details

property	value
status	complete
benchmark	jones6.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.68045306206 seconds
cpu usage	3.434030035
max memory	1.94473984E8

stage attributes

key	value
output-size	4730
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 40 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(a, empty) -> g(a, empty) f(a, cons(x, k)) -> f(cons(x, a), k) g(empty, d) -> d g(cons(x, k), d) -> g(k, cons(x, d)) 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(a, empty) -> g(a, empty) f(a, cons(x, k)) -> f(cons(x, a), k) g(empty, d) -> d g(cons(x, k), d) -> g(k, cons(x, d)) 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: empty0() -> 0 cons0(0, 0) -> 0 f0(0, 0) -> 1 g0(0, 0) -> 2 empty1() -> 3 g1(0, 3) -> 1 cons1(0, 0) -> 4 f1(4, 0) -> 1 cons1(0, 0) -> 5 g1(0, 5) -> 2 g1(4, 3) -> 1 cons1(0, 4) -> 4 cons1(0, 3) -> 5 g1(0, 5) -> 1 cons1(0, 5) -> 5 cons2(0, 3) -> 6 g2(0, 6) -> 1 g2(4, 6) -> 1 cons1(0, 6) -> 5 cons2(0, 6) -> 6 0 -> 2 3 -> 1 5 -> 2 5 -> 1 6 -> 1 ---------------------------------------- popout

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job log

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actions

all output return to Runti Compl Inner Rewri 22807