details

property	value
status	complete
benchmark	Ex16_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.488 seconds
cpu usage	348.605
user time	344.852
system time	3.75248
max virtual memory	3.810658E7
max residence set size	6326736.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 158 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedTrs (11) CompletionProof [UPPER BOUND(ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) CompleteCoflocoProof [FINISHED, 615 ms] (16) BOUNDS(1, n^2) (17) RenamingProof [BOTH BOUNDS(ID, ID), 3 ms] (18) CpxRelTRS (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) typed CpxTrs (21) OrderProof [LOWER BOUND(ID), 0 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 3590 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 43 ms] (30) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: a__f(X, X) -> a__f(a, b) a__b -> a mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(b) -> a__b mark(a) -> a a__f(X1, X2) -> f(X1, X2) a__b -> b S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(a) -> a encArg(b) -> b encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encArg(cons_a__f(x_1, x_2)) -> a__f(encArg(x_1), encArg(x_2)) encArg(cons_a__b) -> a__b encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__f(x_1, x_2) -> a__f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b encode_a__b -> a__b encode_mark(x_1) -> mark(encArg(x_1)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: a__f(X, X) -> a__f(a, b) a__b -> a mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(b) -> a__b mark(a) -> a a__f(X1, X2) -> f(X1, X2) a__b -> b The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) popout

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

job log

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actions

all output return to Derivational Complexity: TRS