details

property	value
status	complete
benchmark	match.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.566 seconds
cpu usage	338.646
user time	335.387
system time	3.25821
max virtual memory	3.7104952E7
max residence set size	5906448.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).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), 259 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), 1 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), 449 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 57 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 8908 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 4555 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 146 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) FinalProof [FINISHED, 0 ms] (36) BOUNDS(1, n^2) (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxRelTRS (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 3 ms] (40) typed CpxTrs (41) OrderProof [LOWER BOUND(ID), 0 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 265 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 26 ms] (46) proven lower bound (47) LowerBoundPropagationProof [FINISHED, 0 ms] (48) BOUNDS(n^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: loop(Cons(x, xs), Nil, pp, ss) -> False loop(Cons(x', xs'), Cons(x, xs), pp, ss) -> loop[Ite](!EQ(x', x), Cons(x', xs'), Cons(x, xs), pp, ss) loop(Nil, s, pp, ss) -> True match1(p, s) -> loop(p, s, p, s) 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 loop[Ite](False, p, s, pp, Cons(x, xs)) -> loop(pp, xs, pp, xs) loop[Ite](True, Cons(x', xs'), Cons(x, xs), pp, ss) -> loop(xs', xs, pp, ss) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) 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: loop(Cons(x, xs), Nil, pp, ss) -> False loop(Cons(x', xs'), Cons(x, xs), pp, ss) -> loop[Ite](!EQ(x', x), Cons(x', xs'), Cons(x, xs), pp, ss) loop(Nil, s, pp, ss) -> True match1(p, s) -> loop(p, s, p, s) popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost