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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313798
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
n018.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.982 seconds
cpu usage
1135.53
user time
1121.26
system time
14.2716
max virtual memory
5.6609764E7
max residence set size
1.486722E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1133.74/291.58 WORST_CASE(Omega(n^1), ?) 1135.17/291.89 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1135.17/291.89 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1135.17/291.89 1135.17/291.89 1135.17/291.89 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1135.17/291.89 1135.17/291.89 (0) CpxRelTRS 1135.17/291.89 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 179 ms] 1135.17/291.89 (2) CpxRelTRS 1135.17/291.89 (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1135.17/291.89 (4) CpxRelTRS 1135.17/291.89 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1135.17/291.89 (6) typed CpxTrs 1135.17/291.89 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1135.17/291.89 (8) typed CpxTrs 1135.17/291.89 (9) RewriteLemmaProof [LOWER BOUND(ID), 273 ms] 1135.17/291.89 (10) typed CpxTrs 1135.17/291.89 (11) RewriteLemmaProof [LOWER BOUND(ID), 53 ms] 1135.17/291.89 (12) BEST 1135.17/291.89 (13) proven lower bound 1135.17/291.89 (14) LowerBoundPropagationProof [FINISHED, 0 ms] 1135.17/291.89 (15) BOUNDS(n^1, INF) 1135.17/291.89 (16) typed CpxTrs 1135.17/291.89 (17) RewriteLemmaProof [LOWER BOUND(ID), 28 ms] 1135.17/291.89 (18) typed CpxTrs 1135.17/291.89 1135.17/291.89 1135.17/291.89 ---------------------------------------- 1135.17/291.89 1135.17/291.89 (0) 1135.17/291.89 Obligation: 1135.17/291.89 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1135.17/291.89 1135.17/291.89 1135.17/291.89 The TRS R consists of the following rules: 1135.17/291.89 1135.17/291.89 remove(x', Cons(x, xs)) -> remove[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) 1135.17/291.89 remove(x, Nil) -> Nil 1135.17/291.89 minsort(Cons(x, xs)) -> appmin(x, xs, Cons(x, xs)) 1135.17/291.89 minsort(Nil) -> Nil 1135.17/291.89 appmin(min, Cons(x, xs), xs') -> appmin[Ite][True][Ite](<(x, min), min, Cons(x, xs), xs') 1135.17/291.89 appmin(min, Nil, xs) -> Cons(min, minsort(remove(min, xs))) 1135.17/291.89 notEmpty(Cons(x, xs)) -> True 1135.17/291.89 notEmpty(Nil) -> False 1135.17/291.89 goal(xs) -> minsort(xs) 1135.17/291.89 1135.17/291.89 The (relative) TRS S consists of the following rules: 1135.17/291.89 1135.17/291.89 !EQ(S(x), S(y)) -> !EQ(x, y) 1135.17/291.89 !EQ(0, S(y)) -> False 1135.17/291.89 !EQ(S(x), 0) -> False 1135.17/291.89 !EQ(0, 0) -> True 1135.17/291.89 <(S(x), S(y)) -> <(x, y) 1135.17/291.89 <(0, S(y)) -> True 1135.17/291.89 <(x, 0) -> False 1135.17/291.89 remove[Ite][True][Ite](False, x', Cons(x, xs)) -> Cons(x, remove(x', xs)) 1135.17/291.89 appmin[Ite][True][Ite](True, min, Cons(x, xs), xs') -> appmin(x, xs, xs') 1135.17/291.89 remove[Ite][True][Ite](True, x', Cons(x, xs)) -> xs 1135.17/291.89 appmin[Ite][True][Ite](False, min, Cons(x, xs), xs') -> appmin(min, xs, xs') 1135.17/291.89 1135.17/291.89 Rewrite Strategy: INNERMOST 1135.17/291.89 ---------------------------------------- 1135.17/291.89 1135.17/291.89 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 1135.17/291.89 proved termination of relative rules 1135.17/291.89 ---------------------------------------- 1135.17/291.89 1135.17/291.89 (2) 1135.17/291.89 Obligation: 1135.17/291.89 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1135.17/291.89 1135.17/291.89 1135.17/291.89 The TRS R consists of the following rules: 1135.17/291.89 1135.17/291.89 remove(x', Cons(x, xs)) -> remove[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) 1135.17/291.89 remove(x, Nil) -> Nil 1135.17/291.89 minsort(Cons(x, xs)) -> appmin(x, xs, Cons(x, xs)) 1135.17/291.89 minsort(Nil) -> Nil 1135.17/291.89 appmin(min, Cons(x, xs), xs') -> appmin[Ite][True][Ite](<(x, min), min, Cons(x, xs), xs') 1135.17/291.89 appmin(min, Nil, xs) -> Cons(min, minsort(remove(min, xs))) 1135.17/291.89 notEmpty(Cons(x, xs)) -> True 1135.17/291.89 notEmpty(Nil) -> False 1135.17/291.89 goal(xs) -> minsort(xs) 1135.17/291.89 1135.17/291.89 The (relative) TRS S consists of the following rules: 1135.17/291.89 1135.17/291.89 !EQ(S(x), S(y)) -> !EQ(x, y) 1135.17/291.89 !EQ(0, S(y)) -> False 1135.17/291.89 !EQ(S(x), 0) -> False 1135.17/291.89 !EQ(0, 0) -> True 1135.17/291.89 <(S(x), S(y)) -> <(x, y) 1135.17/291.89 <(0, S(y)) -> True 1135.17/291.89 <(x, 0) -> False 1135.17/291.89 remove[Ite][True][Ite](False, x', Cons(x, xs)) -> Cons(x, remove(x', xs)) 1135.17/291.89 appmin[Ite][True][Ite](True, min, Cons(x, xs), xs') -> appmin(x, xs, xs') 1135.17/291.89 remove[Ite][True][Ite](True, x', Cons(x, xs)) -> xs 1135.17/291.89 appmin[Ite][True][Ite](False, min, Cons(x, xs), xs') -> appmin(min, xs, xs') 1135.17/291.89 1135.17/291.89 Rewrite Strategy: INNERMOST
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40