details

property	value
status	complete
benchmark	minsort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.583 seconds
cpu usage	1125.84
user time	1112.5
system time	13.3449
max virtual memory	1.9175832E7
max residence set size	1.5036724E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).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), 195 ms] (2) CpxRelTRS (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (4) TRS for Loop Detection (5) DecreasingLoopProof [LOWER BOUND(ID), 37 ms] (6) BEST (7) proven lower bound (8) LowerBoundPropagationProof [FINISHED, 0 ms] (9) BOUNDS(n^1, INF) (10) TRS for Loop Detection ---------------------------------------- (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: remove(x', Cons(x, xs)) -> remove[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) remove(x, Nil) -> Nil 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 goal(xs) -> minsort(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][True][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][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: remove(x', Cons(x, xs)) -> remove[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) remove(x, Nil) -> Nil 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 goal(xs) -> minsort(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][True][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][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) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (4) Obligation: popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost