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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307791
details
property
value
status
complete
benchmark
wiehe12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.525 seconds
cpu usage
306.287
user time
304.677
system time
1.61037
max virtual memory
1.828108E7
max residence set size
5177364.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
306.16/291.48 WORST_CASE(Omega(n^2), ?) 306.16/291.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 306.16/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 306.16/291.49 306.16/291.49 306.16/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 306.16/291.49 306.16/291.49 (0) CpxTRS 306.16/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 306.16/291.49 (2) CpxTRS 306.16/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 306.16/291.49 (4) typed CpxTrs 306.16/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 306.16/291.49 (6) typed CpxTrs 306.16/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] 306.16/291.49 (8) BEST 306.16/291.49 (9) proven lower bound 306.16/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 306.16/291.49 (11) BOUNDS(n^1, INF) 306.16/291.49 (12) typed CpxTrs 306.16/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 105 ms] 306.16/291.49 (14) typed CpxTrs 306.16/291.49 (15) RewriteLemmaProof [LOWER BOUND(ID), 34 ms] 306.16/291.49 (16) typed CpxTrs 306.16/291.49 (17) RewriteLemmaProof [LOWER BOUND(ID), 7 ms] 306.16/291.49 (18) typed CpxTrs 306.16/291.49 (19) RewriteLemmaProof [LOWER BOUND(ID), 537 ms] 306.16/291.49 (20) BEST 306.16/291.49 (21) proven lower bound 306.16/291.49 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 306.16/291.49 (23) BOUNDS(n^2, INF) 306.16/291.49 (24) typed CpxTrs 306.16/291.49 (25) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 306.16/291.49 (26) typed CpxTrs 306.16/291.49 306.16/291.49 306.16/291.49 ---------------------------------------- 306.16/291.49 306.16/291.49 (0) 306.16/291.49 Obligation: 306.16/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 306.16/291.49 306.16/291.49 306.16/291.49 The TRS R consists of the following rules: 306.16/291.49 306.16/291.49 g(s(x), s(y)) -> if(and(f(s(x)), f(s(y))), t(g(k(minus(m(x, y), n(x, y)), s(s(0))), k(n(s(x), s(y)), s(s(0))))), g(minus(m(x, y), n(x, y)), n(s(x), s(y)))) 306.16/291.49 n(0, y) -> 0 306.16/291.49 n(x, 0) -> 0 306.16/291.49 n(s(x), s(y)) -> s(n(x, y)) 306.16/291.49 m(0, y) -> y 306.16/291.49 m(x, 0) -> x 306.16/291.49 m(s(x), s(y)) -> s(m(x, y)) 306.16/291.49 k(0, s(y)) -> 0 306.16/291.49 k(s(x), s(y)) -> s(k(minus(x, y), s(y))) 306.16/291.49 t(x) -> p(x, x) 306.16/291.49 p(s(x), s(y)) -> s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 306.16/291.49 p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x)) 306.16/291.49 p(0, y) -> y 306.16/291.49 p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y)))) 306.16/291.49 minus(x, 0) -> x 306.16/291.49 minus(s(x), s(y)) -> minus(x, y) 306.16/291.49 id(x) -> x 306.16/291.49 if(true, x, y) -> x 306.16/291.49 if(false, x, y) -> y 306.16/291.49 not(x) -> if(x, false, true) 306.16/291.49 and(x, false) -> false 306.16/291.49 and(true, true) -> true 306.16/291.49 f(0) -> true 306.16/291.49 f(s(x)) -> h(x) 306.16/291.49 h(0) -> false 306.16/291.49 h(s(x)) -> f(x) 306.16/291.49 gt(s(x), 0) -> true 306.16/291.49 gt(0, y) -> false 306.16/291.49 gt(s(x), s(y)) -> gt(x, y) 306.16/291.49 306.16/291.49 S is empty. 306.16/291.49 Rewrite Strategy: FULL 306.16/291.49 ---------------------------------------- 306.16/291.49 306.16/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 306.16/291.49 Renamed function symbols to avoid clashes with predefined symbol. 306.16/291.49 ---------------------------------------- 306.16/291.49 306.16/291.49 (2) 306.16/291.49 Obligation: 306.16/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 306.16/291.49 306.16/291.49 306.16/291.49 The TRS R consists of the following rules: 306.16/291.49 306.16/291.49 g(s(x), s(y)) -> if(and(f(s(x)), f(s(y))), t(g(k(minus(m(x, y), n(x, y)), s(s(0'))), k(n(s(x), s(y)), s(s(0'))))), g(minus(m(x, y), n(x, y)), n(s(x), s(y)))) 306.16/291.49 n(0', y) -> 0' 306.16/291.49 n(x, 0') -> 0' 306.16/291.49 n(s(x), s(y)) -> s(n(x, y)) 306.16/291.49 m(0', y) -> y 306.16/291.49 m(x, 0') -> x 306.16/291.49 m(s(x), s(y)) -> s(m(x, y)) 306.16/291.49 k(0', s(y)) -> 0' 306.16/291.49 k(s(x), s(y)) -> s(k(minus(x, y), s(y))) 306.16/291.49 t(x) -> p(x, x)
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