details

property	value
status	complete
benchmark	LengthOfFiniteLists_complete_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.642 seconds
cpu usage	627.431
user time	621.19
system time	6.24121
max virtual memory	1.827932E7
max residence set size	1.0042956E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt, V1) -> a__U12(a__isNatIListKind(V1), V1) a__U12(tt, V1) -> a__U13(a__isNatList(V1)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) a__U22(tt, V1) -> a__U23(a__isNat(V1)) a__U23(tt) -> tt a__U31(tt, V) -> a__U32(a__isNatIListKind(V), V) a__U32(tt, V) -> a__U33(a__isNatList(V)) a__U33(tt) -> tt a__U41(tt, V1, V2) -> a__U42(a__isNatKind(V1), V1, V2) a__U42(tt, V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2) a__U43(tt, V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2) a__U44(tt, V1, V2) -> a__U45(a__isNat(V1), V2) a__U45(tt, V2) -> a__U46(a__isNatIList(V2)) a__U46(tt) -> tt a__U51(tt, V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt) -> tt a__U61(tt) -> tt a__U71(tt) -> tt a__U81(tt, V1, V2) -> a__U82(a__isNatKind(V1), V1, V2) a__U82(tt, V1, V2) -> a__U83(a__isNatIListKind(V2), V1, V2) a__U83(tt, V1, V2) -> a__U84(a__isNatIListKind(V2), V1, V2) a__U84(tt, V1, V2) -> a__U85(a__isNat(V1), V2) a__U85(tt, V2) -> a__U86(a__isNatList(V2)) a__U86(tt) -> tt a__U91(tt, L, N) -> a__U92(a__isNatIListKind(L), L, N) a__U92(tt, L, N) -> a__U93(a__isNat(N), L, N) a__U93(tt, L, N) -> a__U94(a__isNatKind(N), L) a__U94(tt, L) -> s(a__length(mark(L))) a__isNat(0) -> tt a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__U41(a__isNatKind(V1), V1, V2) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2) a__isNatKind(0) -> tt a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__U81(a__isNatKind(V1), V1, V2) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U91(a__isNatList(L), L, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X1, X2)) -> a__U22(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X1, X2)) -> a__U32(mark(X1), X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) mark(U45(X1, X2)) -> a__U45(mark(X1), X2) mark(U46(X)) -> a__U46(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1, X2)) -> a__U51(mark(X1), X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3) mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3) popout

output may be truncated. 'popout' for the full output.

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actions

all output return to Runtime Complexity: TRS