details

property	value
status	complete
benchmark	direct_n_log_n.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	misc

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.2 seconds
cpu usage	4.29357
user time	4.03941
system time	0.254159
max virtual memory	1.8523716E7
max residence set size	217616.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

4.21/2.17 WORST_CASE(?, O(n^1)) 4.21/2.18 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.21/2.18 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.21/2.18 4.21/2.18 4.21/2.18 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(3, 3 + 4 * Arg_0) + nat(8 * Arg_0)). 4.21/2.18 4.21/2.18 (0) CpxIntTrs 4.21/2.18 (1) Koat2 Proof [FINISHED, 133 ms] 4.21/2.18 (2) BOUNDS(1, max(3, 3 + 4 * Arg_0) + nat(8 * Arg_0)) 4.21/2.18 4.21/2.18 4.21/2.18 ---------------------------------------- 4.21/2.18 4.21/2.18 (0) 4.21/2.18 Obligation: 4.21/2.18 Complexity Int TRS consisting of the following rules: 4.21/2.18 start(A) -> Com_1(a(A)) :|: A >= 1 4.21/2.18 start(A) -> Com_1(a(A)) :|: A >= 2 4.21/2.18 start(A) -> Com_1(a(A)) :|: A >= 4 4.21/2.18 a(A) -> Com_1(a(B)) :|: 2 * B >= 2 && A >= 2 * B && A <= 2 * B 4.21/2.18 a(A) -> Com_1(a(B)) :|: 2 * B >= 1 && A >= 2 * B + 1 && A <= 2 * B + 1 4.21/2.18 4.21/2.18 The start-symbols are:[start_1] 4.21/2.18 4.21/2.18 4.21/2.18 ---------------------------------------- 4.21/2.18 4.21/2.18 (1) Koat2 Proof (FINISHED) 4.21/2.18 YES( ?, 3+2*(2*max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])) {O(n)}) 4.21/2.18 4.21/2.18 4.21/2.18 4.21/2.18 Initial Complexity Problem: 4.21/2.18 4.21/2.18 Start: start 4.21/2.18 4.21/2.18 Program_Vars: Arg_0 4.21/2.18 4.21/2.18 Temp_Vars: B 4.21/2.18 4.21/2.18 Locations: a, start 4.21/2.18 4.21/2.18 Transitions: 4.21/2.18 4.21/2.18 a(Arg_0) -> a(B):|:2 <= (2)*B && Arg_0 <= (2)*B && (2)*B <= Arg_0 4.21/2.18 4.21/2.18 a(Arg_0) -> a(B):|:1 <= (2)*B && Arg_0 <= (2)*B+1 && (2)*B+1 <= Arg_0 4.21/2.18 4.21/2.18 start(Arg_0) -> a(Arg_0):|:1 <= Arg_0 4.21/2.18 4.21/2.18 start(Arg_0) -> a(Arg_0):|:2 <= Arg_0 4.21/2.18 4.21/2.18 start(Arg_0) -> a(Arg_0):|:4 <= Arg_0 4.21/2.18 4.21/2.18 4.21/2.18 4.21/2.18 Timebounds: 4.21/2.18 4.21/2.18 Overall timebound: 3+2*(2*max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])) {O(n)} 4.21/2.18 4.21/2.18 3: a->a: 2*max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0]) {O(n)} 4.21/2.18 4.21/2.18 4: a->a: 2*max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0]) {O(n)} 4.21/2.18 4.21/2.18 0: start->a: 1 {O(1)} 4.21/2.18 4.21/2.18 1: start->a: 1 {O(1)} 4.21/2.18 4.21/2.18 2: start->a: 1 {O(1)} 4.21/2.18 4.21/2.18 4.21/2.18 4.21/2.18 Costbounds: 4.21/2.18 4.21/2.18 Overall costbound: 3+2*(2*max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])) {O(n)} 4.21/2.18 4.21/2.18 3: a->a: 2*max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0]) {O(n)} 4.21/2.18 4.21/2.18 4: a->a: 2*max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0])+max([0, Arg_0]) {O(n)} 4.21/2.18 4.21/2.18 0: start->a: 1 {O(1)} 4.21/2.18 4.21/2.18 1: start->a: 1 {O(1)} 4.21/2.18 4.21/2.18 2: start->a: 1 {O(1)} 4.21/2.18 4.21/2.18 4.21/2.18 4.21/2.18 Sizebounds: 4.21/2.18 4.21/2.18 `Lower: 4.21/2.18 4.21/2.18 3: a->a, Arg_0: 1 {O(1)} 4.21/2.18 4.21/2.18 4: a->a, Arg_0: 1 {O(1)} 4.21/2.18 4.21/2.18 0: start->a, Arg_0: 1 {O(1)} 4.21/2.18 4.21/2.18 1: start->a, Arg_0: 2 {O(1)} popout

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all output return to Complexity_ITS 2019-03-21 04.46