details

property	value
status	complete
benchmark	#4.29.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	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.502 seconds
cpu usage	316.315
user time	314.414
system time	1.90154
max virtual memory	1.8282E7
max residence set size	5370828.0

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 223 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 74 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] (16) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) half(0) -> 0 half(s(s(x))) -> s(half(x)) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(0, y) -> 0 times(s(x), y) -> if_times(even(s(x)), s(x), y) if_times(true, s(x), y) -> plus(times(half(s(x)), y), times(half(s(x)), y)) if_times(false, s(x), y) -> plus(y, times(x, y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: even(0') -> true even(s(0')) -> false even(s(s(x))) -> even(x) half(0') -> 0' half(s(s(x))) -> s(half(x)) plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) times(0', y) -> 0' times(s(x), y) -> if_times(even(s(x)), s(x), y) if_times(true, s(x), y) -> plus(times(half(s(x)), y), times(half(s(x)), y)) if_times(false, s(x), y) -> plus(y, times(x, y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: even(0') -> true even(s(0')) -> false even(s(s(x))) -> even(x) half(0') -> 0' half(s(s(x))) -> s(half(x)) plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) times(0', y) -> 0' times(s(x), y) -> if_times(even(s(x)), s(x), y) if_times(true, s(x), y) -> plus(times(half(s(x)), y), times(half(s(x)), y)) if_times(false, s(x), y) -> plus(y, times(x, y)) Types: even :: 0':s -> true:false popout

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all output return to Runtime Complexity: TRS