details

property	value
status	complete
benchmark	parting03_minsort.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	AProVE_08

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.707 seconds
cpu usage	1150.46
user time	1139.97
system time	10.4852
max virtual memory	3.731834E7
max residence set size	1.5060916E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 374 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs 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) eq(0, 0) -> true eq(0, s(y)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) if1(true, x, y, xs) -> min(x, xs) if1(false, x, y, xs) -> min(y, xs) if2(true, x, y, xs) -> xs if2(false, x, y, xs) -> cons(y, del(x, xs)) minsort(nil) -> nil minsort(cons(x, y)) -> cons(min(x, y), minsort(del(min(x, y), cons(x, y)))) min(x, nil) -> x min(x, cons(y, z)) -> if1(le(x, y), x, y, z) del(x, nil) -> nil del(x, cons(y, z)) -> if2(eq(x, y), x, y, z) 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(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(nil) -> nil encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) encArg(cons_if1(x_1, x_2, x_3, x_4)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_if2(x_1, x_2, x_3, x_4)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_minsort(x_1)) -> minsort(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_del(x_1, x_2)) -> del(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) encode_if1(x_1, x_2, x_3, x_4) -> if1(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_if2(x_1, x_2, x_3, x_4) -> if2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_del(x_1, x_2) -> del(encArg(x_1), encArg(x_2)) encode_minsort(x_1) -> minsort(encArg(x_1)) encode_nil -> nil ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS 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) eq(0, 0) -> true eq(0, s(y)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) popout

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

job log

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actions

all output return to Derivational Complexity: TRS Innermost