details

property	value
status	complete
benchmark	bintrees.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	Rubio_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.764 seconds
cpu usage	364.344
user time	360.373
system time	3.97051
max virtual memory	3.8377528E7
max residence set size	6380560.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 154 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (8) CdtProblem (9) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (10) CdtProblem (11) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 94 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 258 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 153 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 172 ms] (24) CdtProblem (25) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (26) BOUNDS(1, 1) (27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (28) TRS for Loop Detection (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (30) BEST (31) proven lower bound (32) LowerBoundPropagationProof [FINISHED, 0 ms] (33) BOUNDS(n^1, INF) (34) 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: concat(leaf, Y) -> Y concat(cons(U, V), Y) -> cons(U, concat(V, Y)) lessleaves(X, leaf) -> false lessleaves(leaf, cons(W, Z)) -> true lessleaves(cons(U, V), cons(W, Z)) -> lessleaves(concat(U, V), concat(W, Z)) 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(leaf) -> leaf encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(false) -> false encArg(true) -> true encArg(cons_concat(x_1, x_2)) -> concat(encArg(x_1), encArg(x_2)) encArg(cons_lessleaves(x_1, x_2)) -> lessleaves(encArg(x_1), encArg(x_2)) encode_concat(x_1, x_2) -> concat(encArg(x_1), encArg(x_2)) encode_leaf -> leaf encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_lessleaves(x_1, x_2) -> lessleaves(encArg(x_1), encArg(x_2)) encode_false -> false encode_true -> true ---------------------------------------- (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: concat(leaf, Y) -> Y concat(cons(U, V), Y) -> cons(U, concat(V, Y)) lessleaves(X, leaf) -> false lessleaves(leaf, cons(W, Z)) -> true lessleaves(cons(U, V), cons(W, Z)) -> lessleaves(concat(U, V), concat(W, Z)) The (relative) TRS S consists of the following rules: encArg(leaf) -> leaf encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(false) -> false popout

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all output return to Derivational Complexity: TRS