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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308281
details
property
value
status
complete
benchmark
LISTUTILITIES_complete_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n125.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
12.6748 seconds
cpu usage
45.6063
user time
44.3783
system time
1.22799
max virtual memory
1.8279832E7
max residence set size
3965804.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
45.13/12.58 WORST_CASE(NON_POLY, ?) 45.13/12.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 45.13/12.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 45.13/12.61 45.13/12.61 45.13/12.61 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 45.13/12.61 45.13/12.61 (0) CpxTRS 45.13/12.61 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 45.13/12.61 (2) TRS for Loop Detection 45.13/12.61 (3) DecreasingLoopProof [LOWER BOUND(ID), 703 ms] 45.13/12.61 (4) BEST 45.13/12.61 (5) proven lower bound 45.13/12.61 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 45.13/12.61 (7) BOUNDS(n^1, INF) 45.13/12.61 (8) TRS for Loop Detection 45.13/12.61 (9) DecreasingLoopProof [FINISHED, 8145 ms] 45.13/12.61 (10) BOUNDS(EXP, INF) 45.13/12.61 45.13/12.61 45.13/12.61 ---------------------------------------- 45.13/12.61 45.13/12.61 (0) 45.13/12.61 Obligation: 45.13/12.61 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 45.13/12.61 45.13/12.61 45.13/12.61 The TRS R consists of the following rules: 45.13/12.61 45.13/12.61 U101(tt, V1, V2) -> U102(isNatural(activate(V1)), activate(V2)) 45.13/12.61 U102(tt, V2) -> U103(isLNat(activate(V2))) 45.13/12.61 U103(tt) -> tt 45.13/12.61 U11(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) 45.13/12.61 U111(tt, V1) -> U112(isLNat(activate(V1))) 45.13/12.61 U112(tt) -> tt 45.13/12.61 U121(tt, V1) -> U122(isNatural(activate(V1))) 45.13/12.61 U122(tt) -> tt 45.13/12.61 U131(tt, V1, V2) -> U132(isNatural(activate(V1)), activate(V2)) 45.13/12.61 U132(tt, V2) -> U133(isLNat(activate(V2))) 45.13/12.61 U133(tt) -> tt 45.13/12.61 U141(tt, V1, V2) -> U142(isLNat(activate(V1)), activate(V2)) 45.13/12.61 U142(tt, V2) -> U143(isLNat(activate(V2))) 45.13/12.61 U143(tt) -> tt 45.13/12.61 U151(tt, V1, V2) -> U152(isNatural(activate(V1)), activate(V2)) 45.13/12.61 U152(tt, V2) -> U153(isLNat(activate(V2))) 45.13/12.61 U153(tt) -> tt 45.13/12.61 U161(tt, N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 45.13/12.61 U171(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) 45.13/12.61 U181(tt, Y) -> activate(Y) 45.13/12.61 U191(tt, XS) -> pair(nil, activate(XS)) 45.13/12.61 U201(tt, N, X, XS) -> U202(splitAt(activate(N), activate(XS)), activate(X)) 45.13/12.61 U202(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 45.13/12.61 U21(tt, X) -> activate(X) 45.13/12.61 U211(tt, XS) -> activate(XS) 45.13/12.61 U221(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) 45.13/12.61 U31(tt, N) -> activate(N) 45.13/12.61 U41(tt, V1, V2) -> U42(isNatural(activate(V1)), activate(V2)) 45.13/12.61 U42(tt, V2) -> U43(isLNat(activate(V2))) 45.13/12.61 U43(tt) -> tt 45.13/12.61 U51(tt, V1, V2) -> U52(isNatural(activate(V1)), activate(V2)) 45.13/12.61 U52(tt, V2) -> U53(isLNat(activate(V2))) 45.13/12.61 U53(tt) -> tt 45.13/12.61 U61(tt, V1) -> U62(isPLNat(activate(V1))) 45.13/12.61 U62(tt) -> tt 45.13/12.61 U71(tt, V1) -> U72(isNatural(activate(V1))) 45.13/12.61 U72(tt) -> tt 45.13/12.61 U81(tt, V1) -> U82(isPLNat(activate(V1))) 45.13/12.61 U82(tt) -> tt 45.13/12.61 U91(tt, V1) -> U92(isLNat(activate(V1))) 45.13/12.61 U92(tt) -> tt 45.13/12.61 afterNth(N, XS) -> U11(and(and(isNatural(N), n__isNaturalKind(N)), n__and(isLNat(XS), n__isLNatKind(XS))), N, XS) 45.13/12.61 and(tt, X) -> activate(X) 45.13/12.61 fst(pair(X, Y)) -> U21(and(and(isLNat(X), n__isLNatKind(X)), n__and(isLNat(Y), n__isLNatKind(Y))), X) 45.13/12.61 head(cons(N, XS)) -> U31(and(and(isNatural(N), n__isNaturalKind(N)), n__and(isLNat(activate(XS)), n__isLNatKind(activate(XS)))), N) 45.13/12.61 isLNat(n__nil) -> tt 45.13/12.61 isLNat(n__afterNth(V1, V2)) -> U41(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) 45.13/12.61 isLNat(n__cons(V1, V2)) -> U51(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) 45.13/12.61 isLNat(n__fst(V1)) -> U61(isPLNatKind(activate(V1)), activate(V1)) 45.13/12.61 isLNat(n__natsFrom(V1)) -> U71(isNaturalKind(activate(V1)), activate(V1)) 45.13/12.61 isLNat(n__snd(V1)) -> U81(isPLNatKind(activate(V1)), activate(V1)) 45.13/12.61 isLNat(n__tail(V1)) -> U91(isLNatKind(activate(V1)), activate(V1)) 45.13/12.61 isLNat(n__take(V1, V2)) -> U101(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) 45.13/12.61 isLNatKind(n__nil) -> tt 45.13/12.61 isLNatKind(n__afterNth(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) 45.13/12.61 isLNatKind(n__cons(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) 45.13/12.61 isLNatKind(n__fst(V1)) -> isPLNatKind(activate(V1)) 45.13/12.61 isLNatKind(n__natsFrom(V1)) -> isNaturalKind(activate(V1)) 45.13/12.61 isLNatKind(n__snd(V1)) -> isPLNatKind(activate(V1)) 45.13/12.61 isLNatKind(n__tail(V1)) -> isLNatKind(activate(V1)) 45.13/12.61 isLNatKind(n__take(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) 45.13/12.61 isNatural(n__0) -> tt 45.13/12.61 isNatural(n__head(V1)) -> U111(isLNatKind(activate(V1)), activate(V1)) 45.13/12.61 isNatural(n__s(V1)) -> U121(isNaturalKind(activate(V1)), activate(V1)) 45.13/12.61 isNatural(n__sel(V1, V2)) -> U131(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) 45.13/12.61 isNaturalKind(n__0) -> tt 45.13/12.61 isNaturalKind(n__head(V1)) -> isLNatKind(activate(V1)) 45.13/12.61 isNaturalKind(n__s(V1)) -> isNaturalKind(activate(V1)) 45.13/12.61 isNaturalKind(n__sel(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) 45.13/12.61 isPLNat(n__pair(V1, V2)) -> U141(and(isLNatKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) 45.13/12.61 isPLNat(n__splitAt(V1, V2)) -> U151(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2))
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