details

property	value
status	complete
benchmark	21.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	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.98063612 seconds
cpu usage	310.498156685
max memory	5.28080896E9

stage attributes

key	value
output-size	4517
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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: cond1(true, x, y, z) -> cond2(gr(y, z), x, y, z) cond2(true, x, y, z) -> cond2(gr(y, z), p(x), p(y), z) cond2(false, x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x eq(0, 0) -> true eq(s(x), 0) -> false eq(0, s(x)) -> false eq(s(x), s(y)) -> eq(x, y) and(true, true) -> true and(false, x) -> false and(x, false) -> false 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: cond1(true, x, y, z) -> cond2(gr(y, z), x, y, z) cond2(true, x, y, z) -> cond2(gr(y, z), p(x), p(y), z) cond2(false, x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x eq(0, 0) -> true eq(s(x), 0) -> false eq(0, s(x)) -> false eq(s(x), s(y)) -> eq(x, y) and(true, true) -> true and(false, x) -> false and(x, false) -> false 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 gr(s(x), s(y)) ->^+ gr(x, y) gives rise to a decreasing loop by considering the right hand sides subterm at position []. 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