/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(23245 + -230 * Arg_0, 15) * max(nat(619992 + -6164 * Arg_0) + max(407 + -4 * Arg_0, 3) + max(46490 + -460 * Arg_0, 30) + nat(22130 + -220 * Arg_0), 7) + max(816 + -8 * Arg_0, 8) + nat(88210 + -880 * Arg_0) + nat(11065 + -110 * Arg_0) + nat(309996 + -3082 * Arg_0) + nat(max(3, 205 + -2 * Arg_0) * max(11065 + -110 * Arg_0, -45) + max(23245 + -230 * Arg_0, 15) * max(11065 + -110 * Arg_0, -45) + nat(11065 + -110 * Arg_0) * max(11065 + -110 * Arg_0, -45) + nat(309996 + -3082 * Arg_0) * max(11065 + -110 * Arg_0, -45)) + nat(115310 + -1146 * Arg_0) + max(1, 1 + max(-1286, 309996 + -3082 * Arg_0) * max(7, max(407 + -4 * Arg_0, 3) + max(46490 + -460 * Arg_0, 30) + nat(22130 + -220 * Arg_0) + nat(619992 + -6164 * Arg_0))) + nat(404 + -4 * Arg_0) + nat(101 + -1 * Arg_0) + max(1, 1 + max(2, 204 + -2 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0) + max(23245 + -230 * Arg_0, 15) * max(-1286, 309996 + -3082 * Arg_0) + nat(11065 + -110 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0) + nat(309996 + -3082 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0)) + max(22, 23252 + -230 * Arg_0)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 10.4 s] (2) BOUNDS(1, max(23245 + -230 * Arg_0, 15) * max(nat(619992 + -6164 * Arg_0) + max(407 + -4 * Arg_0, 3) + max(46490 + -460 * Arg_0, 30) + nat(22130 + -220 * Arg_0), 7) + max(816 + -8 * Arg_0, 8) + nat(88210 + -880 * Arg_0) + nat(11065 + -110 * Arg_0) + nat(309996 + -3082 * Arg_0) + nat(max(3, 205 + -2 * Arg_0) * max(11065 + -110 * Arg_0, -45) + max(23245 + -230 * Arg_0, 15) * max(11065 + -110 * Arg_0, -45) + nat(11065 + -110 * Arg_0) * max(11065 + -110 * Arg_0, -45) + nat(309996 + -3082 * Arg_0) * max(11065 + -110 * Arg_0, -45)) + nat(115310 + -1146 * Arg_0) + max(1, 1 + max(-1286, 309996 + -3082 * Arg_0) * max(7, max(407 + -4 * Arg_0, 3) + max(46490 + -460 * Arg_0, 30) + nat(22130 + -220 * Arg_0) + nat(619992 + -6164 * Arg_0))) + nat(404 + -4 * Arg_0) + nat(101 + -1 * Arg_0) + max(1, 1 + max(2, 204 + -2 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0) + max(23245 + -230 * Arg_0, 15) * max(-1286, 309996 + -3082 * Arg_0) + nat(11065 + -110 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0) + nat(309996 + -3082 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0)) + max(22, 23252 + -230 * Arg_0)) (3) Loat Proof [FINISHED, 602 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalsipma91start(A, B, C, D) -> Com_1(evalsipma91entryin(A, B, C, D)) :|: TRUE evalsipma91entryin(A, B, C, D) -> Com_1(evalsipma91returnin(A, B, C, D)) :|: A >= 101 evalsipma91entryin(A, B, C, D) -> Com_1(evalsipma91bb3in(1, A, C, D)) :|: 100 >= A evalsipma91bb3in(A, B, C, D) -> Com_1(evalsipma91bb2in(A, B, C, D)) :|: 100 >= B evalsipma91bb3in(A, B, C, D) -> Com_1(evalsipma91bb11in(A, B, C, D)) :|: B >= 101 evalsipma91bb2in(A, B, C, D) -> Com_1(evalsipma91bb3in(A + 1, B + 11, C, D)) :|: TRUE evalsipma91bb11in(A, B, C, D) -> Com_1(evalsipma91bb5in(A, B, C, D)) :|: A >= 2 evalsipma91bb11in(A, B, C, D) -> Com_1(evalsipma91returnin(A, B, C, D)) :|: 1 >= A evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: 110 >= B evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: 1 >= A evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: A >= 3 evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb11in(A - 1, B - 10, C, D)) :|: B >= 111 && A >= 2 && A <= 2 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D, C + 1, C, D)) :|: C >= 101 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D, C + 11, C, D)) :|: C >= 101 && 100 >= C evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D + 1, C + 1, C, D)) :|: 100 >= C && C >= 101 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D + 1, C + 11, C, D)) :|: 100 >= C evalsipma91returnin(A, B, C, D) -> Com_1(evalsipma91stop(A, B, C, D)) :|: TRUE The start-symbols are:[evalsipma91start_4] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 7+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([2, 2+2*(101-Arg_0)])+max([2, 2+2*(101-Arg_0)])+max([0, max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])+max([0, (2+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([2, 2+2*(101-Arg_0)])+max([0, max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])])+max([1, 1+max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])])+max([2, 2+2*(101-Arg_0)])+max([0, 2*(101-Arg_0)])+max([0, 2*(101-Arg_0)])+max([0, 101-Arg_0])+max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)}) Initial Complexity Problem: Start: evalsipma91start Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3 Temp_Vars: Locations: evalsipma91bb11in, evalsipma91bb2in, evalsipma91bb3in, evalsipma91entryin, evalsipma91returnin, evalsipma91start, evalsipma91stop, n_evalsipma91bb11in___3, n_evalsipma91bb11in___4, n_evalsipma91bb5in___2, n_evalsipma91bb5in___7, n_evalsipma91bb8in___1, n_evalsipma91bb8in___5, n_evalsipma91bb8in___6 Transitions: 7: evalsipma91bb11in->evalsipma91returnin 2578: evalsipma91bb11in->n_evalsipma91bb5in___7 5: evalsipma91bb2in->evalsipma91bb3in 4: evalsipma91bb3in->evalsipma91bb11in 3: evalsipma91bb3in->evalsipma91bb2in 2: evalsipma91entryin->evalsipma91bb3in 1: evalsipma91entryin->evalsipma91returnin 16: evalsipma91returnin->evalsipma91stop 0: evalsipma91start->evalsipma91entryin 2615: n_evalsipma91bb11in___3->evalsipma91returnin 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2 2616: n_evalsipma91bb11in___4->evalsipma91returnin 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5 2581: n_evalsipma91bb5in___7->evalsipma91bb11in 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4 Timebounds: Overall timebound: 7+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([2, 2+2*(101-Arg_0)])+max([2, 2+2*(101-Arg_0)])+max([0, max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])+max([0, (2+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([2, 2+2*(101-Arg_0)])+max([0, max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])])+max([1, 1+max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])])+max([2, 2+2*(101-Arg_0)])+max([0, 2*(101-Arg_0)])+max([0, 2*(101-Arg_0)])+max([0, 101-Arg_0])+max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 7: evalsipma91bb11in->evalsipma91returnin: 1 {O(1)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7: max([1, 1+2*(101-Arg_0)]) {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in: max([0, 2*(101-Arg_0)]) {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in: max([0, 101-Arg_0]) {O(n)} 4: evalsipma91bb3in->evalsipma91bb11in: 1 {O(1)} 1: evalsipma91entryin->evalsipma91returnin: 1 {O(1)} 2: evalsipma91entryin->evalsipma91bb3in: 1 {O(1)} 16: evalsipma91returnin->evalsipma91stop: 1 {O(1)} 0: evalsipma91start->evalsipma91entryin: 1 {O(1)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2: max([15, -100+115*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])+max([1, 1+max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])]) {O(n^2)} 2615: n_evalsipma91bb11in___3->evalsipma91returnin: 1 {O(1)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7: max([2, 2+2*(101-Arg_0)])+max([0, (2+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2616: n_evalsipma91bb11in___4->evalsipma91returnin: 1 {O(1)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1: max([0, max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5: max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in: max([0, 2*(101-Arg_0)]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5: max([2, 2+2*(101-Arg_0)]) {O(n)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6: max([0, max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3: max([15, -100+115*max([1, 1+2*(101-Arg_0)])]) {O(n)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3: max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4: max([2, 2+2*(101-Arg_0)]) {O(n)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4: max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])]) {O(n)} Costbounds: Overall costbound: 7+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([2, 2+2*(101-Arg_0)])+max([2, 2+2*(101-Arg_0)])+max([0, max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])+max([0, (2+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([2, 2+2*(101-Arg_0)])+max([0, max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])])+max([1, 1+max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])])+max([2, 2+2*(101-Arg_0)])+max([0, 2*(101-Arg_0)])+max([0, 2*(101-Arg_0)])+max([0, 101-Arg_0])+max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 7: evalsipma91bb11in->evalsipma91returnin: 1 {O(1)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7: max([1, 1+2*(101-Arg_0)]) {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in: max([0, 2*(101-Arg_0)]) {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in: max([0, 101-Arg_0]) {O(n)} 4: evalsipma91bb3in->evalsipma91bb11in: 1 {O(1)} 1: evalsipma91entryin->evalsipma91returnin: 1 {O(1)} 2: evalsipma91entryin->evalsipma91bb3in: 1 {O(1)} 16: evalsipma91returnin->evalsipma91stop: 1 {O(1)} 0: evalsipma91start->evalsipma91entryin: 1 {O(1)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2: max([15, -100+115*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])+max([1, 1+max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])*max([7, 1+2*(max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))])]) {O(n^2)} 2615: n_evalsipma91bb11in___3->evalsipma91returnin: 1 {O(1)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7: max([2, 2+2*(101-Arg_0)])+max([0, (2+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2616: n_evalsipma91bb11in___4->evalsipma91returnin: 1 {O(1)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1: max([0, max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5: max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in: max([0, 2*(101-Arg_0)]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5: max([2, 2+2*(101-Arg_0)]) {O(n)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6: max([0, max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3: max([15, -100+115*max([1, 1+2*(101-Arg_0)])]) {O(n)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3: max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4: max([2, 2+2*(101-Arg_0)]) {O(n)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4: max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])]) {O(n)} Sizebounds: `Lower: 7: evalsipma91bb11in->evalsipma91returnin, Arg_0: 1 {O(1)} 7: evalsipma91bb11in->evalsipma91returnin, Arg_1: 101 {O(1)} 7: evalsipma91bb11in->evalsipma91returnin, Arg_2: min([101, min([Arg_2, min([Arg_2, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])])]) {O(n)} 7: evalsipma91bb11in->evalsipma91returnin, Arg_3: min([1, Arg_3]) {O(n)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_0: 2 {O(1)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_1: 101 {O(1)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_2: Arg_2 {O(n)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_3: Arg_3 {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_0: 1 {O(1)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_1: Arg_0 {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_2: Arg_2 {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_3: Arg_3 {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_0: 1 {O(1)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_1: Arg_0 {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_2: Arg_2 {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_3: Arg_3 {O(n)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_0: 1 {O(1)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_1: 101 {O(1)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_2: Arg_2 {O(n)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_3: Arg_3 {O(n)} 1: evalsipma91entryin->evalsipma91returnin, Arg_0: 101 {O(1)} 1: evalsipma91entryin->evalsipma91returnin, Arg_1: Arg_1 {O(n)} 1: evalsipma91entryin->evalsipma91returnin, Arg_2: Arg_2 {O(n)} 1: evalsipma91entryin->evalsipma91returnin, Arg_3: Arg_3 {O(n)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_0: 1 {O(1)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_1: Arg_0 {O(n)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_2: Arg_2 {O(n)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_3: Arg_3 {O(n)} 16: evalsipma91returnin->evalsipma91stop, Arg_0: 1 {O(1)} 16: evalsipma91returnin->evalsipma91stop, Arg_1: min([101, Arg_1]) {O(n)} 16: evalsipma91returnin->evalsipma91stop, Arg_2: min([101, min([Arg_2, min([Arg_2, min([Arg_2, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])])])]) {O(n)} 16: evalsipma91returnin->evalsipma91stop, Arg_3: min([1, Arg_3]) {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_0: Arg_0 {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_1: Arg_1 {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_2: Arg_2 {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_3: Arg_3 {O(n)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_0: 3 {O(1)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_1: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_2: min([91, min([-(10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])+max([-91, -91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])])+max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])), min([-(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])), -(10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])+max([-91, -91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])])+max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])]))])])]) {O(n^2)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_3: 2 {O(1)} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_0: inf {Infinity} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_1: inf {Infinity} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_2: inf {Infinity} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_3: inf {Infinity} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_0: 2 {O(1)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_1: min([101, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_2: