details

property	value
status	complete
benchmark	LengthOfFiniteLists_nosorts_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	4.30811 seconds
cpu usage	13.9719
user time	13.0004
system time	0.971572
max virtual memory	3.6848012E7
max residence set size	3185468.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 302 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection (13) InfiniteLowerBoundProof [FINISHED, 1678 ms] (14) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U11(tt, L) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(zeros) -> zeros encArg(tt) -> tt encArg(s(x_1)) -> s(encArg(x_1)) encArg(nil) -> nil encArg(U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(U12(x_1, x_2)) -> U12(encArg(x_1), encArg(x_2)) encArg(length(x_1)) -> length(encArg(x_1)) encArg(cons_a__zeros) -> a__zeros encArg(cons_a__U11(x_1, x_2)) -> a__U11(encArg(x_1), encArg(x_2)) encArg(cons_a__U12(x_1, x_2)) -> a__U12(encArg(x_1), encArg(x_2)) encArg(cons_a__length(x_1)) -> a__length(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__zeros -> a__zeros encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_zeros -> zeros encode_a__U11(x_1, x_2) -> a__U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_a__U12(x_1, x_2) -> a__U12(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_a__length(x_1) -> a__length(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_nil -> nil encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_U12(x_1, x_2) -> U12(encArg(x_1), encArg(x_2)) encode_length(x_1) -> length(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt, L) -> a__U12(tt, L) popout

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

job log

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actions

all output return to Derivational Complexity: TRS Innermost