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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313688
details
property
value
status
complete
benchmark
parting03_minsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n013.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.741 seconds
cpu usage
1106.19
user time
1092.94
system time
13.2476
max virtual memory
3.7648448E7
max residence set size
1.4795152E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1105.39/291.54 WORST_CASE(Omega(n^2), ?) 1105.99/291.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1105.99/291.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1105.99/291.67 1105.99/291.67 1105.99/291.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1105.99/291.67 1105.99/291.67 (0) CpxTRS 1105.99/291.67 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1105.99/291.67 (2) CpxTRS 1105.99/291.67 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1105.99/291.67 (4) typed CpxTrs 1105.99/291.67 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1105.99/291.67 (6) typed CpxTrs 1105.99/291.67 (7) RewriteLemmaProof [LOWER BOUND(ID), 297 ms] 1105.99/291.67 (8) BEST 1105.99/291.67 (9) proven lower bound 1105.99/291.67 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1105.99/291.67 (11) BOUNDS(n^1, INF) 1105.99/291.67 (12) typed CpxTrs 1105.99/291.67 (13) RewriteLemmaProof [LOWER BOUND(ID), 74 ms] 1105.99/291.67 (14) typed CpxTrs 1105.99/291.67 (15) RewriteLemmaProof [LOWER BOUND(ID), 40 ms] 1105.99/291.67 (16) typed CpxTrs 1105.99/291.67 (17) RewriteLemmaProof [LOWER BOUND(ID), 19 ms] 1105.99/291.67 (18) proven lower bound 1105.99/291.67 (19) LowerBoundPropagationProof [FINISHED, 0 ms] 1105.99/291.67 (20) BOUNDS(n^2, INF) 1105.99/291.67 1105.99/291.67 1105.99/291.67 ---------------------------------------- 1105.99/291.67 1105.99/291.67 (0) 1105.99/291.67 Obligation: 1105.99/291.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1105.99/291.67 1105.99/291.67 1105.99/291.67 The TRS R consists of the following rules: 1105.99/291.67 1105.99/291.67 le(0, y) -> true 1105.99/291.67 le(s(x), 0) -> false 1105.99/291.67 le(s(x), s(y)) -> le(x, y) 1105.99/291.67 eq(0, 0) -> true 1105.99/291.67 eq(0, s(y)) -> false 1105.99/291.67 eq(s(x), 0) -> false 1105.99/291.67 eq(s(x), s(y)) -> eq(x, y) 1105.99/291.67 if1(true, x, y, xs) -> min(x, xs) 1105.99/291.67 if1(false, x, y, xs) -> min(y, xs) 1105.99/291.67 if2(true, x, y, xs) -> xs 1105.99/291.67 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1105.99/291.67 minsort(nil) -> nil 1105.99/291.67 minsort(cons(x, y)) -> cons(min(x, y), minsort(del(min(x, y), cons(x, y)))) 1105.99/291.67 min(x, nil) -> x 1105.99/291.67 min(x, cons(y, z)) -> if1(le(x, y), x, y, z) 1105.99/291.67 del(x, nil) -> nil 1105.99/291.67 del(x, cons(y, z)) -> if2(eq(x, y), x, y, z) 1105.99/291.67 1105.99/291.67 S is empty. 1105.99/291.67 Rewrite Strategy: INNERMOST 1105.99/291.67 ---------------------------------------- 1105.99/291.67 1105.99/291.67 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1105.99/291.67 Renamed function symbols to avoid clashes with predefined symbol. 1105.99/291.67 ---------------------------------------- 1105.99/291.67 1105.99/291.67 (2) 1105.99/291.67 Obligation: 1105.99/291.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1105.99/291.67 1105.99/291.67 1105.99/291.67 The TRS R consists of the following rules: 1105.99/291.67 1105.99/291.67 le(0', y) -> true 1105.99/291.67 le(s(x), 0') -> false 1105.99/291.67 le(s(x), s(y)) -> le(x, y) 1105.99/291.67 eq(0', 0') -> true 1105.99/291.67 eq(0', s(y)) -> false 1105.99/291.67 eq(s(x), 0') -> false 1105.99/291.67 eq(s(x), s(y)) -> eq(x, y) 1105.99/291.67 if1(true, x, y, xs) -> min(x, xs) 1105.99/291.67 if1(false, x, y, xs) -> min(y, xs) 1105.99/291.67 if2(true, x, y, xs) -> xs 1105.99/291.67 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1105.99/291.67 minsort(nil) -> nil 1105.99/291.67 minsort(cons(x, y)) -> cons(min(x, y), minsort(del(min(x, y), cons(x, y)))) 1105.99/291.67 min(x, nil) -> x 1105.99/291.67 min(x, cons(y, z)) -> if1(le(x, y), x, y, z) 1105.99/291.67 del(x, nil) -> nil 1105.99/291.67 del(x, cons(y, z)) -> if2(eq(x, y), x, y, z) 1105.99/291.67 1105.99/291.67 S is empty. 1105.99/291.67 Rewrite Strategy: INNERMOST 1105.99/291.67 ---------------------------------------- 1105.99/291.67 1105.99/291.67 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1105.99/291.67 Infered types. 1105.99/291.67 ---------------------------------------- 1105.99/291.67 1105.99/291.67 (4) 1105.99/291.67 Obligation:
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