details

property	value
status	complete
benchmark	kabasci05.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	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.025710821 seconds
cpu usage	351.374611987
max memory	7.002497024E9

stage attributes

key	value
output-size	4807
starexec-result	WORST_CASE(Omega(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), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) minus(x, 0) -> x minus(s(x), s(y)) -> s(minus(x, y)) gcd(s(x), s(y)) -> gcd(minus(max(x, y), min(x, transform(y))), s(min(x, y))) transform(x) -> s(s(x)) transform(cons(x, y)) -> cons(cons(x, x), x) transform(cons(x, y)) -> y transform(s(x)) -> s(s(transform(x))) cons(x, y) -> y cons(x, cons(y, s(z))) -> cons(y, x) cons(cons(x, z), s(y)) -> transform(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) minus(x, 0) -> x minus(s(x), s(y)) -> s(minus(x, y)) gcd(s(x), s(y)) -> gcd(minus(max(x, y), min(x, transform(y))), s(min(x, y))) transform(x) -> s(s(x)) transform(cons(x, y)) -> cons(cons(x, x), x) transform(cons(x, y)) -> y transform(s(x)) -> s(s(transform(x))) cons(x, y) -> y cons(x, cons(y, s(z))) -> cons(y, x) cons(cons(x, z), s(y)) -> transform(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence minus(s(x), s(y)) ->^+ s(minus(x, y)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [x / s(x), y / s(y)]. The result substitution is [ ]. popout

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actions

all output return to Runti Compl Full Rewri 10127