details

property	value
status	complete
benchmark	thetrickSize.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	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.85208 seconds
cpu usage	22.7678
user time	21.4244
system time	1.34345
max virtual memory	1.9209344E7
max residence set size	3702104.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 159 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 439 ms] (12) BOUNDS(1, n^1) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRelTRS (15) SlicingProof [LOWER BOUND(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), 278 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), 44 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 44 ms] (30) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: lt0(Nil, Cons(x', xs)) -> True lt0(Cons(x', xs'), Cons(x, xs)) -> lt0(xs', xs) g(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) f(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lt0(x, Nil) -> False g(x, Cons(x', xs)) -> g[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) f(x, Cons(x', xs)) -> f[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) number4(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) goal(x, y) -> Cons(f(x, y), Cons(g(x, y), Nil)) The (relative) TRS S consists of the following rules: g[Ite][False][Ite](False, Cons(x, xs), y) -> g(xs, Cons(Cons(Nil, Nil), y)) g[Ite][False][Ite](True, x', Cons(x, xs)) -> g(x', xs) f[Ite][False][Ite](False, Cons(x, xs), y) -> f(xs, Cons(Cons(Nil, Nil), y)) f[Ite][False][Ite](True, x', Cons(x, xs)) -> f(x', xs) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: lt0(Nil, Cons(x', xs)) -> True lt0(Cons(x', xs'), Cons(x, xs)) -> lt0(xs', xs) g(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) f(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lt0(x, Nil) -> False g(x, Cons(x', xs)) -> g[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) f(x, Cons(x', xs)) -> f[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) number4(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) goal(x, y) -> Cons(f(x, y), Cons(g(x, y), Nil)) The (relative) TRS S consists of the following rules: g[Ite][False][Ite](False, Cons(x, xs), y) -> g(xs, Cons(Cons(Nil, Nil), y)) g[Ite][False][Ite](True, x', Cons(x, xs)) -> g(x', xs) f[Ite][False][Ite](False, Cons(x, xs), y) -> f(xs, Cons(Cons(Nil, Nil), y)) f[Ite][False][Ite](True, x', Cons(x, xs)) -> f(x', xs) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost