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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313701
details
property
value
status
complete
benchmark
thiemann34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.576 seconds
cpu usage
1091.92
user time
1084.06
system time
7.86351
max virtual memory
5.7194812E7
max residence set size
6022464.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1091.55/291.51 WORST_CASE(Omega(n^1), O(n^2)) 1091.80/291.54 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1091.80/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1091.80/291.54 1091.80/291.54 1091.80/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1091.80/291.54 1091.80/291.54 (0) CpxTRS 1091.80/291.54 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1091.80/291.54 (2) CpxWeightedTrs 1091.80/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1091.80/291.54 (4) CpxTypedWeightedTrs 1091.80/291.54 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1091.80/291.54 (6) CpxTypedWeightedCompleteTrs 1091.80/291.54 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1091.80/291.54 (8) CpxRNTS 1091.80/291.54 (9) CompleteCoflocoProof [FINISHED, 804 ms] 1091.80/291.54 (10) BOUNDS(1, n^2) 1091.80/291.54 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1091.80/291.54 (12) CpxTRS 1091.80/291.54 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1091.80/291.54 (14) typed CpxTrs 1091.80/291.54 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1091.80/291.54 (16) typed CpxTrs 1091.80/291.54 (17) RewriteLemmaProof [LOWER BOUND(ID), 293 ms] 1091.80/291.54 (18) BEST 1091.80/291.54 (19) proven lower bound 1091.80/291.54 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1091.80/291.54 (21) BOUNDS(n^1, INF) 1091.80/291.54 (22) typed CpxTrs 1091.80/291.54 (23) RewriteLemmaProof [LOWER BOUND(ID), 94 ms] 1091.80/291.54 (24) typed CpxTrs 1091.80/291.54 1091.80/291.54 1091.80/291.54 ---------------------------------------- 1091.80/291.54 1091.80/291.54 (0) 1091.80/291.54 Obligation: 1091.80/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1091.80/291.54 1091.80/291.54 1091.80/291.54 The TRS R consists of the following rules: 1091.80/291.54 1091.80/291.54 gt(s(x), 0) -> true 1091.80/291.54 gt(0, y) -> false 1091.80/291.54 gt(s(x), s(y)) -> gt(x, y) 1091.80/291.54 divides(x, y) -> div(x, y, y) 1091.80/291.54 div(0, 0, z) -> true 1091.80/291.54 div(0, s(x), z) -> false 1091.80/291.54 div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) 1091.80/291.54 div(s(x), s(y), z) -> div(x, y, z) 1091.80/291.54 prime(x) -> test(x, s(s(0))) 1091.80/291.54 test(x, y) -> if1(gt(x, y), x, y) 1091.80/291.54 if1(true, x, y) -> if2(divides(x, y), x, y) 1091.80/291.54 if1(false, x, y) -> true 1091.80/291.54 if2(true, x, y) -> false 1091.80/291.54 if2(false, x, y) -> test(x, s(y)) 1091.80/291.54 1091.80/291.54 S is empty. 1091.80/291.54 Rewrite Strategy: INNERMOST 1091.80/291.54 ---------------------------------------- 1091.80/291.54 1091.80/291.54 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1091.80/291.54 Transformed relative TRS to weighted TRS 1091.80/291.54 ---------------------------------------- 1091.80/291.54 1091.80/291.54 (2) 1091.80/291.54 Obligation: 1091.80/291.54 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1091.80/291.54 1091.80/291.54 1091.80/291.54 The TRS R consists of the following rules: 1091.80/291.54 1091.80/291.54 gt(s(x), 0) -> true [1] 1091.80/291.54 gt(0, y) -> false [1] 1091.80/291.54 gt(s(x), s(y)) -> gt(x, y) [1] 1091.80/291.54 divides(x, y) -> div(x, y, y) [1] 1091.80/291.54 div(0, 0, z) -> true [1] 1091.80/291.54 div(0, s(x), z) -> false [1] 1091.80/291.54 div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) [1] 1091.80/291.54 div(s(x), s(y), z) -> div(x, y, z) [1] 1091.80/291.54 prime(x) -> test(x, s(s(0))) [1] 1091.80/291.54 test(x, y) -> if1(gt(x, y), x, y) [1] 1091.80/291.54 if1(true, x, y) -> if2(divides(x, y), x, y) [1] 1091.80/291.54 if1(false, x, y) -> true [1] 1091.80/291.54 if2(true, x, y) -> false [1] 1091.80/291.54 if2(false, x, y) -> test(x, s(y)) [1] 1091.80/291.54 1091.80/291.54 Rewrite Strategy: INNERMOST 1091.80/291.54 ---------------------------------------- 1091.80/291.54 1091.80/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1091.80/291.54 Infered types. 1091.80/291.54 ---------------------------------------- 1091.80/291.54 1091.80/291.54 (4) 1091.80/291.54 Obligation: 1091.80/291.54 Runtime Complexity Weighted TRS with Types. 1091.80/291.54 The TRS R consists of the following rules: 1091.80/291.54
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