details

property	value
status	complete
benchmark	rsd.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.75838184357 seconds
cpu usage	12.070741371
max memory	4.7489024E8

stage attributes

key	value
output-size	27002
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(6, 6 + 16 * Arg_0) + 4 * nat(2 * Arg_0) * max(2, 2 * Arg_0) + nat(1 + 2 * Arg_0)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 5905 ms] (2) BOUNDS(1, max(6, 6 + 16 * Arg_0) + 4 * nat(2 * Arg_0) * max(2, 2 * Arg_0) + nat(1 + 2 * Arg_0)) (3) Loat Proof [FINISHED, 1010 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H start(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, D, 2 * D, F, 2 * D - 1, H)) :|: A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H start(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, 2 * D, C, D, 2 * D - 1, F, 2 * D - 1, H)) :|: A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H lbl82(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: E >= A && 2 * A >= E && D >= A && D <= A && G + 1 >= A && G + 1 <= A lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, D, E, F, G - 1, H)) :|: G >= A && E >= G + 1 && 2 * A >= E && G + 1 >= A && D >= A && D <= A lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, G, C, D, E - 1, F, E - 1, H)) :|: G >= A && E >= G + 1 && 2 * A >= E && G + 1 >= A && D >= A && D <= A lbl121(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= E + 1 && 2 * A >= E + 1 && B >= A && E + 1 >= B && G >= E && G <= E && D >= A && D <= A lbl121(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, D, E, F, G - 1, H)) :|: E >= A && 2 * A >= E + 1 && B >= A && E + 1 >= B && G >= E && G <= E && D >= A && D <= A lbl121(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, G, C, D, E - 1, F, E - 1, H)) :|: E >= A && 2 * A >= E + 1 && B >= A && E + 1 >= B && G >= E && G <= E && D >= A && D <= A start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE The start-symbols are:[start0_8] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 6+2*2*max([0, 2*Arg_0])*max([2, 2*Arg_0])+2*2*max([0, 2*Arg_0])+max([0, 1+2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0]) {O(n^2)}) Initial Complexity Problem: Start: start0 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7 Temp_Vars: Locations: lbl121, lbl82, start, start0, stop Transitions: lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl121(Arg_0,Arg_6,Arg_2,Arg_3,Arg_4-1,Arg_5,Arg_4-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 2+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= 1+Arg_4 && 0 <= 1+Arg_3+Arg_4 && Arg_3 <= 1+Arg_4 && 0 <= 1+Arg_1+Arg_4 && 0 <= 1+Arg_0+Arg_4 && Arg_0 <= 1+Arg_4 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 0 <= Arg_0 && Arg_0 <= Arg_4 && Arg_4+1 <= (2)*Arg_0 && Arg_0 <= Arg_1 && Arg_1 <= Arg_4+1 && Arg_6 <= Arg_4 && Arg_4 <= Arg_6 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 2+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= 1+Arg_4 && 0 <= 1+Arg_3+Arg_4 && Arg_3 <= 1+Arg_4 && 0 <= 1+Arg_1+Arg_4 && 0 <= 1+Arg_0+Arg_4 && Arg_0 <= 1+Arg_4 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 0 <= Arg_0 && Arg_0 <= Arg_4 && Arg_4+1 <= (2)*Arg_0 && Arg_0 <= Arg_1 && Arg_1 <= Arg_4+1 && Arg_6 <= Arg_4 && Arg_4 <= Arg_6 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= 1+Arg_6 && 0 <= 2+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= 1+Arg_4 && 0 <= 1+Arg_3+Arg_4 && Arg_3 <= 1+Arg_4 && 0 <= 1+Arg_1+Arg_4 && 0 <= 1+Arg_0+Arg_4 && Arg_0 <= 1+Arg_4 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 0 <= Arg_0 && Arg_4+1 <= Arg_0 && Arg_4+1 <= (2)*Arg_0 && Arg_0 <= Arg_1 && Arg_1 <= Arg_4+1 && Arg_6 <= Arg_4 && Arg_4 <= Arg_6 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl121(Arg_0,Arg_6,Arg_2,Arg_3,Arg_4-1,Arg_5,Arg_4-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 1+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && Arg_3 <= Arg_4 && 0 <= Arg_0+Arg_4 && Arg_0 <= Arg_4 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_0 && Arg_0 <= Arg_6 && Arg_6+1 <= Arg_4 && Arg_4 <= (2)*Arg_0 && Arg_0 <= Arg_6+1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 1+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && Arg_3 <= Arg_4 && 0 <= Arg_0+Arg_4 && Arg_0 <= Arg_4 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_0 && Arg_0 <= Arg_6 && Arg_6+1 <= Arg_4 && Arg_4 <= (2)*Arg_0 && Arg_0 <= Arg_6+1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= 1+Arg_6 && 0 <= 1+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && Arg_3 <= Arg_4 && 0 <= Arg_0+Arg_4 && Arg_0 <= Arg_4 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_0 && Arg_0 <= Arg_4 && Arg_4 <= (2)*Arg_0 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_6+1 <= Arg_0 && Arg_0 <= Arg_6+1 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl121(Arg_0,(2)*Arg_3,Arg_2,Arg_3,(2)*Arg_3-1,Arg_5,(2)*Arg_3-1,Arg_7):|:Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_4 && Arg_4 <= Arg_5 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_4 <= Arg_5 && Arg_5 <= Arg_4 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1,Arg_2,Arg_3,(2)*Arg_3,Arg_5,(2)*Arg_3-1,Arg_7):|:Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_4 && Arg_4 <= Arg_5 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_4 <= Arg_5 && Arg_5 <= Arg_4 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_4 && Arg_4 <= Arg_5 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0+1 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_4 <= Arg_5 && Arg_5 <= Arg_4 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> start(Arg_0,Arg_2,Arg_2,Arg_0,Arg_5,Arg_5,Arg_7,Arg_7):|: Timebounds: Overall timebound: 6+2*2*max([0, 2*Arg_0])*max([2, 2*Arg_0])+2*2*max([0, 2*Arg_0])+max([0, 1+2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0]) {O(n^2)} 6: lbl121->stop: 1 {O(1)} 7: lbl121->lbl82: max([0, 1+2*Arg_0])+max([0, 2*Arg_0]) {O(n)} 8: lbl121->lbl121: 2*max([0, 2*Arg_0]) {O(n)} 3: lbl82->stop: 1 {O(1)} 4: lbl82->lbl82: 2*2*max([0, 2*Arg_0])*max([2, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0]) {O(n^2)} 5: lbl82->lbl121: 2*max([0, 2*Arg_0]) {O(n)} 0: start->stop: 1 {O(1)} 1: start->lbl82: 1 {O(1)} popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Compl Integ Trans Syste 26843