details

property	value
status	complete
benchmark	practical1.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	CAV02

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.54057407379 seconds
cpu usage	4.380783557
max memory	2.56458752E8

stage attributes

key	value
output-size	7336
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, max(1, 3 + 2 * Arg_0) + nat(3 * Arg_0) + nat(Arg_0 * max(-3, 3 * Arg_0) + max(-3, 3 * Arg_0))). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 221 ms] (2) BOUNDS(1, max(1, 3 + 2 * Arg_0) + nat(3 * Arg_0) + nat(Arg_0 * max(-3, 3 * Arg_0) + max(-3, 3 * Arg_0))) (3) Loat Proof [FINISHED, 435 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval1(A, B) -> Com_1(eval2(A, 0)) :|: A >= 0 eval2(A, B) -> Com_1(eval2(A, B + 1)) :|: A >= 1 + B eval2(A, B) -> Com_1(eval1(A - 1, B)) :|: B >= A start(A, B) -> Com_1(eval1(A, B)) :|: TRUE The start-symbols are:[start_2] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 1+2*max([0, 1+Arg_0])+max([0, 3*Arg_0])+max([0, (1+Arg_0)*max([-3, 3*Arg_0])]) {O(n^2)}) Initial Complexity Problem: Start: start Program_Vars: Arg_0, Arg_1 Temp_Vars: Locations: eval1, eval2, start Transitions: eval1(Arg_0,Arg_1) -> eval2(Arg_0,0):|:0 <= Arg_0 eval2(Arg_0,Arg_1) -> eval1(Arg_0-1,Arg_1):|:Arg_1 <= Arg_0 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 && Arg_0 <= Arg_1 eval2(Arg_0,Arg_1) -> eval2(Arg_0,Arg_1+1):|:Arg_1 <= Arg_0 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 && 1+Arg_1 <= Arg_0 start(Arg_0,Arg_1) -> eval1(Arg_0,Arg_1):|: Timebounds: Overall timebound: 1+2*max([0, 1+Arg_0])+max([0, 3*Arg_0])+max([0, (1+Arg_0)*max([-3, 3*Arg_0])]) {O(n^2)} 0: eval1->eval2: max([0, 1+Arg_0]) {O(n)} 1: eval2->eval2: max([0, 3*Arg_0])+max([0, (1+Arg_0)*max([-3, 3*Arg_0])]) {O(n^2)} 2: eval2->eval1: max([0, 1+Arg_0]) {O(n)} 3: start->eval1: 1 {O(1)} Costbounds: Overall costbound: 1+2*max([0, 1+Arg_0])+max([0, 3*Arg_0])+max([0, (1+Arg_0)*max([-3, 3*Arg_0])]) {O(n^2)} 0: eval1->eval2: max([0, 1+Arg_0]) {O(n)} 1: eval2->eval2: max([0, 3*Arg_0])+max([0, (1+Arg_0)*max([-3, 3*Arg_0])]) {O(n^2)} 2: eval2->eval1: max([0, 1+Arg_0]) {O(n)} 3: start->eval1: 1 {O(1)} Sizebounds: `Lower: 0: eval1->eval2, Arg_0: 0 {O(1)} 0: eval1->eval2, Arg_1: 0 {O(1)} 1: eval2->eval2, Arg_0: 1 {O(1)} popout

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actions

all output return to Compl Integ Trans Syste 26843