details

property	value
status	complete
benchmark	Hamming.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	2.19952 seconds
cpu usage	5.55289
user time	5.31649
system time	0.236403
max virtual memory	1.8543288E7
max residence set size	363508.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 462 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) InfiniteLowerBoundProof [FINISHED, 52 ms] (8) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: app(app(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(lt, app(s, x)), app(s, y)) -> app(app(lt, x), y) app(app(lt, 0), app(s, y)) -> true app(app(lt, y), 0) -> false app(app(eq, x), x) -> true app(app(eq, app(s, x)), 0) -> false app(app(eq, 0), app(s, x)) -> false app(app(merge, xs), nil) -> xs app(app(merge, nil), ys) -> ys app(app(merge, app(app(cons, x), xs)), app(app(cons, y), ys)) -> app(app(app(if, app(app(lt, x), y)), app(app(cons, x), app(app(merge, xs), app(app(cons, y), ys)))), app(app(app(if, app(app(eq, x), y)), app(app(cons, x), app(app(merge, xs), ys))), app(app(cons, y), app(app(merge, app(app(cons, x), xs)), ys)))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(mult, 0), x) -> 0 app(app(mult, app(s, x)), y) -> app(app(plus, y), app(app(mult, x), y)) app(app(plus, 0), x) -> 0 app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) list1 -> app(app(map, app(mult, app(s, app(s, 0)))), hamming) list2 -> app(app(map, app(mult, app(s, app(s, app(s, 0))))), hamming) list3 -> app(app(map, app(mult, app(s, app(s, app(s, app(s, app(s, 0))))))), hamming) hamming -> app(app(cons, app(s, 0)), app(app(merge, list1), app(app(merge, list2), list3))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(lt) -> lt encArg(s) -> s encArg(0) -> 0 encArg(eq) -> eq encArg(merge) -> merge encArg(nil) -> nil encArg(cons) -> cons encArg(map) -> map encArg(mult) -> mult encArg(plus) -> plus encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encArg(cons_list1) -> list1 encArg(cons_list2) -> list2 encArg(cons_list3) -> list3 encArg(cons_hamming) -> hamming encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_if -> if encode_true -> true encode_false -> false encode_lt -> lt encode_s -> s encode_0 -> 0 encode_eq -> eq encode_merge -> merge encode_nil -> nil encode_cons -> cons encode_map -> map encode_mult -> mult encode_plus -> plus encode_list1 -> list1 encode_hamming -> hamming encode_list2 -> list2 encode_list3 -> list3 ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). popout

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actions

all output return to Derivational Complexity: TRS Innermost