details

property	value
status	complete
benchmark	minsortSize.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	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.649 seconds
cpu usage	1120.45
user time	1106.86
system time	13.5863
max virtual memory	3.79084E7
max residence set size	1.4902444E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).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), 244 ms] (2) CpxRelTRS (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 0 ms] (8) typed CpxTrs (9) RewriteLemmaProof [LOWER BOUND(ID), 252 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 34 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 212 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs ---------------------------------------- (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: minsort(Cons(x, xs)) -> appmin(x, xs, Cons(x, xs)) minsort(Nil) -> Nil appmin(min, Cons(x, xs), xs') -> appmin[Ite][True][Ite](<(x, min), min, Cons(x, xs), xs') appmin(min, Nil, xs) -> Cons(min, minsort(remove(min, xs))) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False remove(x', Cons(x, xs)) -> remove[Ite](!EQ(x', x), x', Cons(x, xs)) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False remove[Ite](False, x', Cons(x, xs)) -> Cons(x, remove(x', xs)) appmin[Ite][True][Ite](True, min, Cons(x, xs), xs') -> appmin(x, xs, xs') remove[Ite](True, x', Cons(x, xs)) -> xs appmin[Ite][True][Ite](False, min, Cons(x, xs), xs') -> appmin(min, xs, 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, INF). The TRS R consists of the following rules: minsort(Cons(x, xs)) -> appmin(x, xs, Cons(x, xs)) minsort(Nil) -> Nil appmin(min, Cons(x, xs), xs') -> appmin[Ite][True][Ite](<(x, min), min, Cons(x, xs), xs') appmin(min, Nil, xs) -> Cons(min, minsort(remove(min, xs))) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False remove(x', Cons(x, xs)) -> remove[Ite](!EQ(x', x), x', Cons(x, xs)) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False remove[Ite](False, x', Cons(x, xs)) -> Cons(x, remove(x', xs)) appmin[Ite][True][Ite](True, min, Cons(x, xs), xs') -> appmin(x, xs, xs') remove[Ite](True, x', Cons(x, xs)) -> xs appmin[Ite][True][Ite](False, min, Cons(x, xs), xs') -> appmin(min, xs, xs') Rewrite Strategy: INNERMOST ---------------------------------------- (3) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. popout

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job log

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actions

all output return to Runtime Complexity: TRS Innermost