details

property	value
status	complete
benchmark	complete3.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	VMCAI04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.15024 seconds
cpu usage	4.36605
user time	4.12103
system time	0.245019
max virtual memory	1.8522764E7
max residence set size	217872.0

stage attributes

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

output

4.27/2.11 WORST_CASE(Omega(n^2), O(n^2)) 4.27/2.11 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.27/2.11 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.27/2.11 4.27/2.11 4.27/2.11 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, max(1, 3 + 2 * Arg_0) + nat(3 * Arg_0) +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 * Arg_0, -3) + max(3 * Arg_0, -3))). 4.27/2.11 4.27/2.11 (0) CpxIntTrs 4.27/2.11 (1) Koat2 Proof [FINISHED, 249 ms] 4.27/2.11 (2) BOUNDS(1, max(1, 3 + 2 * Arg_0) + nat(3 * Arg_0) + nat(Arg_0 * max(3 * Arg_0, -3) + max(3 * Arg_0, -3))) 4.27/2.11 (3) Loat Proof [FINISHED, 416 ms] 4.27/2.11 (4) BOUNDS(n^2, INF) 4.27/2.11 4.27/2.11 4.27/2.11 ---------------------------------------- 4.27/2.11 4.27/2.11 (0) 4.27/2.11 Obligation: 4.27/2.11 Complexity Int TRS consisting of the following rules: 4.27/2.11 eval1(A, B) -> Com_1(eval2(A, 0)) :|: A >= 0 4.27/2.11 eval2(A, B) -> Com_1(eval2(A, B + 1)) :|: A >= 1 + B 4.27/2.11 eval2(A, B) -> Com_1(eval1(A - 1, B)) :|: B >= A 4.27/2.11 start(A, B) -> Com_1(eval1(A, B)) :|: TRUE 4.27/2.11 4.27/2.11 The start-symbols are:[start_2] 4.27/2.11 4.27/2.11 4.27/2.11 ---------------------------------------- 4.27/2.11 4.27/2.11 (1) Koat2 Proof (FINISHED) 4.27/2.11 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)}) 4.27/2.11 4.27/2.11 4.27/2.11 4.27/2.11 Initial Complexity Problem: 4.27/2.11 4.27/2.11 Start: start 4.27/2.11 4.27/2.11 Program_Vars: Arg_0, Arg_1 4.27/2.11 4.27/2.11 Temp_Vars: 4.27/2.11 4.27/2.11 Locations: eval1, eval2, start 4.27/2.11 4.27/2.11 Transitions: 4.27/2.11 4.27/2.11 eval1(Arg_0,Arg_1) -> eval2(Arg_0,0):|:0 <= Arg_0 4.27/2.11 4.27/2.11 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 4.27/2.11 4.27/2.11 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 4.27/2.11 4.27/2.11 start(Arg_0,Arg_1) -> eval1(Arg_0,Arg_1):|: 4.27/2.11 4.27/2.11 4.27/2.11 4.27/2.11 Timebounds: 4.27/2.11 4.27/2.11 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)} 4.27/2.11 4.27/2.11 0: eval1->eval2: max([0, 1+Arg_0]) {O(n)} 4.27/2.11 4.27/2.11 1: eval2->eval2: max([0, 3*Arg_0])+max([0, (1+Arg_0)*max([-3, 3*Arg_0])]) {O(n^2)} 4.27/2.11 4.27/2.11 2: eval2->eval1: max([0, 1+Arg_0]) {O(n)} 4.27/2.11 4.27/2.11 3: start->eval1: 1 {O(1)} 4.27/2.11 4.27/2.11 4.27/2.11 4.27/2.11 Costbounds: 4.27/2.11 4.27/2.11 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)} 4.27/2.11 4.27/2.11 0: eval1->eval2: max([0, 1+Arg_0]) {O(n)} 4.27/2.11 4.27/2.11 1: eval2->eval2: max([0, 3*Arg_0])+max([0, (1+Arg_0)*max([-3, 3*Arg_0])]) {O(n^2)} 4.27/2.11 4.27/2.11 2: eval2->eval1: max([0, 1+Arg_0]) {O(n)} 4.27/2.11 4.27/2.11 3: start->eval1: 1 {O(1)} 4.27/2.11 4.27/2.11 4.27/2.11 4.27/2.11 Sizebounds: 4.27/2.11 4.27/2.11 `Lower: 4.27/2.11 4.27/2.11 0: eval1->eval2, Arg_0: 0 {O(1)} 4.27/2.11 4.27/2.11 0: eval1->eval2, Arg_1: 0 {O(1)} 4.27/2.11 4.27/2.11 1: eval2->eval2, Arg_0: 1 {O(1)} 4.27/2.11 4.27/2.11 1: eval2->eval2, Arg_1: 1 {O(1)} 4.27/2.11 4.27/2.11 2: eval2->eval1, Arg_0: -1 {O(1)} 4.27/2.11 4.27/2.11 2: eval2->eval1, Arg_1: 0 {O(1)} 4.27/2.11 popout

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all output return to Complexity_ITS 2019-03-21 04.46