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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313390
details
property
value
status
complete
benchmark
gcd_triple.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.65 seconds
cpu usage
1148.1
user time
1133.61
system time
14.4834
max virtual memory
5.7094368E7
max residence set size
1.5034128E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1147.54/291.50 WORST_CASE(Omega(n^1), ?) 1147.73/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1147.73/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1147.73/291.52 1147.73/291.52 1147.73/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1147.73/291.52 1147.73/291.52 (0) CpxTRS 1147.73/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1147.73/291.52 (2) TRS for Loop Detection 1147.73/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1147.73/291.52 (4) BEST 1147.73/291.52 (5) proven lower bound 1147.73/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1147.73/291.52 (7) BOUNDS(n^1, INF) 1147.73/291.52 (8) TRS for Loop Detection 1147.73/291.52 1147.73/291.52 1147.73/291.52 ---------------------------------------- 1147.73/291.52 1147.73/291.52 (0) 1147.73/291.52 Obligation: 1147.73/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1147.73/291.52 1147.73/291.52 1147.73/291.52 The TRS R consists of the following rules: 1147.73/291.52 1147.73/291.52 min(x, 0) -> 0 1147.73/291.52 min(0, y) -> 0 1147.73/291.52 min(s(x), s(y)) -> s(min(x, y)) 1147.73/291.52 max(x, 0) -> x 1147.73/291.52 max(0, y) -> y 1147.73/291.52 max(s(x), s(y)) -> s(max(x, y)) 1147.73/291.52 -(x, 0) -> x 1147.73/291.52 -(s(x), s(y)) -> -(x, y) 1147.73/291.52 gcd(s(x), s(y), z) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)), z) 1147.73/291.52 gcd(x, s(y), s(z)) -> gcd(x, -(max(y, z), min(y, z)), s(min(y, z))) 1147.73/291.52 gcd(s(x), y, s(z)) -> gcd(-(max(x, z), min(x, z)), y, s(min(x, z))) 1147.73/291.52 gcd(x, 0, 0) -> x 1147.73/291.52 gcd(0, y, 0) -> y 1147.73/291.52 gcd(0, 0, z) -> z 1147.73/291.52 1147.73/291.52 S is empty. 1147.73/291.52 Rewrite Strategy: INNERMOST 1147.73/291.52 ---------------------------------------- 1147.73/291.52 1147.73/291.52 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1147.73/291.52 Transformed a relative TRS into a decreasing-loop problem. 1147.73/291.52 ---------------------------------------- 1147.73/291.52 1147.73/291.52 (2) 1147.73/291.52 Obligation: 1147.73/291.52 Analyzing the following TRS for decreasing loops: 1147.73/291.52 1147.73/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1147.73/291.52 1147.73/291.52 1147.73/291.52 The TRS R consists of the following rules: 1147.73/291.52 1147.73/291.52 min(x, 0) -> 0 1147.73/291.52 min(0, y) -> 0 1147.73/291.52 min(s(x), s(y)) -> s(min(x, y)) 1147.73/291.52 max(x, 0) -> x 1147.73/291.52 max(0, y) -> y 1147.73/291.52 max(s(x), s(y)) -> s(max(x, y)) 1147.73/291.52 -(x, 0) -> x 1147.73/291.52 -(s(x), s(y)) -> -(x, y) 1147.73/291.52 gcd(s(x), s(y), z) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)), z) 1147.73/291.52 gcd(x, s(y), s(z)) -> gcd(x, -(max(y, z), min(y, z)), s(min(y, z))) 1147.73/291.52 gcd(s(x), y, s(z)) -> gcd(-(max(x, z), min(x, z)), y, s(min(x, z))) 1147.73/291.52 gcd(x, 0, 0) -> x 1147.73/291.52 gcd(0, y, 0) -> y 1147.73/291.52 gcd(0, 0, z) -> z 1147.73/291.52 1147.73/291.52 S is empty. 1147.73/291.52 Rewrite Strategy: INNERMOST 1147.73/291.52 ---------------------------------------- 1147.73/291.52 1147.73/291.52 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1147.73/291.52 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1147.73/291.52 1147.73/291.52 The rewrite sequence 1147.73/291.52 1147.73/291.52 -(s(x), s(y)) ->^+ -(x, y) 1147.73/291.52 1147.73/291.52 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1147.73/291.52 1147.73/291.52 The pumping substitution is [x / s(x), y / s(y)]. 1147.73/291.52 1147.73/291.52 The result substitution is [ ]. 1147.73/291.52 1147.73/291.52 1147.73/291.52 1147.73/291.52 1147.73/291.52 ---------------------------------------- 1147.73/291.52 1147.73/291.52 (4) 1147.73/291.52 Complex Obligation (BEST) 1147.73/291.52 1147.73/291.52 ----------------------------------------
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