details

property	value
status	complete
benchmark	zerolist.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	292.303 seconds
cpu usage	1113.53
user time	1098.92
system time	14.6114
max virtual memory	3.81849E7
max residence set size	1.4702964E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).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), 206 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), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 6452 ms] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 325 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 97 ms] (28) BOUNDS(1, INF) ---------------------------------------- (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: sub(0, 0) -> 0 sub(s(x), 0) -> s(x) sub(0, s(x)) -> 0 sub(s(x), s(y)) -> sub(x, y) zero(nil) -> zero2(0, nil) zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs)) zero2(0, nil) -> nil zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs)) zero2(s(y), nil) -> zero(nil) zero2(s(y), cons(x, xs)) -> zero(cons(x, xs)) 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(cons_sub(x_1, x_2)) -> sub(encArg(x_1), encArg(x_2)) encArg(cons_zero(x_1)) -> zero(encArg(x_1)) encArg(cons_zero2(x_1, x_2)) -> zero2(encArg(x_1), encArg(x_2)) encode_sub(x_1, x_2) -> sub(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_zero(x_1) -> zero(encArg(x_1)) encode_nil -> nil encode_zero2(x_1, x_2) -> zero2(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) ---------------------------------------- (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: sub(0, 0) -> 0 sub(s(x), 0) -> s(x) sub(0, s(x)) -> 0 sub(s(x), s(y)) -> sub(x, y) zero(nil) -> zero2(0, nil) zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs)) zero2(0, nil) -> nil zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs)) zero2(s(y), nil) -> zero(nil) zero2(s(y), cons(x, xs)) -> zero(cons(x, xs)) 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