296.11/290.18 WORST_CASE(Omega(n^1), O(n^1)) 296.11/290.19 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 296.11/290.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 296.11/290.19 296.11/290.19 296.11/290.19 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(2, 1 + Arg_2) + nat(Arg_0)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 + Arg_0, 8) + max(3, 3 * Arg_2) + max(-3 + 3 * Arg_2, 3) + nat(2 * Arg_2)). 296.11/290.19 296.11/290.19 (0) CpxIntTrs 296.11/290.19 (1) Koat2 Proof [FINISHED, 2743 ms] 296.11/290.19 (2) BOUNDS(1, max(2, 1 + Arg_2) + nat(Arg_0) + nat(-1 + Arg_0) + max(8 + Arg_0, 8) + max(3, 3 * Arg_2) + max(-3 + 3 * Arg_2, 3) + nat(2 * Arg_2)) 296.11/290.19 (3) Loat Proof [FINISHED, 288.4 s] 296.11/290.19 (4) BOUNDS(n^1, INF) 296.11/290.19 296.11/290.19 296.11/290.19 ---------------------------------------- 296.11/290.19 296.11/290.19 (0) 296.11/290.19 Obligation: 296.11/290.19 Complexity Int TRS consisting of the following rules: 296.11/290.19 start(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A 296.11/290.19 start(A, B, C, D) -> Com_1(lbl6(A, B, C, D)) :|: A >= 1 && 0 >= C && B >= C && B <= C && D >= A && D <= A 296.11/290.19 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 296.11/290.19 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 296.11/290.19 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 296.11/290.19 lbl6(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: A >= 1 && 0 >= C && D >= A && D <= A && B >= C && B <= C 296.11/290.19 lbl101(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: A >= B && B >= 1 && C >= 2 * B && D >= B && D <= B 296.11/290.19 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 296.11/290.19 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 296.11/290.19 lbl111(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: C >= B && B >= 1 && A >= 2 * B && D >= B && D <= B 296.11/290.19 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 296.11/290.19 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 296.11/290.19 cut(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: A >= B && B >= 1 && C >= B && D >= B && D <= B 296.11/290.19 start0(A, B, C, D) -> Com_1(start(A, C, C, A)) :|: TRUE 296.11/290.19 296.11/290.19 The start-symbols are:[start0_4] 296.11/290.19 296.11/290.19 296.11/290.19 ---------------------------------------- 296.11/290.19 296.11/290.19 (1) Koat2 Proof (FINISHED) 296.11/290.19 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)}) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Initial Complexity Problem: 296.11/290.19 296.11/290.19 Start: start0 296.11/290.19 296.11/290.19 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3 296.11/290.19 296.11/290.19 Temp_Vars: 296.11/290.19 296.11/290.19 Locations: cut, lbl101, lbl111, lbl6, start, start0, stop 296.11/290.19 296.11/290.19 Transitions: 296.11/290.19 296.11/290.19 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_3 296.11/290.19 296.11/290.19 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_3 296.11/290.19 296.11/290.19 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_2 296.11/290.19 296.11/290.19 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_2 296.11/290.19 296.11/290.19 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_3 296.11/290.19 296.11/290.19 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_0 296.11/290.19 296.11/290.19 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_0 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_2 296.11/290.19 296.11/290.19 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_3 296.11/290.19 296.11/290.19 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_3 296.11/290.19 296.11/290.19 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_3 296.11/290.19 296.11/290.19 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_3 296.11/290.19 296.11/290.19 start0(Arg_0,Arg_1,Arg_2,Arg_3) -> start(Arg_0,Arg_2,Arg_2,Arg_0):|: 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Timebounds: 296.11/290.19 296.11/290.19 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)} 296.11/290.19 296.11/290.19 12: cut->stop: 1 {O(1)} 296.11/290.19 296.11/290.19 6: lbl101->cut: 1 {O(1)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101: max([0, -1+Arg_2])+max([0, Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111: max([0, Arg_0])+max([0, Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 9: lbl111->cut: 1 {O(1)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101: max([3, 3*(-1+Arg_2)])+max([3, 3*Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111: max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 5: lbl6->stop: 1 {O(1)} 296.11/290.19 296.11/290.19 0: start->stop: 1 {O(1)} 296.11/290.19 296.11/290.19 1: start->lbl6: 1 {O(1)} 296.11/290.19 296.11/290.19 2: start->cut: 1 {O(1)} 296.11/290.19 296.11/290.19 3: start->lbl101: 1 {O(1)} 296.11/290.19 296.11/290.19 4: start->lbl111: 1 {O(1)} 296.11/290.19 296.11/290.19 13: start0->start: 1 {O(1)} 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Costbounds: 296.11/290.19 296.11/290.19 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)} 296.11/290.19 296.11/290.19 12: cut->stop: 1 {O(1)} 296.11/290.19 296.11/290.19 6: lbl101->cut: 1 {O(1)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101: max([0, -1+Arg_2])+max([0, Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111: max([0, Arg_0])+max([0, Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 9: lbl111->cut: 1 {O(1)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101: max([3, 3*(-1+Arg_2)])+max([3, 3*Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111: max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 5: lbl6->stop: 1 {O(1)} 296.11/290.19 296.11/290.19 0: start->stop: 1 {O(1)} 296.11/290.19 296.11/290.19 1: start->lbl6: 1 {O(1)} 296.11/290.19 296.11/290.19 2: start->cut: 1 {O(1)} 296.11/290.19 296.11/290.19 3: start->lbl101: 1 {O(1)} 296.11/290.19 296.11/290.19 4: start->lbl111: 1 {O(1)} 296.11/290.19 296.11/290.19 13: start0->start: 1 {O(1)} 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Sizebounds: 296.11/290.19 296.11/290.19 `Lower: 296.11/290.19 296.11/290.19 12: cut->stop, Arg_0: 1 {O(1)} 296.11/290.19 296.11/290.19 12: cut->stop, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 12: cut->stop, Arg_2: 1 {O(1)} 296.11/290.19 296.11/290.19 12: cut->stop, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_0: 1 {O(1)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_2: 2 {O(1)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_0: 1 {O(1)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_2: 3 {O(1)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_0: 2 {O(1)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_2: 3 {O(1)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_0: 2 {O(1)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_2: 1 {O(1)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_0: 3 {O(1)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_2: 2 {O(1)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_0: 3 {O(1)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_2: 1 {O(1)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_0: 1 {O(1)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_3: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_0: 1 {O(1)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_0: 1 {O(1)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_2: 1 {O(1)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_0: 1 {O(1)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_2: 2 {O(1)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_0: 2 {O(1)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_1: 1 {O(1)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_2: 1 {O(1)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_3: 1 {O(1)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_3: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 `Upper: 296.11/290.19 296.11/290.19 12: cut->stop, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 12: cut->stop, Arg_1: max([Arg_2, max([Arg_2, max([Arg_2, -1+Arg_2])])]) {O(n)} 296.11/290.19 296.11/290.19 12: cut->stop, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 12: cut->stop, Arg_3: max([Arg_0, max([Arg_0, -1+Arg_0])]) {O(n)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 6: lbl101->cut, Arg_3: max([Arg_0, max([Arg_0, -1+Arg_0])]) {O(n)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_1: max([Arg_2, max([Arg_2, -1+Arg_2])]) {O(n)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 9: lbl111->cut, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 10: lbl111->lbl101, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_1: max([Arg_2, -1+Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 11: lbl111->lbl111, Arg_3: max([Arg_0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_1: 0 {O(1)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_2: 0 {O(1)} 296.11/290.19 296.11/290.19 5: lbl6->stop, Arg_3: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_0: 0 {O(1)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 0: start->stop, Arg_3: 0 {O(1)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_1: 0 {O(1)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_2: 0 {O(1)} 296.11/290.19 296.11/290.19 1: start->lbl6, Arg_3: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 2: start->cut, Arg_3: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_1: -1+Arg_2 {O(n)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 3: start->lbl101, Arg_3: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 4: start->lbl111, Arg_3: -1+Arg_0 {O(n)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_0: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_1: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_2: Arg_2 {O(n)} 296.11/290.19 296.11/290.19 13: start0->start, Arg_3: Arg_0 {O(n)} 296.11/290.19 296.11/290.19 296.11/290.19 ---------------------------------------- 296.11/290.19 296.11/290.19 (2) 296.11/290.19 BOUNDS(1, max(2, 1 + Arg_2) + nat(Arg_0) + nat(-1 + Arg_0) + max(8 + Arg_0, 8) + max(3, 3 * Arg_2) + max(-3 + 3 * Arg_2, 3) + nat(2 * Arg_2)) 296.11/290.19 296.11/290.19 ---------------------------------------- 296.11/290.19 296.11/290.19 (3) Loat Proof (FINISHED) 296.11/290.19 296.11/290.19 