details

property	value
status	complete
benchmark	t001.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.855 seconds
cpu usage	1119.53
user time	1107.5
system time	12.0225
max virtual memory	1.903316E7
max residence set size	1.5096856E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 244 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 2 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), 271 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), 3102 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 31 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 1474 ms] (24) 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) *(x, 0) -> 0 *(x, s(y)) -> +(*(x, y), x) if(true, x, y) -> x if(false, x, y) -> y odd(0) -> false odd(s(0)) -> true odd(s(s(x))) -> odd(x) half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) if(true, x, y) -> true if(false, x, y) -> false pow(x, y) -> f(x, y, s(0)) f(x, 0, z) -> z f(x, s(y), z) -> if(odd(s(y)), f(x, y, *(x, z)), f(*(x, x), half(s(y)), z)) 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(+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2)) 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_odd(x_1)) -> odd(encArg(x_1)) encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_pow(x_1, x_2)) -> pow(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) 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_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_false -> false encode_odd(x_1) -> odd(encArg(x_1)) encode_half(x_1) -> half(encArg(x_1)) encode_pow(x_1, x_2) -> pow(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 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