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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313297
details
property
value
status
complete
benchmark
gcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.80971 seconds
cpu usage
30.7217
user time
28.9323
system time
1.78943
max virtual memory
1.9178464E7
max residence set size
4314700.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
30.58/8.74 WORST_CASE(Omega(n^1), O(n^1)) 30.58/8.75 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 30.58/8.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.58/8.75 30.58/8.75 30.58/8.75 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 30.58/8.75 30.58/8.75 (0) CpxTRS 30.58/8.75 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 30.58/8.75 (2) CpxWeightedTrs 30.58/8.75 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 30.58/8.75 (4) CpxTypedWeightedTrs 30.58/8.75 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 30.58/8.75 (6) CpxTypedWeightedCompleteTrs 30.58/8.75 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 30.58/8.75 (8) CpxRNTS 30.58/8.75 (9) CompleteCoflocoProof [FINISHED, 954 ms] 30.58/8.75 (10) BOUNDS(1, n^1) 30.58/8.75 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 30.58/8.75 (12) TRS for Loop Detection 30.58/8.75 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 30.58/8.75 (14) BEST 30.58/8.75 (15) proven lower bound 30.58/8.75 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 30.58/8.75 (17) BOUNDS(n^1, INF) 30.58/8.75 (18) TRS for Loop Detection 30.58/8.75 30.58/8.75 30.58/8.75 ---------------------------------------- 30.58/8.75 30.58/8.75 (0) 30.58/8.75 Obligation: 30.58/8.75 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 30.58/8.75 30.58/8.75 30.58/8.75 The TRS R consists of the following rules: 30.58/8.75 30.58/8.75 minus(X, s(Y)) -> pred(minus(X, Y)) 30.58/8.75 minus(X, 0) -> X 30.58/8.75 pred(s(X)) -> X 30.58/8.75 le(s(X), s(Y)) -> le(X, Y) 30.58/8.75 le(s(X), 0) -> false 30.58/8.75 le(0, Y) -> true 30.58/8.75 gcd(0, Y) -> 0 30.58/8.75 gcd(s(X), 0) -> s(X) 30.58/8.75 gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y)) 30.58/8.75 if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y)) 30.58/8.75 if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X)) 30.58/8.75 30.58/8.75 S is empty. 30.58/8.75 Rewrite Strategy: INNERMOST 30.58/8.75 ---------------------------------------- 30.58/8.75 30.58/8.75 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 30.58/8.75 Transformed relative TRS to weighted TRS 30.58/8.75 ---------------------------------------- 30.58/8.75 30.58/8.75 (2) 30.58/8.75 Obligation: 30.58/8.75 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 30.58/8.75 30.58/8.75 30.58/8.75 The TRS R consists of the following rules: 30.58/8.75 30.58/8.75 minus(X, s(Y)) -> pred(minus(X, Y)) [1] 30.58/8.75 minus(X, 0) -> X [1] 30.58/8.75 pred(s(X)) -> X [1] 30.58/8.75 le(s(X), s(Y)) -> le(X, Y) [1] 30.58/8.75 le(s(X), 0) -> false [1] 30.58/8.75 le(0, Y) -> true [1] 30.58/8.75 gcd(0, Y) -> 0 [1] 30.58/8.75 gcd(s(X), 0) -> s(X) [1] 30.58/8.75 gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y)) [1] 30.58/8.75 if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y)) [1] 30.58/8.75 if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X)) [1] 30.58/8.75 30.58/8.75 Rewrite Strategy: INNERMOST 30.58/8.75 ---------------------------------------- 30.58/8.75 30.58/8.75 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 30.58/8.75 Infered types. 30.58/8.75 ---------------------------------------- 30.58/8.75 30.58/8.75 (4) 30.58/8.75 Obligation: 30.58/8.75 Runtime Complexity Weighted TRS with Types. 30.58/8.75 The TRS R consists of the following rules: 30.58/8.75 30.58/8.75 minus(X, s(Y)) -> pred(minus(X, Y)) [1] 30.58/8.75 minus(X, 0) -> X [1] 30.58/8.75 pred(s(X)) -> X [1] 30.58/8.75 le(s(X), s(Y)) -> le(X, Y) [1] 30.58/8.75 le(s(X), 0) -> false [1] 30.58/8.75 le(0, Y) -> true [1] 30.58/8.75 gcd(0, Y) -> 0 [1] 30.58/8.75 gcd(s(X), 0) -> s(X) [1] 30.58/8.75 gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y)) [1] 30.58/8.75 if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y)) [1] 30.58/8.75 if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X)) [1] 30.58/8.75
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