details

property	value
status	complete
benchmark	cade03.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	GTSSK07

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.004 seconds
cpu usage	1109.64
user time	1096.5
system time	13.1418
max virtual memory	3.7376868E7
max residence set size	1.4817508E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

output

WORST_CASE(Omega(n^1), O(n^3)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 255 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 27.3 s] (14) BOUNDS(1, n^3) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 6 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) 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(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0 encode_true -> true ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) The (relative) TRS S consists of the following rules: encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) 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