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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313870
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
n173.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.599 seconds
cpu usage
1133.26
user time
1119.08
system time
14.1715
max virtual memory
3.7980304E7
max residence set size
1.4913152E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1132.82/291.50 WORST_CASE(Omega(n^1), ?) 1132.82/291.53 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1132.82/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1132.82/291.53 1132.82/291.53 1132.82/291.53 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1132.82/291.53 1132.82/291.53 (0) CpxRelTRS 1132.82/291.53 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 169 ms] 1132.82/291.53 (2) CpxRelTRS 1132.82/291.53 (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1132.82/291.53 (4) CpxRelTRS 1132.82/291.53 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1132.82/291.53 (6) typed CpxTrs 1132.82/291.53 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1132.82/291.53 (8) typed CpxTrs 1132.82/291.53 (9) RewriteLemmaProof [LOWER BOUND(ID), 286 ms] 1132.82/291.53 (10) typed CpxTrs 1132.82/291.53 (11) RewriteLemmaProof [LOWER BOUND(ID), 76 ms] 1132.82/291.53 (12) typed CpxTrs 1132.82/291.53 (13) RewriteLemmaProof [LOWER BOUND(ID), 188 ms] 1132.82/291.53 (14) BEST 1132.82/291.53 (15) proven lower bound 1132.82/291.53 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1132.82/291.53 (17) BOUNDS(n^1, INF) 1132.82/291.53 (18) typed CpxTrs 1132.82/291.53 1132.82/291.53 1132.82/291.53 ---------------------------------------- 1132.82/291.53 1132.82/291.53 (0) 1132.82/291.53 Obligation: 1132.82/291.53 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1132.82/291.53 1132.82/291.53 1132.82/291.53 The TRS R consists of the following rules: 1132.82/291.53 1132.82/291.53 minsort(Cons(x, xs)) -> appmin(x, xs, Cons(x, xs)) 1132.82/291.53 minsort(Nil) -> Nil 1132.82/291.53 appmin(min, Cons(x, xs), xs') -> appmin[Ite][True][Ite](<(x, min), min, Cons(x, xs), xs') 1132.82/291.53 appmin(min, Nil, xs) -> Cons(min, minsort(remove(min, xs))) 1132.82/291.53 notEmpty(Cons(x, xs)) -> True 1132.82/291.53 notEmpty(Nil) -> False 1132.82/291.53 remove(x', Cons(x, xs)) -> remove[Ite](!EQ(x', x), x', Cons(x, xs)) 1132.82/291.53 1132.82/291.53 The (relative) TRS S consists of the following rules: 1132.82/291.53 1132.82/291.53 !EQ(S(x), S(y)) -> !EQ(x, y) 1132.82/291.53 !EQ(0, S(y)) -> False 1132.82/291.53 !EQ(S(x), 0) -> False 1132.82/291.53 !EQ(0, 0) -> True 1132.82/291.53 <(S(x), S(y)) -> <(x, y) 1132.82/291.53 <(0, S(y)) -> True 1132.82/291.53 <(x, 0) -> False 1132.82/291.53 remove[Ite](False, x', Cons(x, xs)) -> Cons(x, remove(x', xs)) 1132.82/291.53 appmin[Ite][True][Ite](True, min, Cons(x, xs), xs') -> appmin(x, xs, xs') 1132.82/291.53 remove[Ite](True, x', Cons(x, xs)) -> xs 1132.82/291.53 appmin[Ite][True][Ite](False, min, Cons(x, xs), xs') -> appmin(min, xs, xs') 1132.82/291.53 1132.82/291.53 Rewrite Strategy: INNERMOST 1132.82/291.53 ---------------------------------------- 1132.82/291.53 1132.82/291.53 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 1132.82/291.53 proved termination of relative rules 1132.82/291.53 ---------------------------------------- 1132.82/291.53 1132.82/291.53 (2) 1132.82/291.53 Obligation: 1132.82/291.53 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1132.82/291.53 1132.82/291.53 1132.82/291.53 The TRS R consists of the following rules: 1132.82/291.53 1132.82/291.53 minsort(Cons(x, xs)) -> appmin(x, xs, Cons(x, xs)) 1132.82/291.53 minsort(Nil) -> Nil 1132.82/291.53 appmin(min, Cons(x, xs), xs') -> appmin[Ite][True][Ite](<(x, min), min, Cons(x, xs), xs') 1132.82/291.53 appmin(min, Nil, xs) -> Cons(min, minsort(remove(min, xs))) 1132.82/291.53 notEmpty(Cons(x, xs)) -> True 1132.82/291.53 notEmpty(Nil) -> False 1132.82/291.53 remove(x', Cons(x, xs)) -> remove[Ite](!EQ(x', x), x', Cons(x, xs)) 1132.82/291.53 1132.82/291.53 The (relative) TRS S consists of the following rules: 1132.82/291.53 1132.82/291.53 !EQ(S(x), S(y)) -> !EQ(x, y) 1132.82/291.53 !EQ(0, S(y)) -> False 1132.82/291.53 !EQ(S(x), 0) -> False 1132.82/291.53 !EQ(0, 0) -> True 1132.82/291.53 <(S(x), S(y)) -> <(x, y) 1132.82/291.53 <(0, S(y)) -> True 1132.82/291.53 <(x, 0) -> False 1132.82/291.53 remove[Ite](False, x', Cons(x, xs)) -> Cons(x, remove(x', xs)) 1132.82/291.53 appmin[Ite][True][Ite](True, min, Cons(x, xs), xs') -> appmin(x, xs, xs') 1132.82/291.53 remove[Ite](True, x', Cons(x, xs)) -> xs 1132.82/291.53 appmin[Ite][True][Ite](False, min, Cons(x, xs), xs') -> appmin(min, xs, xs') 1132.82/291.53 1132.82/291.53 Rewrite Strategy: INNERMOST 1132.82/291.53 ---------------------------------------- 1132.82/291.53 1132.82/291.53 (3) RenamingProof (BOTH BOUNDS(ID, ID)) 1132.82/291.53 Renamed function symbols to avoid clashes with predefined symbol.
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