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Complexity_ITS 2019-03-21 04.46 pair #429991238
details
property
value
status
complete
benchmark
03.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
Beerendonk
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.66505 seconds
cpu usage
4.2505
user time
4.02224
system time
0.228266
max virtual memory
1.8379624E7
max residence set size
220476.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
4.14/2.63 WORST_CASE(Omega(n^1), O(n^1)) 4.14/2.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.14/2.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.14/2.63 4.14/2.63 4.14/2.63 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(1, 1 + Arg_0 + -1 * Arg_1)). 4.14/2.63 4.14/2.63 (0) CpxIntTrs 4.14/2.63 (1) Koat2 Proof [FINISHED, 85 ms] 4.14/2.63 (2) BOUNDS(1, max(1, 1 + Arg_0 + -1 * Arg_1)) 4.14/2.63 (3) Loat Proof [FINISHED, 480 ms] 4.14/2.63 (4) BOUNDS(n^1, INF) 4.14/2.63 4.14/2.63 4.14/2.63 ---------------------------------------- 4.14/2.63 4.14/2.63 (0) 4.14/2.63 Obligation: 4.14/2.63 Complexity Int TRS consisting of the following rules: 4.14/2.63 eval(A, B) -> Com_1(eval(A, A + B)) :|: A >= 1 && A >= B + 1 4.14/2.63 start(A, B) -> Com_1(eval(A, B)) :|: TRUE 4.14/2.63 4.14/2.63 The start-symbols are:[start_2] 4.14/2.63 4.14/2.63 4.14/2.63 ---------------------------------------- 4.14/2.63 4.14/2.63 (1) Koat2 Proof (FINISHED) 4.14/2.63 YES( ?, max([1, 1+Arg_0-Arg_1]) {O(n)}) 4.14/2.63 4.14/2.63 4.14/2.63 4.14/2.63 Initial Complexity Problem: 4.14/2.63 4.14/2.63 Start: start 4.14/2.63 4.14/2.63 Program_Vars: Arg_0, Arg_1 4.14/2.63 4.14/2.63 Temp_Vars: 4.14/2.63 4.14/2.63 Locations: eval, start 4.14/2.63 4.14/2.63 Transitions: 4.14/2.63 4.14/2.63 eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_0+Arg_1):|:1 <= Arg_0 && Arg_1+1 <= Arg_0 4.14/2.63 4.14/2.63 start(Arg_0,Arg_1) -> eval(Arg_0,Arg_1):|: 4.14/2.63 4.14/2.63 4.14/2.63 4.14/2.63 Timebounds: 4.14/2.63 4.14/2.63 Overall timebound: max([1, 1+Arg_0-Arg_1]) {O(n)} 4.14/2.63 4.14/2.63 0: eval->eval: max([0, Arg_0-Arg_1]) {O(n)} 4.14/2.63 4.14/2.63 1: start->eval: 1 {O(1)} 4.14/2.63 4.14/2.63 4.14/2.63 4.14/2.63 Costbounds: 4.14/2.63 4.14/2.63 Overall costbound: max([1, 1+Arg_0-Arg_1]) {O(n)} 4.14/2.63 4.14/2.63 0: eval->eval: max([0, Arg_0-Arg_1]) {O(n)} 4.14/2.63 4.14/2.63 1: start->eval: 1 {O(1)} 4.14/2.63 4.14/2.63 4.14/2.63 4.14/2.63 Sizebounds: 4.14/2.63 4.14/2.63 `Lower: 4.14/2.63 4.14/2.63 0: eval->eval, Arg_0: 1 {O(1)} 4.14/2.63 4.14/2.63 0: eval->eval, Arg_1: Arg_1 {O(n)} 4.14/2.63 4.14/2.63 1: start->eval, Arg_0: Arg_0 {O(n)} 4.14/2.63 4.14/2.63 1: start->eval, Arg_1: Arg_1 {O(n)} 4.14/2.63 4.14/2.63 `Upper: 4.14/2.63 4.14/2.63 0: eval->eval, Arg_0: Arg_0 {O(n)} 4.14/2.63 4.14/2.63 0: eval->eval, Arg_1: 2*Arg_0 {O(n)} 4.14/2.63 4.14/2.63 1: start->eval, Arg_0: Arg_0 {O(n)} 4.14/2.63 4.14/2.63 1: start->eval, Arg_1: Arg_1 {O(n)} 4.14/2.63 4.14/2.63 4.14/2.63 ---------------------------------------- 4.14/2.63 4.14/2.63 (2) 4.14/2.63 BOUNDS(1, max(1, 1 + Arg_0 + -1 * Arg_1)) 4.14/2.63 4.14/2.63 ---------------------------------------- 4.14/2.63
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