details

property	value
status	complete
benchmark	aprove01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.535 seconds
cpu usage	304.613
user time	302.686
system time	1.92689
max virtual memory	1.8279408E7
max residence set size	5143976.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 283 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), 32 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 43 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 51 ms] (18) BOUNDS(1, INF) ---------------------------------------- (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: times(x, y) -> sum(generate(x, y)) generate(x, y) -> gen(x, y, 0) gen(x, y, z) -> if(ge(z, x), x, y, z) if(true, x, y, z) -> nil if(false, x, y, z) -> cons(y, gen(x, y, s(z))) sum(xs) -> sum2(xs, 0) sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y) ifsum(true, b, xs, y) -> y ifsum(false, b, xs, y) -> ifsum2(b, xs, y) ifsum2(true, xs, y) -> sum2(tail(xs), y) ifsum2(false, xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y)) isNil(nil) -> true isNil(cons(x, xs)) -> false tail(nil) -> nil tail(cons(x, xs)) -> xs head(cons(x, xs)) -> x head(nil) -> error isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) p(0) -> s(s(0)) p(s(0)) -> 0 p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) a -> c a -> d 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: times(x, y) -> sum(generate(x, y)) generate(x, y) -> gen(x, y, 0') gen(x, y, z) -> if(ge(z, x), x, y, z) if(true, x, y, z) -> nil if(false, x, y, z) -> cons(y, gen(x, y, s(z))) sum(xs) -> sum2(xs, 0') sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y) ifsum(true, b, xs, y) -> y ifsum(false, b, xs, y) -> ifsum2(b, xs, y) ifsum2(true, xs, y) -> sum2(tail(xs), y) ifsum2(false, xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y)) isNil(nil) -> true isNil(cons(x, xs)) -> false tail(nil) -> nil tail(cons(x, xs)) -> xs head(cons(x, xs)) -> x head(nil) -> error isZero(0') -> true isZero(s(0')) -> false popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS