details

property	value
status	complete
benchmark	#3.37.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	AG01

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	2.81169 seconds
cpu usage	8.28499
user time	7.87033
system time	0.414659
max virtual memory	1.8345196E7
max residence set size	1181480.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 188 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsTAProof [FINISHED, 702 ms] (8) BOUNDS(1, n^1) (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: not(true) -> false not(false) -> true evenodd(x, 0) -> not(evenodd(x, s(0))) evenodd(0, s(0)) -> false evenodd(s(x), s(0)) -> evenodd(x, 0) 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(true) -> true encArg(false) -> false encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_not(x_1)) -> not(encArg(x_1)) encArg(cons_evenodd(x_1, x_2)) -> evenodd(encArg(x_1), encArg(x_2)) encode_not(x_1) -> not(encArg(x_1)) encode_true -> true encode_false -> false encode_evenodd(x_1, x_2) -> evenodd(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: not(true) -> false not(false) -> true evenodd(x, 0) -> not(evenodd(x, s(0))) evenodd(0, s(0)) -> false evenodd(s(x), s(0)) -> evenodd(x, 0) The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(false) -> false encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_not(x_1)) -> not(encArg(x_1)) encArg(cons_evenodd(x_1, x_2)) -> evenodd(encArg(x_1), encArg(x_2)) encode_not(x_1) -> not(encArg(x_1)) encode_true -> true encode_false -> false encode_evenodd(x_1, x_2) -> evenodd(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) popout

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actions

all output return to Derivational Complexity: TRS Innermost