details

property	value
status	complete
benchmark	otto06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.996 seconds
cpu usage	1149.36
user time	1139.13
system time	10.2301
max virtual memory	1.96005E7
max residence set size	1.5105968E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 817 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), 299 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), 77 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 29.1 s] (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: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) length(nil) -> 0 length(cons(x, y)) -> s(length(y)) helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) if(true, c, l, ys, zs) -> nil if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) helpc(true, ys, zs) -> ys helpc(false, ys, zs) -> zs helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 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(nil) -> nil encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(true) -> true encArg(false) -> false encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_length(x_1)) -> length(encArg(x_1)) encArg(cons_helpa(x_1, x_2, x_3, x_4)) -> helpa(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3, x_4, x_5)) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encArg(cons_greater(x_1, x_2)) -> greater(encArg(x_1), encArg(x_2)) encArg(cons_smaller(x_1, x_2)) -> smaller(encArg(x_1), encArg(x_2)) encArg(cons_helpc(x_1, x_2, x_3)) -> helpc(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_helpb(x_1, x_2, x_3, x_4)) -> helpb(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_helpa(x_1, x_2, x_3, x_4) -> helpa(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_0 -> 0 encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_length(x_1) -> length(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3, x_4, x_5) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_helpb(x_1, x_2, x_3, x_4) -> helpb(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_greater(x_1, x_2) -> greater(encArg(x_1), encArg(x_2)) encode_smaller(x_1, x_2) -> smaller(encArg(x_1), encArg(x_2)) encode_helpc(x_1, x_2, x_3) -> helpc(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) 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