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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313498
details
property
value
status
complete
benchmark
Ex9_Luc04_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n095.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.624 seconds
cpu usage
1124.51
user time
1111.92
system time
12.5983
max virtual memory
3.7965648E7
max residence set size
1.5245112E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1124.11/291.49 WORST_CASE(Omega(n^1), ?) 1124.11/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1124.11/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1124.11/291.50 1124.11/291.50 1124.11/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1124.11/291.50 1124.11/291.50 (0) CpxTRS 1124.11/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1124.11/291.50 (2) TRS for Loop Detection 1124.11/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1124.11/291.50 (4) BEST 1124.11/291.50 (5) proven lower bound 1124.11/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1124.11/291.50 (7) BOUNDS(n^1, INF) 1124.11/291.50 (8) TRS for Loop Detection 1124.11/291.50 1124.11/291.50 1124.11/291.50 ---------------------------------------- 1124.11/291.50 1124.11/291.50 (0) 1124.11/291.50 Obligation: 1124.11/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1124.11/291.50 1124.11/291.50 1124.11/291.50 The TRS R consists of the following rules: 1124.11/291.50 1124.11/291.50 a__f(a, b, X) -> a__f(mark(X), X, mark(X)) 1124.11/291.50 a__c -> a 1124.11/291.50 a__c -> b 1124.11/291.50 mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) 1124.11/291.50 mark(c) -> a__c 1124.11/291.50 mark(a) -> a 1124.11/291.50 mark(b) -> b 1124.11/291.50 a__f(X1, X2, X3) -> f(X1, X2, X3) 1124.11/291.50 a__c -> c 1124.11/291.50 1124.11/291.50 S is empty. 1124.11/291.50 Rewrite Strategy: INNERMOST 1124.11/291.50 ---------------------------------------- 1124.11/291.50 1124.11/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1124.11/291.50 Transformed a relative TRS into a decreasing-loop problem. 1124.11/291.50 ---------------------------------------- 1124.11/291.50 1124.11/291.50 (2) 1124.11/291.50 Obligation: 1124.11/291.50 Analyzing the following TRS for decreasing loops: 1124.11/291.50 1124.11/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1124.11/291.50 1124.11/291.50 1124.11/291.50 The TRS R consists of the following rules: 1124.11/291.50 1124.11/291.50 a__f(a, b, X) -> a__f(mark(X), X, mark(X)) 1124.11/291.50 a__c -> a 1124.11/291.50 a__c -> b 1124.11/291.50 mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) 1124.11/291.50 mark(c) -> a__c 1124.11/291.50 mark(a) -> a 1124.11/291.50 mark(b) -> b 1124.11/291.50 a__f(X1, X2, X3) -> f(X1, X2, X3) 1124.11/291.50 a__c -> c 1124.11/291.50 1124.11/291.50 S is empty. 1124.11/291.50 Rewrite Strategy: INNERMOST 1124.11/291.50 ---------------------------------------- 1124.11/291.50 1124.11/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1124.11/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1124.11/291.50 1124.11/291.50 The rewrite sequence 1124.11/291.50 1124.11/291.50 mark(f(X1, X2, X3)) ->^+ a__f(mark(X1), X2, mark(X3)) 1124.11/291.50 1124.11/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1124.11/291.50 1124.11/291.50 The pumping substitution is [X1 / f(X1, X2, X3)]. 1124.11/291.50 1124.11/291.50 The result substitution is [ ]. 1124.11/291.50 1124.11/291.50 1124.11/291.50 1124.11/291.50 1124.11/291.50 ---------------------------------------- 1124.11/291.50 1124.11/291.50 (4) 1124.11/291.50 Complex Obligation (BEST) 1124.11/291.50 1124.11/291.50 ---------------------------------------- 1124.11/291.50 1124.11/291.50 (5) 1124.11/291.50 Obligation: 1124.11/291.50 Proved the lower bound n^1 for the following obligation: 1124.11/291.50 1124.11/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1124.11/291.50 1124.11/291.50 1124.11/291.50 The TRS R consists of the following rules: 1124.11/291.50
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