details

property	value
status	complete
benchmark	ex6.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.75131 seconds
cpu usage	3.73916
user time	3.57771
system time	0.161449
max virtual memory	1.827736E7
max residence set size	250972.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsTAProof [FINISHED, 21 ms] (4) BOUNDS(1, n^1) (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 ---------------------------------------- (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: g(S(x), y) -> g(x, S(y)) f(y, S(x)) -> f(S(y), x) g(0, x2) -> x2 f(x1, 0) -> g(x1, 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: g(S(x), y) -> g(x, S(y)) f(y, S(x)) -> f(S(y), x) g(0, x2) -> x2 f(x1, 0) -> g(x1, 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsTAProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2] transitions: S0(0) -> 0 00() -> 0 g0(0, 0) -> 1 f0(0, 0) -> 2 S1(0) -> 3 g1(0, 3) -> 1 S1(0) -> 4 f1(4, 0) -> 2 01() -> 5 g1(0, 5) -> 2 S1(3) -> 3 S1(5) -> 3 g1(0, 3) -> 2 S1(4) -> 4 g1(4, 5) -> 2 S2(5) -> 6 g2(0, 6) -> 2 g2(4, 6) -> 2 S1(6) -> 3 S2(6) -> 6 0 -> 1 3 -> 1 3 -> 2 5 -> 2 6 -> 2 ---------------------------------------- (4) BOUNDS(1, n^1) ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) popout

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actions

all output return to Runtime Complexity: TRS Innermost