details

property	value
status	complete
benchmark	gcd2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.226725817 seconds
cpu usage	1092.70777388
max memory	1.5438737408E10

stage attributes

key	value
output-size	174239
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 220 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 109.6 s] (12) BOUNDS(1, n^3) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRelTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 316 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 62 ms] (30) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runti Compl Inner Rewri 22807