296.11/290.19 ### Pre-processing the ITS problem ### 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Initial linear ITS problem 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 0: start -> stop : [ 0>=A && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 1: start -> lbl6 : [ A>=1 && 0>=C && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 2: start -> cut : [ A>=1 && D==A && B==A && C==A ], cost: 1 296.11/290.19 296.11/290.19 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 5: lbl6 -> stop : [ A>=1 && 0>=C && D==A && B==C ], cost: 1 296.11/290.19 296.11/290.19 6: lbl101 -> cut : [ A>=B && B>=1 && C>=2*B && D==B ], cost: 1 296.11/290.19 296.11/290.19 7: lbl101 -> lbl101 : B'=-D+B, [ B>=1+D && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 9: lbl111 -> cut : [ C>=B && B>=1 && A>=2*B && D==B ], cost: 1 296.11/290.19 296.11/290.19 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 11: lbl111 -> lbl111 : D'=D-B, [ D>=1+B && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 12: cut -> stop : [ A>=B && B>=1 && C>=B && D==B ], cost: 1 296.11/290.19 296.11/290.19 13: start0 -> start : B'=C, D'=A, [], cost: 1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Removed unreachable and leaf rules: 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 7: lbl101 -> lbl101 : B'=-D+B, [ B>=1+D && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 11: lbl111 -> lbl111 : D'=D-B, [ D>=1+B && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 13: start0 -> start : B'=C, D'=A, [], cost: 1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 ### Simplification by acceleration and chaining ### 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Accelerating simple loops of location 2. 296.11/290.19 296.11/290.19 Accelerating the following rules: 296.11/290.19 296.11/290.19 7: lbl101 -> lbl101 : B'=-D+B, [ B>=1+D && A>=D && B>=1 && D>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Accelerated rule 7 with backward acceleration, yielding the new rule 14. 296.11/290.19 296.11/290.19 Removing the simple loops: 7. 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Accelerating simple loops of location 3. 296.11/290.19 296.11/290.19 Accelerating the following rules: 296.11/290.19 296.11/290.19 11: lbl111 -> lbl111 : D'=D-B, [ D>=1+B && C>=B && B>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Accelerated rule 11 with backward acceleration, yielding the new rule 15. 296.11/290.19 296.11/290.19 Removing the simple loops: 11. 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Accelerated all simple loops using metering functions (where possible): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 13: start0 -> start : B'=C, D'=A, [], cost: 1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Chained accelerated rules (with incoming rules): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 3: start -> lbl101 : B'=-D+B, [ A>=1 && C>=1+A && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 4: start -> lbl111 : D'=D-B, [ A>=1+C && C>=1 && B==C && D==A ], cost: 1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 13: start0 -> start : B'=C, D'=A, [], cost: 1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Eliminated locations (on tree-shaped paths): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 8: lbl101 -> lbl111 : D'=D-B, [ D>=1+B && A>=D && B>=1 && C>=D+B ], cost: 1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 10: lbl111 -> lbl101 : B'=-D+B, [ B>=1+D && C>=B && B>=1 && D>=1 && A>=D+B ], cost: 1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 20: start0 -> lbl101 : B'=C-A, D'=A, [ A>=1 && C>=1+A ], cost: 2 296.11/290.19 296.11/290.19 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Eliminated location lbl101 (as a last resort): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 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: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 28: start0 -> lbl111 : B'=C-A, D'=-C+2*A, [ A>=1 && C>=1+A && A>=1+C-A ], cost: 3 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Applied pruning (of leafs and parallel rules): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 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: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Accelerating simple loops of location 3. 296.11/290.19 296.11/290.19 Accelerating the following rules: 296.11/290.19 296.11/290.19 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: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Found no metering function for rule 24. 296.11/290.19 296.11/290.19 Found no metering function for rule 25 (rule is too complicated). 296.11/290.19 296.11/290.19 Found no metering function for rule 26 (rule is too complicated). 296.11/290.19 296.11/290.19 Found no metering function for rule 27 (rule is too complicated). 296.11/290.19 296.11/290.19 Removing the simple loops:. 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Accelerated all simple loops using metering functions (where possible): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 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: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Chained accelerated rules (with incoming rules): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 21: start0 -> lbl111 : B'=C, D'=-C+A, [ A>=1+C && C>=1 ], cost: 2 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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: 4 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Removed unreachable locations (and leaf rules with constant cost): 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 ### Computing asymptotic complexity ### 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Fully simplified ITS problem 296.11/290.19 296.11/290.19 Start location: start0 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 23 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 C (+/+!), -2*C+A (+/+!), k_1 (+/+!), 2+k_1 (+), -2*C-C*(-1+k_1)+A (+/+!) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {C==1,k_1==n,A==2*n} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 C (+/+!), -2*C+A (+/+!), k_1 (+/+!), 2+k_1 (+), -2*C-C*(-1+k_1)+A (+/+!) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {C==1} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 1 (+/+!), -1-k_1+A (+/+!), k_1 (+/+!), -2+A (+/+!), 2+k_1 (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (B), deleting 1 (+/+!) 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 -1-k_1+A (+/+!), k_1 (+/+!), -2+A (+/+!), 2+k_1 (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k_1==n,A==3+n} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solution: 296.11/290.19 296.11/290.19 C / 1 296.11/290.19 296.11/290.19 k_1 / n 296.11/290.19 296.11/290.19 A / 2*n 296.11/290.19 296.11/290.19 Resulting cost 2+n has complexity: Poly(n^1) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Found new complexity Poly(n^1). 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 29 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 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] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {C==4+2*n,k_1==n,A==3+2*n} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 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] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {C==1+A} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 1 (+/+!), -1+A (+/+!), -1-k_1+A (+/+!), k_1 (+/+!), 3+k_1 (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (B), deleting 1 (+/+!) 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 -1+A (+/+!), -1-k_1+A (+/+!), k_1 (+/+!), 3+k_1 (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k_1==n,A==2+n} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solution: 296.11/290.19 296.11/290.19 C / 4+2*n 296.11/290.19 296.11/290.19 k_1 / n 296.11/290.19 296.11/290.19 A / 3+2*n 296.11/290.19 296.11/290.19 Resulting cost 3+n has complexity: Poly(n^1) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 30 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 C-2*A-(-1+k)*A (+/+!), k (+/+!), k*A-C+2*A (+/+!), 3+k (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k==-1+n,C==1+2*n,A==2} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solution: 296.11/290.19 296.11/290.19 k / -1+n 296.11/290.19 296.11/290.19 C / 1+2*n 296.11/290.19 296.11/290.19 A / 2 296.11/290.19 296.11/290.19 Resulting cost 2+n has complexity: Poly(n^1) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 31 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 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] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k_1==1} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 1 (+/+!), C-2*A-(-1+k)*A (+/+!), k (+/+!), k*A-C+2*A (+/+!), 2*k*A-2*C+3*A (+/+!), 4+k (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (B), deleting 1 (+/+!) 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 C-2*A-(-1+k)*A (+/+!), k (+/+!), k*A-C+2*A (+/+!), 2*k*A-2*C+3*A (+/+!), 4+k (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k==n,C==4+3*n,A==3} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 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] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k==1} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 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] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (B), deleting 1 (+/+!) 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 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] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {C==3+6*n,k_1==-1+n,A==1+3*n} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solution: 296.11/290.19 296.11/290.19 k / n 296.11/290.19 296.11/290.19 C / 4+3*n 296.11/290.19 296.11/290.19 k_1 / 1 296.11/290.19 296.11/290.19 A / 3 296.11/290.19 296.11/290.19 Resulting cost 4+n has complexity: Poly(n^1) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 33 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 2*C-A+C*k_1 (+/+!), 4+k_1 (+), k_1 (+/+!), -3*C+2*A-2*C*k_1 (+/+!) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {C==3,k_1==-2+n,A==-1+3*n} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solution: 296.11/290.19 296.11/290.19 C / 3 296.11/290.19 296.11/290.19 k_1 / -2+n 296.11/290.19 296.11/290.19 A / -1+3*n 296.11/290.19 296.11/290.19 Resulting cost 2+n has complexity: Poly(n^1) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 34 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 Could not solve the limit problem. 