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Runti Compl Inner Rewri 22807 pair #381904760
details
property
value
status
complete
benchmark
evenodd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.55847501755 seconds
cpu usage
3.563264434
max memory
2.1614592E8
stage attributes
key
value
output-size
5022
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 0 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: odd(Cons(x, xs)) -> even(xs) odd(Nil) -> False even(Cons(x, xs)) -> odd(xs) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False even(Nil) -> True evenodd(x) -> even(x) 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: odd(Cons(x, xs)) -> even(xs) odd(Nil) -> False even(Cons(x, xs)) -> odd(xs) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False even(Nil) -> True evenodd(x) -> even(x) 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 1. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2, 3, 4] transitions: Cons0(0, 0) -> 0 Nil0() -> 0 False0() -> 0 True0() -> 0 odd0(0) -> 1 even0(0) -> 2 notEmpty0(0) -> 3 evenodd0(0) -> 4 even1(0) -> 1 False1() -> 1 odd1(0) -> 2 True1() -> 3 False1() -> 3 True1() -> 2 even1(0) -> 4 even1(0) -> 2 False1() -> 2 odd1(0) -> 1 odd1(0) -> 4 True1() -> 1 True1() -> 4 False1() -> 4
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