details

property	value
status	complete
benchmark	thiemann16.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	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.475 seconds
cpu usage	1135.08
user time	1123.71
system time	11.364
max virtual memory	3.8396044E7
max residence set size	1.4638684E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 240 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), 21 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] (16) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x)))) -> check(s(x)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> timesIter(x, y, 0) timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) p(s(x)) -> x p(0) -> 0 if(zero, x, y, z, u) -> z if(odd, x, y, z, u) -> timesIter(p(x), y, u) if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: check(0') -> zero check(s(0')) -> odd check(s(s(0'))) -> even check(s(s(s(x)))) -> check(s(x)) half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> timesIter(x, y, 0') timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) p(s(x)) -> x p(0') -> 0' if(zero, x, y, z, u) -> z if(odd, x, y, z, u) -> timesIter(p(x), y, u) if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: check(0') -> zero check(s(0')) -> odd check(s(s(0'))) -> even check(s(s(s(x)))) -> check(s(x)) popout

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all output return to Runtime Complexity: TRS Innermost