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Runti Compl Inner Rewri 22807 pair #381904637
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
n072.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.32023096085 seconds
cpu usage
25.570902994
max memory
4.06022144E9
stage attributes
key
value
output-size
28272
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 922 ms] (10) BOUNDS(1, n^1) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: minus(X, s(Y)) -> pred(minus(X, Y)) minus(X, 0) -> X pred(s(X)) -> X le(s(X), s(Y)) -> le(X, Y) le(s(X), 0) -> false le(0, Y) -> true gcd(0, Y) -> 0 gcd(s(X), 0) -> s(X) gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y)) if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y)) if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: minus(X, s(Y)) -> pred(minus(X, Y)) [1] minus(X, 0) -> X [1] pred(s(X)) -> X [1] le(s(X), s(Y)) -> le(X, Y) [1] le(s(X), 0) -> false [1] le(0, Y) -> true [1] gcd(0, Y) -> 0 [1] gcd(s(X), 0) -> s(X) [1] gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y)) [1] if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y)) [1] if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: minus(X, s(Y)) -> pred(minus(X, Y)) [1] minus(X, 0) -> X [1] pred(s(X)) -> X [1] le(s(X), s(Y)) -> le(X, Y) [1] le(s(X), 0) -> false [1] le(0, Y) -> true [1]
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