details

property	value
status	complete
benchmark	inssort_better.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.696 seconds
cpu usage	342.155
user time	338.731
system time	3.42396
max virtual memory	1.9214816E7
max residence set size	5770300.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 199 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 281 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 88 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 1048 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 344 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 320 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 265 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 136 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) FinalProof [FINISHED, 0 ms] (44) BOUNDS(1, n^2) (45) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxRelTRS (47) TypeInferenceProof [BOTH BOUNDS(ID, ID), 4 ms] (48) typed CpxTrs (49) OrderProof [LOWER BOUND(ID), 0 ms] (50) typed CpxTrs (51) RewriteLemmaProof [LOWER BOUND(ID), 244 ms] (52) typed CpxTrs (53) RewriteLemmaProof [LOWER BOUND(ID), 9527 ms] (54) BEST (55) proven lower bound (56) LowerBoundPropagationProof [FINISHED, 0 ms] (57) BOUNDS(n^1, INF) (58) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: isort(Cons(x, xs), r) -> isort(xs, insert(x, r)) insert(x', Cons(x, xs)) -> insert[Ite][False][Ite](<(x', x), x', Cons(x, xs)) isort(Nil, r) -> r insert(x, Nil) -> Cons(x, Nil) inssort(xs) -> isort(xs, Nil) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False insert[Ite][False][Ite](False, x', Cons(x, xs)) -> Cons(x, insert(x', xs)) insert[Ite][False][Ite](True, x, r) -> Cons(x, r) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost