details

property	value
status	complete
benchmark	t003.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.267 seconds
cpu usage	1148.48
user time	1138.57
system time	9.9051
max virtual memory	1.9181268E7
max residence set size	1.5110788E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 333 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 282 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), 50 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 1114 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: -(x, 0) -> x -(s(x), s(y)) -> -(x, y) <=(0, y) -> true <=(s(x), 0) -> false <=(s(x), s(y)) -> <=(x, y) if(true, x, y) -> x if(false, x, y) -> y perfectp(0) -> false perfectp(s(x)) -> f(x, s(0), s(x), s(x)) f(0, y, 0, u) -> true f(0, y, s(z), u) -> false f(s(x), 0, z, u) -> f(x, u, -(z, s(x)), u) f(s(x), s(y), z, u) -> if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u)) 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(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_<=(x_1, x_2)) -> <=(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_perfectp(x_1)) -> perfectp(encArg(x_1)) encArg(cons_f(x_1, x_2, x_3, x_4)) -> f(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_<=(x_1, x_2) -> <=(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_perfectp(x_1) -> perfectp(encArg(x_1)) encode_f(x_1, x_2, x_3, x_4) -> f(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) ---------------------------------------- (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: -(x, 0) -> x -(s(x), s(y)) -> -(x, y) <=(0, y) -> true <=(s(x), 0) -> false <=(s(x), s(y)) -> <=(x, y) if(true, x, y) -> x if(false, x, y) -> y perfectp(0) -> false perfectp(s(x)) -> f(x, s(0), s(x), s(x)) f(0, y, 0, u) -> true f(0, y, s(z), u) -> 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