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Complexity_ITS 2019-03-21 04.46 pair #429990228
details
property
value
status
complete
benchmark
241.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.10943 seconds
cpu usage
4.24994
user time
4.00877
system time
0.241166
max virtual memory
1.8608172E7
max residence set size
213916.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
4.11/2.06 WORST_CASE(Omega(n^2), O(n^2)) 4.11/2.07 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.11/2.07 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.11/2.07 4.11/2.07 4.11/2.07 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, max(1, 1 + -1 * Arg_0 + Arg_0^2) + nat(2 * Arg_0)). 4.11/2.07 4.11/2.07 (0) CpxIntTrs 4.11/2.07 (1) Koat2 Proof [FINISHED, 143 ms] 4.11/2.07 (2) BOUNDS(1, max(1, 1 + -1 * Arg_0 + Arg_0^2) + nat(2 * Arg_0)) 4.11/2.07 (3) Loat Proof [FINISHED, 422 ms] 4.11/2.07 (4) BOUNDS(n^2, INF) 4.11/2.07 4.11/2.07 4.11/2.07 ---------------------------------------- 4.11/2.07 4.11/2.07 (0) 4.11/2.07 Obligation: 4.11/2.07 Complexity Int TRS consisting of the following rules: 4.11/2.07 f1(A, B) -> Com_1(f3(A, A)) :|: A >= 1 4.11/2.07 f3(A, B) -> Com_1(f3(A, B - 1)) :|: B >= 1 4.11/2.07 f3(A, B) -> Com_1(f3(A - 1, A - 1)) :|: 0 >= B && A >= 2 4.11/2.07 4.11/2.07 The start-symbols are:[f1_2] 4.11/2.07 4.11/2.07 4.11/2.07 ---------------------------------------- 4.11/2.07 4.11/2.07 (1) Koat2 Proof (FINISHED) 4.11/2.07 YES( ?, max([1, 1+Arg_0*(-1+Arg_0)])+max([0, Arg_0])+max([0, Arg_0]) {O(n^2)}) 4.11/2.07 4.11/2.07 4.11/2.07 4.11/2.07 Initial Complexity Problem: 4.11/2.07 4.11/2.07 Start: f1 4.11/2.07 4.11/2.07 Program_Vars: Arg_0, Arg_1 4.11/2.07 4.11/2.07 Temp_Vars: 4.11/2.07 4.11/2.07 Locations: f1, f3 4.11/2.07 4.11/2.07 Transitions: 4.11/2.07 4.11/2.07 f1(Arg_0,Arg_1) -> f3(Arg_0,Arg_0):|:1 <= Arg_0 4.11/2.07 4.11/2.07 f3(Arg_0,Arg_1) -> f3(Arg_0,Arg_1-1):|:Arg_1 <= Arg_0 && 1 <= Arg_0 && 1 <= Arg_1 4.11/2.07 4.11/2.07 f3(Arg_0,Arg_1) -> f3(Arg_0-1,Arg_0-1):|:Arg_1 <= Arg_0 && 1 <= Arg_0 && Arg_1 <= 0 && 2 <= Arg_0 4.11/2.07 4.11/2.07 4.11/2.07 4.11/2.07 Timebounds: 4.11/2.07 4.11/2.07 Overall timebound: max([1, 1+Arg_0*(-1+Arg_0)])+max([0, Arg_0])+max([0, Arg_0]) {O(n^2)} 4.11/2.07 4.11/2.07 0: f1->f3: 1 {O(1)} 4.11/2.07 4.11/2.07 1: f3->f3: max([0, Arg_0*(-1+Arg_0)])+max([0, Arg_0]) {O(n^2)} 4.11/2.07 4.11/2.07 2: f3->f3: max([0, Arg_0]) {O(n)} 4.11/2.07 4.11/2.07 4.11/2.07 4.11/2.07 Costbounds: 4.11/2.07 4.11/2.07 Overall costbound: max([1, 1+Arg_0*(-1+Arg_0)])+max([0, Arg_0])+max([0, Arg_0]) {O(n^2)} 4.11/2.07 4.11/2.07 0: f1->f3: 1 {O(1)} 4.11/2.07 4.11/2.07 1: f3->f3: max([0, Arg_0*(-1+Arg_0)])+max([0, Arg_0]) {O(n^2)} 4.11/2.07 4.11/2.07 2: f3->f3: max([0, Arg_0]) {O(n)} 4.11/2.07 4.11/2.07 4.11/2.07 4.11/2.07 Sizebounds: 4.11/2.07 4.11/2.07 `Lower: 4.11/2.07 4.11/2.07 0: f1->f3, Arg_0: 1 {O(1)} 4.11/2.07 4.11/2.07 0: f1->f3, Arg_1: 1 {O(1)} 4.11/2.07 4.11/2.07 1: f3->f3, Arg_0: 1 {O(1)} 4.11/2.07 4.11/2.07 1: f3->f3, Arg_1: 0 {O(1)} 4.11/2.07 4.11/2.07 2: f3->f3, Arg_0: 1 {O(1)} 4.11/2.07 4.11/2.07 2: f3->f3, Arg_1: 1 {O(1)} 4.11/2.07 4.11/2.07 `Upper: 4.11/2.07 4.11/2.07 0: f1->f3, Arg_0: Arg_0 {O(n)} 4.11/2.07 4.11/2.07 0: f1->f3, Arg_1: Arg_0 {O(n)} 4.11/2.07 4.11/2.07 1: f3->f3, Arg_0: Arg_0 {O(n)}
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