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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313683
details
property
value
status
complete
benchmark
fac.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n115.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.713 seconds
cpu usage
1135.63
user time
1126.59
system time
9.04462
max virtual memory
3.7510872E7
max residence set size
9861212.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1135.12/291.58 WORST_CASE(Omega(n^2), ?) 1135.41/291.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1135.41/291.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1135.41/291.61 1135.41/291.61 1135.41/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1135.41/291.61 1135.41/291.61 (0) CpxTRS 1135.41/291.61 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1135.41/291.61 (2) CpxTRS 1135.41/291.61 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1135.41/291.61 (4) typed CpxTrs 1135.41/291.61 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1135.41/291.61 (6) typed CpxTrs 1135.41/291.61 (7) RewriteLemmaProof [LOWER BOUND(ID), 280 ms] 1135.41/291.61 (8) BEST 1135.41/291.61 (9) proven lower bound 1135.41/291.61 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1135.41/291.61 (11) BOUNDS(n^1, INF) 1135.41/291.61 (12) typed CpxTrs 1135.41/291.61 (13) RewriteLemmaProof [LOWER BOUND(ID), 50 ms] 1135.41/291.61 (14) BEST 1135.41/291.61 (15) proven lower bound 1135.41/291.61 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1135.41/291.61 (17) BOUNDS(n^2, INF) 1135.41/291.61 (18) typed CpxTrs 1135.41/291.61 (19) RewriteLemmaProof [LOWER BOUND(ID), 66 ms] 1135.41/291.61 (20) typed CpxTrs 1135.41/291.61 (21) RewriteLemmaProof [LOWER BOUND(ID), 2394 ms] 1135.41/291.61 (22) BOUNDS(1, INF) 1135.41/291.61 1135.41/291.61 1135.41/291.61 ---------------------------------------- 1135.41/291.61 1135.41/291.61 (0) 1135.41/291.61 Obligation: 1135.41/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1135.41/291.61 1135.41/291.61 1135.41/291.61 The TRS R consists of the following rules: 1135.41/291.61 1135.41/291.61 plus(x, 0) -> x 1135.41/291.61 plus(x, s(y)) -> s(plus(x, y)) 1135.41/291.61 times(0, y) -> 0 1135.41/291.61 times(x, 0) -> 0 1135.41/291.61 times(s(x), y) -> plus(times(x, y), y) 1135.41/291.61 p(s(s(x))) -> s(p(s(x))) 1135.41/291.61 p(s(0)) -> 0 1135.41/291.61 fac(s(x)) -> times(fac(p(s(x))), s(x)) 1135.41/291.61 1135.41/291.61 S is empty. 1135.41/291.61 Rewrite Strategy: INNERMOST 1135.41/291.61 ---------------------------------------- 1135.41/291.61 1135.41/291.61 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1135.41/291.61 Renamed function symbols to avoid clashes with predefined symbol. 1135.41/291.61 ---------------------------------------- 1135.41/291.61 1135.41/291.61 (2) 1135.41/291.61 Obligation: 1135.41/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1135.41/291.61 1135.41/291.61 1135.41/291.61 The TRS R consists of the following rules: 1135.41/291.61 1135.41/291.61 plus(x, 0') -> x 1135.41/291.61 plus(x, s(y)) -> s(plus(x, y)) 1135.41/291.61 times(0', y) -> 0' 1135.41/291.61 times(x, 0') -> 0' 1135.41/291.61 times(s(x), y) -> plus(times(x, y), y) 1135.41/291.61 p(s(s(x))) -> s(p(s(x))) 1135.41/291.61 p(s(0')) -> 0' 1135.41/291.61 fac(s(x)) -> times(fac(p(s(x))), s(x)) 1135.41/291.61 1135.41/291.61 S is empty. 1135.41/291.61 Rewrite Strategy: INNERMOST 1135.41/291.61 ---------------------------------------- 1135.41/291.61 1135.41/291.61 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1135.41/291.61 Infered types. 1135.41/291.61 ---------------------------------------- 1135.41/291.61 1135.41/291.61 (4) 1135.41/291.61 Obligation: 1135.41/291.61 Innermost TRS: 1135.41/291.61 Rules: 1135.41/291.61 plus(x, 0') -> x 1135.41/291.61 plus(x, s(y)) -> s(plus(x, y)) 1135.41/291.61 times(0', y) -> 0' 1135.41/291.61 times(x, 0') -> 0' 1135.41/291.61 times(s(x), y) -> plus(times(x, y), y) 1135.41/291.61 p(s(s(x))) -> s(p(s(x))) 1135.41/291.61 p(s(0')) -> 0' 1135.41/291.61 fac(s(x)) -> times(fac(p(s(x))), s(x)) 1135.41/291.61 1135.41/291.61 Types: 1135.41/291.61 plus :: 0':s -> 0':s -> 0':s 1135.41/291.61 0' :: 0':s 1135.41/291.61 s :: 0':s -> 0':s 1135.41/291.61 times :: 0':s -> 0':s -> 0':s
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