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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313717
details
property
value
status
complete
benchmark
thiemann38.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n102.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.675 seconds
cpu usage
1128.39
user time
1114.21
system time
14.1769
max virtual memory
3.7789812E7
max residence set size
1.5103256E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1128.13/291.57 WORST_CASE(Omega(n^1), O(n^2)) 1128.16/291.58 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1128.16/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1128.16/291.58 1128.16/291.58 1128.16/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1128.16/291.58 1128.16/291.58 (0) CpxTRS 1128.16/291.58 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1128.16/291.58 (2) CpxWeightedTrs 1128.16/291.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1128.16/291.58 (4) CpxTypedWeightedTrs 1128.16/291.58 (5) CompletionProof [UPPER BOUND(ID), 1 ms] 1128.16/291.58 (6) CpxTypedWeightedCompleteTrs 1128.16/291.58 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1128.16/291.58 (8) CpxRNTS 1128.16/291.58 (9) CompleteCoflocoProof [FINISHED, 603 ms] 1128.16/291.58 (10) BOUNDS(1, n^2) 1128.16/291.58 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1128.16/291.58 (12) CpxTRS 1128.16/291.58 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1128.16/291.58 (14) typed CpxTrs 1128.16/291.58 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1128.16/291.58 (16) typed CpxTrs 1128.16/291.58 (17) RewriteLemmaProof [LOWER BOUND(ID), 238 ms] 1128.16/291.58 (18) BEST 1128.16/291.58 (19) proven lower bound 1128.16/291.58 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1128.16/291.58 (21) BOUNDS(n^1, INF) 1128.16/291.58 (22) typed CpxTrs 1128.16/291.58 (23) RewriteLemmaProof [LOWER BOUND(ID), 74 ms] 1128.16/291.58 (24) typed CpxTrs 1128.16/291.58 1128.16/291.58 1128.16/291.58 ---------------------------------------- 1128.16/291.58 1128.16/291.58 (0) 1128.16/291.58 Obligation: 1128.16/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1128.16/291.58 1128.16/291.58 1128.16/291.58 The TRS R consists of the following rules: 1128.16/291.58 1128.16/291.58 length(nil) -> 0 1128.16/291.58 length(cons(x, l)) -> s(length(l)) 1128.16/291.58 lt(x, 0) -> false 1128.16/291.58 lt(0, s(y)) -> true 1128.16/291.58 lt(s(x), s(y)) -> lt(x, y) 1128.16/291.58 head(cons(x, l)) -> x 1128.16/291.58 head(nil) -> undefined 1128.16/291.58 tail(nil) -> nil 1128.16/291.58 tail(cons(x, l)) -> l 1128.16/291.58 reverse(l) -> rev(0, l, nil, l) 1128.16/291.58 rev(x, l, accu, orig) -> if(lt(x, length(orig)), x, l, accu, orig) 1128.16/291.58 if(true, x, l, accu, orig) -> rev(s(x), tail(l), cons(head(l), accu), orig) 1128.16/291.58 if(false, x, l, accu, orig) -> accu 1128.16/291.58 1128.16/291.58 S is empty. 1128.16/291.58 Rewrite Strategy: INNERMOST 1128.16/291.58 ---------------------------------------- 1128.16/291.58 1128.16/291.58 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1128.16/291.58 Transformed relative TRS to weighted TRS 1128.16/291.58 ---------------------------------------- 1128.16/291.58 1128.16/291.58 (2) 1128.16/291.58 Obligation: 1128.16/291.58 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1128.16/291.58 1128.16/291.58 1128.16/291.58 The TRS R consists of the following rules: 1128.16/291.58 1128.16/291.58 length(nil) -> 0 [1] 1128.16/291.58 length(cons(x, l)) -> s(length(l)) [1] 1128.16/291.58 lt(x, 0) -> false [1] 1128.16/291.58 lt(0, s(y)) -> true [1] 1128.16/291.58 lt(s(x), s(y)) -> lt(x, y) [1] 1128.16/291.58 head(cons(x, l)) -> x [1] 1128.16/291.58 head(nil) -> undefined [1] 1128.16/291.58 tail(nil) -> nil [1] 1128.16/291.58 tail(cons(x, l)) -> l [1] 1128.16/291.58 reverse(l) -> rev(0, l, nil, l) [1] 1128.16/291.58 rev(x, l, accu, orig) -> if(lt(x, length(orig)), x, l, accu, orig) [1] 1128.16/291.58 if(true, x, l, accu, orig) -> rev(s(x), tail(l), cons(head(l), accu), orig) [1] 1128.16/291.58 if(false, x, l, accu, orig) -> accu [1] 1128.16/291.58 1128.16/291.58 Rewrite Strategy: INNERMOST 1128.16/291.58 ---------------------------------------- 1128.16/291.58 1128.16/291.58 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1128.16/291.58 Infered types. 1128.16/291.58 ---------------------------------------- 1128.16/291.58 1128.16/291.58 (4) 1128.16/291.58 Obligation: 1128.16/291.58 Runtime Complexity Weighted TRS with Types. 1128.16/291.58 The TRS R consists of the following rules: 1128.16/291.58 1128.16/291.58 length(nil) -> 0 [1] 1128.16/291.58 length(cons(x, l)) -> s(length(l)) [1]
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