details

property	value
status	complete
benchmark	16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.705 seconds
cpu usage	1135.82
user time	1121.49
system time	14.3356
max virtual memory	3.7780992E7
max residence set size	1.5063032E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 1563 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 57 ms] (24) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: cond1(true, x, y, z) -> cond2(gr(x, 0), x, y, z) cond2(true, x, y, z) -> cond1(gr(add(x, y), z), p(x), y, z) cond2(false, x, y, z) -> cond3(gr(y, 0), x, y, z) cond3(true, x, y, z) -> cond1(gr(add(x, y), z), x, p(y), z) cond3(false, x, y, z) -> cond1(gr(add(x, y), z), x, y, z) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) add(0, x) -> x add(s(x), y) -> s(add(x, y)) p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: cond1(true, x, y, z) -> cond2(gr(x, 0), x, y, z) [1] cond2(true, x, y, z) -> cond1(gr(add(x, y), z), p(x), y, z) [1] cond2(false, x, y, z) -> cond3(gr(y, 0), x, y, z) [1] cond3(true, x, y, z) -> cond1(gr(add(x, y), z), x, p(y), z) [1] cond3(false, x, y, z) -> cond1(gr(add(x, y), z), x, y, z) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] add(0, x) -> x [1] add(s(x), y) -> s(add(x, y)) [1] p(0) -> 0 [1] p(s(x)) -> x [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond1(true, x, y, z) -> cond2(gr(x, 0), x, y, z) [1] cond2(true, x, y, z) -> cond1(gr(add(x, y), z), p(x), y, z) [1] cond2(false, x, y, z) -> cond3(gr(y, 0), x, y, z) [1] cond3(true, x, y, z) -> cond1(gr(add(x, y), z), x, p(y), z) [1] 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