min([101, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_3: 1 {O(1)} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_0: inf {Infinity} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_1: inf {Infinity} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_2: inf {Infinity} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_3: inf {Infinity} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_0: 3 {O(1)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_1: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_2: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_3: 2 {O(1)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_0: 3 {O(1)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_1: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_2: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_3: 2 {O(1)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_0: 1 {O(1)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_1: 101 {O(1)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_2: min([101, min([Arg_2, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])]) {O(n)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_3: min([1, Arg_3]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_0: 3 {O(1)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_1: min([101, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_2: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_3: 2 {O(1)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_0: 2 {O(1)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_1: min([101, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_2: min([101, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_3: 1 {O(1)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_0: 3 {O(1)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_1: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_2: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_3: 2 {O(1)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_0: 3 {O(1)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_1: min([91, -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])-max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])+-10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n^2)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_2: min([91, min([-(10*max([1, 1+(1+max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]))*max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])+max([-91, -91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])])])+max([0, 10*max([-670, -1110+440*max([1, 1+2*(101-Arg_0)])])])), -(-91+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))])]) {O(n^2)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_3: 2 {O(1)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_0: 2 {O(1)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_1: 102 {O(1)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_2: 101 {O(1)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_3: 2 {O(1)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_0: 2 {O(1)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_1: min([101, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_2: min([101, -(-101+10*max([-436, -1009+573*max([1, 1+2*(101-Arg_0)])]))]) {O(n)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_3: 1 {O(1)} `Upper: 7: evalsipma91bb11in->evalsipma91returnin, Arg_0: 1 {O(1)} 7: evalsipma91bb11in->evalsipma91returnin, Arg_1: max([111, 103+2*(101-Arg_0)]) {O(n)} 7: evalsipma91bb11in->evalsipma91returnin, Arg_2: max([100, max([113, max([Arg_2, max([Arg_2, 113+2*(101-Arg_0)])])])]) {O(n)} 7: evalsipma91bb11in->evalsipma91returnin, Arg_3: max([Arg_3, max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])]) {O(n)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_0: max([1, 1+2*(101-Arg_0)]) {O(n)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_1: 111 {O(1)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_2: Arg_2 {O(n)} 2578: evalsipma91bb11in->n_evalsipma91bb5in___7, Arg_3: Arg_3 {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_0: max([1, 1+2*(101-Arg_0)]) {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_1: 111 {O(1)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_2: Arg_2 {O(n)} 5: evalsipma91bb2in->evalsipma91bb3in, Arg_3: Arg_3 {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_0: max([1, 1+2*(101-Arg_0)]) {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_1: 100 {O(1)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_2: Arg_2 {O(n)} 3: evalsipma91bb3in->evalsipma91bb2in, Arg_3: Arg_3 {O(n)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_0: max([1, 1+2*(101-Arg_0)]) {O(n)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_1: 111 {O(1)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_2: Arg_2 {O(n)} 4: evalsipma91bb3in->evalsipma91bb11in, Arg_3: Arg_3 {O(n)} 1: evalsipma91entryin->evalsipma91returnin, Arg_0: Arg_0 {O(n)} 1: evalsipma91entryin->evalsipma91returnin, Arg_1: Arg_1 {O(n)} 1: evalsipma91entryin->evalsipma91returnin, Arg_2: Arg_2 {O(n)} 1: evalsipma91entryin->evalsipma91returnin, Arg_3: Arg_3 {O(n)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_0: 1 {O(1)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_1: 100 {O(1)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_2: Arg_2 {O(n)} 2: evalsipma91entryin->evalsipma91bb3in, Arg_3: Arg_3 {O(n)} 16: evalsipma91returnin->evalsipma91stop, Arg_0: max([1, Arg_0]) {O(n)} 16: evalsipma91returnin->evalsipma91stop, Arg_1: max([111, max([Arg_1, 103+2*(101-Arg_0)])]) {O(n)} 16: evalsipma91returnin->evalsipma91stop, Arg_2: max([100, max([113, max([Arg_2, max([Arg_2, max([Arg_2, 113+2*(101-Arg_0)])])])])]) {O(n)} 16: evalsipma91returnin->evalsipma91stop, Arg_3: max([Arg_3, max([Arg_3, max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])])]) {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_0: Arg_0 {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_1: Arg_1 {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_2: Arg_2 {O(n)} 0: evalsipma91start->evalsipma91entryin, Arg_3: Arg_3 {O(n)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_1: 111 {O(1)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_2: 100 {O(1)} 2576: n_evalsipma91bb11in___3->n_evalsipma91bb5in___2, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_0: -(inf) {Infinity} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_1: -(inf) {Infinity} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_2: -(inf) {Infinity} 2615: n_evalsipma91bb11in___3->evalsipma91returnin, Arg_3: -(inf) {Infinity} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_1: max([113, 113+2*(101-Arg_0)]) {O(n)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_2: max([100, max([113, 113+2*(101-Arg_0)])]) {O(n)} 2577: n_evalsipma91bb11in___4->n_evalsipma91bb5in___7, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_0: -(inf) {Infinity} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_1: -(inf) {Infinity} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_2: -(inf) {Infinity} 2616: n_evalsipma91bb11in___4->evalsipma91returnin, Arg_3: -(inf) {Infinity} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_1: 110 {O(1)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_2: 100 {O(1)} 2579: n_evalsipma91bb5in___2->n_evalsipma91bb8in___1, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_1: 111 {O(1)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_2: 101 {O(1)} 2580: n_evalsipma91bb5in___2->n_evalsipma91bb8in___5, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_0: 1 {O(1)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_1: max([103, 103+2*(101-Arg_0)]) {O(n)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_2: max([113, max([100, max([Arg_2, 113+2*(101-Arg_0)])])]) {O(n)} 2581: n_evalsipma91bb5in___7->evalsipma91bb11in, Arg_3: max([Arg_3, max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])])]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_0: max([1, max([max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]), 1+2*(101-Arg_0)])]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_1: max([113, 113+2*(101-Arg_0)]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_2: max([113, 113+2*(101-Arg_0)]) {O(n)} 2582: n_evalsipma91bb5in___7->n_evalsipma91bb8in___5, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_0: max([1, max([max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]), 1+2*(101-Arg_0)])]) {O(n)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_1: 110 {O(1)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_2: 100 {O(1)} 2583: n_evalsipma91bb5in___7->n_evalsipma91bb8in___6, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_1: 111 {O(1)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_2: 100 {O(1)} 2584: n_evalsipma91bb8in___1->n_evalsipma91bb11in___3, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_1: 111 {O(1)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_2: 100 {O(1)} 2585: n_evalsipma91bb8in___5->n_evalsipma91bb11in___3, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_1: max([113, 113+2*(101-Arg_0)]) {O(n)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_2: max([113, 113+2*(101-Arg_0)]) {O(n)} 2586: n_evalsipma91bb8in___5->n_evalsipma91bb11in___4, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_0: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_1: 111 {O(1)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_2: 100 {O(1)} 2587: n_evalsipma91bb8in___6->n_evalsipma91bb11in___4, Arg_3: max([1, 1+2*(101-Arg_0)])+max([15, -100+115*max([1, 1+2*(101-Arg_0)])])+max([0, max([-45, -100+55*max([1, 1+2*(101-Arg_0)])])])+max([0, max([-1286, -2827+1541*max([1, 1+2*(101-Arg_0)])])]) {O(n)} ---------------------------------------- (2) BOUNDS(1, max(23245 + -230 * Arg_0, 15) * max(nat(619992 + -6164 * Arg_0) + max(407 + -4 * Arg_0, 3) + max(46490 + -460 * Arg_0, 30) + nat(22130 + -220 * Arg_0), 7) + max(816 + -8 * Arg_0, 8) + nat(88210 + -880 * Arg_0) + nat(11065 + -110 * Arg_0) + nat(309996 + -3082 * Arg_0) + nat(max(3, 205 + -2 * Arg_0) * max(11065 + -110 * Arg_0, -45) + max(23245 + -230 * Arg_0, 15) * max(11065 + -110 * Arg_0, -45) + nat(11065 + -110 * Arg_0) * max(11065 + -110 * Arg_0, -45) + nat(309996 + -3082 * Arg_0) * max(11065 + -110 * Arg_0, -45)) + nat(115310 + -1146 * Arg_0) + max(1, 1 + max(-1286, 309996 + -3082 * Arg_0) * max(7, max(407 + -4 * Arg_0, 3) + max(46490 + -460 * Arg_0, 30) + nat(22130 + -220 * Arg_0) + nat(619992 + -6164 * Arg_0))) + nat(404 + -4 * Arg_0) + nat(101 + -1 * Arg_0) + max(1, 1 + max(2, 204 + -2 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0) + max(23245 + -230 * Arg_0, 15) * max(-1286, 309996 + -3082 * Arg_0) + nat(11065 + -110 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0) + nat(309996 + -3082 * Arg_0) * max(-1286, 309996 + -3082 * Arg_0)) + max(22, 23252 + -230 * Arg_0)) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalsipma91start 0: evalsipma91start -> evalsipma91entryin : [], cost: 1 1: evalsipma91entryin -> evalsipma91returnin : [ A>=101 ], cost: 1 2: evalsipma91entryin -> evalsipma91bb3in : A'=1, B'=A, [ 100>=A ], cost: 1 3: evalsipma91bb3in -> evalsipma91bb2in : [ 100>=B ], cost: 1 4: evalsipma91bb3in -> evalsipma91bb11in : [ B>=101 ], cost: 1 5: evalsipma91bb2in -> evalsipma91bb3in : A'=1+A, B'=11+B, [], cost: 1 6: evalsipma91bb11in -> evalsipma91bb5in : [ A>=2 ], cost: 1 7: evalsipma91bb11in -> evalsipma91returnin : [ 1>=A ], cost: 1 8: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 110>=B ], cost: 1 9: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 1>=A ], cost: 1 10: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ A>=3 ], cost: 1 11: evalsipma91bb5in -> evalsipma91bb11in : A'=-1+A, B'=-10+B, [ B>=111 && A==2 ], cost: 1 12: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=1+C, [ C>=101 ], cost: 1 13: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=11+C, [ C>=101 && 100>=C ], cost: 1 14: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=1+C, [ 100>=C && C>=101 ], cost: 1 15: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=11+C, [ 100>=C ], cost: 1 16: evalsipma91returnin -> evalsipma91stop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalsipma91start -> evalsipma91entryin : [], cost: 1 Removed unreachable and leaf rules: Start location: evalsipma91start 0: evalsipma91start -> evalsipma91entryin : [], cost: 1 2: evalsipma91entryin -> evalsipma91bb3in : A'=1, B'=A, [ 100>=A ], cost: 1 3: evalsipma91bb3in -> evalsipma91bb2in : [ 100>=B ], cost: 1 4: evalsipma91bb3in -> evalsipma91bb11in : [ B>=101 ], cost: 1 5: evalsipma91bb2in -> evalsipma91bb3in : A'=1+A, B'=11+B, [], cost: 1 6: evalsipma91bb11in -> evalsipma91bb5in : [ A>=2 ], cost: 1 8: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 110>=B ], cost: 1 9: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 1>=A ], cost: 1 10: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ A>=3 ], cost: 1 11: evalsipma91bb5in -> evalsipma91bb11in : A'=-1+A, B'=-10+B, [ B>=111 && A==2 ], cost: 1 12: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=1+C, [ C>=101 ], cost: 1 13: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=11+C, [ C>=101 && 100>=C ], cost: 1 14: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=1+C, [ 100>=C && C>=101 ], cost: 1 15: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=11+C, [ 100>=C ], cost: 1 Removed rules with unsatisfiable guard: Start location: evalsipma91start 0: evalsipma91start -> evalsipma91entryin : [], cost: 1 2: evalsipma91entryin -> evalsipma91bb3in : A'=1, B'=A, [ 100>=A ], cost: 1 3: evalsipma91bb3in -> evalsipma91bb2in : [ 100>=B ], cost: 1 4: evalsipma91bb3in -> evalsipma91bb11in : [ B>=101 ], cost: 1 5: evalsipma91bb2in -> evalsipma91bb3in : A'=1+A, B'=11+B, [], cost: 1 6: evalsipma91bb11in -> evalsipma91bb5in : [ A>=2 ], cost: 1 8: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 110>=B ], cost: 1 9: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 1>=A ], cost: 1 10: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ A>=3 ], cost: 1 11: evalsipma91bb5in -> evalsipma91bb11in : A'=-1+A, B'=-10+B, [ B>=111 && A==2 ], cost: 