296.11/290.19 296.11/290.19 Resulting cost 0 has complexity: Unknown 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 35 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 k (+/+!), 3*k*A-3*C+5*A (+/+!), 5+k (+), -2*k*A+2*C-3*A (+/+!) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k==n,C==8+5*n,A==5} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Solution: 296.11/290.19 296.11/290.19 k / n 296.11/290.19 296.11/290.19 C / 8+5*n 296.11/290.19 296.11/290.19 A / 5 296.11/290.19 296.11/290.19 Resulting cost 5+n has complexity: Poly(n^1) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Computing asymptotic complexity for rule 36 296.11/290.19 296.11/290.19 Simplified the guard: 296.11/290.19 296.11/290.19 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_1 296.11/290.19 296.11/290.19 Solved the limit problem by the following transformations: 296.11/290.19 296.11/290.19 Created initial limit problem: 296.11/290.19 296.11/290.19 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] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k_1==1} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 -3*k*A+3*C-4*A (+/+!), 1 (+/+!), 5*k*A-5*C+7*A (+/+!), C-2*A (+/+!), k (+/+!), 6+k (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (B), deleting 1 (+/+!) 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.19 296.11/290.19 -3*k*A+3*C-4*A (+/+!), 5*k*A-5*C+7*A (+/+!), C-2*A (+/+!), k (+/+!), 6+k (+) [not solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 removing all constraints (solved by SMT) 296.11/290.19 296.11/290.19 resulting limit problem: [solved] 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 applying transformation rule (C) using substitution {k==n,C==11+8*n,A==8} 296.11/290.19 296.11/290.19 resulting limit problem: 296.11/290.20 296.11/290.20 [solved] 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 Solution: 296.11/290.20 296.11/290.20 k / n 296.11/290.20 296.11/290.20 C / 11+8*n 296.11/290.20 296.11/290.20 k_1 / 1 296.11/290.20 296.11/290.20 A / 8 296.11/290.20 296.11/290.20 Resulting cost 6+n has complexity: Poly(n^1) 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 Computing asymptotic complexity for rule 37 296.11/290.20 296.11/290.20 Simplified the guard: 296.11/290.20 296.11/290.20 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_1 296.11/290.20 296.11/290.20 Solved the limit problem by the following transformations: 296.11/290.20 296.11/290.20 Created initial limit problem: 296.11/290.20 296.11/290.20 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] 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 removing all constraints (solved by SMT) 296.11/290.20 296.11/290.20 resulting limit problem: [solved] 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 applying transformation rule (C) using substitution {C==4+2*n,k_1==1+n,A==7+4*n} 296.11/290.20 296.11/290.20 resulting limit problem: 296.11/290.20 296.11/290.20 [solved] 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 Solution: 296.11/290.20 296.11/290.20 C / 4+2*n 296.11/290.20 296.11/290.20 k_1 / 1+n 296.11/290.20 296.11/290.20 A / 7+4*n 296.11/290.20 296.11/290.20 Resulting cost 5+n has complexity: Poly(n^1) 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 Computing asymptotic complexity for rule 38 296.11/290.20 296.11/290.20 Simplified the guard: 296.11/290.20 296.11/290.20 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_1 296.11/290.20 296.11/290.20 Could not solve the limit problem. 296.11/290.20 296.11/290.20 Resulting cost 0 has complexity: Unknown 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 Computing asymptotic complexity for rule 39 296.11/290.20 296.11/290.20 Simplified the guard: 296.11/290.20 296.11/290.20 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_1 296.11/290.20 296.11/290.20 Could not solve the limit problem. 296.11/290.20 296.11/290.20 Resulting cost 0 has complexity: Unknown 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 Computing asymptotic complexity for rule 40 296.11/290.20 296.11/290.20 Simplified the guard: 296.11/290.20 296.11/290.20 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_1 296.11/290.20 296.11/290.20 Could not solve the limit problem. 296.11/290.20 296.11/290.20 Resulting cost 0 has complexity: Unknown 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 Obtained the following overall complexity (w.r.t. the length of the input n): 296.11/290.20 296.11/290.20 Complexity: Poly(n^1) 296.11/290.20 296.11/290.20 Cpx degree: 1 296.11/290.20 296.11/290.20 Solved cost: 2+n 296.11/290.20 296.11/290.20 Rule cost: 2+k_1 296.11/290.20 296.11/290.20 Rule guard: [ C>=1 && -C+A>=1+C && k_1>0 && -C-C*(-1+k_1)+A>=1+C ] 296.11/290.20 296.11/290.20 296.11/290.20 296.11/290.20 WORST_CASE(Omega(n^1),?) 296.11/290.20 296.11/290.20 296.11/290.20 ---------------------------------------- 296.11/290.20 296.11/290.20 (4) 296.11/290.20 BOUNDS(n^1, INF) 296.11/290.20 EOF