details

property	value
status	complete
benchmark	thiemann07.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)	291.752 seconds
cpu usage	1109.31
user time	1095.73
system time	13.5825
max virtual memory	3.784754E7
max residence set size	1.4958936E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^2), ?)

output

WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 275 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), 73 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^2, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 29 ms] (20) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: car(cons(x, l)) -> x cddr(nil) -> nil cddr(cons(x, nil)) -> nil cddr(cons(x, cons(y, l))) -> l cadr(cons(x, cons(y, l))) -> y isZero(0) -> true isZero(s(x)) -> false plus(x, y) -> ifplus(isZero(x), x, y) ifplus(true, x, y) -> y ifplus(false, x, y) -> s(plus(p(x), y)) times(x, y) -> iftimes(isZero(x), x, y) iftimes(true, x, y) -> 0 iftimes(false, x, y) -> plus(y, times(p(x), y)) p(s(x)) -> x p(0) -> 0 shorter(nil, y) -> true shorter(cons(x, l), 0) -> false shorter(cons(x, l), s(y)) -> shorter(l, y) prod(l) -> if(shorter(l, 0), shorter(l, s(0)), l) if(true, b, l) -> s(0) if(false, b, l) -> if2(b, l) if2(true, l) -> car(l) if2(false, l) -> prod(cons(times(car(l), cadr(l)), cddr(l))) 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^2, INF). The TRS R consists of the following rules: car(cons(x, l)) -> x cddr(nil) -> nil cddr(cons(x, nil)) -> nil cddr(cons(x, cons(y, l))) -> l cadr(cons(x, cons(y, l))) -> y isZero(0') -> true isZero(s(x)) -> false plus(x, y) -> ifplus(isZero(x), x, y) ifplus(true, x, y) -> y ifplus(false, x, y) -> s(plus(p(x), y)) times(x, y) -> iftimes(isZero(x), x, y) iftimes(true, x, y) -> 0' iftimes(false, x, y) -> plus(y, times(p(x), y)) p(s(x)) -> x p(0') -> 0' shorter(nil, y) -> true shorter(cons(x, l), 0') -> false shorter(cons(x, l), s(y)) -> shorter(l, y) prod(l) -> if(shorter(l, 0'), shorter(l, s(0')), l) if(true, b, l) -> s(0') if(false, b, l) -> if2(b, l) if2(true, l) -> car(l) popout

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

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actions

all output return to Runtime Complexity: TRS Innermost