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Complexity_ITS 2019-03-21 04.46 pair #429990716
details
property
value
status
complete
benchmark
p-4.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.00549 seconds
cpu usage
4.3554
user time
4.1189
system time
0.236498
max virtual memory
3.6523916E7
max residence set size
220288.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
4.13/1.98 WORST_CASE(Omega(n^1), O(n^2)) 4.13/1.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.13/1.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.13/1.98 4.13/1.98 4.13/1.98 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(1, 1 + Arg_1 + -1 * Arg_2) + nat(Arg_0 + -1 * Arg_1) + nat(Arg_0 * Arg_1 + -1 * Arg_0 * Arg_2 + Arg_0 * nat(Arg_0 + -1 * Arg_1) + Arg_1 * Arg_2 + -1 * Arg_1 * nat(Arg_0 + -1 * Arg_1) + -1 * Arg_1^2)). 4.13/1.98 4.13/1.98 (0) CpxIntTrs 4.13/1.98 (1) Koat2 Proof [FINISHED, 201 ms] 4.13/1.98 (2) BOUNDS(1, max(1, 1 + Arg_1 + -1 * Arg_2) + nat(Arg_0 + -1 * Arg_1) + nat(Arg_0 * Arg_1 + -1 * Arg_0 * Arg_2 + Arg_0 * nat(Arg_0 + -1 * Arg_1) + Arg_1 * Arg_2 + -1 * Arg_1 * nat(Arg_0 + -1 * Arg_1) + -1 * Arg_1^2)) 4.13/1.98 (3) Loat Proof [FINISHED, 314 ms] 4.13/1.98 (4) BOUNDS(n^1, INF) 4.13/1.98 4.13/1.98 4.13/1.98 ---------------------------------------- 4.13/1.98 4.13/1.98 (0) 4.13/1.98 Obligation: 4.13/1.98 Complexity Int TRS consisting of the following rules: 4.13/1.98 f1(A, B, C) -> Com_1(f1(A, B + 1, C)) :|: A >= B + 1 4.13/1.98 f3(A, B, C) -> Com_1(f1(A, B, C)) :|: B >= C + 1 4.13/1.98 f1(A, B, C) -> Com_1(f1(A, B, C + 1)) :|: B >= C + 2 && B >= A 4.13/1.99 4.13/1.99 The start-symbols are:[f3_3] 4.13/1.99 4.13/1.99 4.13/1.99 ---------------------------------------- 4.13/1.99 4.13/1.99 (1) Koat2 Proof (FINISHED) 4.13/1.99 YES( ?, 1+max([0, Arg_1-Arg_2])+max([0, (Arg_0-Arg_1)*(Arg_1-Arg_2+max([0, Arg_0-Arg_1]))])+max([0, Arg_0-Arg_1]) {O(n^2)}) 4.13/1.99 4.13/1.99 4.13/1.99 4.13/1.99 Initial Complexity Problem: 4.13/1.99 4.13/1.99 Start: f3 4.13/1.99 4.13/1.99 Program_Vars: Arg_0, Arg_1, Arg_2 4.13/1.99 4.13/1.99 Temp_Vars: 4.13/1.99 4.13/1.99 Locations: f1, f3 4.13/1.99 4.13/1.99 Transitions: 4.13/1.99 4.13/1.99 f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2 <= Arg_1 && Arg_1+1 <= Arg_0 4.13/1.99 4.13/1.99 f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2 <= Arg_1 && Arg_2+2 <= Arg_1 && Arg_0 <= Arg_1 4.13/1.99 4.13/1.99 f3(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,Arg_2):|:Arg_2+1 <= Arg_1 4.13/1.99 4.13/1.99 4.13/1.99 4.13/1.99 Timebounds: 4.13/1.99 4.13/1.99 Overall timebound: 1+max([0, Arg_1-Arg_2])+max([0, (Arg_0-Arg_1)*(Arg_1-Arg_2+max([0, Arg_0-Arg_1]))])+max([0, Arg_0-Arg_1]) {O(n^2)} 4.13/1.99 4.13/1.99 0: f1->f1: max([0, Arg_0-Arg_1]) {O(n)} 4.13/1.99 4.13/1.99 2: f1->f1: max([0, Arg_1-Arg_2])+max([0, (Arg_0-Arg_1)*(Arg_1-Arg_2+max([0, Arg_0-Arg_1]))]) {O(n^2)} 4.13/1.99 4.13/1.99 1: f3->f1: 1 {O(1)} 4.13/1.99 4.13/1.99 4.13/1.99 4.13/1.99 Costbounds: 4.13/1.99 4.13/1.99 Overall costbound: 1+max([0, Arg_1-Arg_2])+max([0, (Arg_0-Arg_1)*(Arg_1-Arg_2+max([0, Arg_0-Arg_1]))])+max([0, Arg_0-Arg_1]) {O(n^2)} 4.13/1.99 4.13/1.99 0: f1->f1: max([0, Arg_0-Arg_1]) {O(n)} 4.13/1.99 4.13/1.99 2: f1->f1: max([0, Arg_1-Arg_2])+max([0, (Arg_0-Arg_1)*(Arg_1-Arg_2+max([0, Arg_0-Arg_1]))]) {O(n^2)} 4.13/1.99 4.13/1.99 1: f3->f1: 1 {O(1)} 4.13/1.99 4.13/1.99 4.13/1.99 4.13/1.99 Sizebounds: 4.13/1.99 4.13/1.99 `Lower: 4.13/1.99 4.13/1.99 0: f1->f1, Arg_0: Arg_0 {O(n)} 4.13/1.99 4.13/1.99 0: f1->f1, Arg_1: Arg_1 {O(n)} 4.13/1.99 4.13/1.99 0: f1->f1, Arg_2: Arg_2 {O(n)} 4.13/1.99 4.13/1.99 2: f1->f1, Arg_0: Arg_0 {O(n)} 4.13/1.99 4.13/1.99 2: f1->f1, Arg_1: Arg_1 {O(n)} 4.13/1.99 4.13/1.99 2: f1->f1, Arg_2: Arg_2 {O(n)} 4.13/1.99 4.13/1.99 1: f3->f1, Arg_0: Arg_0 {O(n)} 4.13/1.99 4.13/1.99 1: f3->f1, Arg_1: Arg_1 {O(n)} 4.13/1.99 4.13/1.99 1: f3->f1, Arg_2: Arg_2 {O(n)} 4.13/1.99 4.13/1.99 `Upper:
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