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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313854
details
property
value
status
complete
benchmark
quicksortSize.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n164.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.877 seconds
cpu usage
1129.66
user time
1115.96
system time
13.7013
max virtual memory
3.7476132E7
max residence set size
1.5071864E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1116.46/291.55 WORST_CASE(Omega(n^1), ?) 1129.25/294.78 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1129.25/294.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1129.25/294.78 1129.25/294.78 1129.25/294.78 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1129.25/294.78 1129.25/294.78 (0) CpxRelTRS 1129.25/294.78 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 235 ms] 1129.25/294.78 (2) CpxRelTRS 1129.25/294.78 (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1129.25/294.78 (4) CpxRelTRS 1129.25/294.78 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1129.25/294.78 (6) typed CpxTrs 1129.25/294.78 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1129.25/294.78 (8) typed CpxTrs 1129.25/294.78 (9) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] 1129.25/294.78 (10) typed CpxTrs 1129.25/294.78 (11) RewriteLemmaProof [LOWER BOUND(ID), 48 ms] 1129.25/294.78 (12) BEST 1129.25/294.78 (13) proven lower bound 1129.25/294.78 (14) LowerBoundPropagationProof [FINISHED, 0 ms] 1129.25/294.78 (15) BOUNDS(n^1, INF) 1129.25/294.78 (16) typed CpxTrs 1129.25/294.78 (17) RewriteLemmaProof [LOWER BOUND(ID), 48 ms] 1129.25/294.78 (18) typed CpxTrs 1129.25/294.78 (19) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 1129.25/294.78 (20) typed CpxTrs 1129.25/294.78 (21) RewriteLemmaProof [LOWER BOUND(ID), 2 ms] 1129.25/294.78 (22) typed CpxTrs 1129.25/294.78 1129.25/294.78 1129.25/294.78 ---------------------------------------- 1129.25/294.78 1129.25/294.78 (0) 1129.25/294.78 Obligation: 1129.25/294.78 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1129.25/294.78 1129.25/294.78 1129.25/294.78 The TRS R consists of the following rules: 1129.25/294.78 1129.25/294.78 quicksort(Cons(x, Cons(x', xs))) -> part(x, Cons(x', xs)) 1129.25/294.78 quicksort(Cons(x, Nil)) -> Cons(x, Nil) 1129.25/294.78 quicksort(Nil) -> Nil 1129.25/294.78 partLt(x', Cons(x, xs)) -> partLt[Ite][True][Ite](<(x, x'), x', Cons(x, xs)) 1129.25/294.78 partLt(x, Nil) -> Nil 1129.25/294.78 partGt(x', Cons(x, xs)) -> partGt[Ite][True][Ite](>(x, x'), x', Cons(x, xs)) 1129.25/294.78 partGt(x, Nil) -> Nil 1129.25/294.78 app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) 1129.25/294.78 app(Nil, ys) -> ys 1129.25/294.78 notEmpty(Cons(x, xs)) -> True 1129.25/294.78 notEmpty(Nil) -> False 1129.25/294.78 part(x, xs) -> app(quicksort(partLt(x, xs)), Cons(x, quicksort(partGt(x, xs)))) 1129.25/294.78 goal(xs) -> quicksort(xs) 1129.25/294.78 1129.25/294.78 The (relative) TRS S consists of the following rules: 1129.25/294.78 1129.25/294.78 <(S(x), S(y)) -> <(x, y) 1129.25/294.78 <(0, S(y)) -> True 1129.25/294.78 <(x, 0) -> False 1129.25/294.78 >(S(x), S(y)) -> >(x, y) 1129.25/294.78 >(0, y) -> False 1129.25/294.78 >(S(x), 0) -> True 1129.25/294.78 partLt[Ite][True][Ite](True, x', Cons(x, xs)) -> Cons(x, partLt(x', xs)) 1129.25/294.78 partGt[Ite][True][Ite](True, x', Cons(x, xs)) -> Cons(x, partGt(x', xs)) 1129.25/294.78 partLt[Ite][True][Ite](False, x', Cons(x, xs)) -> partLt(x', xs) 1129.25/294.78 partGt[Ite][True][Ite](False, x', Cons(x, xs)) -> partGt(x', xs) 1129.25/294.78 1129.25/294.78 Rewrite Strategy: INNERMOST 1129.25/294.78 ---------------------------------------- 1129.25/294.78 1129.25/294.78 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 1129.25/294.78 proved termination of relative rules 1129.25/294.78 ---------------------------------------- 1129.25/294.78 1129.25/294.78 (2) 1129.25/294.78 Obligation: 1129.25/294.78 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1129.25/294.78 1129.25/294.78 1129.25/294.78 The TRS R consists of the following rules: 1129.25/294.78 1129.25/294.78 quicksort(Cons(x, Cons(x', xs))) -> part(x, Cons(x', xs)) 1129.25/294.78 quicksort(Cons(x, Nil)) -> Cons(x, Nil) 1129.25/294.78 quicksort(Nil) -> Nil 1129.25/294.78 partLt(x', Cons(x, xs)) -> partLt[Ite][True][Ite](<(x, x'), x', Cons(x, xs)) 1129.25/294.78 partLt(x, Nil) -> Nil 1129.25/294.78 partGt(x', Cons(x, xs)) -> partGt[Ite][True][Ite](>(x, x'), x', Cons(x, xs)) 1129.25/294.78 partGt(x, Nil) -> Nil 1129.25/294.78 app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) 1129.25/294.78 app(Nil, ys) -> ys 1129.25/294.78 notEmpty(Cons(x, xs)) -> True 1129.25/294.78 notEmpty(Nil) -> False 1129.25/294.78 part(x, xs) -> app(quicksort(partLt(x, xs)), Cons(x, quicksort(partGt(x, xs)))) 1129.25/294.78 goal(xs) -> quicksort(xs) 1129.25/294.78 1129.25/294.78 The (relative) TRS S consists of the following rules: 1129.25/294.78 1129.25/294.78 <(S(x), S(y)) -> <(x, y) 1129.25/294.78 <(0, S(y)) -> True
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
