details

property	value
status	complete
benchmark	12.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	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.825 seconds
cpu usage	1111.38
user time	1098.36
system time	13.0184
max virtual memory	5.5811288E7
max residence set size	1.5085232E7

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 311 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), 15 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 42.5 s] (14) BOUNDS(1, n^3) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true p(0) -> 0 p(s(x)) -> x 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_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_gr0(x_1)) -> gr0(encArg(x_1)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_gr0(x_1) -> gr0(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) 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^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost