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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313689
details
property
value
status
complete
benchmark
parting04_maxsort_h.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.564 seconds
cpu usage
1039.7
user time
1029.48
system time
10.2209
max virtual memory
5.6802628E7
max residence set size
1.4708284E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1039.44/293.47 WORST_CASE(Omega(n^2), ?) 1039.44/293.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1039.44/293.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1039.44/293.48 1039.44/293.48 1039.44/293.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1039.44/293.48 1039.44/293.48 (0) CpxTRS 1039.44/293.48 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1039.44/293.48 (2) CpxTRS 1039.44/293.48 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1039.44/293.48 (4) typed CpxTrs 1039.44/293.48 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1039.44/293.48 (6) typed CpxTrs 1039.44/293.48 (7) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] 1039.44/293.48 (8) BEST 1039.44/293.48 (9) proven lower bound 1039.44/293.48 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1039.44/293.48 (11) BOUNDS(n^1, INF) 1039.44/293.48 (12) typed CpxTrs 1039.44/293.48 (13) RewriteLemmaProof [LOWER BOUND(ID), 27 ms] 1039.44/293.48 (14) typed CpxTrs 1039.44/293.48 (15) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] 1039.44/293.48 (16) typed CpxTrs 1039.44/293.48 (17) RewriteLemmaProof [LOWER BOUND(ID), 74 ms] 1039.44/293.48 (18) typed CpxTrs 1039.44/293.48 (19) RewriteLemmaProof [LOWER BOUND(ID), 70 ms] 1039.44/293.48 (20) proven lower bound 1039.44/293.48 (21) LowerBoundPropagationProof [FINISHED, 0 ms] 1039.44/293.48 (22) BOUNDS(n^2, INF) 1039.44/293.48 1039.44/293.48 1039.44/293.48 ---------------------------------------- 1039.44/293.48 1039.44/293.48 (0) 1039.44/293.48 Obligation: 1039.44/293.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1039.44/293.48 1039.44/293.48 1039.44/293.48 The TRS R consists of the following rules: 1039.44/293.48 1039.44/293.48 max(nil) -> 0 1039.44/293.48 max(cons(x, nil)) -> x 1039.44/293.48 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 1039.44/293.48 if1(true, x, y, xs) -> max(cons(x, xs)) 1039.44/293.48 if1(false, x, y, xs) -> max(cons(y, xs)) 1039.44/293.48 del(x, nil) -> nil 1039.44/293.48 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1039.44/293.48 if2(true, x, y, xs) -> xs 1039.44/293.48 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1039.44/293.48 eq(0, 0) -> true 1039.44/293.48 eq(0, s(y)) -> false 1039.44/293.48 eq(s(x), 0) -> false 1039.44/293.48 eq(s(x), s(y)) -> eq(x, y) 1039.44/293.48 sort(nil) -> nil 1039.44/293.48 sort(cons(x, xs)) -> cons(max(cons(x, xs)), sort(h(del(max(cons(x, xs)), cons(x, xs))))) 1039.44/293.48 ge(0, 0) -> true 1039.44/293.48 ge(s(x), 0) -> true 1039.44/293.48 ge(0, s(x)) -> false 1039.44/293.48 ge(s(x), s(y)) -> ge(x, y) 1039.44/293.48 h(nil) -> nil 1039.44/293.48 h(cons(x, xs)) -> cons(x, h(xs)) 1039.44/293.48 1039.44/293.48 S is empty. 1039.44/293.48 Rewrite Strategy: INNERMOST 1039.44/293.48 ---------------------------------------- 1039.44/293.48 1039.44/293.48 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1039.44/293.48 Renamed function symbols to avoid clashes with predefined symbol. 1039.44/293.48 ---------------------------------------- 1039.44/293.48 1039.44/293.48 (2) 1039.44/293.48 Obligation: 1039.44/293.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1039.44/293.48 1039.44/293.48 1039.44/293.48 The TRS R consists of the following rules: 1039.44/293.48 1039.44/293.48 max(nil) -> 0' 1039.44/293.48 max(cons(x, nil)) -> x 1039.44/293.48 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 1039.44/293.48 if1(true, x, y, xs) -> max(cons(x, xs)) 1039.44/293.48 if1(false, x, y, xs) -> max(cons(y, xs)) 1039.44/293.48 del(x, nil) -> nil 1039.44/293.48 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1039.44/293.48 if2(true, x, y, xs) -> xs 1039.44/293.48 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1039.44/293.48 eq(0', 0') -> true 1039.44/293.48 eq(0', s(y)) -> false 1039.44/293.48 eq(s(x), 0') -> false 1039.44/293.48 eq(s(x), s(y)) -> eq(x, y) 1039.44/293.48 sort(nil) -> nil 1039.44/293.48 sort(cons(x, xs)) -> cons(max(cons(x, xs)), sort(h(del(max(cons(x, xs)), cons(x, xs))))) 1039.44/293.48 ge(0', 0') -> true 1039.44/293.48 ge(s(x), 0') -> true 1039.44/293.48 ge(0', s(x)) -> false 1039.44/293.48 ge(s(x), s(y)) -> ge(x, y) 1039.44/293.48 h(nil) -> nil 1039.44/293.48 h(cons(x, xs)) -> cons(x, h(xs)) 1039.44/293.48
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
