details

property	value
status	complete
benchmark	overlap.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.526 seconds
cpu usage	326.741
user time	323.718
system time	3.02345
max virtual memory	5.5744984E7
max residence set size	5480040.0

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/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).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), 156 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) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 44 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 1 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 351 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 15 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 1068 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 305 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 927 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 382 ms] (40) CpxRNTS (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) FinalProof [FINISHED, 0 ms] (48) BOUNDS(1, n^2) (49) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CpxRelTRS (51) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (52) typed CpxTrs (53) OrderProof [LOWER BOUND(ID), 0 ms] (54) typed CpxTrs (55) RewriteLemmaProof [LOWER BOUND(ID), 288 ms] (56) typed CpxTrs (57) RewriteLemmaProof [LOWER BOUND(ID), 34 ms] (58) BEST (59) proven lower bound (60) LowerBoundPropagationProof [FINISHED, 0 ms] (61) BOUNDS(n^1, INF) (62) typed CpxTrs (63) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (64) BOUNDS(1, INF) ---------------------------------------- (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: overlap(Cons(x, xs), ys) -> overlap[Ite][True][Ite](member(x, ys), Cons(x, xs), ys) overlap(Nil, ys) -> False member(x', Cons(x, xs)) -> member[Ite][True][Ite](!EQ(x, x'), x', Cons(x, xs)) member(x, Nil) -> False notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs, ys) -> overlap(xs, ys) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True overlap[Ite][True][Ite](False, Cons(x, xs), ys) -> overlap(xs, ys) member[Ite][True][Ite](False, x', Cons(x, xs)) -> member(x', xs) overlap[Ite][True][Ite](True, xs, ys) -> True popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost