /T14 1 Tf 72 0 TD (=)Tj /T4 1 Tf 74 -34 TD (\002)Tj /T14 1 Tf 38 35 TD (1)Tj 62 0 TD (0)Tj 63 0 TD (0)Tj 62 0 TD (0)Tj /T4 1 Tf 40.9999 -35 TD (\003)Tj /T13 1 Tf -398.9999 88.9999 TD (b)Tj /T14 1 Tf 58.9999 0 TD (=)Tj /T4 1 Tf 74 -32.9999 TD (\002)Tj /T14 1 Tf 38 34 TD (0)Tj /T4 1 Tf 42 -34 TD (\003)Tj /T13 1 Tf -229 88.9999 TD (B)Tj /T14 1 Tf 75 0 TD (=)Tj /T4 1 Tf 74 -34 TD (\002)Tj /T14 1 Tf 38 35.0001 TD (0)Tj 62 0 TD (0)Tj 63 0 TD (1)Tj 62 0 TD (0)Tj /T4 1 Tf 40.9999 -35.0001 TD (\003)Tj /T14 1 Tf -698.9999 122 TD [(Let)-15000(us)-15000(iden)]TJ 204 0 TD (tify)Tj /T13 1 Tf 76 0 TD (e)Tj /T14 1 Tf 33 0 TD (with)Tj /T13 1 Tf 95 0 TD (\013)Tj /T14 1 Tf 27 0 TD (,)Tj /T13 1 Tf 26.0001 0 TD (t)Tj /T14 1 Tf 28.9999 0 TD (with)Tj /T13 1 Tf 95 0 TD (\014)Tj /T14 1 Tf 25 0 TD [(,)-14000(and)]TJ /T13 1 Tf 106.9999 0 TD (n)Tj /T14 1 Tf 39.0001 0 TD (with)Tj /T13 1 Tf 94.9999 0 TD (\015)Tj /T14 1 Tf 23.0001 0 TD [(.)-20000(Then)]TJ -874.0001 55.0001 TD [(the)-19000(constrain)]TJ 241 0 TD [(ts)-19000(corresp)-1000(onding)-20000(to)-18000(Eq.)-18000(9)-18000(are)-19000(\(note)-18000(that)]TJ -241 54.9999 TD (\()Tj /T13 1 Tf 16 0 TD (A)Tj /T8 1 Tf 30.9999 -15.9999 TD (T)Tj /T17 1 Tf 36.0001 15.9999 TD (\000)Tj /T13 1 Tf 41 0 TD (B)Tj /T8 1 Tf 33 -15.9999 TD (T)Tj /T14 1 Tf 26 15.9999 TD [(\))-14000(and)-14000(\()]TJ /T13 1 Tf 127 0 TD (a)Tj /T8 1 Tf 22 -15.9999 TD (T)Tj /T17 1 Tf 35 15.9999 TD (\000)Tj /T13 1 Tf 42 0 TD (b)Tj /T8 1 Tf 18 -15.9999 TD (T)Tj /T14 1 Tf 25 15.9999 TD [(\))-14000(form)-12000(the)-15000(second)-15000(column\):)]TJ /T4 1 Tf -246 56 TD (2)Tj 0 73.0001 TD (6)Tj 0 24.9999 TD (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj 0 26 TD (4)Tj /T17 1 Tf 48 -213.9998 TD (\000)Tj /T14 1 Tf 32 0 TD (1)Tj 95 0 TD (1)Tj -95 53.9999 TD (0)Tj 95 0 TD (0)Tj -95 55 TD (1)Tj /T17 1 Tf 63 0 TD (\000)Tj /T14 1 Tf 32 0 TD (1)Tj -95 54.9999 TD (1)Tj 95 0 TD (0)Tj -95 55 TD (4)Tj 95 0 TD (0)Tj -95 55 TD (0)Tj 95 0 TD (1)Tj /T4 1 Tf 42 -308.9999 TD (3)Tj 0 73.0001 TD (7)Tj 0 24.9999 TD (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj 0 26 TD (5)Tj 34 -135.9999 TD (\024)Tj /T13 1 Tf 43.0001 31 TD (w)Tj /T8 1 Tf 29.9999 6 TD (1)Tj /T13 1 Tf -9 48.9999 TD (\013)Tj /T4 1 Tf 48 -85.9999 TD (\025)Tj /T17 1 Tf 32.9999 57.9999 TD (\025)Tj /T4 1 Tf 44 -171 TD (2)Tj 0 73.0001 TD (6)Tj 0 24.9999 TD (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj 0 26 TD (4)Tj /T14 1 Tf 80.0001 -213.9998 TD (0)Tj 0 53.9999 TD (0)Tj 0 55 TD (0)Tj T* (0)Tj /T13 1 Tf -31 55 TD (\016)Tj /T12 1 Tf 17.9999 6.0001 TD (ee)Tj /T14 1 Tf 13.0001 48.9999 TD (0)Tj /T4 1 Tf 40.9999 -308.9999 TD (3)Tj 0 73.0001 TD (7)Tj 0 24.9999 TD (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj 0 26 TD (5)Tj /T14 1 Tf -766.9999 147 TD [(Elimination)-11000(of)-13000(the)-14000(nondistinguished)]TJ /T13 1 Tf 663.9999 0 TD (w)Tj /T8 1 Tf 30 6.0001 TD (1)Tj /T14 1 Tf 32.0001 -6.0001 TD [(b)-1000(oils)-13000(this)-14000(do)]TJ 221.9999 0 TD (wn)Tj -947.9999 55 TD (to)Tj 423 55 TD (4)Tj /T13 1 Tf 21 0 TD (\013)Tj /T17 1 Tf 38 0 TD (\025)Tj /T13 1 Tf 44 0 TD (\016)Tj /T12 1 Tf 18 6 TD (ee)Tj /T14 1 Tf -544 72.0001 TD [(The)-27000(dev)]TJ 160 0 TD (elopmen)Tj 150 0 TD [(t)-26000(for)-26000(the)-27000(third)-26000(rule)-27000(with)]TJ /T9 1 Tf 521.0001 0 TD (t)Tj /T14 1 Tf 47.9999 0 TD [(as)-27000(the)]TJ -878.9999 54 TD (recursiv)Tj 140 0 TD [(e)-16000(subgoal)-13000(is)-14000(similar,)-11000(yielding)]TJ 287 93 TD (4)Tj /T13 1 Tf 21 0 TD (\014)Tj /T17 1 Tf 37 0 TD (\025)Tj /T13 1 Tf 43.0001 0 TD (\016)Tj /T12 1 Tf 17.9999 6 TD (tt)Tj /T14 1 Tf 554 -2663.9998 TD [(The)-18000(\014rst)-17000(rule)-18000(with)]TJ /T9 1 Tf 361 0 TD (t)Tj /T14 1 Tf 38.9999 0 TD [(as)-17000(the)-18000(recursiv)]TJ 269.0001 0 TD [(e)-18000(subgoal)-17000(and)-17000(the)]TJ -669 55 TD [(third)-16000(rule)-17000(with)]TJ /T9 1 Tf 289 0 TD (n)Tj /T14 1 Tf 38 0 TD [(as)-16000(the)-17000(recursiv)]TJ 267 0 TD [(e)-18000(subgoal)-15000(pro)-1000(duce)-18000(the)]TJ -594 53.9998 TD [(same)-14000(constrain)]TJ 270 0 TD [(ts)-15000(as)-15000(the)-15000(second)-16000(and)-14000(fourth)-14000(rules,)-15000(whic)]TJ 706.9999 0 TD (h)Tj -976.9999 55.0002 TD [(are)-14000(discussed)-16000(next.)]TJ 41.9999 56.9998 TD [(The)-28000(second)-29000(and)-28000(fourth)-28000(rules)-29000(are)-29000(straigh)]TJ 804 0 TD (tforw)Tj 95 0 TD (ard)Tj -940.9999 55.0005 TD (\(yielding)Tj /T13 1 Tf 174 0 TD (\013)Tj /T17 1 Tf 41.9999 0 TD (\025)Tj /T13 1 Tf 47 0 TD (\014)Tj /T17 1 Tf 41 0 TD (\025)Tj /T13 1 Tf 48.0001 0 TD (\015)Tj /T14 1 Tf 22.9999 0 TD [(\),)-17000(but)-16000(the)-16000(imp)-1000(ortan)]TJ 364 0 TD [(t)-15000(p)-1000(oin)]TJ 110.0002 0 TD [(t)-15000(i)0(s)-16000(that)]TJ -849.0001 54.9998 TD [(their)-14000(constrain)]TJ 264 0 TD [(ts)-15000(force)]TJ /T13 1 Tf 147 0 TD (\016)Tj /T12 1 Tf 17.9999 6 TD (et)Tj /T14 1 Tf 45.0001 -6 TD (and)Tj /T13 1 Tf 81 0 TD (\016)Tj /T12 1 Tf 17.9999 6 TD (tn)Tj /T14 1 Tf 49 -6 TD [(to)-14000(b)-1000(e)-14000(0.)]TJ -580 57 TD (Finally)Tj 126.0001 0 TD [(,)-11000(the)-14000(\014fth)-14000(rule)-14000(giv)]TJ 320 0 TD (es)Tj /T4 1 Tf -258 59 TD (2)Tj 0 72.9998 TD (6)Tj 0 25 TD (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj 0 26 TD (4)Tj /T17 1 Tf 48.9999 -162 TD (\000)Tj /T14 1 Tf 32.0001 0 TD (1)Tj 61.9999 0 TD (1)Tj -61.9999 55.0002 TD (0)Tj 61.9999 0 TD (0)Tj -61.9999 54 TD (0)Tj 61.9999 0 TD (2)Tj -61.9999 55 TD (1)Tj 61.9999 0 TD (0)Tj -61.9999 55 TD (0)Tj 61.9999 0 TD (1)Tj /T4 1 Tf 42.0001 -256 TD (3)Tj 0 72.9998 TD (7)Tj 0 25 TD (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj 0 26 TD (5)Tj 34 -112 TD (\024)Tj /T13 1 Tf 42.9999 32.0002 TD (\013)Tj 3.0001 54.9998 TD (\015)Tj /T4 1 Tf 44 -87 TD (\025)Tj /T17 1 Tf 33.9999 59.0002 TD (\025)Tj /T4 1 Tf 44 -146 TD (2)Tj 0 72.9998 TD (6)Tj 0 25 TD (6)Tj T* (6)Tj T* (6)Tj T* (6)Tj 0 26 TD (4)Tj /T14 1 Tf 84.0001 -162 TD (0)Tj 0 55.0002 TD (0)Tj /T13 1 Tf -36 54 TD (\016)Tj /T12 1 Tf 18 6 TD (ne)Tj /T14 1 Tf 18 49 TD (0)Tj 0 55 TD (0)Tj /T4 1 Tf 41.9999 -256 TD (3)Tj 0 72.9998 TD (7)Tj 0 25 TD (7)Tj T* (7)Tj T* (7)Tj T* (7)Tj 0 26 TD (5)Tj /T14 1 Tf -742.9999 154.0002 TD (whic)Tj 81.9999 0 TD 20 Tc [(hd)20000(o)19000(e)20000(s)]TJ /T6 1 Tf 144.0001 0 TD 0 Tc (not)Tj /T14 1 Tf 82 0 TD (force)Tj /T13 1 Tf 107 0 TD (\016)Tj /T12 1 Tf 18 6 TD (ne)Tj /T14 1 Tf 58.9999 -6 TD [(to)-20000(b)-1000(e)-21000(0)-21000(\()0(b)-1000(ecause)]TJ /T13 1 Tf 338 0 TD (a)Tj /T14 1 Tf 44.0002 0 TD [(=)-23000([2]\).)]TJ -874.0001 55 TD [(These)-15000(constrain)]TJ 284.9999 0 TD [(ts)-15000(reduce)-15000(to:)]TJ /T13 1 Tf 245.0001 0 TD (\015)Tj /T17 1 Tf 35.9999 0 TD (\025)Tj /T13 1 Tf 43 0 TD (\013)Tj /T14 1 Tf 41.0001 0 TD [(and)-14000(2)]TJ /T13 1 Tf 101.9999 0 TD (\015)Tj /T17 1 Tf 35 0 TD (\025)Tj /T13 1 Tf 44 0 TD (\016)Tj /T12 1 Tf 18.0002 6 TD (ne)Tj /T14 1 Tf 38 -6 TD (.)Tj -845.0002 57 TD [(Besides)-20000(self-lo)-1000(ops,)-20000(the)-20000(dep)-1000(endency)-21000(graph)-19000(has)-19000(edges)]TJ -41.9999 55 TD (\()Tj /T13 1 Tf 15.9999 0 TD [(e;)-7000(t)]TJ /T14 1 Tf 53 0 TD [(\),)-14000(\()]TJ /T13 1 Tf 58.0001 0 TD [(t;)-7000(n)]TJ /T14 1 Tf 59 0 TD [(\),)-13000(and)-13000(\()]TJ /T13 1 Tf 136.9999 0 TD [(n;)-7000(e)]TJ /T14 1 Tf 63.0001 0 TD [(\).)-19000(As)-14000(men)]TJ 184 0 TD (tioned,)Tj /T13 1 Tf 137 0 TD (\016)Tj /T12 1 Tf 18.0001 5.9998 TD (et)Tj /T14 1 Tf 44.9998 -5.9998 TD (and)Tj /T13 1 Tf 81 0 TD (\016)Tj /T12 1 Tf 18.0002 5.9998 TD (tn)Tj /T14 1 Tf 48.9998 -5.9998 TD (w)Tj 29 0 TD (ere)Tj -946.9999 54.9999 TD [(required)-12000(to)-10000(b)-1000(e)-12000(0.)-16000(Ho)]TJ 361 0 TD (w)Tj 29 0 TD (ev)Tj 38.9999 0 TD [(er,)-12000(assigning)-10000(the)-11000(\\w)]TJ 351 0 TD (eigh)Tj 73 0 TD (t")Tj /T13 1 Tf 47.0002 0 TD (\016)Tj /T12 1 Tf 17.9998 6 TD (ne)Tj /T14 1 Tf 50 -6 TD (=)Tj -967.9999 54 TD [(1)-9000(results)-11000(in)-9000(no)-10000(zero-w)]TJ 371.9999 0 TD (eigh)Tj 73.0001 0 TD [(t)-9000(cycles,)-12000(so)-9000(the)-10000(termination)-8000(test)]TJ -445 55 TD [(is)-16000(able)-16000(to)-16000(con)]TJ 247.9999 0 TD (tin)Tj 50 0 TD [(ue.)-25000(Of)-16000(course,)]TJ /T13 1 Tf 280 0 TD (\016)Tj /T12 1 Tf 18.0001 5.9999 TD (ee)Tj /T14 1 Tf 50 -5.9999 TD (and)Tj /T13 1 Tf 82.9999 0 TD (\016)Tj /T12 1 Tf 18 5.9999 TD (tt)Tj /T14 1 Tf 44 -5.9999 TD [(are)-16000(1.)-25000(No)]TJ 180 0 TD (w)Tj -970.9999 54.9999 TD (straigh)Tj 124 0 TD (tforw)Tj 94.9999 0 TD [(ard)-13000(computation)-13000(leads)-14000(to)]TJ /T13 1 Tf 129 101 TD (\013)Tj /T14 1 Tf 38.0001 0 TD (=)Tj /T13 1 Tf 44 0 TD (\014)Tj /T14 1 Tf 37 0 TD (=)Tj /T13 1 Tf 43.9999 0 TD (\015)Tj /T17 1 Tf 35.0001 0 TD (\025)Tj /T14 1 Tf 44 0 TD (1)Tj /T13 1 Tf 21 0 TD (=)Tj /T14 1 Tf 21 0 TD (2)Tj -632 100 TD [(so)-14000(termination)-12000(is)-14000(pro)]TJ 377.9999 0 TD (v)Tj 21.0001 0 TD (ed.)Tj ET q 8.16 0 0 -0.48 430.776 403.4041 cm BI /W 1 /H 1 /BPC 1 /IM true /F /CCF /DP <> ID P EI Q q 0.48 0 0 -8.16 430.776 403.1641 cm BI /W 1 /H 1 /BPC 1 /IM true /F /CCF /DP <> ID P EI Q q 0.48 0 0 -8.16 438.456 403.1641 cm BI /W 1 /H 1 /BPC 1 /IM true /F /CCF /DP <> ID P EI Q q 8.16 0 0 -0.48 430.776 395.0041 cm BI /W 1 /H 1 /BPC 1 /IM true /F /CCF /DP <> ID P EI Q BT /T15 1 Tf 0.24 0 0 -0.24 318 366.18 Tm (7)Tj 70 0 TD (Limitations)Tj /T14 1 Tf -70 75.9999 TD [(A)-12000(set)-13000(of)-11000(rules)-13000(ma)]TJ 305 0 TD [(y)-10000(terminate)-11000(in)-12000(top-do)]TJ 383 0 TD [(wn)-11000(execution)-13000(due)]TJ -688 55.0001 TD [(to)-18000(the)-19000(inabilit)]TJ 261 0 TD [(y)-16000(o)0(f)-18000(certain)-19000(terms)-18000(to)-18000(unify)]TJ 497.9999 0 TD [(,)-17000(rather)-19000(than)]TJ -758.9999 55 TD [(b)-1000(ecause)-12000(of)-11000(term)-10000(size)-11000(reduction.)