/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(2, 1 + Arg_2) + nat(Arg_0) + nat(-1 + Arg_0) + max(8, 8 + Arg_0) + max(3, 3 * Arg_2) + max(3, -3 + 3 * Arg_2) + nat(2 * Arg_2)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 2745 ms] (2) BOUNDS(1, max(2, 1 + Arg_2) + nat(Arg_0) + nat(-1 + Arg_0) + max(8, 8 + Arg_0) + max(3, 3 * Arg_2) + max(3, -3 + 3 * Arg_2) + nat(2 * Arg_2)) (3) Loat Proof [FINISHED, 288.2 s] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: start(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A start(A, B, C, D) -> Com_1(lbl6(A, B, C, D)) :|: A >= 1 && 0 >= C && B >= C && B <= C && D >= A && D <= A start(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: A >= 1 && D >= A && D <= A && B >= A && B <= A && C >= A && C <= A start(A, B, C, D) -> Com_1(lbl101(A, B - D, C, D)) :|: A >= 1 && C >= A + 1 && B >= C && B <= C && D >= A && D <= A start(A, B, C, D) -> Com_1(lbl111(A, B, C, D - B)) :|: A >= C + 1 && C >= 1 && B >= C && B <= C && D >= A && D <= A lbl6(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: A >= 1 && 0 >= C && D >= A && D <= A && B >= C && B <= C lbl101(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: A >= B && B >= 1 && C >= 2 * B && D >= B && D <= B lbl101(A, B, C, D) -> Com_1(lbl101(A, B - D, C, D)) :|: B >= D + 1 && A >= D && B >= 1 && D >= 1 && C >= D + B lbl101(A, B, C, D) -> Com_1(lbl111(A, B, C, D - B)) :|: D >= B + 1 && A >= D && B >= 1 && D >= 1 && C >= D + B lbl111(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: C >= B && B >= 1 && A >= 2 * B && D >= B && D <= B lbl111(A, B, C, D) -> Com_1(lbl101(A, B - D, C, D)) :|: B >= D + 1 && C >= B && B >= 1 && D >= 1 && A >= D + B lbl111(A, B, C, D) -> Com_1(lbl111(A, B, C, D - B)) :|: D >= B + 1 && C >= B && B >= 1 && D >= 1 && A >= D + B cut(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: A >= B && B >= 1 && C >= B && D >= B && D <= B start0(A, B, C, D) -> Com_1(start(A, C, C, A)) :|: TRUE The start-symbols are:[start0_4] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 8+max([0, Arg_0])+max([3, 3*Arg_2])+max([3, 3*(-1+Arg_2)])+max([0, Arg_2])+max([2, 1+Arg_2])+max([0, Arg_2])+max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)}) Initial Complexity Problem: Start: start0 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3 Temp_Vars: Locations: cut, lbl101, lbl111, lbl6, start, start0, stop Transitions: cut(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 2 <= Arg_0+Arg_2 && Arg_1 <= Arg_0 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1 <= Arg_0 && 1 <= Arg_1 && Arg_1 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_3 lbl101(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3 <= Arg_2 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 2 <= Arg_0+Arg_3 && 2 <= Arg_2 && 3 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1 <= Arg_0 && 1 <= Arg_1 && (2)*Arg_1 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_3 lbl101(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl101(Arg_0,Arg_1-Arg_3,Arg_2,Arg_3):|:1+Arg_3 <= Arg_2 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 2 <= Arg_0+Arg_3 && 2 <= Arg_2 && 3 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_3 <= Arg_0 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_2 lbl101(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_1):|:1+Arg_3 <= Arg_2 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 2 <= Arg_0+Arg_3 && 2 <= Arg_2 && 3 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1+1 <= Arg_3 && Arg_3 <= Arg_0 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_2 lbl111(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 1+Arg_1 <= Arg_0 && 1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1 <= Arg_2 && 1 <= Arg_1 && (2)*Arg_1 <= Arg_0 && Arg_3 <= Arg_1 && Arg_1 <= Arg_3 lbl111(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl101(Arg_0,Arg_1-Arg_3,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 1+Arg_1 <= Arg_0 && 1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_0 lbl111(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_1):|:1+Arg_3 <= Arg_0 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 1+Arg_1 <= Arg_0 && 1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1+1 <= Arg_3 && Arg_1 <= Arg_2 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_0 lbl6(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && 1 <= Arg_3 && 1+Arg_2 <= Arg_3 && 1+Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && Arg_2 <= 0 && Arg_2 <= Arg_1 && Arg_1+Arg_2 <= 0 && 1+Arg_2 <= Arg_0 && Arg_1 <= Arg_2 && Arg_1 <= 0 && 1+Arg_1 <= Arg_0 && 1 <= Arg_0 && 1 <= Arg_0 && Arg_2 <= 0 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 start(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_0 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_1 <= Arg_0 && Arg_0 <= Arg_1 && Arg_2 <= Arg_0 && Arg_0 <= Arg_2 start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl101(Arg_0,Arg_1-Arg_3,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_0 && Arg_0+1 <= Arg_2 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_1):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_2+1 <= Arg_0 && 1 <= Arg_2 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl6(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_0 && Arg_2 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 start0(Arg_0,Arg_1,Arg_2,Arg_3) -> start(Arg_0,Arg_2,Arg_2,Arg_0):|: Timebounds: Overall timebound: 8+max([0, Arg_0])+max([3, 3*Arg_2])+max([3, 3*(-1+Arg_2)])+max([0, Arg_2])+max([2, 1+Arg_2])+max([0, Arg_2])+max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)} 12: cut->stop: 1 {O(1)} 6: lbl101->cut: 1 {O(1)} 7: lbl101->lbl101: max([0, -1+Arg_2])+max([0, Arg_2]) {O(n)} 8: lbl101->lbl111: max([0, Arg_0])+max([0, Arg_2]) {O(n)} 9: lbl111->cut: 1 {O(1)} 10: lbl111->lbl101: max([3, 3*(-1+Arg_2)])+max([3, 3*Arg_2]) {O(n)} 11: lbl111->lbl111: max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)} 5: lbl6->stop: 1 {O(1)} 0: start->stop: 1 {O(1)} 1: start->lbl6: 1 {O(1)} 2: start->cut: 1 {O(1)} 3: start->lbl101: 1 {O(1)} 4: start->lbl111: 1 {O(1)} 13: start0->start: 1 {O(1)} Costbounds: Overall costbound: 8+max([0, Arg_0])+max([3, 3*Arg_2])+max([3, 3*(-1+Arg_2)])+max([0, Arg_2])+max([2, 1+Arg_2])+max([0, Arg_2])+max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)} 12: cut->stop: 1 {O(1)} 6: lbl101->cut: 1 {O(1)} 7: lbl101->lbl101: max([0, -1+Arg_2])+max([0, Arg_2]) {O(n)} 8: lbl101->lbl111: max([0, Arg_0])+max([0, Arg_2]) {O(n)} 9: lbl111->cut: 1 {O(1)} 10: lbl111->lbl101: max([3, 3*(-1+Arg_2)])+max([3, 3*Arg_2]) {O(n)} 11: lbl111->lbl111: max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)} 5: lbl6->stop: 1 {O(1)} 0: start->stop: 1 {O(1)} 1: start->lbl6: 1 {O(1)} 2: start->cut: 1 {O(1)} 3: start->lbl101: 1 {O(1)} 4: start->lbl111: 1 {O(1)} 13: start0->start: 1 {O(1)} Sizebounds: `Lower: 12: cut->stop, Arg_0: 1 {O(1)} 12: cut->stop, Arg_1: 1 {O(1)} 12: cut->stop, Arg_2: 1 {O(1)} 12: cut->stop, Arg_3: 1 {O(1)} 6: lbl101->cut, Arg_0: 1 {O(1)} 6: lbl101->cut, Arg_1: 1 {O(1)} 6: lbl101->cut, Arg_2: 2 {O(1)} 6: lbl101->cut, Arg_3: 1 {O(1)} 7: lbl101->lbl101, Arg_0: 1 {O(1)} 7: lbl101->lbl101, Arg_1: 1 {O(1)} 7: lbl101->lbl101, Arg_2: 3 {O(1)} 7: lbl101->lbl101, Arg_3: 1 {O(1)} 8: lbl101->lbl111, Arg_0: 2 {O(1)} 8: lbl101->lbl111, Arg_1: 1 {O(1)} 8: lbl101->lbl111, Arg_2: 3 {O(1)} 8: lbl101->lbl111, Arg_3: 1 {O(1)} 9: lbl111->cut, Arg_0: 2 {O(1)} 9: lbl111->cut, Arg_1: 1 {O(1)} 9: lbl111->cut, Arg_2: 1 {O(1)} 9: lbl111->cut, Arg_3: 1 {O(1)} 10: lbl111->lbl101, Arg_0: 3 {O(1)} 10: lbl111->lbl101, Arg_1: 1 {O(1)} 10: lbl111->lbl101, Arg_2: 2 {O(1)} 10: lbl111->lbl101, Arg_3: 1 {O(1)} 11: lbl111->lbl111, Arg_0: 3 {O(1)} 11: lbl111->lbl111, Arg_1: 1 {O(1)} 11: lbl111->lbl111, Arg_2: 1 {O(1)} 11: lbl111->lbl111, Arg_3: 1 {O(1)} 5: lbl6->stop, Arg_0: 1 {O(1)} 5: lbl6->stop, Arg_1: Arg_2 {O(n)} 5: lbl6->stop, Arg_2: Arg_2 {O(n)} 5: lbl6->stop, Arg_3: 1 {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_0 {O(n)} 1: start->lbl6, Arg_0: 1 {O(1)} 1: start->lbl6, Arg_1: Arg_2 {O(n)} 1: start->lbl6, Arg_2: Arg_2 {O(n)} 1: start->lbl6, Arg_3: 1 {O(1)} 2: start->cut, Arg_0: 1 {O(1)} 2: start->cut, Arg_1: 1 {O(1)} 2: start->cut, Arg_2: 1 {O(1)} 2: start->cut, Arg_3: 1 {O(1)} 3: start->lbl101, Arg_0: 1 {O(1)} 3: start->lbl101, Arg_1: 1 {O(1)} 3: start->lbl101, Arg_2: 2 {O(1)} 3: start->lbl101, Arg_3: 1 {O(1)} 4: start->lbl111, Arg_0: 2 {O(1)} 4: start->lbl111, Arg_1: 1 {O(1)} 4: start->lbl111, Arg_2: 1 {O(1)} 4: start->lbl111, Arg_3: 1 {O(1)} 13: start0->start, Arg_0: Arg_0 {O(n)} 13: start0->start, Arg_1: Arg_2 {O(n)} 13: start0->start, Arg_2: Arg_2 {O(n)} 13: start0->start, Arg_3: Arg_0 {O(n)} `Upper: 12: cut->stop, Arg_0: Arg_0 {O(n)} 12: cut->stop, Arg_1: max([Arg_2, max([Arg_2, max([Arg_2, -1+Arg_2])])]) {O(n)} 12: cut->stop, Arg_2: Arg_2 {O(n)} 12: cut->stop, Arg_3: max([Arg_0, max([Arg_0, -1+Arg_0])]) {O(n)} 6: lbl101->cut, Arg_0: Arg_0 {O(n)} 6: lbl101->cut, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 6: lbl101->cut, Arg_2: Arg_2 {O(n)} 6: lbl101->cut, Arg_3: max([Arg_0, max([Arg_0, -1+Arg_0])]) {O(n)} 7: lbl101->lbl101, Arg_0: Arg_0 {O(n)} 7: lbl101->lbl101, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 7: lbl101->lbl101, Arg_2: Arg_2 {O(n)} 7: lbl101->lbl101, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 8: lbl101->lbl111, Arg_0: Arg_0 {O(n)} 8: lbl101->lbl111, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 8: lbl101->lbl111, Arg_2: Arg_2 {O(n)} 8: lbl101->lbl111, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 9: lbl111->cut, Arg_0: Arg_0 {O(n)} 9: lbl111->cut, Arg_1: max([Arg_2, max([Arg_2, -1+Arg_2])]) {O(n)} 9: lbl111->cut, Arg_2: Arg_2 {O(n)} 9: lbl111->cut, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 10: lbl111->lbl101, Arg_0: Arg_0 {O(n)} 10: lbl111->lbl101, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 10: lbl111->lbl101, Arg_2: Arg_2 {O(n)} 10: lbl111->lbl101, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 11: lbl111->lbl111, Arg_0: Arg_0 {O(n)} 11: lbl111->lbl111, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 11: lbl111->lbl111, Arg_2: Arg_2 {O(n)} 11: lbl111->lbl111, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 5: lbl6->stop, Arg_0: Arg_0 {O(n)} 5: lbl6->stop, Arg_1: 0 {O(1)} 5: lbl6->stop, Arg_2: 0 {O(1)} 5: lbl6->stop, Arg_3: Arg_0 {O(n)} 0: start->stop, Arg_0: 0 {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: 0 {O(1)} 1: start->lbl6, Arg_0: Arg_0 {O(n)} 1: start->lbl6, Arg_1: 0 {O(1)} 1: start->lbl6, Arg_2: 0 {O(1)} 1: start->lbl6, Arg_3: Arg_0 {O(n)} 2: start->cut, Arg_0: Arg_0 {O(n)} 2: start->cut, Arg_1: Arg_2 {O(n)} 2: start->cut, Arg_2: Arg_2 {O(n)} 2: start->cut, Arg_3: Arg_0 {O(n)} 3: start->lbl101, Arg_0: Arg_0 {O(n)} 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_0 {O(n)} 4: start->lbl111, Arg_0: Arg_0 {O(n)} 4: start->lbl111, Arg_1: Arg_2 {O(n)} 4: start->lbl111, Arg_2: Arg_2 {O(n)} 4: start->lbl111, Arg_3: -1+Arg_0 {O(n)} 13: start0->start, Arg_0: Arg_0 {O(n)} 13: start0->start, Arg_1: Arg_2 {O(n)} 13: start0->start, Arg_2: Arg_2 {O(n)} 13: start0->start, Arg_3: Arg_0 {O(n)} ---------------------------------------- (2) BOUNDS(1, max(2, 1 + Arg_2) + nat(Arg_0) + nat(-1 + Arg_0) + max(8, 8 + Arg_0) + max(3, 3 * Arg_2) + max(3, -3 + 3 * Arg_2) + nat(2 * Arg_2)) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start0 0: start -> stop : [ 0>=A && B==C && D==A ], cost: 1 1: start -> lbl6 : [ A>=1 && 0>=C && B==C && D==A ], cost: 1 2: start -> cut : [ A>=1 && D==A && B==A && C==A ], cost: 1 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 5: lbl6 -> stop : [ A>=1 && 0>=C && D==A && B==C ], cost: 1 6: lbl101 -> cut : [ A>=B && B>=1 && C>=2*B && D==B ], cost: 1 7: lbl101 -> lbl101 : B'=-D+B, [ B>=1+D && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 9: lbl111 -> cut : [ C>=B && B>=1 && A>=2*B && D==B ], cost: 1 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 11: lbl111 -> lbl111 : D'=D-B, [ D>=1+B && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 12: cut -> stop : [ A>=B && B>=1 && C>=B && D==B ], cost: 1 13: start0 -> start : B'=C, D'=A, [], cost: 1 Removed unreachable and leaf rules: Start location: start0 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 7: lbl101 -> lbl101 : B'=-D+B, [ B>=1+D && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 11: lbl111 -> lbl111 : D'=D-B, [ D>=1+B && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 13: start0 -> start : B'=C, D'=A, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 7: lbl101 -> lbl101 : B'=-D+B, [ B>=1+D && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 Accelerated rule 7 with backward acceleration, yielding the new rule 14. Removing the simple loops: 7. Accelerating simple loops of location 3. Accelerating the following rules: 11: lbl111 -> lbl111 : D'=D-B, [ D>=1+B && C>=B && B>=1 && A>=D+B ], cost: 1 Accelerated rule 11 with backward acceleration, yielding the new rule 15. Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: start0 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B ], cost: 1 14: lbl101 -> lbl101 : B'=-k*D+B, [ B>=1+D && A>=D && B>=1 && D>=1 && C>=D+B && k>0 && -(-1+k)*D+B>=1+D && -(-1+k)*D+B>=1 && C>=D-(-1+k)*D+B ], cost: k 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 15: lbl111 -> lbl111 : D'=-k_1*B+D, [ D>=1+B && C>=B && B>=1 && A>=D+B && k_1>0 && -(-1+k_1)*B+D>=1+B && A>=-(-1+k_1)*B+D+B ], cost: k_1 13: start0 -> start : B'=C, D'=A, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start0 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 16: start -> lbl101 : B'=-k*D-D+B, [ A>=1 && C>=1+A && B==C && D==A && -D+B>=1+D && -D+B>=1 && D>=1 && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B ], cost: 1+k 18: start -> lbl111 : D'=-k_1*B+D-B, [ A>=1+C && C>=1 && B==C && D==A && D-B>=1+B && B>=1 && k_1>0 && -(-1+k_1)*B+D-B>=1+B && A>=-(-1+k_1)*B+D ], cost: 1+k_1 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B ], cost: 1 19: lbl101 -> lbl111 : D'=-k_1*B+D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B && D-B>=1+B && C>=B && k_1>0 && -(-1+k_1)*B+D-B>=1+B && A>=-(-1+k_1)*B+D ], cost: 1+k_1 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 17: lbl111 -> lbl101 : B'=-k*D-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B ], cost: 1+k 13: start0 -> start : B'=C, D'=A, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start0 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B ], cost: 1 19: lbl101 -> lbl111 : D'=-k_1*B+D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B && D-B>=1+B && C>=B && k_1>0 && -(-1+k_1)*B+D-B>=1+B && A>=-(-1+k_1)*B+D ], cost: 1+k_1 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 17: lbl111 -> lbl101 : B'=-k*D-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B ], cost: 1+k 20: start0 -> lbl101 : B'=C-A, D'=A, [ A>=1 && C>=1+A ], cost: 2 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 22: start0 -> lbl101 : B'=-k*A+C-A, D'=A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A ], cost: 2+k 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A ], cost: 2+k_1 Eliminated location lbl101 (as a last resort): Start location: start0 24: lbl111 -> lbl111 : B'=-D+B, D'=2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D ], cost: 2 25: lbl111 -> lbl111 : B'=-D+B, D'=(D-B)*k_1+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D && 2*D-B>=1-D+B && C>=-D+B && k_1>0 && 2*D+(D-B)*(-1+k_1)-B>=1-D+B && A>=D+(D-B)*(-1+k_1) ], cost: 2+k_1 26: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B ], cost: 2+k 27: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D+k_1*(k*D+D-B)-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B && k*D+2*D-B>=1-k*D-D+B && C>=-k*D-D+B && k_1>0 && (-1+k_1)*(k*D+D-B)+k*D+2*D-B>=1-k*D-D+B && A>=(-1+k_1)*(k*D+D-B)+D ], cost: 2+k+k_1 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A ], cost: 2+k_1 28: start0 -> lbl111 : B'=C-A, D'=-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A ], cost: 3 29: start0 -> lbl111 : B'=C-A, D'=-k_1*(C-A)-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) ], cost: 3+k_1 30: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C ], cost: 3+k 31: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A+(k*A-C+A)*k_1-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) ], cost: 3+k+k_1 Applied pruning (of leafs and parallel rules): Start location: start0 24: lbl111 -> lbl111 : B'=-D+B, D'=2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D ], cost: 2 25: lbl111 -> lbl111 : B'=-D+B, D'=(D-B)*k_1+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D && 2*D-B>=1-D+B && C>=-D+B && k_1>0 && 2*D+(D-B)*(-1+k_1)-B>=1-D+B && A>=D+(D-B)*(-1+k_1) ], cost: 2+k_1 26: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B ], cost: 2+k 27: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D+k_1*(k*D+D-B)-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B && k*D+2*D-B>=1-k*D-D+B && C>=-k*D-D+B && k_1>0 && (-1+k_1)*(k*D+D-B)+k*D+2*D-B>=1-k*D-D+B && A>=(-1+k_1)*(k*D+D-B)+D ], cost: 2+k+k_1 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A ], cost: 2+k_1 29: start0 -> lbl111 : B'=C-A, D'=-k_1*(C-A)-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) ], cost: 3+k_1 30: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C ], cost: 3+k 31: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A+(k*A-C+A)*k_1-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) ], cost: 3+k+k_1 Accelerating simple loops of location 3. Accelerating the following rules: 24: lbl111 -> lbl111 : B'=-D+B, D'=2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D ], cost: 2 25: lbl111 -> lbl111 : B'=-D+B, D'=(D-B)*k_1+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D && 2*D-B>=1-D+B && C>=-D+B && k_1>0 && 2*D+(D-B)*(-1+k_1)-B>=1-D+B && A>=D+(D-B)*(-1+k_1) ], cost: 2+k_1 26: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B ], cost: 2+k 27: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D+k_1*(k*D+D-B)-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B && k*D+2*D-B>=1-k*D-D+B && C>=-k*D-D+B && k_1>0 && (-1+k_1)*(k*D+D-B)+k*D+2*D-B>=1-k*D-D+B && A>=(-1+k_1)*(k*D+D-B)+D ], cost: 2+k+k_1 Found no metering function for rule 24. Found no metering function for rule 25 (rule is too complicated). Found no metering function for rule 26 (rule is too complicated). Found no metering function for rule 27 (rule is too complicated). Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: start0 24: lbl111 -> lbl111 : B'=-D+B, D'=2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D ], cost: 2 25: lbl111 -> lbl111 : B'=-D+B, D'=(D-B)*k_1+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && D>=1-D+B && A>=D && 2*D-B>=1-D+B && C>=-D+B && k_1>0 && 2*D+(D-B)*(-1+k_1)-B>=1-D+B && A>=D+(D-B)*(-1+k_1) ], cost: 2+k_1 26: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B ], cost: 2+k 27: lbl111 -> lbl111 : B'=-k*D-D+B, D'=k*D+2*D+k_1*(k*D+D-B)-B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B && -D+B>=1+D && A>=D && k>0 && -D-(-1+k)*D+B>=1+D && -D-(-1+k)*D+B>=1 && C>=-(-1+k)*D+B && D>=1-k*D-D+B && C>=-k*D+B && k*D+2*D-B>=1-k*D-D+B && C>=-k*D-D+B && k_1>0 && (-1+k_1)*(k*D+D-B)+k*D+2*D-B>=1-k*D-D+B && A>=(-1+k_1)*(k*D+D-B)+D ], cost: 2+k+k_1 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A ], cost: 2+k_1 29: start0 -> lbl111 : B'=C-A, D'=-k_1*(C-A)-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) ], cost: 3+k_1 30: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C ], cost: 3+k 31: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A+(k*A-C+A)*k_1-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) ], cost: 3+k+k_1 Chained accelerated rules (with incoming rules): Start location: start0 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A ], cost: 2+k_1 29: start0 -> lbl111 : B'=C-A, D'=-k_1*(C-A)-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) ], cost: 3+k_1 30: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C ], cost: 3+k 31: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A+(k*A-C+A)*k_1-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) ], cost: 3+k+k_1 32: start0 -> lbl111 : B'=2*C-A, D'=-3*C+2*A, [ A>=1+C && C>=1 && C>=1-C+A && -C+A>=1+2*C-A ], cost: 4 33: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-2*C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && -C+A-C*k_1>=1+2*C-A+C*k_1 && A>=-C+A-C*k_1 ], cost: 4+k_1 34: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C+5*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C+2*A ], cost: 5+k_1 35: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A ], cost: 5+k 36: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(k*A-C+A)*k_1-C+2*A ], cost: 5+k+k_1 37: start0 -> lbl111 : B'=2*C-A, D'=-3*C-(2*C-A)*k_1+2*A, [ A>=1+C && C>=1 && C>=1-C+A && -C+A>=1+2*C-A && -3*C+2*A>=1+2*C-A && k_1>0 && -3*C-(2*C-A)*(-1+k_1)+2*A>=1+2*C-A && A>=-C-(2*C-A)*(-1+k_1)+A ], cost: 4+k_1 38: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-(2*C-A+C*k_1)*k_1-2*C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && -C+A-C*k_1>=1+2*C-A+C*k_1 && A>=-C+A-C*k_1 && -3*C+2*A-2*C*k_1>=1+2*C-A+C*k_1 && -3*C-(2*C-A+C*k_1)*(-1+k_1)+2*A-2*C*k_1>=1+2*C-A+C*k_1 && A>=-C-(2*C-A+C*k_1)*(-1+k_1)+A-C*k_1 ], cost: 4+2*k_1 39: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C-(k_1*(C-A)+2*C-3*A)*k_1+5*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C+2*A && -2*k_1*(C-A)-3*C+5*A>=1+k_1*(C-A)+2*C-3*A && C>=k_1*(C-A)+2*C-3*A && -2*k_1*(C-A)-3*C-(-1+k_1)*(k_1*(C-A)+2*C-3*A)+5*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C-(-1+k_1)*(k_1*(C-A)+2*C-3*A)+2*A ], cost: 5+2*k_1 40: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A+(2*k*A-2*C+3*A)*k_1, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A && 3*k*A-3*C+5*A>=1-2*k*A+2*C-3*A && C>=-2*k*A+2*C-3*A && k_1>0 && 3*k*A+(2*k*A-2*C+3*A)*(-1+k_1)-3*C+5*A>=1-2*k*A+2*C-3*A && A>=k*A+(2*k*A-2*C+3*A)*(-1+k_1)-C+2*A ], cost: 5+k+k_1 41: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+5*A+k_1*(2*k*A+(k*A-C+A)*k_1-2*C+3*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && 3*k*A+2*(k*A-C+A)*k_1-3*C+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && C>=-2*k*A-(k*A-C+A)*k_1+2*C-3*A && 3*k*A+(-1+k_1)*(2*k*A+(k*A-C+A)*k_1-2*C+3*A)+2*(k*A-C+A)*k_1-3*C+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(-1+k_1)*(2*k*A+(k*A-C+A)*k_1-2*C+3*A)+(k*A-C+A)*k_1-C+2*A ], cost: 5+k+2*k_1 42: start0 -> lbl111 : B'=2*C-A+k*(C-A), D'=-3*C+2*A-k*(C-A), [ A>=1+C && C>=1 && C>=1-C+A && 2*C-A>=1-C+A && k>0 && (-1+k)*(C-A)+2*C-A>=1-C+A && (-1+k)*(C-A)+2*C-A>=1 && C>=(-1+k)*(C-A)+C && -C+A>=1+2*C-A+k*(C-A) && C>=C+k*(C-A) ], cost: 4+k 43: start0 -> lbl111 : B'=2*C-A+C*k_1+k*(C-A+C*k_1), D'=-3*C+2*A-2*C*k_1-k*(C-A+C*k_1), [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && 2*C-A+C*k_1>=1-C+A-C*k_1 && A>=-C+A-C*k_1 && k>0 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1-C+A-C*k_1 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1 && C>=(-1+k)*(C-A+C*k_1)+C && -C+A-C*k_1>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=C+k*(C-A+C*k_1) ], cost: 4+k+k_1 44: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A), D'=-2*k_1*(C-A)-3*C+5*A-k*(k_1*(C-A)+C-2*A), [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)-C+2*A && k>0 && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1 && C>=(-1+k)*(k_1*(C-A)+C-2*A)+C-A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=C-A+k*(k_1*(C-A)+C-2*A) ], cost: 5+k+k_1 45: start0 -> lbl111 : B'=-2*k*A+2*C-3*A-k*(k*A-C+2*A), D'=3*k*A-3*C+5*A+k*(k*A-C+2*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && -2*k*A+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A-C+2*A)+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-k*A+C-A-k*(k*A-C+2*A) ], cost: 5+2*k 46: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && -2*k*A-(k*A-C+A)*k_1+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+C-A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-k*A+C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-A ], cost: 5+2*k+k_1 47: start0 -> lbl111 : B'=2*C-A+k*(C-A), D'=-3*C+2*A-k_1*(2*C-A+k*(C-A))-k*(C-A), [ A>=1+C && C>=1 && C>=1-C+A && 2*C-A>=1-C+A && k>0 && (-1+k)*(C-A)+2*C-A>=1-C+A && (-1+k)*(C-A)+2*C-A>=1 && C>=(-1+k)*(C-A)+C && -C+A>=1+2*C-A+k*(C-A) && C>=C+k*(C-A) && -3*C+2*A-k*(C-A)>=1+2*C-A+k*(C-A) && C>=2*C-A+k*(C-A) && k_1>0 && -(-1+k_1)*(2*C-A+k*(C-A))-3*C+2*A-k*(C-A)>=1+2*C-A+k*(C-A) && A>=-(-1+k_1)*(2*C-A+k*(C-A))-C+A ], cost: 4+k+k_1 48: start0 -> lbl111 : B'=2*C-A+C*k_1+k*(C-A+C*k_1), D'=-3*C+2*A-2*C*k_1-k*(C-A+C*k_1)-k_1*(2*C-A+C*k_1+k*(C-A+C*k_1)), [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && 2*C-A+C*k_1>=1-C+A-C*k_1 && A>=-C+A-C*k_1 && k>0 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1-C+A-C*k_1 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1 && C>=(-1+k)*(C-A+C*k_1)+C && -C+A-C*k_1>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=C+k*(C-A+C*k_1) && -3*C+2*A-2*C*k_1-k*(C-A+C*k_1)>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=2*C-A+C*k_1+k*(C-A+C*k_1) && -(-1+k_1)*(2*C-A+C*k_1+k*(C-A+C*k_1))-3*C+2*A-2*C*k_1-k*(C-A+C*k_1)>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && A>=-(-1+k_1)*(2*C-A+C*k_1+k*(C-A+C*k_1))-C+A-C*k_1 ], cost: 4+k+2*k_1 49: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A), D'=-2*k_1*(C-A)-3*C-k_1*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+5*A-k*(k_1*(C-A)+C-2*A), [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)-C+2*A && k>0 && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1 && C>=(-1+k)*(k_1*(C-A)+C-2*A)+C-A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=C-A+k*(k_1*(C-A)+C-2*A) && -2*k_1*(C-A)-3*C+5*A-k*(k_1*(C-A)+C-2*A)>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && -2*k_1*(C-A)-3*C-(-1+k_1)*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+5*A-k*(k_1*(C-A)+C-2*A)>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && A>=-k_1*(C-A)-C-(-1+k_1)*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+2*A ], cost: 5+k+2*k_1 50: start0 -> lbl111 : B'=-2*k*A+2*C-3*A-k*(k*A-C+2*A), D'=3*k*A-3*C+5*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*k_1+k*(k*A-C+2*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && -2*k*A+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A-C+2*A)+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-k*A+C-A-k*(k*A-C+2*A) && 3*k*A-3*C+5*A+k*(k*A-C+2*A)>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-2*k*A+2*C-3*A-k*(k*A-C+2*A) && k_1>0 && 3*k*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*(-1+k_1)-3*C+5*A+k*(k*A-C+2*A)>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && A>=k*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*(-1+k_1)-C+2*A ], cost: 5+2*k+k_1 51: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*k_1+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && -2*k*A-(k*A-C+A)*k_1+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+C-A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-k*A+C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-A && 3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && 3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*(-1+k_1)+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && A>=k*A+(k*A-C+A)*k_1-C+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*(-1+k_1)+2*A ], cost: 5+2*k+2*k_1 Removed unreachable locations (and leaf rules with constant cost): Start location: start0 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A ], cost: 2+k_1 29: start0 -> lbl111 : B'=C-A, D'=-k_1*(C-A)-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) ], cost: 3+k_1 30: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C ], cost: 3+k 31: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A+(k*A-C+A)*k_1-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) ], cost: 3+k+k_1 33: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-2*C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && -C+A-C*k_1>=1+2*C-A+C*k_1 && A>=-C+A-C*k_1 ], cost: 4+k_1 34: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C+5*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C+2*A ], cost: 5+k_1 35: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A ], cost: 5+k 36: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(k*A-C+A)*k_1-C+2*A ], cost: 5+k+k_1 37: start0 -> lbl111 : B'=2*C-A, D'=-3*C-(2*C-A)*k_1+2*A, [ A>=1+C && C>=1 && C>=1-C+A && -C+A>=1+2*C-A && -3*C+2*A>=1+2*C-A && k_1>0 && -3*C-(2*C-A)*(-1+k_1)+2*A>=1+2*C-A && A>=-C-(2*C-A)*(-1+k_1)+A ], cost: 4+k_1 38: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-(2*C-A+C*k_1)*k_1-2*C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && -C+A-C*k_1>=1+2*C-A+C*k_1 && A>=-C+A-C*k_1 && -3*C+2*A-2*C*k_1>=1+2*C-A+C*k_1 && -3*C-(2*C-A+C*k_1)*(-1+k_1)+2*A-2*C*k_1>=1+2*C-A+C*k_1 && A>=-C-(2*C-A+C*k_1)*(-1+k_1)+A-C*k_1 ], cost: 4+2*k_1 39: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C-(k_1*(C-A)+2*C-3*A)*k_1+5*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C+2*A && -2*k_1*(C-A)-3*C+5*A>=1+k_1*(C-A)+2*C-3*A && C>=k_1*(C-A)+2*C-3*A && -2*k_1*(C-A)-3*C-(-1+k_1)*(k_1*(C-A)+2*C-3*A)+5*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C-(-1+k_1)*(k_1*(C-A)+2*C-3*A)+2*A ], cost: 5+2*k_1 40: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A+(2*k*A-2*C+3*A)*k_1, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A && 3*k*A-3*C+5*A>=1-2*k*A+2*C-3*A && C>=-2*k*A+2*C-3*A && k_1>0 && 3*k*A+(2*k*A-2*C+3*A)*(-1+k_1)-3*C+5*A>=1-2*k*A+2*C-3*A && A>=k*A+(2*k*A-2*C+3*A)*(-1+k_1)-C+2*A ], cost: 5+k+k_1 41: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+5*A+k_1*(2*k*A+(k*A-C+A)*k_1-2*C+3*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && 3*k*A+2*(k*A-C+A)*k_1-3*C+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && C>=-2*k*A-(k*A-C+A)*k_1+2*C-3*A && 3*k*A+(-1+k_1)*(2*k*A+(k*A-C+A)*k_1-2*C+3*A)+2*(k*A-C+A)*k_1-3*C+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(-1+k_1)*(2*k*A+(k*A-C+A)*k_1-2*C+3*A)+(k*A-C+A)*k_1-C+2*A ], cost: 5+k+2*k_1 42: start0 -> lbl111 : B'=2*C-A+k*(C-A), D'=-3*C+2*A-k*(C-A), [ A>=1+C && C>=1 && C>=1-C+A && 2*C-A>=1-C+A && k>0 && (-1+k)*(C-A)+2*C-A>=1-C+A && (-1+k)*(C-A)+2*C-A>=1 && C>=(-1+k)*(C-A)+C && -C+A>=1+2*C-A+k*(C-A) && C>=C+k*(C-A) ], cost: 4+k 43: start0 -> lbl111 : B'=2*C-A+C*k_1+k*(C-A+C*k_1), D'=-3*C+2*A-2*C*k_1-k*(C-A+C*k_1), [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && 2*C-A+C*k_1>=1-C+A-C*k_1 && A>=-C+A-C*k_1 && k>0 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1-C+A-C*k_1 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1 && C>=(-1+k)*(C-A+C*k_1)+C && -C+A-C*k_1>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=C+k*(C-A+C*k_1) ], cost: 4+k+k_1 44: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A), D'=-2*k_1*(C-A)-3*C+5*A-k*(k_1*(C-A)+C-2*A), [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)-C+2*A && k>0 && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1 && C>=(-1+k)*(k_1*(C-A)+C-2*A)+C-A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=C-A+k*(k_1*(C-A)+C-2*A) ], cost: 5+k+k_1 45: start0 -> lbl111 : B'=-2*k*A+2*C-3*A-k*(k*A-C+2*A), D'=3*k*A-3*C+5*A+k*(k*A-C+2*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && -2*k*A+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A-C+2*A)+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-k*A+C-A-k*(k*A-C+2*A) ], cost: 5+2*k 46: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && -2*k*A-(k*A-C+A)*k_1+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+C-A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-k*A+C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-A ], cost: 5+2*k+k_1 47: start0 -> lbl111 : B'=2*C-A+k*(C-A), D'=-3*C+2*A-k_1*(2*C-A+k*(C-A))-k*(C-A), [ A>=1+C && C>=1 && C>=1-C+A && 2*C-A>=1-C+A && k>0 && (-1+k)*(C-A)+2*C-A>=1-C+A && (-1+k)*(C-A)+2*C-A>=1 && C>=(-1+k)*(C-A)+C && -C+A>=1+2*C-A+k*(C-A) && C>=C+k*(C-A) && -3*C+2*A-k*(C-A)>=1+2*C-A+k*(C-A) && C>=2*C-A+k*(C-A) && k_1>0 && -(-1+k_1)*(2*C-A+k*(C-A))-3*C+2*A-k*(C-A)>=1+2*C-A+k*(C-A) && A>=-(-1+k_1)*(2*C-A+k*(C-A))-C+A ], cost: 4+k+k_1 48: start0 -> lbl111 : B'=2*C-A+C*k_1+k*(C-A+C*k_1), D'=-3*C+2*A-2*C*k_1-k*(C-A+C*k_1)-k_1*(2*C-A+C*k_1+k*(C-A+C*k_1)), [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && 