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Derivational Complexity: TRS Innermost pair #487108206
details
property
value
status
complete
benchmark
LISTUTILITIES_nokinds_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
298.397 seconds
cpu usage
1168.16
user time
1157.9
system time
10.2534
max virtual memory
2.01288E7
max residence set size
1.476598E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 1208 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 9 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: U101(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) U11(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) U21(tt, X) -> activate(X) U31(tt, N) -> activate(N) U41(tt, N) -> cons(activate(N), n__natsFrom(n__s(activate(N)))) U51(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) U61(tt, Y) -> activate(Y) U71(tt, XS) -> pair(nil, activate(XS)) U81(tt, N, X, XS) -> U82(splitAt(activate(N), activate(XS)), activate(X)) U82(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) U91(tt, XS) -> activate(XS) afterNth(N, XS) -> U11(and(isNatural(N), n__isLNat(XS)), N, XS) and(tt, X) -> activate(X) fst(pair(X, Y)) -> U21(and(isLNat(X), n__isLNat(Y)), X) head(cons(N, XS)) -> U31(and(isNatural(N), n__isLNat(activate(XS))), N) isLNat(n__nil) -> tt isLNat(n__afterNth(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) isLNat(n__cons(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) isLNat(n__fst(V1)) -> isPLNat(activate(V1)) isLNat(n__natsFrom(V1)) -> isNatural(activate(V1)) isLNat(n__snd(V1)) -> isPLNat(activate(V1)) isLNat(n__tail(V1)) -> isLNat(activate(V1)) isLNat(n__take(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) isNatural(n__0) -> tt isNatural(n__head(V1)) -> isLNat(activate(V1)) isNatural(n__s(V1)) -> isNatural(activate(V1)) isNatural(n__sel(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) isPLNat(n__pair(V1, V2)) -> and(isLNat(activate(V1)), n__isLNat(activate(V2))) isPLNat(n__splitAt(V1, V2)) -> and(isNatural(activate(V1)), n__isLNat(activate(V2))) natsFrom(N) -> U41(isNatural(N), N) sel(N, XS) -> U51(and(isNatural(N), n__isLNat(XS)), N, XS) snd(pair(X, Y)) -> U61(and(isLNat(X), n__isLNat(Y)), Y) splitAt(0, XS) -> U71(isLNat(XS), XS) splitAt(s(N), cons(X, XS)) -> U81(and(isNatural(N), n__and(n__isNatural(X), n__isLNat(activate(XS)))), N, X, activate(XS)) tail(cons(N, XS)) -> U91(and(isNatural(N), n__isLNat(activate(XS))), activate(XS)) take(N, XS) -> U101(and(isNatural(N), n__isLNat(XS)), N, XS) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) isLNat(X) -> n__isLNat(X) nil -> n__nil afterNth(X1, X2) -> n__afterNth(X1, X2) cons(X1, X2) -> n__cons(X1, X2) fst(X) -> n__fst(X) snd(X) -> n__snd(X) tail(X) -> n__tail(X) take(X1, X2) -> n__take(X1, X2) 0 -> n__0 head(X) -> n__head(X) sel(X1, X2) -> n__sel(X1, X2) pair(X1, X2) -> n__pair(X1, X2) splitAt(X1, X2) -> n__splitAt(X1, X2) and(X1, X2) -> n__and(X1, X2) isNatural(X) -> n__isNatural(X) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__isLNat(X)) -> isLNat(X) activate(n__nil) -> nil activate(n__afterNth(X1, X2)) -> afterNth(activate(X1), activate(X2)) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__fst(X)) -> fst(activate(X)) activate(n__snd(X)) -> snd(activate(X)) activate(n__tail(X)) -> tail(activate(X)) activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) activate(n__0) -> 0 activate(n__head(X)) -> head(activate(X)) activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2)) activate(n__pair(X1, X2)) -> pair(activate(X1), activate(X2)) activate(n__splitAt(X1, X2)) -> splitAt(activate(X1), activate(X2)) activate(n__and(X1, X2)) -> and(activate(X1), X2)
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