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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308377
details
property
value
status
complete
benchmark
LISTUTILITIES_nokinds_Z.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)
291.63 seconds
cpu usage
396.522
user time
393.526
system time
2.99544
max virtual memory
1.8277336E7
max residence set size
6278880.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
396.43/291.58 WORST_CASE(Omega(n^1), ?) 396.43/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 396.43/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 396.43/291.59 396.43/291.59 396.43/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 396.43/291.59 396.43/291.59 (0) CpxTRS 396.43/291.59 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 396.43/291.59 (2) TRS for Loop Detection 396.43/291.59 (3) DecreasingLoopProof [LOWER BOUND(ID), 211 ms] 396.43/291.59 (4) BEST 396.43/291.59 (5) proven lower bound 396.43/291.59 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 396.43/291.59 (7) BOUNDS(n^1, INF) 396.43/291.59 (8) TRS for Loop Detection 396.43/291.59 396.43/291.59 396.43/291.59 ---------------------------------------- 396.43/291.59 396.43/291.59 (0) 396.43/291.59 Obligation: 396.43/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 396.43/291.59 396.43/291.59 396.43/291.59 The TRS R consists of the following rules: 396.43/291.59 396.43/291.59 U101(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) 396.43/291.59 U11(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) 396.43/291.59 U21(tt, X) -> activate(X) 396.43/291.59 U31(tt, N) -> activate(N) 396.43/291.59 U41(tt, N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 396.43/291.59 U51(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) 396.43/291.59 U61(tt, Y) -> activate(Y) 396.43/291.59 U71(tt, XS) -> pair(nil, activate(XS)) 396.43/291.59 U81(tt, N, X, XS) -> U82(splitAt(activate(N), activate(XS)), activate(X)) 396.43/291.59 U82(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 396.43/291.59 U91(tt, XS) -> activate(XS) 396.43/291.59 afterNth(N, XS) -> U11(and(isNatural(N), n__isLNat(XS)), N, XS) 396.43/291.59 and(tt, X) -> activate(X) 396.43/291.59 fst(pair(X, Y)) -> U21(and(isLNat(X), n__isLNat(Y)), X) 396.43/291.59 head(cons(N, XS)) -> U31(and(isNatural(N), n__isLNat(activate(XS))), N) 396.43/291.59 isLNat(n__nil) -> tt 396.43/291.59 isLNat(n__afterNth(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) 396.43/291.59 isLNat(n__cons(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) 396.43/291.59 isLNat(n__fst(V1)) -> isPLNat(activate(V1)) 396.43/291.59 isLNat(n__natsFrom(V1)) -> isNatural(activate(V1)) 396.43/291.59 isLNat(n__snd(V1)) -> isPLNat(activate(V1)) 396.43/291.59 isLNat(n__tail(V1)) -> isLNat(activate(V1)) 396.43/291.59 isLNat(n__take(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) 396.43/291.59 isNatural(n__0) -> tt 396.43/291.59 isNatural(n__head(V1)) -> isLNat(activate(V1)) 396.43/291.59 isNatural(n__s(V1)) -> isNatural(activate(V1)) 396.43/291.59 isNatural(n__sel(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) 396.43/291.59 isPLNat(n__pair(V1, V2)) -> and(isLNat(activate(V1)), n__isLNat(activate(V2))) 396.43/291.59 isPLNat(n__splitAt(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) 396.43/291.59 natsFrom(N) -> U41(isNatural(N), N) 396.43/291.59 sel(N, XS) -> U51(and(isNatural(N), n__isLNat(XS)), N, XS) 396.43/291.59 snd(pair(X, Y)) -> U61(and(isLNat(X), n__isLNat(Y)), Y) 396.43/291.59 splitAt(0, XS) -> U71(isLNat(XS), XS) 396.43/291.59 splitAt(s(N), cons(X, XS)) -> U81(and(isNatural(N), n__and(isNatural(X), n__isLNat(activate(XS)))), N, X, activate(XS)) 396.43/291.59 tail(cons(N, XS)) -> U91(and(isNatural(N), n__isLNat(activate(XS))), activate(XS)) 396.43/291.59 take(N, XS) -> U101(and(isNatural(N), n__isLNat(XS)), N, XS) 396.43/291.59 natsFrom(X) -> n__natsFrom(X) 396.43/291.59 isLNat(X) -> n__isLNat(X) 396.43/291.59 nil -> n__nil 396.43/291.59 afterNth(X1, X2) -> n__afterNth(X1, X2) 396.43/291.59 cons(X1, X2) -> n__cons(X1, X2) 396.43/291.59 fst(X) -> n__fst(X) 396.43/291.59 snd(X) -> n__snd(X) 396.43/291.59 tail(X) -> n__tail(X) 396.43/291.59 take(X1, X2) -> n__take(X1, X2) 396.43/291.59 0 -> n__0 396.43/291.59 head(X) -> n__head(X) 396.43/291.59 s(X) -> n__s(X) 396.43/291.59 sel(X1, X2) -> n__sel(X1, X2) 396.43/291.59 pair(X1, X2) -> n__pair(X1, X2) 396.43/291.59 splitAt(X1, X2) -> n__splitAt(X1, X2) 396.43/291.59 and(X1, X2) -> n__and(X1, X2) 396.43/291.59 activate(n__natsFrom(X)) -> natsFrom(X) 396.43/291.59 activate(n__isLNat(X)) -> isLNat(X) 396.43/291.59 activate(n__nil) -> nil 396.43/291.59 activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 396.43/291.59 activate(n__cons(X1, X2)) -> cons(X1, X2) 396.43/291.59 activate(n__fst(X)) -> fst(X) 396.43/291.59 activate(n__snd(X)) -> snd(X) 396.43/291.59 activate(n__tail(X)) -> tail(X) 396.43/291.59 activate(n__take(X1, X2)) -> take(X1, X2) 396.43/291.59 activate(n__0) -> 0 396.43/291.59 activate(n__head(X)) -> head(X) 396.43/291.59 activate(n__s(X)) -> s(X) 396.43/291.59 activate(n__sel(X1, X2)) -> sel(X1, X2) 396.43/291.59 activate(n__pair(X1, X2)) -> pair(X1, X2) 396.43/291.59 activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 396.43/291.59 activate(n__and(X1, X2)) -> and(X1, X2) 396.43/291.59 activate(X) -> X 396.43/291.59 396.43/291.59 S is empty. 396.43/291.59 Rewrite Strategy: FULL 396.43/291.59 ----------------------------------------
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