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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307789
details
property
value
status
complete
benchmark
wiehe09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.619 seconds
cpu usage
318.537
user time
315.558
system time
2.97885
max virtual memory
1.8279384E7
max residence set size
6508396.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
318.46/291.56 WORST_CASE(Omega(n^1), ?) 318.46/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 318.46/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 318.46/291.57 318.46/291.57 318.46/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 318.46/291.57 318.46/291.57 (0) CpxTRS 318.46/291.57 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 318.46/291.57 (2) CpxTRS 318.46/291.57 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 318.46/291.57 (4) typed CpxTrs 318.46/291.57 (5) OrderProof [LOWER BOUND(ID), 0 ms] 318.46/291.57 (6) typed CpxTrs 318.46/291.57 (7) RewriteLemmaProof [LOWER BOUND(ID), 538 ms] 318.46/291.57 (8) BEST 318.46/291.57 (9) proven lower bound 318.46/291.57 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 318.46/291.57 (11) BOUNDS(n^1, INF) 318.46/291.57 (12) typed CpxTrs 318.46/291.57 (13) RewriteLemmaProof [LOWER BOUND(ID), 238 ms] 318.46/291.57 (14) typed CpxTrs 318.46/291.57 318.46/291.57 318.46/291.57 ---------------------------------------- 318.46/291.57 318.46/291.57 (0) 318.46/291.57 Obligation: 318.46/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 318.46/291.57 318.46/291.57 318.46/291.57 The TRS R consists of the following rules: 318.46/291.57 318.46/291.57 minus(x, 0) -> x 318.46/291.57 minus(s(x), s(y)) -> minus(x, y) 318.46/291.57 quot(0, s(y)) -> 0 318.46/291.57 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 318.46/291.57 minus(minus(x, y), z) -> minus(x, plus(y, z)) 318.46/291.57 plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 318.46/291.57 plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 318.46/291.57 plus(zero, y) -> y 318.46/291.57 plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 318.46/291.57 id(x) -> x 318.46/291.57 if(true, x, y) -> x 318.46/291.57 if(false, x, y) -> y 318.46/291.57 not(x) -> if(x, false, true) 318.46/291.57 gt(s(x), zero) -> true 318.46/291.57 gt(zero, y) -> false 318.46/291.57 gt(s(x), s(y)) -> gt(x, y) 318.46/291.57 318.46/291.57 S is empty. 318.46/291.57 Rewrite Strategy: FULL 318.46/291.57 ---------------------------------------- 318.46/291.57 318.46/291.57 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 318.46/291.57 Renamed function symbols to avoid clashes with predefined symbol. 318.46/291.57 ---------------------------------------- 318.46/291.57 318.46/291.57 (2) 318.46/291.57 Obligation: 318.46/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 318.46/291.57 318.46/291.57 318.46/291.57 The TRS R consists of the following rules: 318.46/291.57 318.46/291.57 minus(x, 0') -> x 318.46/291.57 minus(s(x), s(y)) -> minus(x, y) 318.46/291.57 quot(0', s(y)) -> 0' 318.46/291.57 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 318.46/291.57 minus(minus(x, y), z) -> minus(x, plus(y, z)) 318.46/291.57 plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 318.46/291.57 plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 318.46/291.57 plus(zero, y) -> y 318.46/291.57 plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 318.46/291.57 id(x) -> x 318.46/291.57 if(true, x, y) -> x 318.46/291.57 if(false, x, y) -> y 318.46/291.57 not(x) -> if(x, false, true) 318.46/291.57 gt(s(x), zero) -> true 318.46/291.57 gt(zero, y) -> false 318.46/291.57 gt(s(x), s(y)) -> gt(x, y) 318.46/291.57 318.46/291.57 S is empty. 318.46/291.57 Rewrite Strategy: FULL 318.46/291.57 ---------------------------------------- 318.46/291.57 318.46/291.57 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 318.46/291.57 Infered types. 318.46/291.57 ---------------------------------------- 318.46/291.57 318.46/291.57 (4) 318.46/291.57 Obligation: 318.46/291.57 TRS: 318.46/291.57 Rules: 318.46/291.57 minus(x, 0') -> x 318.46/291.57 minus(s(x), s(y)) -> minus(x, y) 318.46/291.57 quot(0', s(y)) -> 0' 318.46/291.57 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 318.46/291.57 minus(minus(x, y), z) -> minus(x, plus(y, z)) 318.46/291.57 plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
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