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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313459
details
property
value
status
complete
benchmark
Ex4_7_37_Bor03_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n094.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.645 seconds
cpu usage
1036.99
user time
1020.54
system time
16.4523
max virtual memory
3.7847996E7
max residence set size
1.499618E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1036.52/291.52 WORST_CASE(Omega(n^1), ?) 1036.52/291.54 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1036.52/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1036.52/291.54 1036.52/291.54 1036.52/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1036.52/291.54 1036.52/291.54 (0) CpxTRS 1036.52/291.54 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1036.52/291.54 (2) TRS for Loop Detection 1036.52/291.54 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1036.52/291.54 (4) BEST 1036.52/291.54 (5) proven lower bound 1036.52/291.54 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1036.52/291.54 (7) BOUNDS(n^1, INF) 1036.52/291.54 (8) TRS for Loop Detection 1036.52/291.54 1036.52/291.54 1036.52/291.54 ---------------------------------------- 1036.52/291.54 1036.52/291.54 (0) 1036.52/291.54 Obligation: 1036.52/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1036.52/291.54 1036.52/291.54 1036.52/291.54 The TRS R consists of the following rules: 1036.52/291.54 1036.52/291.54 from(X) -> cons(X, n__from(s(X))) 1036.52/291.54 sel(0, cons(X, XS)) -> X 1036.52/291.54 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 1036.52/291.54 minus(X, 0) -> 0 1036.52/291.54 minus(s(X), s(Y)) -> minus(X, Y) 1036.52/291.54 quot(0, s(Y)) -> 0 1036.52/291.54 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 1036.52/291.54 zWquot(XS, nil) -> nil 1036.52/291.54 zWquot(nil, XS) -> nil 1036.52/291.54 zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 1036.52/291.54 from(X) -> n__from(X) 1036.52/291.54 zWquot(X1, X2) -> n__zWquot(X1, X2) 1036.52/291.54 activate(n__from(X)) -> from(X) 1036.52/291.54 activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) 1036.52/291.54 activate(X) -> X 1036.52/291.54 1036.52/291.54 S is empty. 1036.52/291.54 Rewrite Strategy: INNERMOST 1036.52/291.54 ---------------------------------------- 1036.52/291.54 1036.52/291.54 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1036.52/291.54 Transformed a relative TRS into a decreasing-loop problem. 1036.52/291.54 ---------------------------------------- 1036.52/291.54 1036.52/291.54 (2) 1036.52/291.54 Obligation: 1036.52/291.54 Analyzing the following TRS for decreasing loops: 1036.52/291.54 1036.52/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1036.52/291.54 1036.52/291.54 1036.52/291.54 The TRS R consists of the following rules: 1036.52/291.54 1036.52/291.54 from(X) -> cons(X, n__from(s(X))) 1036.52/291.54 sel(0, cons(X, XS)) -> X 1036.52/291.54 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 1036.52/291.54 minus(X, 0) -> 0 1036.52/291.54 minus(s(X), s(Y)) -> minus(X, Y) 1036.52/291.54 quot(0, s(Y)) -> 0 1036.52/291.54 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 1036.52/291.54 zWquot(XS, nil) -> nil 1036.52/291.54 zWquot(nil, XS) -> nil 1036.52/291.54 zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 1036.52/291.54 from(X) -> n__from(X) 1036.52/291.54 zWquot(X1, X2) -> n__zWquot(X1, X2) 1036.52/291.54 activate(n__from(X)) -> from(X) 1036.52/291.54 activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) 1036.52/291.54 activate(X) -> X 1036.52/291.54 1036.52/291.54 S is empty. 1036.52/291.54 Rewrite Strategy: INNERMOST 1036.52/291.54 ---------------------------------------- 1036.52/291.54 1036.52/291.54 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1036.52/291.54 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1036.52/291.54 1036.52/291.54 The rewrite sequence 1036.52/291.54 1036.52/291.54 minus(s(X), s(Y)) ->^+ minus(X, Y) 1036.52/291.54 1036.52/291.54 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1036.52/291.54 1036.52/291.54 The pumping substitution is [X / s(X), Y / s(Y)]. 1036.52/291.54 1036.52/291.54 The result substitution is [ ]. 1036.52/291.54 1036.52/291.54 1036.52/291.54 1036.52/291.54 1036.52/291.54 ---------------------------------------- 1036.52/291.54 1036.52/291.54 (4) 1036.52/291.54 Complex Obligation (BEST)
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