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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313595
details
property
value
status
complete
benchmark
2.13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.92711 seconds
cpu usage
15.1309
user time
13.7125
system time
1.41843
max virtual memory
1.913674E7
max residence set size
4089508.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
14.76/4.80 WORST_CASE(Omega(n^1), O(n^1)) 14.76/4.82 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.76/4.82 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.76/4.82 14.76/4.82 14.76/4.82 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 14.76/4.82 14.76/4.82 (0) CpxTRS 14.76/4.82 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 14.76/4.82 (2) CpxWeightedTrs 14.76/4.82 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 14.76/4.82 (4) CpxWeightedTrs 14.76/4.82 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 14.76/4.82 (6) CpxTypedWeightedTrs 14.76/4.82 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 14.76/4.82 (8) CpxTypedWeightedCompleteTrs 14.76/4.82 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 14.76/4.82 (10) CpxRNTS 14.76/4.82 (11) CompleteCoflocoProof [FINISHED, 39 ms] 14.76/4.82 (12) BOUNDS(1, n^1) 14.76/4.82 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 14.76/4.82 (14) CpxTRS 14.76/4.82 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 14.76/4.82 (16) typed CpxTrs 14.76/4.82 (17) OrderProof [LOWER BOUND(ID), 0 ms] 14.76/4.82 (18) typed CpxTrs 14.76/4.82 (19) RewriteLemmaProof [LOWER BOUND(ID), 288 ms] 14.76/4.82 (20) BEST 14.76/4.82 (21) proven lower bound 14.76/4.82 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 14.76/4.82 (23) BOUNDS(n^1, INF) 14.76/4.82 (24) typed CpxTrs 14.76/4.82 (25) RewriteLemmaProof [LOWER BOUND(ID), 166 ms] 14.76/4.82 (26) BOUNDS(1, INF) 14.76/4.82 14.76/4.82 14.76/4.82 ---------------------------------------- 14.76/4.82 14.76/4.82 (0) 14.76/4.82 Obligation: 14.76/4.82 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 14.76/4.82 14.76/4.82 14.76/4.82 The TRS R consists of the following rules: 14.76/4.82 14.76/4.82 double(0) -> 0 14.76/4.82 double(s(x)) -> s(s(double(x))) 14.76/4.82 +(x, 0) -> x 14.76/4.82 +(x, s(y)) -> s(+(x, y)) 14.76/4.82 +(s(x), y) -> s(+(x, y)) 14.76/4.82 double(x) -> +(x, x) 14.76/4.82 14.76/4.82 S is empty. 14.76/4.82 Rewrite Strategy: INNERMOST 14.76/4.82 ---------------------------------------- 14.76/4.82 14.76/4.82 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 14.76/4.82 Transformed relative TRS to weighted TRS 14.76/4.82 ---------------------------------------- 14.76/4.82 14.76/4.82 (2) 14.76/4.82 Obligation: 14.76/4.82 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 14.76/4.82 14.76/4.82 14.76/4.82 The TRS R consists of the following rules: 14.76/4.82 14.76/4.82 double(0) -> 0 [1] 14.76/4.82 double(s(x)) -> s(s(double(x))) [1] 14.76/4.82 +(x, 0) -> x [1] 14.76/4.82 +(x, s(y)) -> s(+(x, y)) [1] 14.76/4.82 +(s(x), y) -> s(+(x, y)) [1] 14.76/4.82 double(x) -> +(x, x) [1] 14.76/4.82 14.76/4.82 Rewrite Strategy: INNERMOST 14.76/4.82 ---------------------------------------- 14.76/4.82 14.76/4.82 (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) 14.76/4.82 Renamed defined symbols to avoid conflicts with arithmetic symbols: 14.76/4.82 14.76/4.82 + => plus 14.76/4.82 14.76/4.82 ---------------------------------------- 14.76/4.82 14.76/4.82 (4) 14.76/4.82 Obligation: 14.76/4.82 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 14.76/4.82 14.76/4.82 14.76/4.82 The TRS R consists of the following rules: 14.76/4.82 14.76/4.82 double(0) -> 0 [1] 14.76/4.82 double(s(x)) -> s(s(double(x))) [1] 14.76/4.82 plus(x, 0) -> x [1] 14.76/4.82 plus(x, s(y)) -> s(plus(x, y)) [1] 14.76/4.82 plus(s(x), y) -> s(plus(x, y)) [1] 14.76/4.82 double(x) -> plus(x, x) [1] 14.76/4.82 14.76/4.82 Rewrite Strategy: INNERMOST 14.76/4.82 ----------------------------------------
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