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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313494
details
property
value
status
complete
benchmark
LISTUTILITIES_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
296.798 seconds
cpu usage
1139.53
user time
1129.54
system time
9.99246
max virtual memory
1.8879924E7
max residence set size
1.4873048E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1119.51/291.72 WORST_CASE(Omega(n^1), ?) 1139.44/296.73 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1139.44/296.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1139.44/296.73 1139.44/296.73 1139.44/296.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1139.44/296.73 1139.44/296.73 (0) CpxTRS 1139.44/296.73 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1139.44/296.73 (2) TRS for Loop Detection 1139.44/296.73 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1139.44/296.73 (4) BEST 1139.44/296.73 (5) proven lower bound 1139.44/296.73 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1139.44/296.73 (7) BOUNDS(n^1, INF) 1139.44/296.73 (8) TRS for Loop Detection 1139.44/296.73 1139.44/296.73 1139.44/296.73 ---------------------------------------- 1139.44/296.73 1139.44/296.73 (0) 1139.44/296.73 Obligation: 1139.44/296.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1139.44/296.73 1139.44/296.73 1139.44/296.73 The TRS R consists of the following rules: 1139.44/296.73 1139.44/296.73 a__U101(tt, V1, V2) -> a__U102(a__isNatural(V1), V2) 1139.44/296.73 a__U102(tt, V2) -> a__U103(a__isLNat(V2)) 1139.44/296.73 a__U103(tt) -> tt 1139.44/296.73 a__U11(tt, N, XS) -> a__snd(a__splitAt(mark(N), mark(XS))) 1139.44/296.73 a__U111(tt, V1) -> a__U112(a__isLNat(V1)) 1139.44/296.73 a__U112(tt) -> tt 1139.44/296.73 a__U121(tt, V1) -> a__U122(a__isNatural(V1)) 1139.44/296.73 a__U122(tt) -> tt 1139.44/296.73 a__U131(tt, V1, V2) -> a__U132(a__isNatural(V1), V2) 1139.44/296.73 a__U132(tt, V2) -> a__U133(a__isLNat(V2)) 1139.44/296.73 a__U133(tt) -> tt 1139.44/296.73 a__U141(tt, V1, V2) -> a__U142(a__isLNat(V1), V2) 1139.44/296.73 a__U142(tt, V2) -> a__U143(a__isLNat(V2)) 1139.44/296.73 a__U143(tt) -> tt 1139.44/296.73 a__U151(tt, V1, V2) -> a__U152(a__isNatural(V1), V2) 1139.44/296.73 a__U152(tt, V2) -> a__U153(a__isLNat(V2)) 1139.44/296.73 a__U153(tt) -> tt 1139.44/296.73 a__U161(tt, N) -> cons(mark(N), natsFrom(s(N))) 1139.44/296.73 a__U171(tt, N, XS) -> a__head(a__afterNth(mark(N), mark(XS))) 1139.44/296.73 a__U181(tt, Y) -> mark(Y) 1139.44/296.73 a__U191(tt, XS) -> pair(nil, mark(XS)) 1139.44/296.73 a__U201(tt, N, X, XS) -> a__U202(a__splitAt(mark(N), mark(XS)), X) 1139.44/296.73 a__U202(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS)) 1139.44/296.73 a__U21(tt, X) -> mark(X) 1139.44/296.73 a__U211(tt, XS) -> mark(XS) 1139.44/296.73 a__U221(tt, N, XS) -> a__fst(a__splitAt(mark(N), mark(XS))) 1139.44/296.73 a__U31(tt, N) -> mark(N) 1139.44/296.73 a__U41(tt, V1, V2) -> a__U42(a__isNatural(V1), V2) 1139.44/296.73 a__U42(tt, V2) -> a__U43(a__isLNat(V2)) 1139.44/296.73 a__U43(tt) -> tt 1139.44/296.73 a__U51(tt, V1, V2) -> a__U52(a__isNatural(V1), V2) 1139.44/296.73 a__U52(tt, V2) -> a__U53(a__isLNat(V2)) 1139.44/296.73 a__U53(tt) -> tt 1139.44/296.73 a__U61(tt, V1) -> a__U62(a__isPLNat(V1)) 1139.44/296.73 a__U62(tt) -> tt 1139.44/296.73 a__U71(tt, V1) -> a__U72(a__isNatural(V1)) 1139.44/296.73 a__U72(tt) -> tt 1139.44/296.73 a__U81(tt, V1) -> a__U82(a__isPLNat(V1)) 1139.44/296.73 a__U82(tt) -> tt 1139.44/296.73 a__U91(tt, V1) -> a__U92(a__isLNat(V1)) 1139.44/296.73 a__U92(tt) -> tt 1139.44/296.73 a__afterNth(N, XS) -> a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS) 1139.44/296.73 a__and(tt, X) -> mark(X) 1139.44/296.73 a__fst(pair(X, Y)) -> a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), X) 1139.44/296.73 a__head(cons(N, XS)) -> a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N) 1139.44/296.73 a__isLNat(nil) -> tt 1139.44/296.73 a__isLNat(afterNth(V1, V2)) -> a__U41(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2) 1139.44/296.73 a__isLNat(cons(V1, V2)) -> a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2) 1139.44/296.73 a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1) 1139.44/296.73 a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1) 1139.44/296.73 a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1) 1139.44/296.73 a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1) 1139.44/296.73 a__isLNat(take(V1, V2)) -> a__U101(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2) 1139.44/296.73 a__isLNatKind(nil) -> tt 1139.44/296.73 a__isLNatKind(afterNth(V1, V2)) -> a__and(a__isNaturalKind(V1), isLNatKind(V2)) 1139.44/296.73 a__isLNatKind(cons(V1, V2)) -> a__and(a__isNaturalKind(V1), isLNatKind(V2)) 1139.44/296.73 a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1) 1139.44/296.73 a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1) 1139.44/296.73 a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1) 1139.44/296.73 a__isLNatKind(tail(V1)) -> a__isLNatKind(V1) 1139.44/296.73 a__isLNatKind(take(V1, V2)) -> a__and(a__isNaturalKind(V1), isLNatKind(V2)) 1139.44/296.73 a__isNatural(0) -> tt 1139.44/296.73 a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1), V1) 1139.44/296.73 a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1), V1) 1139.44/296.73 a__isNatural(sel(V1, V2)) -> a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2) 1139.44/296.73 a__isNaturalKind(0) -> tt 1139.44/296.73 a__isNaturalKind(head(V1)) -> a__isLNatKind(V1) 1139.44/296.73 a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1) 1139.44/296.73 a__isNaturalKind(sel(V1, V2)) -> a__and(a__isNaturalKind(V1), isLNatKind(V2)) 1139.44/296.73 a__isPLNat(pair(V1, V2)) -> a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)), V1, V2) 1139.44/296.73 a__isPLNat(splitAt(V1, V2)) -> a__U151(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2) 1139.44/296.73 a__isPLNatKind(pair(V1, V2)) -> a__and(a__isLNatKind(V1), isLNatKind(V2)) 1139.44/296.73 a__isPLNatKind(splitAt(V1, V2)) -> a__and(a__isNaturalKind(V1), isLNatKind(V2))
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40