-18000(Sometimes)-8000(the)-12000(syn)]TJ 899.0001 0 TD (tactic)Tj -899.0001 54.9999 TD [(transformations)-17000(describ)-1000(ed)-20000(in)-18000(App)-1000(endix)-19000(A)-18000(clarify)-17000(suc)]TJ 975.9999 0 TD (h)Tj -975.9999 54 TD [(situations)-23000(b)-1000(efore)-24000(termination)-21000(detection)-24000(b)-1000(egins.)]TJ 928.9999 0 TD (The)Tj -928.9999 55.0001 TD (argumen)Tj 156.9999 0 TD [(t)-17000(mapping)-15000(metho)-1000(d)-17000([BS89b)]TJ 490 0 TD [(,)-18000(BS91])-17000(pa)]TJ 196 0 TD [(ys)-17000(closer)]TJ -842.9999 55 TD (atten)Tj 93 0 TD [(tion)-15000(to)-15000(uni\014cation)-14000(issues)-16000(than)-15000(w)]TJ 589 0 TD [(e)-15000(do,)-15000(and)-15000(has)-15000(the)]TJ -682 55 TD (remark)Tj 127 0 TD [(able)-19000(prop)-1000(ert)]TJ 225.9999 0 TD [(y)-22000(o)0(f)-20000(detecting)-22000(certain)-21000(cases)-22000(where)]TJ -352.9999 54.9999 TD [(uni\014cation)-13000(fails)-13000(due)-14000(to)-14000(the)-15000(\\o)-1000(ccurs)-15000(c)]TJ 658.9999 0 TD (hec)Tj 58 0 TD (k".)Tj -675 56.0001 TD [(Also,)-29000(it)-26000(is)-27000(p)-1000(ossible)-27000(that)-27000(b)-1000(ound)-27000(argumen)]TJ 800 0 TD [(ts)-26000(really)]TJ -841.9999 54.9998 TD [(do)-26000(shrink)-27000(during)-26000(recursion,)-30000(but)-26000(the)-27000(in)]TJ 763.9999 0 TD (ter-argumen)Tj 221 0 TD (t)Tj -984.9999 55 TD (constrain)Tj 165 0 TD [(ts)-10000(to)-9000(pro)]TJ 147 0 TD (v)Tj 21 0 TD [(e)-10000(that)-9000(fact)-10000(are)-9000(not)-10000(deriv)]TJ 413.9999 0 TD [(able)-9000(b)]TJ 105 0 TD [(y)-9000(kno)]TJ 96 0 TD (wn)Tj -947.9999 55 TD [(metho)-1000(ds.)]TJ 208 0 TD (F)Tj 23.9999 0 TD [(or)-22000(instance,)-25000(the)-22000(feasible)-22000(region)-22000(ma)]TJ 666 0 TD [(y)-20000(not)]TJ -897.9999 55.0001 TD [(b)-1000(e)-25000(accurately)-24000(c)]TJ 293 0 TD [(haracterized)-26000(b)]TJ 268 0 TD [(y)-23000(a)-24000(\014nite)-24000(set)-25000(of)-23000(linear)]TJ -561 53.9999 TD (constrain)Tj 165 0 TD (ts.)Tj /T15 1 Tf -165 120 TD (8)Tj 70 0 TD (Conclusion)Tj /T14 1 Tf -70 77 TD (W)Tj 40 0 TD 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