details

property	value
status	complete
benchmark	append.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.67142 seconds
cpu usage	18.8573
user time	17.5519
system time	1.30534
max virtual memory	1.887734E7
max residence set size	3270684.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 18 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: is_empty(nil) -> true is_empty(cons(x, l)) -> false hd(cons(x, l)) -> x tl(cons(x, l)) -> l append(l1, l2) -> ifappend(l1, l2, l1) ifappend(l1, l2, nil) -> l2 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS does not nest defined symbols, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: is_empty(nil) -> true is_empty(cons(x, l)) -> false hd(cons(x, l)) -> x tl(cons(x, l)) -> l append(l1, l2) -> ifappend(l1, l2, l1) ifappend(l1, l2, nil) -> l2 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: is_empty(nil) -> true is_empty(cons(z0, z1)) -> false hd(cons(z0, z1)) -> z0 tl(cons(z0, z1)) -> z1 append(z0, z1) -> ifappend(z0, z1, z0) ifappend(z0, z1, nil) -> z1 ifappend(z0, z1, cons(z2, z3)) -> cons(z2, append(z3, z1)) Tuples: IS_EMPTY(nil) -> c IS_EMPTY(cons(z0, z1)) -> c1 HD(cons(z0, z1)) -> c2 TL(cons(z0, z1)) -> c3 APPEND(z0, z1) -> c4(IFAPPEND(z0, z1, z0)) IFAPPEND(z0, z1, nil) -> c5 IFAPPEND(z0, z1, cons(z2, z3)) -> c6(APPEND(z3, z1)) popout

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actions

all output return to Runtime Complexity: TRS