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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313909
details
property
value
status
complete
benchmark
maxsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.468 seconds
cpu usage
1120.37
user time
1107.76
system time
12.612
max virtual memory
5.6805028E7
max residence set size
1.4864404E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1108.68/291.48 WORST_CASE(Omega(n^2), ?) 1120.08/294.39 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1120.08/294.39 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1120.08/294.39 1120.08/294.39 1120.08/294.39 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1120.08/294.39 1120.08/294.39 (0) CpxTRS 1120.08/294.39 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1120.08/294.39 (2) CpxTRS 1120.08/294.39 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1120.08/294.39 (4) typed CpxTrs 1120.08/294.39 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1120.08/294.39 (6) typed CpxTrs 1120.08/294.39 (7) RewriteLemmaProof [LOWER BOUND(ID), 308 ms] 1120.08/294.39 (8) BEST 1120.08/294.39 (9) proven lower bound 1120.08/294.39 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1120.08/294.39 (11) BOUNDS(n^1, INF) 1120.08/294.39 (12) typed CpxTrs 1120.08/294.39 (13) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] 1120.08/294.39 (14) typed CpxTrs 1120.08/294.39 (15) RewriteLemmaProof [LOWER BOUND(ID), 43 ms] 1120.08/294.39 (16) typed CpxTrs 1120.08/294.39 (17) RewriteLemmaProof [LOWER BOUND(ID), 48 ms] 1120.08/294.39 (18) proven lower bound 1120.08/294.39 (19) LowerBoundPropagationProof [FINISHED, 0 ms] 1120.08/294.39 (20) BOUNDS(n^2, INF) 1120.08/294.39 1120.08/294.39 1120.08/294.39 ---------------------------------------- 1120.08/294.39 1120.08/294.39 (0) 1120.08/294.39 Obligation: 1120.08/294.39 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1120.08/294.39 1120.08/294.39 1120.08/294.39 The TRS R consists of the following rules: 1120.08/294.39 1120.08/294.39 max(nil) -> 0 1120.08/294.39 max(cons(x, nil)) -> x 1120.08/294.39 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 1120.08/294.39 if1(true, x, y, xs) -> max(cons(x, xs)) 1120.08/294.39 if1(false, x, y, xs) -> max(cons(y, xs)) 1120.08/294.39 del(x, nil) -> nil 1120.08/294.39 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1120.08/294.39 if2(true, x, y, xs) -> xs 1120.08/294.39 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1120.08/294.39 eq(0, 0) -> true 1120.08/294.39 eq(0, s(y)) -> false 1120.08/294.39 eq(s(x), 0) -> false 1120.08/294.39 eq(s(x), s(y)) -> eq(x, y) 1120.08/294.39 sort(nil) -> nil 1120.08/294.39 sort(cons(x, xs)) -> cons(max(cons(x, xs)), sort(del(max(cons(x, xs)), cons(x, xs)))) 1120.08/294.39 ge(x, 0) -> true 1120.08/294.39 ge(0, s(x)) -> false 1120.08/294.39 ge(s(x), s(y)) -> ge(x, y) 1120.08/294.39 1120.08/294.39 S is empty. 1120.08/294.39 Rewrite Strategy: INNERMOST 1120.08/294.39 ---------------------------------------- 1120.08/294.39 1120.08/294.39 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1120.08/294.39 Renamed function symbols to avoid clashes with predefined symbol. 1120.08/294.39 ---------------------------------------- 1120.08/294.39 1120.08/294.39 (2) 1120.08/294.39 Obligation: 1120.08/294.39 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1120.08/294.39 1120.08/294.39 1120.08/294.39 The TRS R consists of the following rules: 1120.08/294.39 1120.08/294.39 max(nil) -> 0' 1120.08/294.39 max(cons(x, nil)) -> x 1120.08/294.39 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 1120.08/294.39 if1(true, x, y, xs) -> max(cons(x, xs)) 1120.08/294.39 if1(false, x, y, xs) -> max(cons(y, xs)) 1120.08/294.39 del(x, nil) -> nil 1120.08/294.39 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1120.08/294.39 if2(true, x, y, xs) -> xs 1120.08/294.39 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1120.08/294.39 eq(0', 0') -> true 1120.08/294.39 eq(0', s(y)) -> false 1120.08/294.39 eq(s(x), 0') -> false 1120.08/294.39 eq(s(x), s(y)) -> eq(x, y) 1120.08/294.39 sort(nil) -> nil 1120.08/294.39 sort(cons(x, xs)) -> cons(max(cons(x, xs)), sort(del(max(cons(x, xs)), cons(x, xs)))) 1120.08/294.39 ge(x, 0') -> true 1120.08/294.39 ge(0', s(x)) -> false 1120.08/294.39 ge(s(x), s(y)) -> ge(x, y) 1120.08/294.39 1120.08/294.39 S is empty. 1120.08/294.39 Rewrite Strategy: INNERMOST 1120.08/294.39 ---------------------------------------- 1120.08/294.39 1120.08/294.39 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1120.08/294.39 Infered types. 1120.08/294.39 ---------------------------------------- 1120.08/294.39
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