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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313704
details
property
value
status
complete
benchmark
thiemann10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n134.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.8832 seconds
cpu usage
32.5125
user time
30.2928
system time
2.21968
max virtual memory
1.9170132E7
max residence set size
4149300.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
32.25/10.83 WORST_CASE(Omega(n^1), O(n^1)) 32.25/10.84 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 32.25/10.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 32.25/10.84 32.25/10.84 32.25/10.84 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 32.25/10.84 32.25/10.84 (0) CpxTRS 32.25/10.84 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 32.25/10.84 (2) CpxWeightedTrs 32.25/10.84 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 32.25/10.84 (4) CpxTypedWeightedTrs 32.25/10.84 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 32.25/10.84 (6) CpxTypedWeightedCompleteTrs 32.25/10.84 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 32.25/10.84 (8) CpxRNTS 32.25/10.84 (9) CompleteCoflocoProof [FINISHED, 662 ms] 32.25/10.84 (10) BOUNDS(1, n^1) 32.25/10.84 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 32.25/10.84 (12) TRS for Loop Detection 32.25/10.84 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 32.25/10.84 (14) BEST 32.25/10.84 (15) proven lower bound 32.25/10.84 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 32.25/10.84 (17) BOUNDS(n^1, INF) 32.25/10.84 (18) TRS for Loop Detection 32.25/10.84 32.25/10.84 32.25/10.84 ---------------------------------------- 32.25/10.84 32.25/10.84 (0) 32.25/10.84 Obligation: 32.25/10.84 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 32.25/10.84 32.25/10.84 32.25/10.84 The TRS R consists of the following rules: 32.25/10.84 32.25/10.84 half(0) -> 0 32.25/10.84 half(s(0)) -> 0 32.25/10.84 half(s(s(x))) -> s(half(x)) 32.25/10.84 lastbit(0) -> 0 32.25/10.84 lastbit(s(0)) -> s(0) 32.25/10.84 lastbit(s(s(x))) -> lastbit(x) 32.25/10.84 zero(0) -> true 32.25/10.84 zero(s(x)) -> false 32.25/10.84 conv(x) -> conviter(x, cons(0, nil)) 32.25/10.84 conviter(x, l) -> if(zero(x), x, l) 32.25/10.84 if(true, x, l) -> l 32.25/10.84 if(false, x, l) -> conviter(half(x), cons(lastbit(x), l)) 32.25/10.84 32.25/10.84 S is empty. 32.25/10.84 Rewrite Strategy: INNERMOST 32.25/10.84 ---------------------------------------- 32.25/10.84 32.25/10.84 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 32.25/10.84 Transformed relative TRS to weighted TRS 32.25/10.84 ---------------------------------------- 32.25/10.84 32.25/10.84 (2) 32.25/10.84 Obligation: 32.25/10.84 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 32.25/10.84 32.25/10.84 32.25/10.84 The TRS R consists of the following rules: 32.25/10.84 32.25/10.84 half(0) -> 0 [1] 32.25/10.84 half(s(0)) -> 0 [1] 32.25/10.84 half(s(s(x))) -> s(half(x)) [1] 32.25/10.84 lastbit(0) -> 0 [1] 32.25/10.84 lastbit(s(0)) -> s(0) [1] 32.25/10.84 lastbit(s(s(x))) -> lastbit(x) [1] 32.25/10.84 zero(0) -> true [1] 32.25/10.84 zero(s(x)) -> false [1] 32.25/10.84 conv(x) -> conviter(x, cons(0, nil)) [1] 32.25/10.84 conviter(x, l) -> if(zero(x), x, l) [1] 32.25/10.84 if(true, x, l) -> l [1] 32.25/10.84 if(false, x, l) -> conviter(half(x), cons(lastbit(x), l)) [1] 32.25/10.84 32.25/10.84 Rewrite Strategy: INNERMOST 32.25/10.84 ---------------------------------------- 32.25/10.84 32.25/10.84 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 32.25/10.84 Infered types. 32.25/10.84 ---------------------------------------- 32.25/10.84 32.25/10.84 (4) 32.25/10.84 Obligation: 32.25/10.84 Runtime Complexity Weighted TRS with Types. 32.25/10.84 The TRS R consists of the following rules: 32.25/10.84 32.25/10.84 half(0) -> 0 [1] 32.25/10.84 half(s(0)) -> 0 [1] 32.25/10.84 half(s(s(x))) -> s(half(x)) [1] 32.25/10.84 lastbit(0) -> 0 [1] 32.25/10.84 lastbit(s(0)) -> s(0) [1] 32.25/10.84 lastbit(s(s(x))) -> lastbit(x) [1] 32.25/10.84 zero(0) -> true [1] 32.25/10.84 zero(s(x)) -> false [1] 32.25/10.84 conv(x) -> conviter(x, cons(0, nil)) [1] 32.25/10.84 conviter(x, l) -> if(zero(x), x, l) [1]
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