1 12: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=1+C, [ C>=101 ], cost: 1 15: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=11+C, [ 100>=C ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalsipma91start 17: evalsipma91start -> evalsipma91bb3in : A'=1, B'=A, [ 100>=A ], cost: 2 4: evalsipma91bb3in -> evalsipma91bb11in : [ B>=101 ], cost: 1 18: evalsipma91bb3in -> evalsipma91bb3in : A'=1+A, B'=11+B, [ 100>=B ], cost: 2 6: evalsipma91bb11in -> evalsipma91bb5in : [ A>=2 ], cost: 1 8: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 110>=B ], cost: 1 9: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 1>=A ], cost: 1 10: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ A>=3 ], cost: 1 11: evalsipma91bb5in -> evalsipma91bb11in : A'=-1+A, B'=-10+B, [ B>=111 && A==2 ], cost: 1 12: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=1+C, [ C>=101 ], cost: 1 15: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=11+C, [ 100>=C ], cost: 1 Accelerating simple loops of location 2. Accelerating the following rules: 18: evalsipma91bb3in -> evalsipma91bb3in : A'=1+A, B'=11+B, [ 100>=B ], cost: 2 Accelerated rule 18 with metering function meter (where 11*meter==100-B), yielding the new rule 19. Removing the simple loops: 18. Accelerated all simple loops using metering functions (where possible): Start location: evalsipma91start 17: evalsipma91start -> evalsipma91bb3in : A'=1, B'=A, [ 100>=A ], cost: 2 4: evalsipma91bb3in -> evalsipma91bb11in : [ B>=101 ], cost: 1 19: evalsipma91bb3in -> evalsipma91bb3in : A'=meter+A, B'=11*meter+B, [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2*meter 6: evalsipma91bb11in -> evalsipma91bb5in : [ A>=2 ], cost: 1 8: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 110>=B ], cost: 1 9: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 1>=A ], cost: 1 10: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ A>=3 ], cost: 1 11: evalsipma91bb5in -> evalsipma91bb11in : A'=-1+A, B'=-10+B, [ B>=111 && A==2 ], cost: 1 12: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=1+C, [ C>=101 ], cost: 1 15: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=11+C, [ 100>=C ], cost: 1 Chained accelerated rules (with incoming rules): Start location: evalsipma91start 17: evalsipma91start -> evalsipma91bb3in : A'=1, B'=A, [ 100>=A ], cost: 2 20: evalsipma91start -> evalsipma91bb3in : A'=1+meter, B'=11*meter+A, [ 100>=A && 11*meter==100-A && meter>=1 ], cost: 2+2*meter 4: evalsipma91bb3in -> evalsipma91bb11in : [ B>=101 ], cost: 1 6: evalsipma91bb11in -> evalsipma91bb5in : [ A>=2 ], cost: 1 8: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 110>=B ], cost: 1 9: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 1>=A ], cost: 1 10: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ A>=3 ], cost: 1 11: evalsipma91bb5in -> evalsipma91bb11in : A'=-1+A, B'=-10+B, [ B>=111 && A==2 ], cost: 1 12: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=1+C, [ C>=101 ], cost: 1 15: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=11+C, [ 100>=C ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalsipma91start 21: evalsipma91start -> [10] : [ 100>=A && 11*meter==100-A && meter>=1 ], cost: 2+2*meter 6: evalsipma91bb11in -> evalsipma91bb5in : [ A>=2 ], cost: 1 8: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 110>=B ], cost: 1 9: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ 1>=A ], cost: 1 10: evalsipma91bb5in -> evalsipma91bb8in : C'=-10+B, D'=-1+A, [ A>=3 ], cost: 1 11: evalsipma91bb5in -> evalsipma91bb11in : A'=-1+A, B'=-10+B, [ B>=111 && A==2 ], cost: 1 12: evalsipma91bb8in -> evalsipma91bb11in : A'=D, B'=1+C, [ C>=101 ], cost: 1 15: evalsipma91bb8in -> evalsipma91bb11in : A'=1+D, B'=11+C, [ 100>=C ], cost: 1 Applied pruning (of leafs and parallel rules): Start location: evalsipma91start 21: evalsipma91start -> [10] : [ 100>=A && 11*meter==100-A && meter>=1 ], cost: 2+2*meter ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalsipma91start 21: evalsipma91start -> [10] : [ 100>=A && 11*meter==100-A && meter>=1 ], cost: 2+2*meter Computing asymptotic complexity for rule 21 Simplified the guard: 21: evalsipma91start -> [10] : [ 11*meter==100-A && meter>=1 ], cost: 2+2*meter Solved the limit problem by the following transformations: Created initial limit problem: meter (+/+!), 101-11*meter-A (+/+!), 2+2*meter (+), -99+11*meter+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n,A==100-11*n} resulting limit problem: [solved] Solution: meter / n A / 100-11*n Resulting cost 2+2*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 2+2*n Rule cost: 2+2*meter Rule guard: [ 11*meter==100-A && meter>=1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)