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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307792
details
property
value
status
complete
benchmark
thiemann28.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.598 seconds
cpu usage
303.988
user time
301.8
system time
2.18781
max virtual memory
1.8279384E7
max residence set size
5257716.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
303.88/291.56 WORST_CASE(Omega(n^1), ?) 303.88/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 303.88/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 303.88/291.57 303.88/291.57 303.88/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.88/291.57 303.88/291.57 (0) CpxTRS 303.88/291.57 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 303.88/291.57 (2) CpxTRS 303.88/291.57 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 303.88/291.57 (4) typed CpxTrs 303.88/291.57 (5) OrderProof [LOWER BOUND(ID), 0 ms] 303.88/291.57 (6) typed CpxTrs 303.88/291.57 (7) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] 303.88/291.57 (8) BEST 303.88/291.57 (9) proven lower bound 303.88/291.57 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 303.88/291.57 (11) BOUNDS(n^1, INF) 303.88/291.57 (12) typed CpxTrs 303.88/291.57 (13) RewriteLemmaProof [LOWER BOUND(ID), 68 ms] 303.88/291.57 (14) typed CpxTrs 303.88/291.57 303.88/291.57 303.88/291.57 ---------------------------------------- 303.88/291.57 303.88/291.57 (0) 303.88/291.57 Obligation: 303.88/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.88/291.57 303.88/291.57 303.88/291.57 The TRS R consists of the following rules: 303.88/291.57 303.88/291.57 ge(x, 0) -> true 303.88/291.57 ge(0, s(y)) -> false 303.88/291.57 ge(s(x), s(y)) -> ge(x, y) 303.88/291.57 minus(x, 0) -> x 303.88/291.57 minus(0, y) -> 0 303.88/291.57 minus(s(x), s(y)) -> minus(x, y) 303.88/291.57 id_inc(x) -> x 303.88/291.57 id_inc(x) -> s(x) 303.88/291.57 div(x, y) -> if(ge(y, s(0)), ge(x, y), x, y) 303.88/291.57 if(false, b, x, y) -> div_by_zero 303.88/291.57 if(true, false, x, y) -> 0 303.88/291.57 if(true, true, x, y) -> id_inc(div(minus(x, y), y)) 303.88/291.57 303.88/291.57 S is empty. 303.88/291.57 Rewrite Strategy: FULL 303.88/291.57 ---------------------------------------- 303.88/291.57 303.88/291.57 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 303.88/291.57 Renamed function symbols to avoid clashes with predefined symbol. 303.88/291.57 ---------------------------------------- 303.88/291.57 303.88/291.57 (2) 303.88/291.57 Obligation: 303.88/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.88/291.57 303.88/291.57 303.88/291.57 The TRS R consists of the following rules: 303.88/291.57 303.88/291.57 ge(x, 0') -> true 303.88/291.57 ge(0', s(y)) -> false 303.88/291.57 ge(s(x), s(y)) -> ge(x, y) 303.88/291.57 minus(x, 0') -> x 303.88/291.57 minus(0', y) -> 0' 303.88/291.57 minus(s(x), s(y)) -> minus(x, y) 303.88/291.57 id_inc(x) -> x 303.88/291.57 id_inc(x) -> s(x) 303.88/291.57 div(x, y) -> if(ge(y, s(0')), ge(x, y), x, y) 303.88/291.57 if(false, b, x, y) -> div_by_zero 303.88/291.57 if(true, false, x, y) -> 0' 303.88/291.57 if(true, true, x, y) -> id_inc(div(minus(x, y), y)) 303.88/291.57 303.88/291.57 S is empty. 303.88/291.57 Rewrite Strategy: FULL 303.88/291.57 ---------------------------------------- 303.88/291.57 303.88/291.57 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 303.88/291.57 Infered types. 303.88/291.57 ---------------------------------------- 303.88/291.57 303.88/291.57 (4) 303.88/291.57 Obligation: 303.88/291.57 TRS: 303.88/291.57 Rules: 303.88/291.57 ge(x, 0') -> true 303.88/291.57 ge(0', s(y)) -> false 303.88/291.57 ge(s(x), s(y)) -> ge(x, y) 303.88/291.57 minus(x, 0') -> x 303.88/291.57 minus(0', y) -> 0' 303.88/291.57 minus(s(x), s(y)) -> minus(x, y) 303.88/291.57 id_inc(x) -> x 303.88/291.57 id_inc(x) -> s(x) 303.88/291.57 div(x, y) -> if(ge(y, s(0')), ge(x, y), x, y) 303.88/291.57 if(false, b, x, y) -> div_by_zero 303.88/291.57 if(true, false, x, y) -> 0' 303.88/291.57 if(true, true, x, y) -> id_inc(div(minus(x, y), y)) 303.88/291.57 303.88/291.57 Types:
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