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Compl Integ Trans Syste 26843 pair #381744225
details
property
value
status
complete
benchmark
sect1-lin.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
KoAT-2013
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.96058797836 seconds
cpu usage
4.314692341
max memory
2.4805376E8
stage attributes
key
value
output-size
5738
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(Arg_1 + nat(Arg_0), Arg_1, 0) + max(2, 2 + Arg_0)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 145 ms] (2) BOUNDS(1, max(Arg_1 + nat(Arg_0), Arg_1, 0) + max(2, 2 + Arg_0)) (3) Loat Proof [FINISHED, 236 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: l0(A, B) -> Com_1(l1(A, B)) :|: TRUE l1(A, B) -> Com_1(l1(A - 1, B + 1)) :|: A >= 1 l1(A, B) -> Com_1(l2(A, B)) :|: 0 >= A l2(A, B) -> Com_1(l2(A, B - 1)) :|: B >= 1 The start-symbols are:[l0_2] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, max([0, max([Arg_1, Arg_1+max([0, Arg_0])])])+max([2, 2+Arg_0]) {O(n)}) Initial Complexity Problem: Start: l0 Program_Vars: Arg_0, Arg_1 Temp_Vars: Locations: l0, l1, l2 Transitions: l0(Arg_0,Arg_1) -> l1(Arg_0,Arg_1):|: l1(Arg_0,Arg_1) -> l1(Arg_0-1,Arg_1+1):|:1 <= Arg_0 l1(Arg_0,Arg_1) -> l2(Arg_0,Arg_1):|:Arg_0 <= 0 l2(Arg_0,Arg_1) -> l2(Arg_0,Arg_1-1):|:Arg_0 <= 0 && 1 <= Arg_1 Timebounds: Overall timebound: max([0, max([Arg_1, Arg_1+max([0, Arg_0])])])+max([2, 2+Arg_0]) {O(n)} 0: l0->l1: 1 {O(1)} 1: l1->l1: max([0, Arg_0]) {O(n)} 2: l1->l2: 1 {O(1)} 3: l2->l2: max([0, max([Arg_1, Arg_1+max([0, Arg_0])])]) {O(n)} Costbounds: Overall costbound: max([0, max([Arg_1, Arg_1+max([0, Arg_0])])])+max([2, 2+Arg_0]) {O(n)} 0: l0->l1: 1 {O(1)} 1: l1->l1: max([0, Arg_0]) {O(n)} 2: l1->l2: 1 {O(1)} 3: l2->l2: max([0, max([Arg_1, Arg_1+max([0, Arg_0])])]) {O(n)} Sizebounds: `Lower: 0: l0->l1, Arg_0: Arg_0 {O(n)} 0: l0->l1, Arg_1: Arg_1 {O(n)} 1: l1->l1, Arg_0: 0 {O(1)}
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