details

property	value
status	complete
benchmark	p-55.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.38678312302 seconds
cpu usage	4.954887542
max memory	2.9390848E8

stage attributes

key	value
output-size	8500
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(-99 * Arg_1) + max(2, 2 + -1 * Arg_1) + nat(Arg_1 * Arg_0 + -99 * Arg_1) + nat(-1 * Arg_0)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 535 ms] (2) BOUNDS(1, nat(-99 * Arg_1) + max(2, 2 + -1 * Arg_1) + nat(Arg_1 * Arg_0 + -99 * Arg_1) + nat(-1 * Arg_0)) (3) Loat Proof [FINISHED, 729 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f300(A, B, C) -> Com_1(f300(-(99) + A, 0, C)) :|: 0 >= A + 1 && B + 1 >= 0 && B + 1 <= 0 f300(A, B, C) -> Com_1(f300(1 + A, 1 + B, C)) :|: 0 >= A + 1 && B >= 0 f300(A, B, C) -> Com_1(f300(1 + A, 1 + B, C)) :|: 0 >= A + 1 && 0 >= 2 + B f300(A, B, C) -> Com_1(f1(A, B, D)) :|: A >= 0 f2(A, B, C) -> Com_1(f300(A, B, C)) :|: TRUE The start-symbols are:[f2_3] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, max([0, -99*Arg_1])+max([2, 2-Arg_1])+max([0, -(Arg_1)*(99-Arg_0)])+max([0, -(Arg_0)]) {O(n^2)}) Initial Complexity Problem: Start: f2 Program_Vars: Arg_0, Arg_1, Arg_2 Temp_Vars: D Locations: f1, f2, f300 Transitions: f2(Arg_0,Arg_1,Arg_2) -> f300(Arg_0,Arg_1,Arg_2):|: f300(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,D):|:0 <= Arg_0 f300(Arg_0,Arg_1,Arg_2) -> f300(-99+Arg_0,0,Arg_2):|:Arg_0+1 <= 0 && Arg_1+1 <= 0 && 0 <= 1+Arg_1 f300(Arg_0,Arg_1,Arg_2) -> f300(1+Arg_0,1+Arg_1,Arg_2):|:Arg_0+1 <= 0 && 0 <= Arg_1 f300(Arg_0,Arg_1,Arg_2) -> f300(1+Arg_0,1+Arg_1,Arg_2):|:Arg_0+1 <= 0 && 2+Arg_1 <= 0 Timebounds: Overall timebound: max([0, -99*Arg_1])+max([2, 2-Arg_1])+max([0, -(Arg_1)*(99-Arg_0)])+max([0, -(Arg_0)]) {O(n^2)} 4: f2->f300: 1 {O(1)} 0: f300->f300: max([0, -(Arg_1)]) {O(n)} 1: f300->f300: max([0, -(Arg_1)*(99-Arg_0)])+max([0, -(Arg_0)]) {O(n^2)} 2: f300->f300: max([0, -99*Arg_1]) {O(n)} 3: f300->f1: 1 {O(1)} Costbounds: Overall costbound: max([0, -99*Arg_1])+max([2, 2-Arg_1])+max([0, -(Arg_1)*(99-Arg_0)])+max([0, -(Arg_0)]) {O(n^2)} 4: f2->f300: 1 {O(1)} 0: f300->f300: max([0, -(Arg_1)]) {O(n)} 1: f300->f300: max([0, -(Arg_1)*(99-Arg_0)])+max([0, -(Arg_0)]) {O(n^2)} 2: f300->f300: max([0, -99*Arg_1]) {O(n)} 3: f300->f1: 1 {O(1)} Sizebounds: `Lower: popout

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actions

all output return to Compl Integ Trans Syste 26843