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Runti Compl Full Rewri 10127 pair #381902449
details
property
value
status
complete
benchmark
id_inc.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.034727097 seconds
cpu usage
335.180260166
max memory
9.08822528E9
stage attributes
key
value
output-size
3755
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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: f(s(x)) -> f(id_inc(c(x, x))) f(c(s(x), y)) -> g(c(x, y)) g(c(s(x), y)) -> g(c(y, x)) g(c(x, s(y))) -> g(c(y, x)) g(c(x, x)) -> f(x) id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) id_inc(s(x)) -> s(id_inc(x)) id_inc(0) -> 0 id_inc(0) -> s(0) 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: f(s(x)) -> f(id_inc(c(x, x))) f(c(s(x), y)) -> g(c(x, y)) g(c(s(x), y)) -> g(c(y, x)) g(c(x, s(y))) -> g(c(y, x)) g(c(x, x)) -> f(x) id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) id_inc(s(x)) -> s(id_inc(x)) id_inc(0) -> 0 id_inc(0) -> s(0) 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 id_inc(c(x, y)) ->^+ c(id_inc(x), id_inc(y)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [x / c(x, y)]. The result substitution is [ ]. ---------------------------------------- (4) Complex Obligation (BEST) ---------------------------------------- (5) Obligation: Proved the lower bound n^1 for the following obligation:
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