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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313853
details
property
value
status
complete
benchmark
power.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n001.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.581 seconds
cpu usage
734.314
user time
728.82
system time
5.49397
max virtual memory
3.7968848E7
max residence set size
7739184.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
734.15/291.52 WORST_CASE(Omega(n^2), ?) 734.15/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 734.15/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 734.15/291.54 734.15/291.54 734.15/291.54 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). 734.15/291.54 734.15/291.54 (0) CpxRelTRS 734.15/291.54 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 155 ms] 734.15/291.54 (2) CpxRelTRS 734.15/291.54 (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 734.15/291.54 (4) CpxRelTRS 734.15/291.54 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 734.15/291.54 (6) typed CpxTrs 734.15/291.54 (7) OrderProof [LOWER BOUND(ID), 0 ms] 734.15/291.54 (8) typed CpxTrs 734.15/291.54 (9) RewriteLemmaProof [LOWER BOUND(ID), 285 ms] 734.15/291.54 (10) BEST 734.15/291.54 (11) proven lower bound 734.15/291.54 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 734.15/291.54 (13) BOUNDS(n^1, INF) 734.15/291.54 (14) typed CpxTrs 734.15/291.54 (15) RewriteLemmaProof [LOWER BOUND(ID), 40 ms] 734.15/291.54 (16) BEST 734.15/291.54 (17) proven lower bound 734.15/291.54 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 734.15/291.54 (19) BOUNDS(n^2, INF) 734.15/291.54 (20) typed CpxTrs 734.15/291.54 (21) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] 734.15/291.54 (22) BOUNDS(1, INF) 734.15/291.54 734.15/291.54 734.15/291.54 ---------------------------------------- 734.15/291.54 734.15/291.54 (0) 734.15/291.54 Obligation: 734.15/291.54 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). 734.15/291.54 734.15/291.54 734.15/291.54 The TRS R consists of the following rules: 734.15/291.54 734.15/291.54 power(x', S(x)) -> mult(x', power(x', x)) 734.15/291.54 mult(x', S(x)) -> add0(x', mult(x', x)) 734.15/291.54 add0(x', S(x)) -> +(S(0), add0(x', x)) 734.15/291.54 power(x, 0) -> S(0) 734.15/291.54 mult(x, 0) -> 0 734.15/291.54 add0(x, 0) -> x 734.15/291.54 734.15/291.54 The (relative) TRS S consists of the following rules: 734.15/291.54 734.15/291.54 +(x, S(0)) -> S(x) 734.15/291.54 +(S(0), y) -> S(y) 734.15/291.54 734.15/291.54 Rewrite Strategy: INNERMOST 734.15/291.54 ---------------------------------------- 734.15/291.54 734.15/291.54 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 734.15/291.54 proved termination of relative rules 734.15/291.54 ---------------------------------------- 734.15/291.54 734.15/291.54 (2) 734.15/291.54 Obligation: 734.15/291.54 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). 734.15/291.54 734.15/291.54 734.15/291.54 The TRS R consists of the following rules: 734.15/291.54 734.15/291.54 power(x', S(x)) -> mult(x', power(x', x)) 734.15/291.54 mult(x', S(x)) -> add0(x', mult(x', x)) 734.15/291.54 add0(x', S(x)) -> +(S(0), add0(x', x)) 734.15/291.54 power(x, 0) -> S(0) 734.15/291.54 mult(x, 0) -> 0 734.15/291.54 add0(x, 0) -> x 734.15/291.54 734.15/291.54 The (relative) TRS S consists of the following rules: 734.15/291.54 734.15/291.54 +(x, S(0)) -> S(x) 734.15/291.54 +(S(0), y) -> S(y) 734.15/291.54 734.15/291.54 Rewrite Strategy: INNERMOST 734.15/291.54 ---------------------------------------- 734.15/291.54 734.15/291.54 (3) RenamingProof (BOTH BOUNDS(ID, ID)) 734.15/291.54 Renamed function symbols to avoid clashes with predefined symbol. 734.15/291.54 ---------------------------------------- 734.15/291.54 734.15/291.54 (4) 734.15/291.54 Obligation: 734.15/291.54 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). 734.15/291.54 734.15/291.54 734.15/291.54 The TRS R consists of the following rules: 734.15/291.54 734.15/291.54 power(x', S(x)) -> mult(x', power(x', x)) 734.15/291.54 mult(x', S(x)) -> add0(x', mult(x', x)) 734.15/291.54 add0(x', S(x)) -> +'(S(0'), add0(x', x)) 734.15/291.54 power(x, 0') -> S(0') 734.15/291.54 mult(x, 0') -> 0' 734.15/291.54 add0(x, 0') -> x 734.15/291.54
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