details

property	value
status	complete
benchmark	Ex6_Luc98_Z.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	complexity
runtime (wallclock)	4.09823 seconds
cpu usage	12.0214
user time	11.0489
system time	0.972571
max virtual memory	7.4515108E7
max residence set size	3197364.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 63 ms] (8) CdtProblem (9) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (10) BOUNDS(1, 1) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) from(X) -> cons(X, n__from(s(X))) first(X1, X2) -> n__first(X1, X2) from(X) -> n__from(X) activate(n__first(X1, X2)) -> first(X1, X2) activate(n__from(X)) -> from(X) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: first(0, z0) -> nil first(s(z0), cons(z1, z2)) -> cons(z1, n__first(z0, activate(z2))) first(z0, z1) -> n__first(z0, z1) from(z0) -> cons(z0, n__from(s(z0))) from(z0) -> n__from(z0) activate(n__first(z0, z1)) -> first(z0, z1) activate(n__from(z0)) -> from(z0) activate(z0) -> z0 Tuples: FIRST(0, z0) -> c FIRST(s(z0), cons(z1, z2)) -> c1(ACTIVATE(z2)) FIRST(z0, z1) -> c2 FROM(z0) -> c3 FROM(z0) -> c4 ACTIVATE(n__first(z0, z1)) -> c5(FIRST(z0, z1)) ACTIVATE(n__from(z0)) -> c6(FROM(z0)) ACTIVATE(z0) -> c7 S tuples: FIRST(0, z0) -> c FIRST(s(z0), cons(z1, z2)) -> c1(ACTIVATE(z2)) FIRST(z0, z1) -> c2 FROM(z0) -> c3 FROM(z0) -> c4 ACTIVATE(n__first(z0, z1)) -> c5(FIRST(z0, z1)) ACTIVATE(n__from(z0)) -> c6(FROM(z0)) ACTIVATE(z0) -> c7 K tuples:none Defined Rule Symbols: first_2, from_1, activate_1 Defined Pair Symbols: FIRST_2, FROM_1, ACTIVATE_1 Compound Symbols: c, c1_1, c2, c3, c4, c5_1, c6_1, c7 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: FROM(z0) -> c4 FIRST(z0, z1) -> c2 FIRST(0, z0) -> c popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost