details

property	value
status	complete
benchmark	Ex23_Luc06_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.518 seconds
cpu usage	336.497
user time	332.981
system time	3.51587
max virtual memory	1.8985136E7
max residence set size	6104984.0

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/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 51 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (16) CdtProblem (17) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 112 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 45 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 145 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 101 ms] (26) CdtProblem (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 85 ms] (28) CdtProblem (29) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 81 ms] (30) CdtProblem (31) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (32) BOUNDS(1, 1) (33) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (34) TRS for Loop Detection (35) DecreasingLoopProof [LOWER BOUND(ID), 8 ms] (36) BEST (37) proven lower bound (38) LowerBoundPropagationProof [FINISHED, 0 ms] (39) BOUNDS(n^1, INF) (40) TRS for Loop Detection ---------------------------------------- (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: f(f(a)) -> c(n__f(n__g(n__f(n__a)))) f(X) -> n__f(X) g(X) -> n__g(X) a -> n__a activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) activate(n__a) -> a activate(X) -> X 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(c(x_1)) -> c(encArg(x_1)) encArg(n__f(x_1)) -> n__f(encArg(x_1)) encArg(n__g(x_1)) -> n__g(encArg(x_1)) encArg(n__a) -> n__a encArg(cons_f(x_1)) -> f(encArg(x_1)) encArg(cons_g(x_1)) -> g(encArg(x_1)) encArg(cons_a) -> a encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_f(x_1) -> f(encArg(x_1)) encode_a -> a encode_c(x_1) -> c(encArg(x_1)) encode_n__f(x_1) -> n__f(encArg(x_1)) encode_n__g(x_1) -> n__g(encArg(x_1)) encode_n__a -> n__a encode_g(x_1) -> g(encArg(x_1)) encode_activate(x_1) -> activate(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). popout

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actions

all output return to Derivational Complexity: TRS