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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313702
details
property
value
status
complete
benchmark
thiemann26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
17.5308 seconds
cpu usage
64.2468
user time
61.5381
system time
2.7087
max virtual memory
3.7308332E7
max residence set size
4294208.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
64.04/17.46 WORST_CASE(Omega(n^1), O(n^1)) 64.04/17.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 64.04/17.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 64.04/17.48 64.04/17.48 64.04/17.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 64.04/17.48 64.04/17.48 (0) CpxTRS 64.04/17.48 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 64.04/17.48 (2) CpxWeightedTrs 64.04/17.48 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 64.04/17.48 (4) CpxTypedWeightedTrs 64.04/17.48 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 64.04/17.48 (6) CpxTypedWeightedCompleteTrs 64.04/17.48 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 64.04/17.48 (8) CpxRNTS 64.04/17.48 (9) CompleteCoflocoProof [FINISHED, 1105 ms] 64.04/17.48 (10) BOUNDS(1, n^1) 64.04/17.48 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 64.04/17.48 (12) CpxTRS 64.04/17.48 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 64.04/17.48 (14) typed CpxTrs 64.04/17.48 (15) OrderProof [LOWER BOUND(ID), 0 ms] 64.04/17.48 (16) typed CpxTrs 64.04/17.48 (17) RewriteLemmaProof [LOWER BOUND(ID), 301 ms] 64.04/17.48 (18) BEST 64.04/17.48 (19) proven lower bound 64.04/17.48 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 64.04/17.48 (21) BOUNDS(n^1, INF) 64.04/17.48 (22) typed CpxTrs 64.04/17.48 (23) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] 64.04/17.48 (24) typed CpxTrs 64.04/17.48 64.04/17.48 64.04/17.48 ---------------------------------------- 64.04/17.48 64.04/17.48 (0) 64.04/17.48 Obligation: 64.04/17.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 64.04/17.48 64.04/17.48 64.04/17.48 The TRS R consists of the following rules: 64.04/17.48 64.04/17.48 ge(x, 0) -> true 64.04/17.48 ge(0, s(y)) -> false 64.04/17.48 ge(s(x), s(y)) -> ge(x, y) 64.04/17.48 minus(x, 0) -> x 64.04/17.48 minus(0, y) -> 0 64.04/17.48 minus(s(x), s(y)) -> minus(x, y) 64.04/17.48 id_inc(x) -> x 64.04/17.48 id_inc(x) -> s(x) 64.04/17.48 quot(x, y) -> div(x, y, 0) 64.04/17.48 div(x, y, z) -> if(ge(y, s(0)), ge(x, y), x, y, z) 64.04/17.48 if(false, b, x, y, z) -> div_by_zero 64.04/17.48 if(true, false, x, y, z) -> z 64.04/17.48 if(true, true, x, y, z) -> div(minus(x, y), y, id_inc(z)) 64.04/17.48 64.04/17.48 S is empty. 64.04/17.48 Rewrite Strategy: INNERMOST 64.04/17.48 ---------------------------------------- 64.04/17.48 64.04/17.48 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 64.04/17.48 Transformed relative TRS to weighted TRS 64.04/17.48 ---------------------------------------- 64.04/17.48 64.04/17.48 (2) 64.04/17.48 Obligation: 64.04/17.48 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 64.04/17.48 64.04/17.48 64.04/17.48 The TRS R consists of the following rules: 64.04/17.48 64.04/17.48 ge(x, 0) -> true [1] 64.04/17.48 ge(0, s(y)) -> false [1] 64.04/17.48 ge(s(x), s(y)) -> ge(x, y) [1] 64.04/17.48 minus(x, 0) -> x [1] 64.04/17.48 minus(0, y) -> 0 [1] 64.04/17.48 minus(s(x), s(y)) -> minus(x, y) [1] 64.04/17.48 id_inc(x) -> x [1] 64.04/17.48 id_inc(x) -> s(x) [1] 64.04/17.48 quot(x, y) -> div(x, y, 0) [1] 64.04/17.48 div(x, y, z) -> if(ge(y, s(0)), ge(x, y), x, y, z) [1] 64.04/17.48 if(false, b, x, y, z) -> div_by_zero [1] 64.04/17.48 if(true, false, x, y, z) -> z [1] 64.04/17.48 if(true, true, x, y, z) -> div(minus(x, y), y, id_inc(z)) [1] 64.04/17.48 64.04/17.48 Rewrite Strategy: INNERMOST 64.04/17.48 ---------------------------------------- 64.04/17.48 64.04/17.48 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 64.04/17.48 Infered types. 64.04/17.48 ---------------------------------------- 64.04/17.48 64.04/17.48 (4) 64.04/17.48 Obligation: 64.04/17.48 Runtime Complexity Weighted TRS with Types. 64.04/17.48 The TRS R consists of the following rules: 64.04/17.48 64.04/17.48 ge(x, 0) -> true [1] 64.04/17.48 ge(0, s(y)) -> false [1]
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