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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313475
details
property
value
status
complete
benchmark
MYNAT_nosorts_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.236 seconds
cpu usage
1099.71
user time
1087.74
system time
11.9674
max virtual memory
3.7252356E7
max residence set size
1.5094164E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1098.69/291.93 WORST_CASE(Omega(n^2), ?) 1099.35/292.13 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1099.35/292.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1099.35/292.13 1099.35/292.13 1099.35/292.13 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1099.35/292.13 1099.35/292.13 (0) CpxTRS 1099.35/292.13 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.35/292.13 (2) CpxTRS 1099.35/292.13 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.35/292.13 (4) typed CpxTrs 1099.35/292.13 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1099.35/292.13 (6) typed CpxTrs 1099.35/292.13 (7) RewriteLemmaProof [LOWER BOUND(ID), 575 ms] 1099.35/292.13 (8) BEST 1099.35/292.13 (9) proven lower bound 1099.35/292.13 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1099.35/292.13 (11) BOUNDS(n^1, INF) 1099.35/292.13 (12) typed CpxTrs 1099.35/292.13 (13) RewriteLemmaProof [LOWER BOUND(ID), 743 ms] 1099.35/292.13 (14) BEST 1099.35/292.13 (15) proven lower bound 1099.35/292.13 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1099.35/292.13 (17) BOUNDS(n^2, INF) 1099.35/292.13 (18) typed CpxTrs 1099.35/292.13 (19) RewriteLemmaProof [LOWER BOUND(ID), 365 ms] 1099.35/292.13 (20) typed CpxTrs 1099.35/292.13 (21) RewriteLemmaProof [LOWER BOUND(ID), 16 ms] 1099.35/292.13 (22) typed CpxTrs 1099.35/292.13 (23) RewriteLemmaProof [LOWER BOUND(ID), 743 ms] 1099.35/292.13 (24) BOUNDS(1, INF) 1099.35/292.13 1099.35/292.13 1099.35/292.13 ---------------------------------------- 1099.35/292.13 1099.35/292.13 (0) 1099.35/292.13 Obligation: 1099.35/292.13 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1099.35/292.13 1099.35/292.13 1099.35/292.13 The TRS R consists of the following rules: 1099.35/292.13 1099.35/292.13 a__and(tt, X) -> mark(X) 1099.35/292.13 a__plus(N, 0) -> mark(N) 1099.35/292.13 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1099.35/292.13 a__x(N, 0) -> 0 1099.35/292.13 a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1099.35/292.13 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1099.35/292.13 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1099.35/292.13 mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1099.35/292.13 mark(tt) -> tt 1099.35/292.13 mark(0) -> 0 1099.35/292.13 mark(s(X)) -> s(mark(X)) 1099.35/292.13 a__and(X1, X2) -> and(X1, X2) 1099.35/292.13 a__plus(X1, X2) -> plus(X1, X2) 1099.35/292.13 a__x(X1, X2) -> x(X1, X2) 1099.35/292.13 1099.35/292.13 S is empty. 1099.35/292.13 Rewrite Strategy: INNERMOST 1099.35/292.13 ---------------------------------------- 1099.35/292.13 1099.35/292.13 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1099.35/292.13 Renamed function symbols to avoid clashes with predefined symbol. 1099.35/292.13 ---------------------------------------- 1099.35/292.13 1099.35/292.13 (2) 1099.35/292.13 Obligation: 1099.35/292.13 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1099.35/292.13 1099.35/292.13 1099.35/292.13 The TRS R consists of the following rules: 1099.35/292.13 1099.35/292.13 a__and(tt, X) -> mark(X) 1099.35/292.13 a__plus(N, 0') -> mark(N) 1099.35/292.13 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1099.35/292.13 a__x(N, 0') -> 0' 1099.35/292.13 a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1099.35/292.13 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1099.35/292.13 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1099.35/292.13 mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1099.35/292.13 mark(tt) -> tt 1099.35/292.13 mark(0') -> 0' 1099.35/292.13 mark(s(X)) -> s(mark(X)) 1099.35/292.13 a__and(X1, X2) -> and(X1, X2) 1099.35/292.13 a__plus(X1, X2) -> plus(X1, X2) 1099.35/292.13 a__x(X1, X2) -> x(X1, X2) 1099.35/292.13 1099.35/292.13 S is empty. 1099.35/292.13 Rewrite Strategy: INNERMOST 1099.35/292.13 ---------------------------------------- 1099.35/292.13 1099.35/292.13 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1099.35/292.13 Infered types. 1099.35/292.13 ---------------------------------------- 1099.35/292.13 1099.35/292.13 (4) 1099.35/292.13 Obligation: 1099.35/292.13 Innermost TRS: 1099.35/292.13 Rules:
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