details

property	value
status	complete
benchmark	subsets.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	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.505 seconds
cpu usage	1135.19
user time	1127.43
system time	7.7626
max virtual memory	1.9483828E7
max residence set size	9672628.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 150 ms] (2) CpxRelTRS (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) SlicingProof [LOWER BOUND(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), 1428 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), 43 ms] (18) BOUNDS(1, INF) ---------------------------------------- (0) 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: subsets(Cons(x, xs)) -> subsets[Ite][True][Let](Cons(x, xs), subsets(xs)) subsets(Nil) -> Cons(Nil, Nil) mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) mapconsapp(x, Nil, rest) -> rest notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs) -> subsets(xs) The (relative) TRS S consists of the following rules: subsets[Ite][True][Let](Cons(x, xs), subs) -> mapconsapp(x, subs, subs) 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, INF). The TRS R consists of the following rules: subsets(Cons(x, xs)) -> subsets[Ite][True][Let](Cons(x, xs), subsets(xs)) subsets(Nil) -> Cons(Nil, Nil) mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) mapconsapp(x, Nil, rest) -> rest notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs) -> subsets(xs) The (relative) TRS S consists of the following rules: subsets[Ite][True][Let](Cons(x, xs), subs) -> mapconsapp(x, subs, subs) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (4) 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: subsets(Cons(x, xs)) -> subsets[Ite][True][Let](Cons(x, xs), subsets(xs)) subsets(Nil) -> Cons(Nil, Nil) mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) mapconsapp(x, Nil, rest) -> rest notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs) -> subsets(xs) The (relative) TRS S consists of the following rules: subsets[Ite][True][Let](Cons(x, xs), subs) -> mapconsapp(x, subs, subs) popout

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all output return to Runtime Complexity: TRS Innermost