/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(-4 * Arg_2 + max(-4 + -4 * Arg_0 + 4 * Arg_4, -4 + 4 * Arg_4)) + nat(-4 * Arg_2 + 4 * Arg_4) + max(6 + -1 * Arg_2 + Arg_4, 7) + nat(-3 * Arg_2 + 3 * Arg_4) + nat(-2 + -2 * Arg_2 + 2 * Arg_4)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 4044 ms] (2) BOUNDS(1, nat(-4 * Arg_2 + max(-4 + -4 * Arg_0 + 4 * Arg_4, -4 + 4 * Arg_4)) + nat(-4 * Arg_2 + 4 * Arg_4) + max(6 + -1 * Arg_2 + Arg_4, 7) + nat(-3 * Arg_2 + 3 * Arg_4) + nat(-2 + -2 * Arg_2 + 2 * Arg_4)) (3) Loat Proof [FINISHED, 288.5 s] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: 0 >= A + 1 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: A >= 0 && C >= E + 1 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A start(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D - 1 - F, E, F)) :|: A >= 0 && E >= C && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A start(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + F + B, C, D, E, F)) :|: A >= 0 && E >= C && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A lbl91(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: B >= D + 1 && B >= C && A >= 0 && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A lbl91(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: D >= B && 0 >= A + 1 && B >= C && A >= 0 && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A lbl91(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D - 1 - F, E, F)) :|: A >= 0 && D >= B && B >= C && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A lbl91(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + F + B, C, D, E, F)) :|: A >= 0 && D >= B && B >= C && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A lbl101(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: B >= D + 1 && E >= D && A >= 0 && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A lbl101(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: D >= B && 0 >= A + 1 && E >= D && A >= 0 && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A lbl101(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D - 1 - F, E, F)) :|: A >= 0 && D >= B && E >= D && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A lbl101(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + F + B, C, D, E, F)) :|: A >= 0 && D >= B && E >= D && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, E, E, A)) :|: TRUE The start-symbols are:[start0_6] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 7+max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+4*Arg_4])+max([0, Arg_4-Arg_2]) {O(n)}) Initial Complexity Problem: Start: start0 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5 Temp_Vars: Locations: lbl101, lbl91, start, start0, stop Transitions: lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,1+Arg_5+Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_2 <= Arg_3 && 1+Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_3 <= Arg_4 && Arg_0+Arg_2+1 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl91(Arg_0,Arg_1,Arg_2,Arg_3-1-Arg_5,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_2 <= Arg_3 && 1+Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_3 <= Arg_4 && Arg_0+Arg_2+1 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_2 <= Arg_3 && 1+Arg_2 <= Arg_1 && 0 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_3 <= Arg_4 && 0 <= Arg_0 && Arg_0+Arg_2+1 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 lbl91(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,1+Arg_5+Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_1 <= Arg_4 && Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_0+Arg_3+1 <= Arg_4 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 lbl91(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl91(Arg_0,Arg_1,Arg_2,Arg_3-1-Arg_5,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_1 <= Arg_4 && Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_0+Arg_3+1 <= Arg_4 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 lbl91(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_1 <= Arg_4 && Arg_2 <= Arg_1 && 0 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_2 <= Arg_1 && 0 <= Arg_0 && Arg_1 <= Arg_0+Arg_3+1 && Arg_0+Arg_3+1 <= Arg_4 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,1+Arg_5+Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_2 <= Arg_4 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl91(Arg_0,Arg_1,Arg_2,Arg_3-1-Arg_5,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_2 <= Arg_4 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0+1 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_4+1 <= Arg_2 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> start(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_0):|: Timebounds: Overall timebound: 7+max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+4*Arg_4])+max([0, Arg_4-Arg_2]) {O(n)} 8: lbl101->stop: 1 {O(1)} 10: lbl101->lbl91: max([0, -4*Arg_2+4*Arg_4])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]) {O(n)} 11: lbl101->lbl101: max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]) {O(n)} 4: lbl91->stop: 1 {O(1)} 6: lbl91->lbl91: max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]) {O(n)} 7: lbl91->lbl101: max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]) {O(n)} 0: start->stop: 1 {O(1)} 1: start->stop: 1 {O(1)} 2: start->lbl91: 1 {O(1)} 3: start->lbl101: 1 {O(1)} 12: start0->start: 1 {O(1)} Costbounds: Overall costbound: 7+max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+4*Arg_4])+max([0, Arg_4-Arg_2]) {O(n)} 8: lbl101->stop: 1 {O(1)} 10: lbl101->lbl91: max([0, -4*Arg_2+4*Arg_4])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]) {O(n)} 11: lbl101->lbl101: max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]) {O(n)} 4: lbl91->stop: 1 {O(1)} 6: lbl91->lbl91: max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]) {O(n)} 7: lbl91->lbl101: max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]) {O(n)} 0: start->stop: 1 {O(1)} 1: start->stop: 1 {O(1)} 2: start->lbl91: 1 {O(1)} 3: start->lbl101: 1 {O(1)} 12: start0->start: 1 {O(1)} Sizebounds: `Lower: 8: lbl101->stop, Arg_0: 0 {O(1)} 8: lbl101->stop, Arg_1: min([Arg_2, -(-1-Arg_2)]) {O(n)} 8: lbl101->stop, Arg_2: Arg_2 {O(n)} 8: lbl101->stop, Arg_3: min([Arg_4, -((max([0, -4*Arg_2+4*Arg_4])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([0, max([-(Arg_4), max([-(Arg_4), 1+Arg_0-Arg_4])])]))]) {O(n^2)} 8: lbl101->stop, Arg_4: Arg_4 {O(n)} 8: lbl101->stop, Arg_5: 0 {O(1)} 10: lbl101->lbl91, Arg_0: 0 {O(1)} 10: lbl101->lbl91, Arg_1: min([Arg_2, -(-1-Arg_2)]) {O(n)} 10: lbl101->lbl91, Arg_2: Arg_2 {O(n)} 10: lbl101->lbl91, Arg_3: min([0, min([Arg_4, min([Arg_4, -(1+Arg_0-Arg_4)])])])+(min([0, -(-4*Arg_2+4*Arg_4)])-max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]))*max([1, 1+Arg_0])+(min([0, -(-1+Arg_4-Arg_2)])-max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0]) {O(n^2)} 10: lbl101->lbl91, Arg_4: Arg_4 {O(n)} 10: lbl101->lbl91, Arg_5: 0 {O(1)} 11: lbl101->lbl101, Arg_0: 0 {O(1)} 11: lbl101->lbl101, Arg_1: min([Arg_2, -(-1-Arg_2)]) {O(n)} 11: lbl101->lbl101, Arg_2: Arg_2 {O(n)} 11: lbl101->lbl101, Arg_3: min([0, min([Arg_4, min([Arg_4, -(1+Arg_0-Arg_4)])])])+(min([0, -(-4*Arg_2+4*Arg_4)])-max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]))*max([1, 1+Arg_0])+(min([0, -(-1+Arg_4-Arg_2)])-max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0]) {O(n^2)} 11: lbl101->lbl101, Arg_4: Arg_4 {O(n)} 11: lbl101->lbl101, Arg_5: 0 {O(1)} 4: lbl91->stop, Arg_0: 0 {O(1)} 4: lbl91->stop, Arg_1: min([Arg_2, min([Arg_2, -(-1-Arg_2)])]) {O(n)} 4: lbl91->stop, Arg_2: Arg_2 {O(n)} 4: lbl91->stop, Arg_3: min([-((max([0, -4*Arg_2+4*Arg_4])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([0, max([-(Arg_4), max([-(Arg_4), 1+Arg_0-Arg_4])])])), min([-(1+Arg_0-Arg_4), -((max([0, -4*Arg_2+4*Arg_4])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([0, max([-(Arg_4), max([-(Arg_4), 1+Arg_0-Arg_4])])]))])]) {O(n^2)} 4: lbl91->stop, Arg_4: Arg_4 {O(n)} 4: lbl91->stop, Arg_5: 0 {O(1)} 6: lbl91->lbl91, Arg_0: 0 {O(1)} 6: lbl91->lbl91, Arg_1: min([Arg_2, -(-1-Arg_2)]) {O(n)} 6: lbl91->lbl91, Arg_2: Arg_2 {O(n)} 6: lbl91->lbl91, Arg_3: min([0, min([Arg_4, min([Arg_4, -(1+Arg_0-Arg_4)])])])+(min([0, -(-4*Arg_2+4*Arg_4)])-max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]))*max([1, 1+Arg_0])+(min([0, -(-1+Arg_4-Arg_2)])-max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0]) {O(n^2)} 6: lbl91->lbl91, Arg_4: Arg_4 {O(n)} 6: lbl91->lbl91, Arg_5: 0 {O(1)} 7: lbl91->lbl101, Arg_0: 0 {O(1)} 7: lbl91->lbl101, Arg_1: min([Arg_2, -(-1-Arg_2)]) {O(n)} 7: lbl91->lbl101, Arg_2: Arg_2 {O(n)} 7: lbl91->lbl101, Arg_3: min([0, min([Arg_4, min([Arg_4, -(1+Arg_0-Arg_4)])])])+(min([0, -(-4*Arg_2+4*Arg_4)])-max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]))*max([1, 1+Arg_0])+(min([0, -(-1+Arg_4-Arg_2)])-max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0]) {O(n^2)} 7: lbl91->lbl101, Arg_4: Arg_4 {O(n)} 7: lbl91->lbl101, Arg_5: 0 {O(1)} 0: start->stop, Arg_0: Arg_0 {O(n)} 0: start->stop, Arg_1: Arg_2 {O(n)} 0: start->stop, Arg_2: Arg_2 {O(n)} 0: start->stop, Arg_3: Arg_4 {O(n)} 0: start->stop, Arg_4: Arg_4 {O(n)} 0: start->stop, Arg_5: Arg_0 {O(n)} 1: start->stop, Arg_0: 0 {O(1)} 1: start->stop, Arg_1: Arg_2 {O(n)} 1: start->stop, Arg_2: Arg_2 {O(n)} 1: start->stop, Arg_3: Arg_4 {O(n)} 1: start->stop, Arg_4: Arg_4 {O(n)} 1: start->stop, Arg_5: 0 {O(1)} 2: start->lbl91, Arg_0: 0 {O(1)} 2: start->lbl91, Arg_1: Arg_2 {O(n)} 2: start->lbl91, Arg_2: Arg_2 {O(n)} 2: start->lbl91, Arg_3: -1+Arg_4-Arg_0 {O(n)} 2: start->lbl91, Arg_4: Arg_4 {O(n)} 2: start->lbl91, Arg_5: 0 {O(1)} 3: start->lbl101, Arg_0: 0 {O(1)} 3: start->lbl101, Arg_1: 1+Arg_2 {O(n)} 3: start->lbl101, Arg_2: Arg_2 {O(n)} 3: start->lbl101, Arg_3: Arg_4 {O(n)} 3: start->lbl101, Arg_4: Arg_4 {O(n)} 3: start->lbl101, Arg_5: 0 {O(1)} 12: start0->start, Arg_0: Arg_0 {O(n)} 12: start0->start, Arg_1: Arg_2 {O(n)} 12: start0->start, Arg_2: Arg_2 {O(n)} 12: start0->start, Arg_3: Arg_4 {O(n)} 12: start0->start, Arg_4: Arg_4 {O(n)} 12: start0->start, Arg_5: Arg_0 {O(n)} `Upper: 8: lbl101->stop, Arg_0: Arg_0 {O(n)} 8: lbl101->stop, Arg_1: max([(max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([Arg_0, max([Arg_2, max([Arg_0, 1+Arg_2+Arg_0])])]), max([1+Arg_2+Arg_0, (max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([Arg_0, max([Arg_2, max([Arg_0, 1+Arg_2+Arg_0])])])])]) {O(n^2)} 8: lbl101->stop, Arg_2: Arg_2 {O(n)} 8: lbl101->stop, Arg_3: max([Arg_4, max([Arg_4, -1+Arg_4])]) {O(n)} 8: lbl101->stop, Arg_4: Arg_4 {O(n)} 8: lbl101->stop, Arg_5: Arg_0 {O(n)} 10: lbl101->lbl91, Arg_0: Arg_0 {O(n)} 10: lbl101->lbl91, Arg_1: (max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([Arg_0, max([Arg_2, max([Arg_0, 1+Arg_2+Arg_0])])]) {O(n^2)} 10: lbl101->lbl91, Arg_2: Arg_2 {O(n)} 10: lbl101->lbl91, Arg_3: max([Arg_4, -1+Arg_4]) {O(n)} 10: lbl101->lbl91, Arg_4: Arg_4 {O(n)} 10: lbl101->lbl91, Arg_5: Arg_0 {O(n)} 11: lbl101->lbl101, Arg_0: Arg_0 {O(n)} 11: lbl101->lbl101, Arg_1: (max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([Arg_0, max([Arg_2, max([Arg_0, 1+Arg_2+Arg_0])])]) {O(n^2)} 11: lbl101->lbl101, Arg_2: Arg_2 {O(n)} 11: lbl101->lbl101, Arg_3: max([Arg_4, -1+Arg_4]) {O(n)} 11: lbl101->lbl101, Arg_4: Arg_4 {O(n)} 11: lbl101->lbl101, Arg_5: Arg_0 {O(n)} 4: lbl91->stop, Arg_0: Arg_0 {O(n)} 4: lbl91->stop, Arg_1: max([Arg_2, (max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([Arg_0, max([Arg_2, max([Arg_0, 1+Arg_2+Arg_0])])])]) {O(n^2)} 4: lbl91->stop, Arg_2: Arg_2 {O(n)} 4: lbl91->stop, Arg_3: max([Arg_4, -1+Arg_4]) {O(n)} 4: lbl91->stop, Arg_4: Arg_4 {O(n)} 4: lbl91->stop, Arg_5: Arg_0 {O(n)} 6: lbl91->lbl91, Arg_0: Arg_0 {O(n)} 6: lbl91->lbl91, Arg_1: (max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([Arg_0, max([Arg_2, max([Arg_0, 1+Arg_2+Arg_0])])]) {O(n^2)} 6: lbl91->lbl91, Arg_2: Arg_2 {O(n)} 6: lbl91->lbl91, Arg_3: max([Arg_4, -1+Arg_4]) {O(n)} 6: lbl91->lbl91, Arg_4: Arg_4 {O(n)} 6: lbl91->lbl91, Arg_5: Arg_0 {O(n)} 7: lbl91->lbl101, Arg_0: Arg_0 {O(n)} 7: lbl91->lbl101, Arg_1: (max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]))*max([1, 1+Arg_0])+(max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]))*max([1, 1+Arg_0])+max([Arg_0, max([Arg_2, max([Arg_0, 1+Arg_2+Arg_0])])]) {O(n^2)} 7: lbl91->lbl101, Arg_2: Arg_2 {O(n)} 7: lbl91->lbl101, Arg_3: max([Arg_4, -1+Arg_4]) {O(n)} 7: lbl91->lbl101, Arg_4: Arg_4 {O(n)} 7: lbl91->lbl101, Arg_5: Arg_0 {O(n)} 0: start->stop, Arg_0: -1 {O(1)} 0: start->stop, Arg_1: Arg_2 {O(n)} 0: start->stop, Arg_2: Arg_2 {O(n)} 0: start->stop, Arg_3: Arg_4 {O(n)} 0: start->stop, Arg_4: Arg_4 {O(n)} 0: start->stop, Arg_5: -1 {O(1)} 1: start->stop, Arg_0: Arg_0 {O(n)} 1: start->stop, Arg_1: Arg_2 {O(n)} 1: start->stop, Arg_2: Arg_2 {O(n)} 1: start->stop, Arg_3: Arg_4 {O(n)} 1: start->stop, Arg_4: Arg_4 {O(n)} 1: start->stop, Arg_5: Arg_0 {O(n)} 2: start->lbl91, Arg_0: Arg_0 {O(n)} 2: start->lbl91, Arg_1: Arg_2 {O(n)} 2: start->lbl91, Arg_2: Arg_2 {O(n)} 2: start->lbl91, Arg_3: -1+Arg_4 {O(n)} 2: start->lbl91, Arg_4: Arg_4 {O(n)} 2: start->lbl91, Arg_5: Arg_0 {O(n)} 3: start->lbl101, Arg_0: Arg_0 {O(n)} 3: start->lbl101, Arg_1: 1+Arg_2+Arg_0 {O(n)} 3: start->lbl101, Arg_2: Arg_2 {O(n)} 3: start->lbl101, Arg_3: Arg_4 {O(n)} 3: start->lbl101, Arg_4: Arg_4 {O(n)} 3: start->lbl101, Arg_5: Arg_0 {O(n)} 12: start0->start, Arg_0: Arg_0 {O(n)} 12: start0->start, Arg_1: Arg_2 {O(n)} 12: start0->start, Arg_2: Arg_2 {O(n)} 12: start0->start, Arg_3: Arg_4 {O(n)} 12: start0->start, Arg_4: Arg_4 {O(n)} 12: start0->start, Arg_5: Arg_0 {O(n)} ---------------------------------------- (2) BOUNDS(1, nat(-4 * Arg_2 + max(-4 + -4 * Arg_0 + 4 * Arg_4, -4 + 4 * Arg_4)) + nat(-4 * Arg_2 + 4 * Arg_4) + max(6 + -1 * Arg_2 + Arg_4, 7) + nat(-3 * Arg_2 + 3 * Arg_4) + nat(-2 + -2 * Arg_2 + 2 * Arg_4)) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start0 0: start -> stop : [ 0>=1+A && B==C && D==E && F==A ], cost: 1 1: start -> stop : [ A>=0 && C>=1+E && B==C && D==E && F==A ], cost: 1 2: start -> lbl91 : D'=-1-F+D, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 3: start -> lbl101 : B'=1+F+B, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 4: lbl91 -> stop : [ B>=1+D && B>=C && A>=0 && 1+D+A>=B && E>=1+D+A && F==A ], cost: 1 5: lbl91 -> stop : [ D>=B && 0>=1+A && B>=C && A>=0 && 1+D+A>=B && E>=1+D+A && F==A ], cost: 1 6: lbl91 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && B>=C && 1+D+A>=B && E>=1+D+A && F==A ], cost: 1 7: lbl91 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && B>=C && 1+D+A>=B && E>=1+D+A && F==A ], cost: 1 8: lbl101 -> stop : [ B>=1+D && E>=D && A>=0 && B>=1+C+A && 1+D+A>=B && F==A ], cost: 1 9: lbl101 -> stop : [ D>=B && 0>=1+A && E>=D && A>=0 && B>=1+C+A && 1+D+A>=B && F==A ], cost: 1 10: lbl101 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && 1+D+A>=B && F==A ], cost: 1 11: lbl101 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && E>=D && B>=1+C+A && 1+D+A>=B && F==A ], cost: 1 12: start0 -> start : B'=C, D'=E, F'=A, [], cost: 1 Removed unreachable and leaf rules: Start location: start0 2: start -> lbl91 : D'=-1-F+D, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 3: start -> lbl101 : B'=1+F+B, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 6: lbl91 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && B>=C && 1+D+A>=B && E>=1+D+A && F==A ], cost: 1 7: lbl91 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && B>=C && 1+D+A>=B && E>=1+D+A && F==A ], cost: 1 10: lbl101 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && 1+D+A>=B && F==A ], cost: 1 11: lbl101 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && E>=D && B>=1+C+A && 1+D+A>=B && F==A ], cost: 1 12: start0 -> start : B'=C, D'=E, F'=A, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 6: lbl91 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && B>=C && E>=1+D+A && F==A ], cost: 1 Accelerated rule 6 with backward acceleration, yielding the new rule 13. Removing the simple loops: 6. Accelerating simple loops of location 2. Accelerating the following rules: 11: lbl101 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A ], cost: 1 Accelerated rule 11 with backward acceleration, yielding the new rule 14. Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: start0 2: start -> lbl91 : D'=-1-F+D, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 3: start -> lbl101 : B'=1+F+B, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 7: lbl91 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && B>=C && E>=1+D+A && F==A ], cost: 1 13: lbl91 -> lbl91 : D'=D-k-F*k, [ A>=0 && D>=B && B>=C && E>=1+D+A && F==A && k>0 && 1+D-k-F*(-1+k)>=B && E>=2+D+A-k-F*(-1+k) ], cost: k 10: lbl101 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A ], cost: 1 14: lbl101 -> lbl101 : B'=k_1+k_1*F+B, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && k_1>0 && D>=-1+k_1+F*(-1+k_1)+B && -1+k_1+F*(-1+k_1)+B>=1+C+A ], cost: k_1 12: start0 -> start : B'=C, D'=E, F'=A, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start0 2: start -> lbl91 : D'=-1-F+D, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 3: start -> lbl101 : B'=1+F+B, [ A>=0 && E>=C && B==C && D==E && F==A ], cost: 1 15: start -> lbl91 : D'=-1-F+D-k-F*k, [ A>=0 && E>=C && B==C && D==E && F==A && -1-F+D>=B && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) ], cost: 1+k 17: start -> lbl101 : B'=1+k_1+F+k_1*F+B, [ A>=0 && E>=C && B==C && D==E && F==A && D>=1+F+B && 1+F+B>=1+C+A && k_1>0 && D>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 1+k_1 7: lbl91 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && B>=C && E>=1+D+A && F==A ], cost: 1 18: lbl91 -> lbl101 : B'=1+k_1+F+k_1*F+B, [ A>=0 && D>=B && B>=C && E>=1+D+A && F==A && D>=1+F+B && E>=D && 1+F+B>=1+C+A && k_1>0 && D>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 1+k_1 10: lbl101 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A ], cost: 1 16: lbl101 -> lbl91 : D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) ], cost: 1+k 12: start0 -> start : B'=C, D'=E, F'=A, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start0 7: lbl91 -> lbl101 : B'=1+F+B, [ A>=0 && D>=B && B>=C && E>=1+D+A && F==A ], cost: 1 18: lbl91 -> lbl101 : B'=1+k_1+F+k_1*F+B, [ A>=0 && D>=B && B>=C && E>=1+D+A && F==A && D>=1+F+B && E>=D && 1+F+B>=1+C+A && k_1>0 && D>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 1+k_1 10: lbl101 -> lbl91 : D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A ], cost: 1 16: lbl101 -> lbl91 : D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) ], cost: 1+k 19: start0 -> lbl91 : B'=C, D'=-1-A+E, F'=A, [ A>=0 && E>=C ], cost: 2 20: start0 -> lbl101 : B'=1+C+A, D'=E, F'=A, [ A>=0 && E>=C ], cost: 2 21: start0 -> lbl91 : B'=C, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E ], cost: 2+k 22: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 2+k_1 Eliminated location lbl91 (as a last resort): Start location: start0 23: lbl101 -> lbl101 : B'=1+F+B, D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A ], cost: 2 24: lbl101 -> lbl101 : B'=1+k_1+F+k_1*F+B, D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && -1-F+D>=1+F+B && E>=-1-F+D && 1+F+B>=1+C+A && k_1>0 && -1-F+D>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 2+k_1 25: lbl101 -> lbl101 : B'=1+F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k ], cost: 2+k 26: lbl101 -> lbl101 : B'=1+k_1+F+k_1*F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k && -1-F+D-k-F*k>=1+F+B && E>=-1-F+D-k-F*k && 1+F+B>=1+C+A && k_1>0 && -1-F+D-k-F*k>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 2+k_1+k 20: start0 -> lbl101 : B'=1+C+A, D'=E, F'=A, [ A>=0 && E>=C ], cost: 2 22: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 2+k_1 27: start0 -> lbl101 : B'=1+C+A, D'=-1-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C ], cost: 3 28: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1 29: start0 -> lbl101 : B'=1+C+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E ], cost: 3+k 30: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1+k Applied pruning (of leafs and parallel rules): Start location: start0 23: lbl101 -> lbl101 : B'=1+F+B, D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A ], cost: 2 24: lbl101 -> lbl101 : B'=1+k_1+F+k_1*F+B, D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && -1-F+D>=1+F+B && E>=-1-F+D && 1+F+B>=1+C+A && k_1>0 && -1-F+D>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 2+k_1 25: lbl101 -> lbl101 : B'=1+F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k ], cost: 2+k 26: lbl101 -> lbl101 : B'=1+k_1+F+k_1*F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k && -1-F+D-k-F*k>=1+F+B && E>=-1-F+D-k-F*k && 1+F+B>=1+C+A && k_1>0 && -1-F+D-k-F*k>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 2+k_1+k 20: start0 -> lbl101 : B'=1+C+A, D'=E, F'=A, [ A>=0 && E>=C ], cost: 2 22: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 2+k_1 28: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1 29: start0 -> lbl101 : B'=1+C+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E ], cost: 3+k 30: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1+k Accelerating simple loops of location 2. Accelerating the following rules: 23: lbl101 -> lbl101 : B'=1+F+B, D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A ], cost: 2 24: lbl101 -> lbl101 : B'=1+k_1+F+k_1*F+B, D'=-1-F+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && -1-F+D>=1+F+B && E>=-1-F+D && 1+F+B>=1+C+A && k_1>0 && -1-F+D>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 2+k_1 25: lbl101 -> lbl101 : B'=1+F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k ], cost: 2+k 26: lbl101 -> lbl101 : B'=1+k_1+F+k_1*F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k && -1-F+D-k-F*k>=1+F+B && E>=-1-F+D-k-F*k && 1+F+B>=1+C+A && k_1>0 && -1-F+D-k-F*k>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 2+k_1+k Accelerated rule 23 with backward acceleration, yielding the new rule 31. Accelerated rule 24 with backward acceleration, yielding the new rule 32. Found no metering function for rule 25 (rule is too complicated). Found no metering function for rule 26 (rule is too complicated). Removing the simple loops: 23 24. Accelerated all simple loops using metering functions (where possible): Start location: start0 25: lbl101 -> lbl101 : B'=1+F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k ], cost: 2+k 26: lbl101 -> lbl101 : B'=1+k_1+F+k_1*F+B, D'=-1-F+D-k-F*k, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k>0 && -F+D-k-F*(-1+k)>=B && E>=1-F+D+A-k-F*(-1+k) && -1-F+D-k-F*k>=B && E>=-F+D+A-k-F*k && -1-F+D-k-F*k>=1+F+B && E>=-1-F+D-k-F*k && 1+F+B>=1+C+A && k_1>0 && -1-F+D-k-F*k>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A ], cost: 2+k_1+k 31: lbl101 -> lbl101 : B'=k_2+F*k_2+B, D'=-k_2-F*k_2+D, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && k_2>0 && 1-F*(-1+k_2)-k_2+D>=-1+F*(-1+k_2)+k_2+B && E>=1-F*(-1+k_2)-k_2+D && -1+F*(-1+k_2)+k_2+B>=1+C+A && -F*(-1+k_2)-F-k_2+D>=-1+F*(-1+k_2)+k_2+B && -1+F*(-1+k_2)+k_2+B>=C && E>=1-F*(-1+k_2)-F-k_2+D+A ], cost: 2*k_2 32: lbl101 -> lbl101 : B'=k_1*k_3+F*k_3+k_1*F*k_3+k_3+B, D'=D-F*k_3-k_3, [ A>=0 && D>=B && E>=D && B>=1+C+A && F==A && -1-F+D>=B && B>=C && E>=-F+D+A && -1-F+D>=1+F+B && E>=-1-F+D && 1+F+B>=1+C+A && k_1>0 && -1-F+D>=k_1+F+F*(-1+k_1)+B && k_1+F+F*(-1+k_1)+B>=1+C+A && k_3>0 && 1-F*(-1+k_3)+D-k_3>=-1+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+k_3+B && E>=1-F*(-1+k_3)+D-k_3 && -1+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+k_3+B>=1+C+A && -F-F*(-1+k_3)+D-k_3>=-1+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+k_3+B && -1+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+k_3+B>=C && E>=1-F-F*(-1+k_3)+D+A-k_3 && -F-F*(-1+k_3)+D-k_3>=F+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+k_3+B && E>=-F-F*(-1+k_3)+D-k_3 && F+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+k_3+B>=1+C+A && -F-F*(-1+k_3)+D-k_3>=-1+k_1+F+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+F*(-1+k_1)+k_3+B && -1+k_1+F+k_1*F*(-1+k_3)+F*(-1+k_3)+k_1*(-1+k_3)+F*(-1+k_1)+k_3+B>=1+C+A ], cost: k_1*k_3+2*k_3 20: start0 -> lbl101 : B'=1+C+A, D'=E, F'=A, [ A>=0 && E>=C ], cost: 2 22: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 2+k_1 28: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1 29: start0 -> lbl101 : B'=1+C+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E ], cost: 3+k 30: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1+k Chained accelerated rules (with incoming rules): Start location: start0 20: start0 -> lbl101 : B'=1+C+A, D'=E, F'=A, [ A>=0 && E>=C ], cost: 2 22: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 2+k_1 28: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1 29: start0 -> lbl101 : B'=1+C+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E ], cost: 3+k 30: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1+k 33: start0 -> lbl101 : B'=2+C+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k>0 && -A*(-1+k)-A-k+E>=1+C+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+C+A && E>=-A*k-k+E ], cost: 4+k 34: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -A*(-1+k)-A-k+E>=1+k_1+C+k_1*A+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && E>=-A*k-k+E ], cost: 4+k_1+k 35: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-A*k-2*A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -1-A*(-1+k)-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-A*(-1+k)-A-k+E && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-1-A*k-A-k+E ], cost: 5+k_1+k 36: start0 -> lbl101 : B'=2+C+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+C+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+C+A && E>=-1-2*A*k-A-2*k+E ], cost: 5+2*k 37: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-1-2*A*k-A-2*k+E ], cost: 5+k_1+2*k 38: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k>0 && -A*(-1+k)-A-k+E>=1+C+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+C+A && E>=-A*k-k+E && -1-A*k-A-k+E>=2+C+2*A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A ], cost: 4+k_1+k 39: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -A*(-1+k)-A-k+E>=1+k_1+C+k_1*A+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && E>=-A*k-k+E && -1-A*k-A-k+E>=2+k_1+C+k_1*A+2*A && E>=-1-A*k-A-k+E && -1-A*k-A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 4+2*k_1+k 40: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-2-A*k-2*A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -1-A*(-1+k)-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-A*(-1+k)-A-k+E && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=2+k_1+C+k_1*A+2*A && E>=-2-A*k-2*A-k+E && -2-A*k-2*A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+2*k_1+k 41: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+C+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+C+A && E>=-1-2*A*k-A-2*k+E && -2-2*A*k-2*A-2*k+E>=2+C+2*A && E>=-2-2*A*k-2*A-2*k+E && k_1>0 && -2-2*A*k-2*A-2*k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+k_1+2*k 42: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-1-2*A*k-A-2*k+E && -2-2*A*k-2*A-2*k+E>=2+k_1+C+k_1*A+2*A && E>=-2-2*A*k-2*A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+2*k_1+2*k 43: start0 -> lbl101 : B'=1+C+k_2*A+k_2+A, D'=-k_2*A-k_2+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k_2>0 && 1-k_2-(-1+k_2)*A+E>=C+k_2+(-1+k_2)*A+A && E>=1-k_2-(-1+k_2)*A+E && -k_2-(-1+k_2)*A-A+E>=C+k_2+(-1+k_2)*A+A && C+k_2+(-1+k_2)*A+A>=C ], cost: 2+2*k_2 44: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-k_2*A-k_2+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && 1-k_2-(-1+k_2)*A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=1-k_2-(-1+k_2)*A+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -k_2-(-1+k_2)*A-A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 2+k_1+2*k_2 45: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-1-k_2*A-k_2-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && -k_2-(-1+k_2)*A-A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=-k_2-(-1+k_2)*A-A+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-2*A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 3+k_1+2*k_2 46: start0 -> lbl101 : B'=1+C+k_2*A+k_2+A, D'=-1-k_2*A-k_2-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && k_2>0 && -k_2-(-1+k_2)*A-A*k-A-k+E>=C+k_2+(-1+k_2)*A+A && E>=-k_2-(-1+k_2)*A-A*k-A-k+E && C+k_2+(-1+k_2)*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-A*k-2*A-k+E>=C+k_2+(-1+k_2)*A+A && C+k_2+(-1+k_2)*A+A>=C ], cost: 3+2*k_2+k 47: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-1-k_2*A-k_2-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && -k_2-(-1+k_2)*A-A*k-A-k+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=-k_2-(-1+k_2)*A-A*k-A-k+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-A*k-2*A-k+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 3+k_1+2*k_2+k 48: start0 -> lbl101 : B'=1+k_1*k_3+C+A+k_1*A*k_3+A*k_3+k_3, D'=-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && -1-A+E>=2+C+2*A && k_1>0 && -1-A+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && 1+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=1+E-k_3-(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -A+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -A+E-k_3-(-1+k_3)*A>=1+C+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && -A+E-k_3-(-1+k_3)*A>=k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 2+k_1*k_3+2*k_3 49: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A+E>=2+k_1+C+k_1*A+2*A && -1-A+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && 1+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=1+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -A+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && -A+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 2+k_1+k_1*k_3+2*k_3 50: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -2-2*A+E>=2+k_1+C+k_1*A+2*A && E>=-2-2*A+E && -2-2*A+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-2*A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-2*A+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-2*A+E-k_3-(-1+k_3)*A && -1-2*A+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1+k_1*k_3+2*k_3 51: start0 -> lbl101 : B'=1+k_1*k_3+C+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A*k-A-A*k_3-k+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -2-A*k-2*A-k+E>=2+C+2*A && E>=-2-A*k-2*A-k+E && k_1>0 && -2-A*k-2*A-k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A*k-A-k+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A*k-A-k+E-k_3-(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=1+C+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-A*k-2*A-k+E-k_3-(-1+k_3)*A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1*k_3+k+2*k_3 52: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A*k-A-A*k_3-k+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -2-A*k-2*A-k+E>=2+k_1+C+k_1*A+2*A && E>=-2-A*k-2*A-k+E && -2-A*k-2*A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A*k-A-k+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A*k-A-k+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-A*k-2*A-k+E-k_3-(-1+k_3)*A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1+k_1*k_3+k+2*k_3 Removed unreachable locations (and leaf rules with constant cost): Start location: start0 22: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 2+k_1 28: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1 29: start0 -> lbl101 : B'=1+C+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E ], cost: 3+k 30: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1+k 33: start0 -> lbl101 : B'=2+C+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k>0 && -A*(-1+k)-A-k+E>=1+C+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+C+A && E>=-A*k-k+E ], cost: 4+k 34: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -A*(-1+k)-A-k+E>=1+k_1+C+k_1*A+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && E>=-A*k-k+E ], cost: 4+k_1+k 35: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-A*k-2*A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -1-A*(-1+k)-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-A*(-1+k)-A-k+E && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-1-A*k-A-k+E ], cost: 5+k_1+k 36: start0 -> lbl101 : B'=2+C+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+C+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+C+A && E>=-1-2*A*k-A-2*k+E ], cost: 5+2*k 37: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-1-2*A*k-A-2*k+E ], cost: 5+k_1+2*k 38: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k>0 && -A*(-1+k)-A-k+E>=1+C+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+C+A && E>=-A*k-k+E && -1-A*k-A-k+E>=2+C+2*A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A ], cost: 4+k_1+k 39: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -A*(-1+k)-A-k+E>=1+k_1+C+k_1*A+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && E>=-A*k-k+E && -1-A*k-A-k+E>=2+k_1+C+k_1*A+2*A && E>=-1-A*k-A-k+E && -1-A*k-A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 4+2*k_1+k 40: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-2-A*k-2*A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -1-A*(-1+k)-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-A*(-1+k)-A-k+E && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=2+k_1+C+k_1*A+2*A && E>=-2-A*k-2*A-k+E && -2-A*k-2*A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+2*k_1+k 41: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+C+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+C+A && E>=-1-2*A*k-A-2*k+E && -2-2*A*k-2*A-2*k+E>=2+C+2*A && E>=-2-2*A*k-2*A-2*k+E && k_1>0 && -2-2*A*k-2*A-2*k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+k_1+2*k 42: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-1-2*A*k-A-2*k+E && -2-2*A*k-2*A-2*k+E>=2+k_1+C+k_1*A+2*A && E>=-2-2*A*k-2*A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+2*k_1+2*k 43: start0 -> lbl101 : B'=1+C+k_2*A+k_2+A, D'=-k_2*A-k_2+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k_2>0 && 1-k_2-(-1+k_2)*A+E>=C+k_2+(-1+k_2)*A+A && E>=1-k_2-(-1+k_2)*A+E && -k_2-(-1+k_2)*A-A+E>=C+k_2+(-1+k_2)*A+A && C+k_2+(-1+k_2)*A+A>=C ], cost: 2+2*k_2 44: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-k_2*A-k_2+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && 1-k_2-(-1+k_2)*A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=1-k_2-(-1+k_2)*A+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -k_2-(-1+k_2)*A-A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 2+k_1+2*k_2 45: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-1-k_2*A-k_2-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && -k_2-(-1+k_2)*A-A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=-k_2-(-1+k_2)*A-A+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-2*A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 3+k_1+2*k_2 46: start0 -> lbl101 : B'=1+C+k_2*A+k_2+A, D'=-1-k_2*A-k_2-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && k_2>0 && -k_2-(-1+k_2)*A-A*k-A-k+E>=C+k_2+(-1+k_2)*A+A && E>=-k_2-(-1+k_2)*A-A*k-A-k+E && C+k_2+(-1+k_2)*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-A*k-2*A-k+E>=C+k_2+(-1+k_2)*A+A && C+k_2+(-1+k_2)*A+A>=C ], cost: 3+2*k_2+k 47: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-1-k_2*A-k_2-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && -k_2-(-1+k_2)*A-A*k-A-k+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=-k_2-(-1+k_2)*A-A*k-A-k+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-A*k-2*A-k+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 3+k_1+2*k_2+k 48: start0 -> lbl101 : B'=1+k_1*k_3+C+A+k_1*A*k_3+A*k_3+k_3, D'=-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && -1-A+E>=2+C+2*A && k_1>0 && -1-A+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && 1+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=1+E-k_3-(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -A+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -A+E-k_3-(-1+k_3)*A>=1+C+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && -A+E-k_3-(-1+k_3)*A>=k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 2+k_1*k_3+2*k_3 49: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A+E>=2+k_1+C+k_1*A+2*A && -1-A+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && 1+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=1+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -A+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && -A+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 2+k_1+k_1*k_3+2*k_3 