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Runti Compl Inner Rewri 22807 pair #381904041
details
property
value
status
complete
benchmark
tower_sizeChange.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_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.229116917 seconds
cpu usage
1111.79554164
max memory
1.2043251712E10
stage attributes
key
value
output-size
3935
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 12 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 (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: tower(x) -> f(a, x, s(0)) f(a, 0, y) -> y f(a, s(x), y) -> f(b, y, s(x)) f(b, y, x) -> f(a, half(x), exp(y)) exp(0) -> s(0) exp(s(x)) -> double(exp(x)) double(0) -> 0 double(s(x)) -> s(s(double(x))) half(0) -> double(0) half(s(0)) -> half(0) half(s(s(x))) -> s(half(x)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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 (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: tower(x) -> f(a, x, s(0)) f(a, 0, y) -> y f(a, s(x), y) -> f(b, y, s(x)) f(b, y, x) -> f(a, half(x), exp(y)) exp(0) -> s(0) exp(s(x)) -> double(exp(x)) double(0) -> 0 double(s(x)) -> s(s(double(x))) half(0) -> double(0) half(s(0)) -> half(0) half(s(s(x))) -> s(half(x)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence exp(s(x)) ->^+ double(exp(x)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [x / s(x)]. The result substitution is [ ]. ---------------------------------------- (4) Complex Obligation (BEST) ----------------------------------------
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