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Runti Compl Inner Rewri 22807 pair #381905038
details
property
value
status
complete
benchmark
thiemann06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
41.2225039005 seconds
cpu usage
160.174671185
max memory
6.824349696E9
stage attributes
key
value
output-size
24525
starexec-result
WORST_CASE(Omega(n^1), O(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), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 709 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 285 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: p(s(x)) -> x p(0) -> 0 le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) average(x, y) -> if(le(x, 0), le(y, 0), le(y, s(0)), le(y, s(s(0))), x, y) if(true, b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y) if(false, b1, b2, b3, x, y) -> average(p(x), s(y)) if2(true, b2, b3, x, y) -> 0 if2(false, b2, b3, x, y) -> if3(b2, b3, x, y) if3(true, b3, x, y) -> 0 if3(false, b3, x, y) -> if4(b3, x, y) if4(true, x, y) -> s(0) if4(false, x, y) -> average(s(x), p(p(y))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: p(s(x)) -> x [1] p(0) -> 0 [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] average(x, y) -> if(le(x, 0), le(y, 0), le(y, s(0)), le(y, s(s(0))), x, y) [1] if(true, b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y) [1] if(false, b1, b2, b3, x, y) -> average(p(x), s(y)) [1] if2(true, b2, b3, x, y) -> 0 [1] if2(false, b2, b3, x, y) -> if3(b2, b3, x, y) [1] if3(true, b3, x, y) -> 0 [1] if3(false, b3, x, y) -> if4(b3, x, y) [1] if4(true, x, y) -> s(0) [1] if4(false, x, y) -> average(s(x), p(p(y))) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4)
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