details

property	value
status	complete
benchmark	LengthOfFiniteLists_complete-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.807 seconds
cpu usage	1166.36
user time	1158.37
system time	7.99775
max virtual memory	1.9322872E7
max residence set size	1.2174832E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 2484 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 247 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: zeros -> cons(0, n__zeros) U11(tt, V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) U12(tt, V1) -> U13(isNatList(activate(V1))) U13(tt) -> tt U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) U22(tt, V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt, V) -> U32(isNatIListKind(activate(V)), activate(V)) U32(tt, V) -> U33(isNatList(activate(V))) U33(tt) -> tt U41(tt, V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)) U42(tt, V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) U43(tt, V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) U44(tt, V1, V2) -> U45(isNat(activate(V1)), activate(V2)) U45(tt, V2) -> U46(isNatIList(activate(V2))) U46(tt) -> tt U51(tt, V2) -> U52(isNatIListKind(activate(V2))) U52(tt) -> tt U61(tt) -> tt U71(tt) -> tt U81(tt, V1, V2) -> U82(isNatKind(activate(V1)), activate(V1), activate(V2)) U82(tt, V1, V2) -> U83(isNatIListKind(activate(V2)), activate(V1), activate(V2)) U83(tt, V1, V2) -> U84(isNatIListKind(activate(V2)), activate(V1), activate(V2)) U84(tt, V1, V2) -> U85(isNat(activate(V1)), activate(V2)) U85(tt, V2) -> U86(isNatList(activate(V2))) U86(tt) -> tt U91(tt, L, N) -> U92(isNatIListKind(activate(L)), activate(L), activate(N)) U92(tt, L, N) -> U93(isNat(activate(N)), activate(L), activate(N)) U93(tt, L, N) -> U94(isNatKind(activate(N)), activate(L)) U94(tt, L) -> s(length(activate(L))) isNat(n__0) -> tt isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) isNatIList(n__zeros) -> tt isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)) isNatIListKind(n__nil) -> tt isNatIListKind(n__zeros) -> tt isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)) isNatKind(n__0) -> tt isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1))) isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1))) isNatList(n__nil) -> tt isNatList(n__cons(V1, V2)) -> U81(isNatKind(activate(V1)), activate(V1), activate(V2)) length(nil) -> 0 length(cons(N, L)) -> U91(isNatList(activate(L)), activate(L), N) zeros -> n__zeros 0 -> n__0 length(X) -> n__length(X) s(X) -> n__s(X) cons(X1, X2) -> n__cons(X1, X2) nil -> n__nil activate(n__zeros) -> zeros activate(n__0) -> 0 activate(n__length(X)) -> length(X) activate(n__s(X)) -> s(X) activate(n__cons(X1, X2)) -> cons(X1, X2) activate(n__nil) -> nil activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(n__zeros) -> n__zeros encArg(tt) -> tt popout

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job log

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actions

all output return to Derivational Complexity: TRS Innermost