details

property	value
status	complete
benchmark	thiemann13.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	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.512 seconds
cpu usage	309.559
user time	307.731
system time	1.82818
max virtual memory	1.8279408E7
max residence set size	5223520.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 246 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), 57 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 56 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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) inc(0) -> 0 inc(s(x)) -> s(inc(x)) minus(0, y) -> 0 minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) log(x) -> log2(x, 0) log2(x, y) -> if(le(x, 0), le(x, s(0)), x, inc(y)) if(true, b, x, y) -> log_undefined if(false, b, x, y) -> if2(b, x, y) if2(true, x, s(y)) -> y if2(false, x, y) -> log2(quot(x, s(s(0))), 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: le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) minus(0', y) -> 0' minus(x, 0') -> x minus(s(x), s(y)) -> minus(x, y) quot(0', s(y)) -> 0' quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, 0'), le(x, s(0')), x, inc(y)) if(true, b, x, y) -> log_undefined if(false, b, x, y) -> if2(b, x, y) if2(true, x, s(y)) -> y if2(false, x, y) -> log2(quot(x, s(s(0'))), y) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' popout

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all output return to Runtime Complexity: TRS