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Runti Compl Full Rewri 10127 pair #381902321
details
property
value
status
complete
benchmark
quotminus.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.455441952 seconds
cpu usage
930.671288052
max memory
1.5473037312E10
stage attributes
key
value
output-size
3555
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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: plus(0, Y) -> Y plus(s(X), Y) -> s(plus(X, Y)) min(X, 0) -> X min(s(X), s(Y)) -> min(X, Y) min(min(X, Y), Z) -> min(X, plus(Y, Z)) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) 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: plus(0, Y) -> Y plus(s(X), Y) -> s(plus(X, Y)) min(X, 0) -> X min(s(X), s(Y)) -> min(X, Y) min(min(X, Y), Z) -> min(X, plus(Y, Z)) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) 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 min(s(X), s(Y)) ->^+ min(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 [ ]. ---------------------------------------- (4) Complex Obligation (BEST) ---------------------------------------- (5) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
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