50: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -2-2*A+E>=2+k_1+C+k_1*A+2*A && E>=-2-2*A+E && -2-2*A+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-2*A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-2*A+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-2*A+E-k_3-(-1+k_3)*A && -1-2*A+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1+k_1*k_3+2*k_3 51: start0 -> lbl101 : B'=1+k_1*k_3+C+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A*k-A-A*k_3-k+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -2-A*k-2*A-k+E>=2+C+2*A && E>=-2-A*k-2*A-k+E && k_1>0 && -2-A*k-2*A-k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A*k-A-k+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A*k-A-k+E-k_3-(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=1+C+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-A*k-2*A-k+E-k_3-(-1+k_3)*A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1*k_3+k+2*k_3 52: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A*k-A-A*k_3-k+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -2-A*k-2*A-k+E>=2+k_1+C+k_1*A+2*A && E>=-2-A*k-2*A-k+E && -2-A*k-2*A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A*k-A-k+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A*k-A-k+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-A*k-2*A-k+E-k_3-(-1+k_3)*A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1+k_1*k_3+k+2*k_3 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start0 22: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 2+k_1 28: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1 29: start0 -> lbl101 : B'=1+C+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E ], cost: 3+k 30: start0 -> lbl101 : B'=1+k_1+C+k_1*A+A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A ], cost: 3+k_1+k 33: start0 -> lbl101 : B'=2+C+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k>0 && -A*(-1+k)-A-k+E>=1+C+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+C+A && E>=-A*k-k+E ], cost: 4+k 34: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -A*(-1+k)-A-k+E>=1+k_1+C+k_1*A+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && E>=-A*k-k+E ], cost: 4+k_1+k 35: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-A*k-2*A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -1-A*(-1+k)-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-A*(-1+k)-A-k+E && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-1-A*k-A-k+E ], cost: 5+k_1+k 36: start0 -> lbl101 : B'=2+C+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+C+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+C+A && E>=-1-2*A*k-A-2*k+E ], cost: 5+2*k 37: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-1-2*A*k-A-2*k+E ], cost: 5+k_1+2*k 38: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k>0 && -A*(-1+k)-A-k+E>=1+C+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+C+A && E>=-A*k-k+E && -1-A*k-A-k+E>=2+C+2*A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A ], cost: 4+k_1+k 39: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-1-A*k-A-k+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -A*(-1+k)-A-k+E>=1+k_1+C+k_1*A+A && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && E>=-A*k-k+E && -1-A*k-A-k+E>=2+k_1+C+k_1*A+2*A && E>=-1-A*k-A-k+E && -1-A*k-A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 4+2*k_1+k 40: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-2-A*k-2*A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k>0 && -1-A*(-1+k)-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-A*(-1+k)-A-k+E && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=2+k_1+C+k_1*A+2*A && E>=-2-A*k-2*A-k+E && -2-A*k-2*A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+2*k_1+k 41: start0 -> lbl101 : B'=2+k_1+C+k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+C+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+C+A && E>=-1-2*A*k-A-2*k+E && -2-2*A*k-2*A-2*k+E>=2+C+2*A && E>=-2-2*A*k-2*A-2*k+E && k_1>0 && -2-2*A*k-2*A-2*k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+k_1+2*k 42: start0 -> lbl101 : B'=2+2*k_1+C+2*k_1*A+2*A, D'=-2-2*A*k-2*A-2*k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A*k-A*(-1+k)-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-A*k-A*(-1+k)-A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+k_1+C+k_1*A+A && E>=-1-2*A*k-A-2*k+E && -2-2*A*k-2*A-2*k+E>=2+k_1+C+k_1*A+2*A && E>=-2-2*A*k-2*A-2*k+E && -2-2*A*k-2*A-2*k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A ], cost: 5+2*k_1+2*k 43: start0 -> lbl101 : B'=1+C+k_2*A+k_2+A, D'=-k_2*A-k_2+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && k_2>0 && 1-k_2-(-1+k_2)*A+E>=C+k_2+(-1+k_2)*A+A && E>=1-k_2-(-1+k_2)*A+E && -k_2-(-1+k_2)*A-A+E>=C+k_2+(-1+k_2)*A+A && C+k_2+(-1+k_2)*A+A>=C ], cost: 2+2*k_2 44: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-k_2*A-k_2+E, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && 1-k_2-(-1+k_2)*A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=1-k_2-(-1+k_2)*A+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -k_2-(-1+k_2)*A-A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 2+k_1+2*k_2 45: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-1-k_2*A-k_2-A+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && -k_2-(-1+k_2)*A-A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=-k_2-(-1+k_2)*A-A+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-2*A+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 3+k_1+2*k_2 46: start0 -> lbl101 : B'=1+C+k_2*A+k_2+A, D'=-1-k_2*A-k_2-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && k_2>0 && -k_2-(-1+k_2)*A-A*k-A-k+E>=C+k_2+(-1+k_2)*A+A && E>=-k_2-(-1+k_2)*A-A*k-A-k+E && C+k_2+(-1+k_2)*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-A*k-2*A-k+E>=C+k_2+(-1+k_2)*A+A && C+k_2+(-1+k_2)*A+A>=C ], cost: 3+2*k_2+k 47: start0 -> lbl101 : B'=1+k_1+C+k_2*A+k_2+k_1*A+A, D'=-1-k_2*A-k_2-A*k-A-k+E, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && k_2>0 && -k_2-(-1+k_2)*A-A*k-A-k+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && E>=-k_2-(-1+k_2)*A-A*k-A-k+E && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=1+C+A && -1-k_2-(-1+k_2)*A-A*k-2*A-k+E>=k_1+C+k_2+(-1+k_2)*A+k_1*A+A && k_1+C+k_2+(-1+k_2)*A+k_1*A+A>=C ], cost: 3+k_1+2*k_2+k 48: start0 -> lbl101 : B'=1+k_1*k_3+C+A+k_1*A*k_3+A*k_3+k_3, D'=-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && E>=1+C+A && -1-A+E>=1+C+A && -1-A+E>=2+C+2*A && k_1>0 && -1-A+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && 1+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=1+E-k_3-(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -A+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -A+E-k_3-(-1+k_3)*A>=1+C+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && -A+E-k_3-(-1+k_3)*A>=k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 2+k_1*k_3+2*k_3 49: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -1-A+E>=2+k_1+C+k_1*A+2*A && -1-A+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && 1+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=1+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -A+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && -A+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 2+k_1+k_1*k_3+2*k_3 50: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A-A*k_3+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && -1-A+E>=1+C+A && k_1>0 && -1-A+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-2*A+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -2-2*A+E>=2+k_1+C+k_1*A+2*A && E>=-2-2*A+E && -2-2*A+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-2*A+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-2*A+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-2*A+E-k_3-(-1+k_3)*A && -1-2*A+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1+k_1*k_3+2*k_3 51: start0 -> lbl101 : B'=1+k_1*k_3+C+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A*k-A-A*k_3-k+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && -2-A*k-2*A-k+E>=1+C+A && -2-A*k-2*A-k+E>=2+C+2*A && E>=-2-A*k-2*A-k+E && k_1>0 && -2-A*k-2*A-k+E>=1+k_1+C+2*A+(-1+k_1)*A && 1+k_1+C+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A*k-A-k+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A*k-A-k+E-k_3-(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && C+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=1+C+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-A*k-2*A-k+E-k_3-(-1+k_3)*A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1*k_3+k+2*k_3 52: start0 -> lbl101 : B'=1+k_1+k_1*k_3+C+k_1*A+A+k_1*A*k_3+A*k_3+k_3, D'=-1-A*k-A-A*k_3-k+E-k_3, F'=A, [ A>=0 && E>=C && -1-A+E>=C && k>0 && -A*(-1+k)-A-k+E>=C && E>=1-A*(-1+k)-k+E && -1-A*k-A-k+E>=C && E>=-A*k-k+E && -1-A*k-A-k+E>=1+C+A && E>=-1-A*k-A-k+E && k_1>0 && -1-A*k-A-k+E>=k_1+C+A+(-1+k_1)*A && k_1+C+A+(-1+k_1)*A>=1+C+A && -1-A*k-A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=1+C+A && -2-A*k-2*A-k+E>=1+k_1+C+k_1*A+A && 1+k_1+C+k_1*A+A>=C && -2-A*k-2*A-k+E>=2+k_1+C+k_1*A+2*A && E>=-2-A*k-2*A-k+E && -2-A*k-2*A-k+E>=1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A && 1+2*k_1+C+k_1*A+2*A+(-1+k_1)*A>=1+C+A && k_3>0 && -A*k-A-k+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-A*k-A-k+E-k_3-(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && k_1+C+k_1*A+A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=C && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=1+k_1+C+k_1*A+2*A+k_1*(-1+k_3)+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && E>=-1-A*k-2*A-k+E-k_3-(-1+k_3)*A && -1-A*k-2*A-k+E-k_3-(-1+k_3)*A>=2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A && 2*k_1+C+k_1*A+2*A+k_1*(-1+k_3)+(-1+k_1)*A+k_3+(-1+k_3)*A+k_1*(-1+k_3)*A>=1+C+A ], cost: 3+k_1+k_1*k_3+k+2*k_3 Computing asymptotic complexity for rule 22 Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,C==-2*n,A==0,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 2+k_1 (+) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 2+k_1 (+) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), 2+k_1 (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), 2+k_1 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1+n,A==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+(-1+k_1)*A (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+(-1+k_1)*A (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 2+k_1 (+) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), 2+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 2+k_1 (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), k_1 (+/+!), -C+E (+/+!), 2+k_1 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,C==-n,E==1} resulting limit problem: [solved] Solution: k_1 / n C / -2*n A / 0 E / 0 Resulting cost 2+n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 28 Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), 3+k_1 (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,C==-2*n,A==0,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), 3+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), -1-C+E (+/+!), 3+k_1 (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A (+/+!), 3+k_1 (+), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 2+A (+/+!), A (+/+!), 3+k_1 (+), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), 3+k_1 (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), -1-C+E (+/+!), 3+k_1 (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), -1-C+E (+/+!), 3+k_1 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,C==0,E==2*n} resulting limit problem: [solved] Solution: k_1 / n C / -2*n A / 0 E / 0 Resulting cost 3+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 29 Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==-2*n,A==0,k==n,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+k (+), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==1,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), 1+A*k+A (+/+!), 3+k (+), 2+A*k+A (+/+!), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1+A*k+A (+/+!), 3+k (+), 2+A*k+A (+/+!), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==0,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A*k-A*(-1+k) (+/+!), 2+A*k+A+k (+/+!), k (+/+!), 1+A*k+k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+k (+), 2+A*k-A*(-1+k) (+/+!), 2+A*k+A+k (+/+!), k (+/+!), 1+A*k+k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==0,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), 3+k (+), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+k (+), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==1,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+k (+), 2+A (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), 3+k (+), -C-A+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -C+E (+/+!), 3+k (+), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==-2*n,k==n,E==0} resulting limit problem: [solved] Solution: C / -2*n A / 0 k / n E / 0 Resulting cost 3+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 30 Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1+n,C==-3*n,A==0,k==1+n,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), 4+k (+), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), 4+k (+), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==1,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: A*k+A (+/+!), 1 (+/+!), k_1 (+/+!), 1+A*k+A (+/+!), 1-k_1+A*k+A (+/+!), 2+A*k+A (+/+!), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: A*k+A (+/+!), 1 (+/+!), 1+A*k+A (+/+!), 2+A*k+A (+/+!), 4+k (+), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: A*k+A (+/+!), 1+A*k+A (+/+!), 2+A*k+A (+/+!), 4+k (+), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==1,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), 4+k (+), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), 4+k (+), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==1,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 2+A (+/+!), 4+k (+), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), 4+k (+), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), 4+k (+), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==0,k==-2+n,E==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), 4+k (+), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), 4+k (+), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==0,A==0,k==-1+n,E==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 4+k_1 (+), -2-C+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A*(-1+k)+A+k (+/+!), -1-k_1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)+A+k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A*(-1+k)+A+k (+/+!), -1-k_1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)+A+k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), -1+A*(-1+k)+A+k (+/+!), -1-k_1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)+A+k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==0,k==3+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-k_1-C-3*A-(-1+k_1)*A+E (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), A*(-1+k)+k (+/+!), -1-k_1+A*(-1+k)-2*A+k-(-1+k_1)*A (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)-2*A+k (+/+!), -1+A*(-1+k)-A+k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), A*(-1+k)+k (+/+!), -1-k_1+A*(-1+k)-2*A+k-(-1+k_1)*A (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)-2*A+k (+/+!), -1+A*(-1+k)-A+k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), A*(-1+k)+k (+/+!), -1-k_1+A*(-1+k)-2*A+k-(-1+k_1)*A (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)-2*A+k (+/+!), -1+A*(-1+k)-A+k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==0,k==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1,A==n,k==-1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1,k==1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 4+k_1 (+), -2-C+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A*k+A+k (+/+!), A*k+A+k (+/+!), -k_1+A*k+A+k (+/+!), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), -1+A*k+A+k (+/+!), A*k+A+k (+/+!), -k_1+A*k+A+k (+/+!), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==2*n,A==1,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-k_1-C-3*A-(-1+k_1)*A+E (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), -1+A*k-2*A+k (+/+!), 4+k_1 (+), A*k-A+k (+/+!), 2+A*k+A+k (+/+!), 1+A*k+k (+/+!), 1+A (+/+!), -k_1+A*k-2*A+k-(-1+k_1)*A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), -1+A*k-2*A+k (+/+!), 4+k_1 (+), A*k-A+k (+/+!), 2+A*k+A+k (+/+!), 1+A*k+k (+/+!), 1+A (+/+!), -k_1+A*k-2*A+k-(-1+k_1)*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==0,k==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1,A==n,k==-1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: A*k+A (+/+!), 1 (+/+!), k_1 (+/+!), 1+A*k+A (+/+!), 1-k_1+A*k+A (+/+!), 2+A*k+A (+/+!), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: A*k+A (+/+!), k_1 (+/+!), 1+A*k+A (+/+!), 1-k_1+A*k+A (+/+!), 2+A*k+A (+/+!), 1+A*k+A+k (+/+!), 2+A*k+A+k (+/+!), k (+/+!), 3+k_1+k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==2+n,A==1,k==1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 4+k_1 (+), -2-C+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A*(-1+k)+A+k (+/+!), -1-k_1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)+A+k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), -1+A*(-1+k)+A+k (+/+!), -1-k_1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)+A+k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==0,k==3+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-k_1-C-3*A-(-1+k_1)*A+E (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), A*(-1+k)+k (+/+!), -1-k_1+A*(-1+k)-2*A+k-(-1+k_1)*A (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)-2*A+k (+/+!), -1+A*(-1+k)-A+k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), A*(-1+k)+k (+/+!), -1-k_1+A*(-1+k)-2*A+k-(-1+k_1)*A (+/+!), 1+A*(-1+k)+A+k (+/+!), -2+A*(-1+k)-2*A+k (+/+!), -1+A*(-1+k)-A+k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==0,k==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1,A==n,k==-1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), -1+A*(-1+k)+A (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), A*(-1+k)+A (+/+!), -k_1+A*(-1+k)+A (+/+!), k (+/+!), 3+k_1+k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1,k==1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1 (+), -1+A (+/+!), 2+A (+/+!), A (+/+!), -k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), 4+k_1 (+), -2-C+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), k_1 (+/+!), -C+E (+/+!), 4+k_1 (+), -2-C+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,C==0,E==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), 4+k_1 (+), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-k_1-C-3*A-(-1+k_1)*A+E (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1 (+), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-k_1-C-3*A-(-1+k_1)*A+E (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,C==-2*n,A==0,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 1-k_1+A-k (+/+!), 2+A-k (+/+!), k (+/+!), 3+k_1+k (+), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1,A==n,k==-1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -k_1-C-A*k-2*A-k-(-1+k_1)*A+E (+/+!), 1-C+E (+/+!), k_1 (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), k (+/+!), 3+k_1+k (+), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), k_1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), k (+/+!), 3+k_1+k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,C==-n,k==1,E==3} resulting limit problem: [solved] Solution: k_1 / 1+n C / -3*n A / 0 k / 1+n E / 0 Resulting cost 5+2*n has complexity: Poly(n^1) Computing asymptotic complexity for rule 33 Solved the limit problem by the following transformations: Created initial limit problem: -C-A*(-1+k)-2*A-k+E (+/+!), 1-C+E (+/+!), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), 4+k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==-2*n,A==0,k==n,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -C-A*(-1+k)-2*A-k+E (+/+!), 1-C+E (+/+!), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), 4+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 4+k (+), -1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), 2+A (+/+!), 4+k (+), A-k (+/+!), A (+/+!), 1+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 2+A (+/+!), 4+k (+), A-k (+/+!), A (+/+!), 1+A-k (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: -C-A*(-1+k)-2*A-k+E (+/+!), 1-C+E (+/+!), -1-C-2*A+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), 4+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 4+k (+), -1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -C+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 4+k (+), -1-C+E (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==-2*n,k==n,E==0} resulting limit problem: [solved] Solution: C / -2*n A / 0 k / n E / 0 Resulting cost 4+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 34 Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1,C==-2*n,A==0,k==1+n,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1 (+), -2+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 5+k_1 (+), -2+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), k_1*A+A (+/+!), 4+k_1+k (+), 1+k_1*A+A-k (+/+!), 1+k_1*A+A (+/+!), 1+k_1+k_1*A+A (+/+!), k_1*A+A-k (+/+!), 2+k_1+k_1*A+A (+/+!), 2+k_1*A+A (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), k_1*A+A (+/+!), 5+k_1 (+), 1+k_1*A+A (+/+!), 1+k_1+k_1*A+A (+/+!), 2+k_1+k_1*A+A (+/+!), 2+k_1*A+A (+/+!), -1+k_1*A+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), k_1*A+A (+/+!), 5+k_1 (+), 1+k_1*A+A (+/+!), 1+k_1+k_1*A+A (+/+!), 2+k_1+k_1*A+A (+/+!), 2+k_1*A+A (+/+!), -1+k_1*A+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1 (+), -2+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 5+k_1 (+), -2+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 5+k_1 (+), -1-k_1+A (+/+!), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1 (+), -2-k_1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1 (+), -2-k_1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-3+n,C==0,E==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), 5+k_1 (+), -2-k_1-C-k_1*A-3*A+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), k_1 (+/+!), 5+k_1 (+), -2-k_1-C-k_1*A-3*A+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,C==0,A==0,E==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C+E (+/+!), -1-C-k+E (+/+!), -2-C-k+E (+/+!), 5+k (+), -1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), -1+k_1+A-k+(-1+k_1)*A (+/+!), -2+k_1+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+k_1+A+(-1+k_1)*A (+/+!), 5+k (+), -2+k_1+A-k+(-1+k_1)*A (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), -1+k_1+A-k+(-1+k_1)*A (+/+!), -2+k_1+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+k_1+A+(-1+k_1)*A (+/+!), 5+k (+), -2+k_1+A-k+(-1+k_1)*A (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+k_1+A-k+(-1+k_1)*A (+/+!), -2+k_1+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+k_1+A+(-1+k_1)*A (+/+!), 5+k (+), -2+k_1+A-k+(-1+k_1)*A (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==2*n,A==0,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -1-C-2*A+E (+/+!), -1-C-A*(-1+k)-3*A-k+E (+/+!), -C-A+E (+/+!), 5+k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), -1+k_1-A+(-1+k_1)*A (+/+!), -1+k_1-A*(-1+k)-2*A-k+(-1+k_1)*A (+/+!), -2+k_1-2*A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+(-1+k_1)*A (+/+!), -2+k_1-A*k-2*A-k+(-1+k_1)*A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), -1+k_1-A+(-1+k_1)*A (+/+!), -1+k_1-A*(-1+k)-2*A-k+(-1+k_1)*A (+/+!), -2+k_1-2*A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+(-1+k_1)*A (+/+!), -2+k_1-A*k-2*A-k+(-1+k_1)*A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+k_1-A+(-1+k_1)*A (+/+!), -1+k_1-A*(-1+k)-2*A-k+(-1+k_1)*A (+/+!), -2+k_1-2*A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+(-1+k_1)*A (+/+!), -2+k_1-A*k-2*A-k+(-1+k_1)*A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==2*n,A==0,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,A==n,k==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1,k==-2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C+E (+/+!), -1-C-k+E (+/+!), -2-C-k+E (+/+!), 5+k (+), -1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1+k_1*A+A (+/+!), 1+k_1+k_1*A+A (+/+!), k_1+k_1*A+A-k (+/+!), 2+k_1+k_1*A+A (+/+!), 5+k (+), k (+/+!), -1+k_1+k_1*A+A-k (+/+!), -1+k_1+k_1*A+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1+k_1*A+A (+/+!), 1+k_1+k_1*A+A (+/+!), k_1+k_1*A+A-k (+/+!), 2+k_1+k_1*A+A (+/+!), 5+k (+), k (+/+!), -1+k_1+k_1*A+A-k (+/+!), -1+k_1+k_1*A+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-1-2*n,A==-2,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -1-C-2*A+E (+/+!), -1-C-A*(-1+k)-3*A-k+E (+/+!), -C-A+E (+/+!), 5+k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: k_1+k_1*A-A*(-1+k)-2*A-k (+/+!), 1 (+/+!), 1+k_1+k_1*A (+/+!), 2+k_1+k_1*A+A (+/+!), 5+k (+), -1+k_1+k_1*A-2*A (+/+!), k (+/+!), k_1+k_1*A-A (+/+!), -1+k_1+k_1*A-A*k-2*A-k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1+k_1*A-A*(-1+k)-2*A-k (+/+!), 1+k_1+k_1*A (+/+!), 2+k_1+k_1*A+A (+/+!), 5+k (+), -1+k_1+k_1*A-2*A (+/+!), k (+/+!), k_1+k_1*A-A (+/+!), -1+k_1+k_1*A-A*k-2*A-k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==2*n,A==0,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,A==n,k==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+k_1+C+k_1*A+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), k_1*A+A (+/+!), 4+k_1+k (+), 1+k_1*A+A-k (+/+!), 1+k_1*A+A (+/+!), 1+k_1+k_1*A+A (+/+!), k_1*A+A-k (+/+!), 2+k_1+k_1*A+A (+/+!), 2+k_1*A+A (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), k_1*A+A (+/+!), 4+k_1+k (+), 1+k_1*A+A-k (+/+!), 1+k_1*A+A (+/+!), 1+k_1+k_1*A+A (+/+!), k_1*A+A-k (+/+!), 2+k_1+k_1*A+A (+/+!), 2+k_1*A+A (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1+n,A==2,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C+E (+/+!), -1-C-k+E (+/+!), -2-C-k+E (+/+!), 5+k (+), -1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), -1+k_1+A-k+(-1+k_1)*A (+/+!), -2+k_1+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+k_1+A+(-1+k_1)*A (+/+!), 5+k (+), -2+k_1+A-k+(-1+k_1)*A (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+k_1+A-k+(-1+k_1)*A (+/+!), -2+k_1+A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+k_1+A+(-1+k_1)*A (+/+!), 5+k (+), -2+k_1+A-k+(-1+k_1)*A (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==2*n,A==0,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -1-C-2*A+E (+/+!), -1-C-A*(-1+k)-3*A-k+E (+/+!), -C-A+E (+/+!), 5+k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), -1+k_1-A+(-1+k_1)*A (+/+!), -1+k_1-A*(-1+k)-2*A-k+(-1+k_1)*A (+/+!), -2+k_1-2*A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+(-1+k_1)*A (+/+!), -2+k_1-A*k-2*A-k+(-1+k_1)*A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+k_1-A+(-1+k_1)*A (+/+!), -1+k_1-A*(-1+k)-2*A-k+(-1+k_1)*A (+/+!), -2+k_1-2*A+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), k_1+(-1+k_1)*A (+/+!), -2+k_1-A*k-2*A-k+(-1+k_1)*A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==2*n,A==0,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,A==n,k==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==k_1+C+A+(-1+k_1)*A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1+k (+), -1+A-k+(-1+k_1)*A (+/+!), 1+k_1+A+(-1+k_1)*A (+/+!), 1+A+(-1+k_1)*A (+/+!), A+(-1+k_1)*A (+/+!), k_1+A+(-1+k_1)*A (+/+!), -1+A+(-1+k_1)*A (+/+!), k (+/+!), A-k+(-1+k_1)*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==1,k==-2+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A (+/+!), -1+A-k (+/+!), 2+A (+/+!), A-k (+/+!), A (+/+!), 5+k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C+E (+/+!), -1-C-k+E (+/+!), -2-C-k+E (+/+!), 5+k (+), -1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -C+E (+/+!), -2-C+E (+/+!), -1-C-k+E (+/+!), -2-C-k+E (+/+!), 5+k (+), -1-C+E (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==-n,k==n,E==3} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -1-C-2*A+E (+/+!), -1-C-A*(-1+k)-3*A-k+E (+/+!), -C-A+E (+/+!), 5+k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -1-C-2*A+E (+/+!), -1-C-A*(-1+k)-3*A-k+E (+/+!), -C-A+E (+/+!), 5+k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==-2*n,A==0,k==n,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {E==1+C+A} resulting limit problem: 1 (+/+!), k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 4+k_1+k (+), 2+A (+/+!), 2-k_1+A (+/+!), -k_1+A-k (+/+!), 1-k_1+A-k (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,A==n,k==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), k_1 (+/+!), 4+k_1+k (+), -1-k_1-C-k_1*A-A*k-2*A-k+E (+/+!), 1-k_1-C-A-(-1+k_1)*A+E (+/+!), -C-A+E (+/+!), -k_1-C-k_1*A-A+E (+/+!), k (+/+!), -k_1-C-k_1*A-A*(-1+k)-2*A-k+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), 1-k_1-C+E (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 4+k_1+k (+), -1-k_1-C-k+E (+/+!), -k_1-C-k+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1,C==-2*n,k==n,E==0} resulting limit problem: [solved] Solution: k_1 / 1 C / -2*n A / 0 k / 1+n E / 0 Resulting cost 6+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 35 Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==1,C==-2*n,A==0,k==1+n,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1+k (+), -2-k_1-C+E (+/+!), -1-k_1-C-k+E (+/+!), -2-k_1-C-k+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-k_1+A (+/+!), -1-k_1+A-k (+/+!), 2+A (+/+!), -k_1+A-k (+/+!), A (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 6+k_1 (+), 1 (+/+!), k_1 (+/+!), -1-k_1+A (+/+!), 2+A (+/+!), A (+/+!), -2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 6+k_1 (+), k_1 (+/+!), -1-k_1+A (+/+!), 2+A (+/+!), A (+/+!), -2-k_1+A (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==n,A==3+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1+k (+), -2-k_1-C+E (+/+!), -1-k_1-C-k+E (+/+!), -2-k_1-C-k+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 6+k_1 (+), 1-C+E (+/+!), -3-k_1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), -2-k_1-C+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 6+k_1 (+), 1-C+E (+/+!), -3-k_1-C+E (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), -2-k_1-C+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,C==-n,E==2} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 6+k_1 (+), 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -3-k_1-C-k_1*A-4*A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 6+k_1 (+), 1-C+E (+/+!), k_1 (+/+!), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -3-k_1-C-k_1*A-4*A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,C==0,A==0,E==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1+k (+), -2-k_1-C+E (+/+!), -1-k_1-C-k+E (+/+!), -2-k_1-C-k+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-k_1+A (+/+!), -1-k_1+A-k (+/+!), 2+A (+/+!), -k_1+A-k (+/+!), A (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1+A-k (+/+!), -2+A-k (+/+!), 6+k (+), 2+A (+/+!), A (+/+!), -2+A (+/+!), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A (+/+!), -1+A-k (+/+!), -2+A-k (+/+!), 6+k (+), 2+A (+/+!), A (+/+!), -2+A (+/+!), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1+k (+), -2-k_1-C+E (+/+!), -1-k_1-C-k+E (+/+!), -2-k_1-C-k+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), -3-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C+E (+/+!), 6+k (+), -3-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -3-C+E (+/+!), -C+E (+/+!), -2-C+E (+/+!), 6+k (+), -3-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C+E (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==0,k==-4+n,E==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1-C+E (+/+!), -3-C-A*k-4*A-k+E (+/+!), 1 (+/+!), -3-C-4*A+E (+/+!), -1-C-2*A+E (+/+!), -2-C-A*(-1+k)-4*A-k+E (+/+!), -C-A+E (+/+!), 6+k (+), k (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -3-C-A*k-4*A-k+E (+/+!), -3-C-4*A+E (+/+!), -1-C-2*A+E (+/+!), -2-C-A*(-1+k)-4*A-k+E (+/+!), -C-A+E (+/+!), 6+k (+), k (+/+!), -2-C-3*A+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==-2*n,A==0,k==n,E==0} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1+k (+), -2-k_1-C+E (+/+!), -1-k_1-C-k+E (+/+!), -2-k_1-C-k+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-k_1+A (+/+!), -1-k_1+A-k (+/+!), 2+A (+/+!), -k_1+A-k (+/+!), A (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: k_1 (+/+!), 5+k_1+k (+), -1-k_1+A (+/+!), -1-k_1+A-k (+/+!), 2+A (+/+!), -k_1+A-k (+/+!), A (+/+!), k (+/+!), -k_1+A (+/+!), 1-k_1+A (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-2+n,A==1+n,k==1} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -2-k_1-C-k_1*A-A*k-3*A-k+E (+/+!), k_1 (+/+!), 5+k_1+k (+), -1-C-2*A+E (+/+!), -2-k_1-C-k_1*A-3*A+E (+/+!), -C-A+E (+/+!), -k_1-C-2*A-(-1+k_1)*A+E (+/+!), -1-k_1-C-k_1*A-A*(-1+k)-3*A-k+E (+/+!), k (+/+!), -1-k_1-C-k_1*A-2*A+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1+k (+), -2-k_1-C+E (+/+!), -1-k_1-C-k+E (+/+!), -2-k_1-C-k+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), k_1 (+/+!), -k_1-C+E (+/+!), -C+E (+/+!), 5+k_1+k (+), -2-k_1-C+E (+/+!), -1-k_1-C-k+E (+/+!), -2-k_1-C-k+E (+/+!), -1-C+E (+/+!), -1-k_1-C+E (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k_1==-4+n,C==0,k==1,E==n} resulting limit problem: [solved] Solution: k_1 / 1 C / -2*n A / 0 k / 1+n E / 0 Resulting cost 7+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 36 Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==0,A==0,k==-2+n,E==1+2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==3*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), -1+A*(-1+k)+A (+/+!), -2+A*(-1+k)+A-k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), -1+A*(-1+k)+A-k (+/+!), A*(-1+k)+A (+/+!), -2+A*(-1+k)+A (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), -1+A*(-1+k)+A (+/+!), -2+A*(-1+k)+A-k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), -1+A*(-1+k)+A-k (+/+!), A*(-1+k)+A (+/+!), -2+A*(-1+k)+A (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A*(-1+k)+A (+/+!), -2+A*(-1+k)+A-k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), -1+A*(-1+k)+A-k (+/+!), A*(-1+k)+A (+/+!), -2+A*(-1+k)+A (+/+!), 5+2*k (+), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==3*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A*k-A-k+E} resulting limit problem: A*k+A (+/+!), 1 (+/+!), 1+A*k+A (+/+!), A*k+A-k (+/+!), 2+A*k+A (+/+!), 1+A*k+A+k (+/+!), -1+A*k+A-k (+/+!), 5+2*k (+), 2+A*k+A+k (+/+!), k (+/+!), -1+A*k+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: A*k+A (+/+!), 1+A*k+A (+/+!), A*k+A-k (+/+!), 2+A*k+A (+/+!), 1+A*k+A+k (+/+!), -1+A*k+A-k (+/+!), 5+2*k (+), 2+A*k+A+k (+/+!), k (+/+!), -1+A*k+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==3*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-A*(-1+k)-A-k+E} resulting limit problem: 1 (+/+!), -1+A*(-1+k)+A (+/+!), -2+A*(-1+k)+A-k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), -1+A*(-1+k)+A-k (+/+!), A*(-1+k)+A (+/+!), -2+A*(-1+k)+A (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A*(-1+k)+A (+/+!), -2+A*(-1+k)+A-k (+/+!), A*(-1+k)+A+k (+/+!), 1+A*(-1+k)+A (+/+!), 1+A*(-1+k)+A+k (+/+!), -1+A*(-1+k)+A-k (+/+!), A*(-1+k)+A (+/+!), -2+A*(-1+k)+A (+/+!), 5+2*k (+), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==2,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (C) using substitution {C==-1-A+E} resulting limit problem: 1 (+/+!), A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: A-2*k (+/+!), -1+A-k (+/+!), -1+A-2*k (+/+!), 2+A (+/+!), A-k (+/+!), 1+A-k (+/+!), 2+A-k (+/+!), 5+2*k (+), k (+/+!), 1+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==3*n,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1-C+E (+/+!), -1-C-A*k-A*(-1+k)-3*A-2*k+E (+/+!), -C-A+E (+/+!), -1-C-A*k-2*A-k+E (+/+!), -C-A*k-A-k+E (+/+!), -2-C-2*A*k-3*A-2*k+E (+/+!), 5+2*k (+), -2-C-A*k-3*A-k+E (+/+!), k (+/+!), 1-C-A*(-1+k)-A-k+E (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1-C+E (+/+!), 1 (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-C+E (+/+!), -C+E (+/+!), -2-C-2*k+E (+/+!), -1-C-k+E (+/+!), -C-k+E (+/+!), 1-C-k+E (+/+!), -2-C-k+E (+/+!), -1-C-2*k+E (+/+!), 5+2*k (+), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==0,k==-2+n,E==2*n} resulting limit problem: [solved] Solution: C / 0 A / 0 k / -2+n E / 1+2*n Resulting cost 1+2*n has complexity: Poly(n^1) Computing asymptotic complexity for rule 37 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 2+n Rule cost: 2+k_1 Rule guard: [ A>=0 && E>=C && E>=1+C+A && k_1>0 && E>=k_1+C+A+(-1+k_1)*A ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)