details

property	value
status	complete
benchmark	modulo.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.177 seconds
cpu usage	1135.01
user time	1124.7
system time	10.3073
max virtual memory	3.7931756E7
max residence set size	1.5006252E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 275 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 4 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 246 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 56 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 480 ms] (20) BOUNDS(1, INF) ---------------------------------------- (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) minus(x, x) -> 0 minus(x, 0) -> x minus(0, x) -> 0 minus(s(x), s(y)) -> minus(x, y) isZero(0) -> true isZero(s(x)) -> false mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y)) if_mod(true, b, x, y, z) -> divByZeroError if_mod(false, false, x, y, z) -> x if_mod(false, true, x, y, z) -> mod(z, y) 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(divByZeroError) -> divByZeroError encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_isZero(x_1)) -> isZero(encArg(x_1)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encArg(cons_if_mod(x_1, x_2, x_3, x_4, x_5)) -> if_mod(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) 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_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_isZero(x_1) -> isZero(encArg(x_1)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) encode_if_mod(x_1, x_2, x_3, x_4, x_5) -> if_mod(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encode_divByZeroError -> divByZeroError ---------------------------------------- (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) minus(x, x) -> 0 minus(x, 0) -> x minus(0, x) -> 0 minus(s(x), s(y)) -> minus(x, y) isZero(0) -> true isZero(s(x)) -> false 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