details

property	value
status	complete
benchmark	z23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.27500200272 seconds
cpu usage	6.684495821
max memory	6.37947904E8

stage attributes

key	value
output-size	5195
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 403 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: f(x, a(b(c(y)))) -> f(b(c(a(b(x)))), y) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) f(c(x), y) -> f(x, c(y)) 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: f(x, a(b(c(y)))) -> f(b(c(a(b(x)))), y) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) f(c(x), y) -> f(x, c(y)) 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 3. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1] transitions: a0(0) -> 0 b0(0) -> 0 c0(0) -> 0 f0(0, 0) -> 1 b1(0) -> 5 a1(5) -> 4 c1(4) -> 3 b1(3) -> 2 f1(2, 0) -> 1 a1(0) -> 6 f1(0, 6) -> 1 b1(0) -> 7 f1(0, 7) -> 1 c1(0) -> 8 f1(0, 8) -> 1 b1(2) -> 5 a1(6) -> 6 a1(7) -> 6 a1(8) -> 6 b1(6) -> 7 b1(7) -> 7 b1(8) -> 7 b2(0) -> 9 f2(3, 9) -> 1 c1(6) -> 8 c1(7) -> 8 c1(8) -> 8 b2(0) -> 13 popout

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actions

all output return to Runti Compl Inner Rewri 22807