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Runti Compl Full Rewri 10127 pair #381902683
details
property
value
status
complete
benchmark
double.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.512068033 seconds
cpu usage
314.205518926
max memory
5.462867968E9
stage attributes
key
value
output-size
4808
starexec-result
WORST_CASE(Omega(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), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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: double(x) -> permute(x, x, a) permute(x, y, a) -> permute(isZero(x), x, b) permute(false, x, b) -> permute(ack(x, x), p(x), c) permute(true, x, b) -> 0 permute(y, x, c) -> s(s(permute(x, y, a))) p(0) -> 0 p(s(x)) -> x ack(0, x) -> plus(x, s(0)) ack(s(x), 0) -> ack(x, s(0)) ack(s(x), s(y)) -> ack(x, ack(s(x), y)) plus(0, y) -> y plus(s(x), y) -> plus(x, s(y)) plus(x, s(s(y))) -> s(plus(s(x), y)) plus(x, s(0)) -> s(x) plus(x, 0) -> x isZero(0) -> true isZero(s(x)) -> 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: double(x) -> permute(x, x, a) permute(x, y, a) -> permute(isZero(x), x, b) permute(false, x, b) -> permute(ack(x, x), p(x), c) permute(true, x, b) -> 0 permute(y, x, c) -> s(s(permute(x, y, a))) p(0) -> 0 p(s(x)) -> x ack(0, x) -> plus(x, s(0)) ack(s(x), 0) -> ack(x, s(0)) ack(s(x), s(y)) -> ack(x, ack(s(x), y)) plus(0, y) -> y plus(s(x), y) -> plus(x, s(y)) plus(x, s(s(y))) -> s(plus(s(x), y)) plus(x, s(0)) -> s(x) plus(x, 0) -> x isZero(0) -> true isZero(s(x)) -> 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 plus(x, s(s(y))) ->^+ s(plus(s(x), y)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [y / s(s(y))].
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