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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313614
details
property
value
status
complete
benchmark
2.19.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.02166 seconds
cpu usage
23.9599
user time
22.4297
system time
1.5302
max virtual memory
1.9207632E7
max residence set size
4340608.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
23.56/6.94 WORST_CASE(Omega(n^2), O(n^2)) 23.85/6.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 23.85/6.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.85/6.96 23.85/6.96 23.85/6.96 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 23.85/6.96 23.85/6.96 (0) CpxTRS 23.85/6.96 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 23.85/6.96 (2) CpxWeightedTrs 23.85/6.96 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 4 ms] 23.85/6.96 (4) CpxWeightedTrs 23.85/6.96 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 23.85/6.96 (6) CpxTypedWeightedTrs 23.85/6.96 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 23.85/6.96 (8) CpxTypedWeightedCompleteTrs 23.85/6.96 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 23.85/6.96 (10) CpxRNTS 23.85/6.96 (11) CompleteCoflocoProof [FINISHED, 208 ms] 23.85/6.96 (12) BOUNDS(1, n^2) 23.85/6.96 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 23.85/6.96 (14) CpxTRS 23.85/6.96 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 23.85/6.96 (16) typed CpxTrs 23.85/6.96 (17) OrderProof [LOWER BOUND(ID), 0 ms] 23.85/6.96 (18) typed CpxTrs 23.85/6.96 (19) RewriteLemmaProof [LOWER BOUND(ID), 334 ms] 23.85/6.96 (20) BEST 23.85/6.96 (21) proven lower bound 23.85/6.96 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 23.85/6.96 (23) BOUNDS(n^1, INF) 23.85/6.96 (24) typed CpxTrs 23.85/6.96 (25) RewriteLemmaProof [LOWER BOUND(ID), 81 ms] 23.85/6.96 (26) typed CpxTrs 23.85/6.96 (27) RewriteLemmaProof [LOWER BOUND(ID), 105 ms] 23.85/6.96 (28) proven lower bound 23.85/6.96 (29) LowerBoundPropagationProof [FINISHED, 0 ms] 23.85/6.96 (30) BOUNDS(n^2, INF) 23.85/6.96 23.85/6.96 23.85/6.96 ---------------------------------------- 23.85/6.96 23.85/6.96 (0) 23.85/6.96 Obligation: 23.85/6.96 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 23.85/6.96 23.85/6.96 23.85/6.96 The TRS R consists of the following rules: 23.85/6.96 23.85/6.96 sqr(0) -> 0 23.85/6.96 sqr(s(x)) -> +(sqr(x), s(double(x))) 23.85/6.96 double(0) -> 0 23.85/6.96 double(s(x)) -> s(s(double(x))) 23.85/6.96 +(x, 0) -> x 23.85/6.96 +(x, s(y)) -> s(+(x, y)) 23.85/6.96 sqr(s(x)) -> s(+(sqr(x), double(x))) 23.85/6.96 23.85/6.96 S is empty. 23.85/6.96 Rewrite Strategy: INNERMOST 23.85/6.96 ---------------------------------------- 23.85/6.96 23.85/6.96 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 23.85/6.96 Transformed relative TRS to weighted TRS 23.85/6.96 ---------------------------------------- 23.85/6.96 23.85/6.96 (2) 23.85/6.96 Obligation: 23.85/6.96 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 23.85/6.96 23.85/6.96 23.85/6.96 The TRS R consists of the following rules: 23.85/6.96 23.85/6.96 sqr(0) -> 0 [1] 23.85/6.96 sqr(s(x)) -> +(sqr(x), s(double(x))) [1] 23.85/6.96 double(0) -> 0 [1] 23.85/6.96 double(s(x)) -> s(s(double(x))) [1] 23.85/6.96 +(x, 0) -> x [1] 23.85/6.96 +(x, s(y)) -> s(+(x, y)) [1] 23.85/6.96 sqr(s(x)) -> s(+(sqr(x), double(x))) [1] 23.85/6.96 23.85/6.96 Rewrite Strategy: INNERMOST 23.85/6.96 ---------------------------------------- 23.85/6.96 23.85/6.96 (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) 23.85/6.96 Renamed defined symbols to avoid conflicts with arithmetic symbols: 23.85/6.96 23.85/6.96 + => plus 23.85/6.96 23.85/6.96 ---------------------------------------- 23.85/6.96 23.85/6.96 (4) 23.85/6.96 Obligation: 23.85/6.96 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 23.85/6.96 23.85/6.96 23.85/6.96 The TRS R consists of the following rules: 23.85/6.96 23.85/6.96 sqr(0) -> 0 [1] 23.85/6.96 sqr(s(x)) -> plus(sqr(x), s(double(x))) [1] 23.85/6.96 double(0) -> 0 [1]
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