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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313903
details
property
value
status
complete
benchmark
4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n063.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.25345 seconds
cpu usage
28.5263
user time
26.5203
system time
2.00603
max virtual memory
3.7245212E7
max residence set size
4306512.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
27.94/8.19 WORST_CASE(Omega(n^1), O(n^1)) 28.43/8.20 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 28.43/8.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.43/8.20 28.43/8.20 28.43/8.20 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.43/8.20 28.43/8.20 (0) CpxTRS 28.43/8.20 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 28.43/8.20 (2) CpxWeightedTrs 28.43/8.20 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 28.43/8.20 (4) CpxTypedWeightedTrs 28.43/8.20 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 28.43/8.20 (6) CpxTypedWeightedCompleteTrs 28.43/8.20 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 28.43/8.20 (8) CpxRNTS 28.43/8.20 (9) CompleteCoflocoProof [FINISHED, 222 ms] 28.43/8.20 (10) BOUNDS(1, n^1) 28.43/8.20 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 28.43/8.20 (12) TRS for Loop Detection 28.43/8.20 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 28.43/8.20 (14) BEST 28.43/8.20 (15) proven lower bound 28.43/8.20 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 28.43/8.20 (17) BOUNDS(n^1, INF) 28.43/8.20 (18) TRS for Loop Detection 28.43/8.20 28.43/8.20 28.43/8.20 ---------------------------------------- 28.43/8.20 28.43/8.20 (0) 28.43/8.20 Obligation: 28.43/8.20 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.43/8.20 28.43/8.20 28.43/8.20 The TRS R consists of the following rules: 28.43/8.20 28.43/8.20 cond(true, x, y) -> cond(gr(x, y), y, x) 28.43/8.20 gr(0, x) -> false 28.43/8.20 gr(s(x), 0) -> true 28.43/8.20 gr(s(x), s(y)) -> gr(x, y) 28.43/8.20 28.43/8.20 S is empty. 28.43/8.20 Rewrite Strategy: INNERMOST 28.43/8.20 ---------------------------------------- 28.43/8.20 28.43/8.20 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 28.43/8.20 Transformed relative TRS to weighted TRS 28.43/8.20 ---------------------------------------- 28.43/8.20 28.43/8.20 (2) 28.43/8.20 Obligation: 28.43/8.20 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 28.43/8.20 28.43/8.20 28.43/8.20 The TRS R consists of the following rules: 28.43/8.20 28.43/8.20 cond(true, x, y) -> cond(gr(x, y), y, x) [1] 28.43/8.20 gr(0, x) -> false [1] 28.43/8.20 gr(s(x), 0) -> true [1] 28.43/8.20 gr(s(x), s(y)) -> gr(x, y) [1] 28.43/8.20 28.43/8.20 Rewrite Strategy: INNERMOST 28.43/8.20 ---------------------------------------- 28.43/8.20 28.43/8.20 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 28.43/8.20 Infered types. 28.43/8.20 ---------------------------------------- 28.43/8.20 28.43/8.20 (4) 28.43/8.20 Obligation: 28.43/8.20 Runtime Complexity Weighted TRS with Types. 28.43/8.20 The TRS R consists of the following rules: 28.43/8.20 28.43/8.20 cond(true, x, y) -> cond(gr(x, y), y, x) [1] 28.43/8.20 gr(0, x) -> false [1] 28.43/8.20 gr(s(x), 0) -> true [1] 28.43/8.20 gr(s(x), s(y)) -> gr(x, y) [1] 28.43/8.20 28.43/8.20 The TRS has the following type information: 28.43/8.20 cond :: true:false -> 0:s -> 0:s -> cond 28.43/8.20 true :: true:false 28.43/8.20 gr :: 0:s -> 0:s -> true:false 28.43/8.20 0 :: 0:s 28.43/8.20 false :: true:false 28.43/8.20 s :: 0:s -> 0:s 28.43/8.20 28.43/8.20 Rewrite Strategy: INNERMOST 28.43/8.20 ---------------------------------------- 28.43/8.20 28.43/8.20 (5) CompletionProof (UPPER BOUND(ID)) 28.43/8.20 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 28.43/8.20 28.43/8.20 cond(v0, v1, v2) -> null_cond [0] 28.43/8.20 28.43/8.20 And the following fresh constants: null_cond 28.43/8.20 28.43/8.20 ---------------------------------------- 28.43/8.20 28.43/8.20 (6)
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