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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313278
details
property
value
status
complete
benchmark
tpa5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.197 seconds
cpu usage
1154.26
user time
1143.6
system time
10.6617
max virtual memory
3.8502776E7
max residence set size
1.504402E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1147.81/291.55 WORST_CASE(Omega(n^1), ?) 1153.96/293.12 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1153.96/293.12 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1153.96/293.12 1153.96/293.12 1153.96/293.12 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1153.96/293.12 1153.96/293.12 (0) CpxTRS 1153.96/293.12 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1153.96/293.12 (2) CpxTRS 1153.96/293.12 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1153.96/293.12 (4) typed CpxTrs 1153.96/293.12 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1153.96/293.12 (6) typed CpxTrs 1153.96/293.12 (7) RewriteLemmaProof [LOWER BOUND(ID), 288 ms] 1153.96/293.12 (8) BEST 1153.96/293.12 (9) proven lower bound 1153.96/293.12 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1153.96/293.12 (11) BOUNDS(n^1, INF) 1153.96/293.12 (12) typed CpxTrs 1153.96/293.12 (13) RewriteLemmaProof [LOWER BOUND(ID), 83 ms] 1153.96/293.12 (14) typed CpxTrs 1153.96/293.12 (15) RewriteLemmaProof [LOWER BOUND(ID), 79 ms] 1153.96/293.12 (16) typed CpxTrs 1153.96/293.12 1153.96/293.12 1153.96/293.12 ---------------------------------------- 1153.96/293.12 1153.96/293.12 (0) 1153.96/293.12 Obligation: 1153.96/293.12 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1153.96/293.12 1153.96/293.12 1153.96/293.12 The TRS R consists of the following rules: 1153.96/293.12 1153.96/293.12 -(x, 0) -> x 1153.96/293.12 -(s(x), s(y)) -> -(x, y) 1153.96/293.12 min(x, 0) -> 0 1153.96/293.12 min(0, y) -> 0 1153.96/293.12 min(s(x), s(y)) -> s(min(x, y)) 1153.96/293.12 twice(0) -> 0 1153.96/293.12 twice(s(x)) -> s(s(twice(x))) 1153.96/293.12 f(s(x), s(y)) -> f(-(y, min(x, y)), s(twice(min(x, y)))) 1153.96/293.12 f(s(x), s(y)) -> f(-(x, min(x, y)), s(twice(min(x, y)))) 1153.96/293.12 1153.96/293.12 S is empty. 1153.96/293.12 Rewrite Strategy: INNERMOST 1153.96/293.12 ---------------------------------------- 1153.96/293.12 1153.96/293.12 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1153.96/293.12 Renamed function symbols to avoid clashes with predefined symbol. 1153.96/293.12 ---------------------------------------- 1153.96/293.12 1153.96/293.12 (2) 1153.96/293.12 Obligation: 1153.96/293.12 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1153.96/293.12 1153.96/293.12 1153.96/293.12 The TRS R consists of the following rules: 1153.96/293.12 1153.96/293.12 -(x, 0') -> x 1153.96/293.12 -(s(x), s(y)) -> -(x, y) 1153.96/293.12 min(x, 0') -> 0' 1153.96/293.12 min(0', y) -> 0' 1153.96/293.12 min(s(x), s(y)) -> s(min(x, y)) 1153.96/293.12 twice(0') -> 0' 1153.96/293.12 twice(s(x)) -> s(s(twice(x))) 1153.96/293.12 f(s(x), s(y)) -> f(-(y, min(x, y)), s(twice(min(x, y)))) 1153.96/293.12 f(s(x), s(y)) -> f(-(x, min(x, y)), s(twice(min(x, y)))) 1153.96/293.12 1153.96/293.12 S is empty. 1153.96/293.12 Rewrite Strategy: INNERMOST 1153.96/293.12 ---------------------------------------- 1153.96/293.12 1153.96/293.12 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1153.96/293.12 Infered types. 1153.96/293.12 ---------------------------------------- 1153.96/293.12 1153.96/293.12 (4) 1153.96/293.12 Obligation: 1153.96/293.12 Innermost TRS: 1153.96/293.12 Rules: 1153.96/293.12 -(x, 0') -> x 1153.96/293.12 -(s(x), s(y)) -> -(x, y) 1153.96/293.12 min(x, 0') -> 0' 1153.96/293.12 min(0', y) -> 0' 1153.96/293.12 min(s(x), s(y)) -> s(min(x, y)) 1153.96/293.12 twice(0') -> 0' 1153.96/293.12 twice(s(x)) -> s(s(twice(x))) 1153.96/293.12 f(s(x), s(y)) -> f(-(y, min(x, y)), s(twice(min(x, y)))) 1153.96/293.12 f(s(x), s(y)) -> f(-(x, min(x, y)), s(twice(min(x, y)))) 1153.96/293.12 1153.96/293.12 Types: 1153.96/293.12 - :: 0':s -> 0':s -> 0':s 1153.96/293.12 0' :: 0':s 1153.96/293.12 s :: 0':s -> 0':s 1153.96/293.12 min :: 0':s -> 0':s -> 0':s 1153.96/293.12 twice :: 0':s -> 0':s 1153.96/293.12 f :: 0':s -> 0':s -> f 1153.96/293.12 hole_0':s1_0 :: 0':s
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