2*C-A+C*k_1>=1-C+A-C*k_1 && A>=-C+A-C*k_1 && k>0 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1-C+A-C*k_1 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1 && C>=(-1+k)*(C-A+C*k_1)+C && -C+A-C*k_1>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=C+k*(C-A+C*k_1) && -3*C+2*A-2*C*k_1-k*(C-A+C*k_1)>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=2*C-A+C*k_1+k*(C-A+C*k_1) && -(-1+k_1)*(2*C-A+C*k_1+k*(C-A+C*k_1))-3*C+2*A-2*C*k_1-k*(C-A+C*k_1)>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && A>=-(-1+k_1)*(2*C-A+C*k_1+k*(C-A+C*k_1))-C+A-C*k_1 ], cost: 4+k+2*k_1 49: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A), D'=-2*k_1*(C-A)-3*C-k_1*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+5*A-k*(k_1*(C-A)+C-2*A), [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)-C+2*A && k>0 && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1 && C>=(-1+k)*(k_1*(C-A)+C-2*A)+C-A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=C-A+k*(k_1*(C-A)+C-2*A) && -2*k_1*(C-A)-3*C+5*A-k*(k_1*(C-A)+C-2*A)>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && -2*k_1*(C-A)-3*C-(-1+k_1)*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+5*A-k*(k_1*(C-A)+C-2*A)>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && A>=-k_1*(C-A)-C-(-1+k_1)*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+2*A ], cost: 5+k+2*k_1 50: start0 -> lbl111 : B'=-2*k*A+2*C-3*A-k*(k*A-C+2*A), D'=3*k*A-3*C+5*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*k_1+k*(k*A-C+2*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && -2*k*A+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A-C+2*A)+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-k*A+C-A-k*(k*A-C+2*A) && 3*k*A-3*C+5*A+k*(k*A-C+2*A)>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-2*k*A+2*C-3*A-k*(k*A-C+2*A) && k_1>0 && 3*k*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*(-1+k_1)-3*C+5*A+k*(k*A-C+2*A)>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && A>=k*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*(-1+k_1)-C+2*A ], cost: 5+2*k+k_1 51: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*k_1+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && -2*k*A-(k*A-C+A)*k_1+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+C-A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-k*A+C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-A && 3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && 3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*(-1+k_1)+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && A>=k*A+(k*A-C+A)*k_1-C+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*(-1+k_1)+2*A ], cost: 5+2*k+2*k_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start0 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A ], cost: 2+k_1 29: start0 -> lbl111 : B'=C-A, D'=-k_1*(C-A)-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) ], cost: 3+k_1 30: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C ], cost: 3+k 31: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A+(k*A-C+A)*k_1-C+2*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) ], cost: 3+k+k_1 33: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-2*C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && -C+A-C*k_1>=1+2*C-A+C*k_1 && A>=-C+A-C*k_1 ], cost: 4+k_1 34: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C+5*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C+2*A ], cost: 5+k_1 35: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A ], cost: 5+k 36: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(k*A-C+A)*k_1-C+2*A ], cost: 5+k+k_1 37: start0 -> lbl111 : B'=2*C-A, D'=-3*C-(2*C-A)*k_1+2*A, [ A>=1+C && C>=1 && C>=1-C+A && -C+A>=1+2*C-A && -3*C+2*A>=1+2*C-A && k_1>0 && -3*C-(2*C-A)*(-1+k_1)+2*A>=1+2*C-A && A>=-C-(2*C-A)*(-1+k_1)+A ], cost: 4+k_1 38: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-(2*C-A+C*k_1)*k_1-2*C*k_1, [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && -C+A-C*k_1>=1+2*C-A+C*k_1 && A>=-C+A-C*k_1 && -3*C+2*A-2*C*k_1>=1+2*C-A+C*k_1 && -3*C-(2*C-A+C*k_1)*(-1+k_1)+2*A-2*C*k_1>=1+2*C-A+C*k_1 && A>=-C-(2*C-A+C*k_1)*(-1+k_1)+A-C*k_1 ], cost: 4+2*k_1 39: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C-(k_1*(C-A)+2*C-3*A)*k_1+5*A, [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C+2*A && -2*k_1*(C-A)-3*C+5*A>=1+k_1*(C-A)+2*C-3*A && C>=k_1*(C-A)+2*C-3*A && -2*k_1*(C-A)-3*C-(-1+k_1)*(k_1*(C-A)+2*C-3*A)+5*A>=1+k_1*(C-A)+2*C-3*A && A>=-k_1*(C-A)-C-(-1+k_1)*(k_1*(C-A)+2*C-3*A)+2*A ], cost: 5+2*k_1 40: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A+(2*k*A-2*C+3*A)*k_1, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A && 3*k*A-3*C+5*A>=1-2*k*A+2*C-3*A && C>=-2*k*A+2*C-3*A && k_1>0 && 3*k*A+(2*k*A-2*C+3*A)*(-1+k_1)-3*C+5*A>=1-2*k*A+2*C-3*A && A>=k*A+(2*k*A-2*C+3*A)*(-1+k_1)-C+2*A ], cost: 5+k+k_1 41: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+5*A+k_1*(2*k*A+(k*A-C+A)*k_1-2*C+3*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && 3*k*A+2*(k*A-C+A)*k_1-3*C+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && C>=-2*k*A-(k*A-C+A)*k_1+2*C-3*A && 3*k*A+(-1+k_1)*(2*k*A+(k*A-C+A)*k_1-2*C+3*A)+2*(k*A-C+A)*k_1-3*C+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A && A>=k*A+(-1+k_1)*(2*k*A+(k*A-C+A)*k_1-2*C+3*A)+(k*A-C+A)*k_1-C+2*A ], cost: 5+k+2*k_1 42: start0 -> lbl111 : B'=2*C-A+k*(C-A), D'=-3*C+2*A-k*(C-A), [ A>=1+C && C>=1 && C>=1-C+A && 2*C-A>=1-C+A && k>0 && (-1+k)*(C-A)+2*C-A>=1-C+A && (-1+k)*(C-A)+2*C-A>=1 && C>=(-1+k)*(C-A)+C && -C+A>=1+2*C-A+k*(C-A) && C>=C+k*(C-A) ], cost: 4+k 43: start0 -> lbl111 : B'=2*C-A+C*k_1+k*(C-A+C*k_1), D'=-3*C+2*A-2*C*k_1-k*(C-A+C*k_1), [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && 2*C-A+C*k_1>=1-C+A-C*k_1 && A>=-C+A-C*k_1 && k>0 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1-C+A-C*k_1 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1 && C>=(-1+k)*(C-A+C*k_1)+C && -C+A-C*k_1>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=C+k*(C-A+C*k_1) ], cost: 4+k+k_1 44: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A), D'=-2*k_1*(C-A)-3*C+5*A-k*(k_1*(C-A)+C-2*A), [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)-C+2*A && k>0 && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1 && C>=(-1+k)*(k_1*(C-A)+C-2*A)+C-A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=C-A+k*(k_1*(C-A)+C-2*A) ], cost: 5+k+k_1 45: start0 -> lbl111 : B'=-2*k*A+2*C-3*A-k*(k*A-C+2*A), D'=3*k*A-3*C+5*A+k*(k*A-C+2*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && -2*k*A+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A-C+2*A)+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-k*A+C-A-k*(k*A-C+2*A) ], cost: 5+2*k 46: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && -2*k*A-(k*A-C+A)*k_1+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+C-A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-k*A+C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-A ], cost: 5+2*k+k_1 47: start0 -> lbl111 : B'=2*C-A+k*(C-A), D'=-3*C+2*A-k_1*(2*C-A+k*(C-A))-k*(C-A), [ A>=1+C && C>=1 && C>=1-C+A && 2*C-A>=1-C+A && k>0 && (-1+k)*(C-A)+2*C-A>=1-C+A && (-1+k)*(C-A)+2*C-A>=1 && C>=(-1+k)*(C-A)+C && -C+A>=1+2*C-A+k*(C-A) && C>=C+k*(C-A) && -3*C+2*A-k*(C-A)>=1+2*C-A+k*(C-A) && C>=2*C-A+k*(C-A) && k_1>0 && -(-1+k_1)*(2*C-A+k*(C-A))-3*C+2*A-k*(C-A)>=1+2*C-A+k*(C-A) && A>=-(-1+k_1)*(2*C-A+k*(C-A))-C+A ], cost: 4+k+k_1 48: start0 -> lbl111 : B'=2*C-A+C*k_1+k*(C-A+C*k_1), D'=-3*C+2*A-2*C*k_1-k*(C-A+C*k_1)-k_1*(2*C-A+C*k_1+k*(C-A+C*k_1)), [ A>=1+C && C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C && A>=-C*(-1+k_1)+A && C>=1-C+A-C*k_1 && A>=A-C*k_1 && 2*C-A+C*k_1>=1-C+A-C*k_1 && A>=-C+A-C*k_1 && k>0 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1-C+A-C*k_1 && (-1+k)*(C-A+C*k_1)+2*C-A+C*k_1>=1 && C>=(-1+k)*(C-A+C*k_1)+C && -C+A-C*k_1>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=C+k*(C-A+C*k_1) && -3*C+2*A-2*C*k_1-k*(C-A+C*k_1)>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && C>=2*C-A+C*k_1+k*(C-A+C*k_1) && -(-1+k_1)*(2*C-A+C*k_1+k*(C-A+C*k_1))-3*C+2*A-2*C*k_1-k*(C-A+C*k_1)>=1+2*C-A+C*k_1+k*(C-A+C*k_1) && A>=-(-1+k_1)*(2*C-A+C*k_1+k*(C-A+C*k_1))-C+A-C*k_1 ], cost: 4+k+2*k_1 49: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A), D'=-2*k_1*(C-A)-3*C-k_1*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+5*A-k*(k_1*(C-A)+C-2*A), [ A>=1 && C>=1+A && A>=1+C-A && -C+2*A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)+A && k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && A>=-k_1*(C-A)-C+2*A && k>0 && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1-k_1*(C-A)-C+2*A && (-1+k)*(k_1*(C-A)+C-2*A)+k_1*(C-A)+2*C-3*A>=1 && C>=(-1+k)*(k_1*(C-A)+C-2*A)+C-A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=C-A+k*(k_1*(C-A)+C-2*A) && -2*k_1*(C-A)-3*C+5*A-k*(k_1*(C-A)+C-2*A)>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && C>=k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && -2*k_1*(C-A)-3*C-(-1+k_1)*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+5*A-k*(k_1*(C-A)+C-2*A)>=1+k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A) && A>=-k_1*(C-A)-C-(-1+k_1)*(k_1*(C-A)+2*C-3*A+k*(k_1*(C-A)+C-2*A))+2*A ], cost: 5+k+2*k_1 50: start0 -> lbl111 : B'=-2*k*A+2*C-3*A-k*(k*A-C+2*A), D'=3*k*A-3*C+5*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*k_1+k*(k*A-C+2*A), [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && -k*A+C-A>=1+k*A-C+2*A && C>=-k*A+C-A && -2*k*A+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1+k*A-C+2*A && -2*k*A-(-1+k)*(k*A-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A-C+2*A)+C-A && k*A-C+2*A>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-k*A+C-A-k*(k*A-C+2*A) && 3*k*A-3*C+5*A+k*(k*A-C+2*A)>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && C>=-2*k*A+2*C-3*A-k*(k*A-C+2*A) && k_1>0 && 3*k*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*(-1+k_1)-3*C+5*A+k*(k*A-C+2*A)>=1-2*k*A+2*C-3*A-k*(k*A-C+2*A) && A>=k*A+(2*k*A-2*C+3*A+k*(k*A-C+2*A))*(-1+k_1)-C+2*A ], cost: 5+2*k+k_1 51: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*k_1+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A, [ A>=1 && C>=1+A && C-A>=1+A && k>0 && C-A-(-1+k)*A>=1+A && C-A-(-1+k)*A>=1 && C>=C-(-1+k)*A && A>=1-k*A+C-A && C>=-k*A+C && k*A-C+2*A>=1-k*A+C-A && C>=-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=(k*A-C+A)*k_1+A && -2*k*A-(k*A-C+A)*k_1+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && A>=k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1+k*A+(k*A-C+A)*k_1-C+2*A && -2*k*A-(k*A-C+A)*k_1-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+2*C-3*A>=1 && C>=-k*A-(-1+k)*(k*A+(k*A-C+A)*k_1-C+2*A)+C-A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-k*A+C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-A && 3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && C>=-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && 3*k*A+2*(k*A-C+A)*k_1-3*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*(-1+k_1)+5*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-k*(k*A+(k*A-C+A)*k_1-C+2*A)-3*A && A>=k*A+(k*A-C+A)*k_1-C+(2*k*A+(k*A-C+A)*k_1-2*C+k*(k*A+(k*A-C+A)*k_1-C+2*A)+3*A)*(-1+k_1)+2*A ], cost: 5+2*k+2*k_1 Computing asymptotic complexity for rule 23 Simplified the guard: 23: start0 -> lbl111 : B'=C, D'=-C+A-C*k_1, [ C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C ], cost: 2+k_1 Solved the limit problem by the following transformations: Created initial limit problem: C (+/+!), -2*C+A (+/+!), k_1 (+/+!), 2+k_1 (+), -2*C-C*(-1+k_1)+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==1,k_1==n,A==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: C (+/+!), -2*C+A (+/+!), k_1 (+/+!), 2+k_1 (+), -2*C-C*(-1+k_1)+A (+/+!) [not solved] applying transformation rule (C) using substitution {C==1} resulting limit problem: 1 (+/+!), -1-k_1+A (+/+!), k_1 (+/+!), -2+A (+/+!), 2+k_1 (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1-k_1+A (+/+!), k_1 (+/+!), -2+A (+/+!), 2+k_1 (+) [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] Solution: C / 1 k_1 / n A / 2*n Resulting cost 2+n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 29 Simplified the guard: 29: start0 -> lbl111 : B'=C-A, D'=-k_1*(C-A)-C+2*A, [ C>=1+A && A>=1+C-A && k_1>0 && -C+2*A-(-1+k_1)*(C-A)>=1+C-A && A>=A-(-1+k_1)*(C-A) ], cost: 3+k_1 Solved the limit problem by the following transformations: Created initial limit problem: 1+(-1+k_1)*(C-A) (+/+!), -2*C+3*A-(-1+k_1)*(C-A) (+/+!), k_1 (+/+!), C-A (+/+!), 3+k_1 (+), -C+2*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==4+2*n,k_1==n,A==3+2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 1+(-1+k_1)*(C-A) (+/+!), -2*C+3*A-(-1+k_1)*(C-A) (+/+!), k_1 (+/+!), C-A (+/+!), 3+k_1 (+), -C+2*A (+/+!) [not solved] applying transformation rule (C) using substitution {C==1+A} resulting limit problem: 1 (+/+!), -1+A (+/+!), -1-k_1+A (+/+!), k_1 (+/+!), 3+k_1 (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -1+A (+/+!), -1-k_1+A (+/+!), k_1 (+/+!), 3+k_1 (+) [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] Solution: C / 4+2*n k_1 / n A / 3+2*n Resulting cost 3+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 30 Simplified the guard: 30: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A-C+2*A, [ k>0 && C-A-(-1+k)*A>=1+A && A>=1-k*A+C-A ], cost: 3+k Solved the limit problem by the following transformations: Created initial limit problem: C-2*A-(-1+k)*A (+/+!), k (+/+!), k*A-C+2*A (+/+!), 3+k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k==-1+n,C==1+2*n,A==2} resulting limit problem: [solved] Solution: k / -1+n C / 1+2*n A / 2 Resulting cost 2+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 31 Simplified the guard: 31: start0 -> lbl111 : B'=-k*A+C-A, D'=k*A+(k*A-C+A)*k_1-C+2*A, [ k>0 && C-A-(-1+k)*A>=1+A && A>=1-k*A+C-A && k_1>0 && k*A-C+2*A+(k*A-C+A)*(-1+k_1)>=1-k*A+C-A && A>=A+(k*A-C+A)*(-1+k_1) ], cost: 3+k+k_1 Solved the limit problem by the following transformations: Created initial limit problem: C-2*A-(-1+k)*A (+/+!), k (+/+!), 2*k*A-2*C+3*A+(k*A-C+A)*(-1+k_1) (+/+!), k*A-C+2*A (+/+!), k_1 (+/+!), 1-(k*A-C+A)*(-1+k_1) (+/+!), 3+k+k_1 (+) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: 1 (+/+!), C-2*A-(-1+k)*A (+/+!), k (+/+!), k*A-C+2*A (+/+!), 2*k*A-2*C+3*A (+/+!), 4+k (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: C-2*A-(-1+k)*A (+/+!), k (+/+!), k*A-C+2*A (+/+!), 2*k*A-2*C+3*A (+/+!), 4+k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k==n,C==4+3*n,A==3} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: C-2*A-(-1+k)*A (+/+!), k (+/+!), 2*k*A-2*C+3*A+(k*A-C+A)*(-1+k_1) (+/+!), k*A-C+2*A (+/+!), k_1 (+/+!), 1-(k*A-C+A)*(-1+k_1) (+/+!), 3+k+k_1 (+) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), 4+k_1 (+), C-2*A (+/+!), 1+(C-2*A)*(-1+k_1) (+/+!), k_1 (+/+!), -C+3*A (+/+!), -2*C+5*A-(C-2*A)*(-1+k_1) (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 4+k_1 (+), C-2*A (+/+!), 1+(C-2*A)*(-1+k_1) (+/+!), k_1 (+/+!), -C+3*A (+/+!), -2*C+5*A-(C-2*A)*(-1+k_1) (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==6*n,k_1==1+n,A==-1+3*n} resulting limit problem: [solved] Solution: k / n C / 4+3*n k_1 / 1 A / 3 Resulting cost 4+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 33 Simplified the guard: 33: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-2*C*k_1, [ k_1>0 && C>=1-C+A-C*k_1 && -C+A-C*k_1>=1+2*C-A+C*k_1 ], cost: 4+k_1 Solved the limit problem by the following transformations: Created initial limit problem: 2*C-A+C*k_1 (+/+!), 4+k_1 (+), k_1 (+/+!), -3*C+2*A-2*C*k_1 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==3,k_1==-2+n,A==-1+3*n} resulting limit problem: [solved] Solution: C / 3 k_1 / -2+n A / -1+3*n Resulting cost 2+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 34 Simplified the guard: 34: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C+5*A, [ A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A ], cost: 5+k_1 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 35 Simplified the guard: 35: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A, [ k>0 && -k*A+C-A>=1+k*A-C+2*A && k*A-C+2*A>=1-2*k*A+2*C-3*A ], cost: 5+k Solved the limit problem by the following transformations: Created initial limit problem: k (+/+!), 3*k*A-3*C+5*A (+/+!), 5+k (+), -2*k*A+2*C-3*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k==n,C==8+5*n,A==5} resulting limit problem: [solved] Solution: k / n C / 8+5*n A / 5 Resulting cost 5+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 36 Simplified the guard: 36: start0 -> lbl111 : B'=-2*k*A-(k*A-C+A)*k_1+2*C-3*A, D'=3*k*A+2*(k*A-C+A)*k_1-3*C+5*A, [ C-A>=1+A && k>0 && k_1>0 && A>=A+(k*A-C+A)*(-1+k_1) && -k*A+C-A>=1+k*A+(k*A-C+A)*k_1-C+2*A && k*A+(k*A-C+A)*k_1-C+2*A>=1-2*k*A-(k*A-C+A)*k_1+2*C-3*A ], cost: 5+k+k_1 Solved the limit problem by the following transformations: Created initial limit problem: 5+k+k_1 (+), C-2*A (+/+!), k (+/+!), -2*k*A-(k*A-C+A)*k_1+2*C-3*A (+/+!), k_1 (+/+!), 1-(k*A-C+A)*(-1+k_1) (+/+!), 3*k*A+2*(k*A-C+A)*k_1-3*C+5*A (+/+!) [not solved] applying transformation rule (C) using substitution {k_1==1} resulting limit problem: -3*k*A+3*C-4*A (+/+!), 1 (+/+!), 5*k*A-5*C+7*A (+/+!), C-2*A (+/+!), k (+/+!), 6+k (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -3*k*A+3*C-4*A (+/+!), 5*k*A-5*C+7*A (+/+!), C-2*A (+/+!), k (+/+!), 6+k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {k==n,C==11+8*n,A==8} resulting limit problem: [solved] Solution: k / n C / 11+8*n k_1 / 1 A / 8 Resulting cost 6+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 37 Simplified the guard: 37: start0 -> lbl111 : B'=2*C-A, D'=-3*C-(2*C-A)*k_1+2*A, [ C>=1-C+A && -C+A>=1+2*C-A && -3*C+2*A>=1+2*C-A && k_1>0 && -3*C-(2*C-A)*(-1+k_1)+2*A>=1+2*C-A ], cost: 4+k_1 Solved the limit problem by the following transformations: Created initial limit problem: 4+k_1 (+), 2*C-A (+/+!), -3*C+2*A (+/+!), k_1 (+/+!), -5*C-(2*C-A)*(-1+k_1)+3*A (+/+!), -5*C+3*A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==1+2*n,k_1==n,A==1+4*n} resulting limit problem: [solved] Solution: C / 1+2*n k_1 / n A / 1+4*n Resulting cost 4+n has complexity: Poly(n^1) Computing asymptotic complexity for rule 38 Simplified the guard: 38: start0 -> lbl111 : B'=2*C-A+C*k_1, D'=-3*C+2*A-(2*C-A+C*k_1)*k_1-2*C*k_1, [ k_1>0 && C>=1-C+A-C*k_1 && -3*C+2*A-2*C*k_1>=1+2*C-A+C*k_1 && -3*C-(2*C-A+C*k_1)*(-1+k_1)+2*A-2*C*k_1>=1+2*C-A+C*k_1 && A>=-C-(2*C-A+C*k_1)*(-1+k_1)+A-C*k_1 ], cost: 4+2*k_1 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 39 Simplified the guard: 39: start0 -> lbl111 : B'=k_1*(C-A)+2*C-3*A, D'=-2*k_1*(C-A)-3*C-(k_1*(C-A)+2*C-3*A)*k_1+5*A, [ k_1>0 && A>=A-(-1+k_1)*(C-A) && C-A>=1-k_1*(C-A)-C+2*A && -k_1*(C-A)-C+2*A>=1+k_1*(C-A)+2*C-3*A && -2*k_1*(C-A)-3*C+5*A>=1+k_1*(C-A)+2*C-3*A && -2*k_1*(C-A)-3*C-(-1+k_1)*(k_1*(C-A)+2*C-3*A)+5*A>=1+k_1*(C-A)+2*C-3*A ], cost: 5+2*k_1 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 40 Simplified the guard: 40: start0 -> lbl111 : B'=-2*k*A+2*C-3*A, D'=3*k*A-3*C+5*A+(2*k*A-2*C+3*A)*k_1, [ k>0 && -k*A+C-A>=1+k*A-C+2*A && k*A-C+2*A>=1-2*k*A+2*C-3*A && 3*k*A-3*C+5*A>=1-2*k*A+2*C-3*A && k_1>0 && 3*k*A+(2*k*A-2*C+3*A)*(-1+k_1)-3*C+5*A>=1-2*k*A+2*C-3*A ], cost: 5+k+k_1 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: [ C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)