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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313522
details
property
value
status
timeout (wallclock)
benchmark
Ex7_BLR02_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
300.082 seconds
cpu usage
1155.35
user time
1142.31
system time
13.04
max virtual memory
3.7111248E7
max residence set size
1452.0
stage attributes
unavailable
output
1155.12/299.98 WORST_CASE(Omega(n^1), ?) 1155.12/300.02 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1155.12/300.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1155.12/300.02 1155.12/300.02 1155.12/300.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1155.12/300.02 1155.12/300.02 (0) CpxTRS 1155.12/300.02 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1155.12/300.02 (2) TRS for Loop Detection 1155.12/300.02 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1155.12/300.02 (4) BEST 1155.12/300.02 (5) proven lower bound 1155.12/300.02 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1155.12/300.02 (7) BOUNDS(n^1, INF) 1155.12/300.02 (8) TRS for Loop Detection 1155.12/300.02 1155.12/300.02 1155.12/300.02 ---------------------------------------- 1155.12/300.02 1155.12/300.02 (0) 1155.12/300.02 Obligation: 1155.12/300.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1155.12/300.02 1155.12/300.02 1155.12/300.02 The TRS R consists of the following rules: 1155.12/300.02 1155.12/300.02 a__from(X) -> cons(mark(X), from(s(X))) 1155.12/300.02 a__head(cons(X, XS)) -> mark(X) 1155.12/300.02 a__2nd(cons(X, XS)) -> a__head(mark(XS)) 1155.12/300.02 a__take(0, XS) -> nil 1155.12/300.02 a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) 1155.12/300.02 a__sel(0, cons(X, XS)) -> mark(X) 1155.12/300.02 a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1155.12/300.02 mark(from(X)) -> a__from(mark(X)) 1155.12/300.02 mark(head(X)) -> a__head(mark(X)) 1155.12/300.02 mark(2nd(X)) -> a__2nd(mark(X)) 1155.12/300.02 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1155.12/300.02 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1155.12/300.02 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1155.12/300.02 mark(s(X)) -> s(mark(X)) 1155.12/300.02 mark(0) -> 0 1155.12/300.02 mark(nil) -> nil 1155.12/300.02 a__from(X) -> from(X) 1155.12/300.02 a__head(X) -> head(X) 1155.12/300.02 a__2nd(X) -> 2nd(X) 1155.12/300.02 a__take(X1, X2) -> take(X1, X2) 1155.12/300.02 a__sel(X1, X2) -> sel(X1, X2) 1155.12/300.02 1155.12/300.02 S is empty. 1155.12/300.02 Rewrite Strategy: INNERMOST 1155.12/300.02 ---------------------------------------- 1155.12/300.02 1155.12/300.02 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1155.12/300.02 Transformed a relative TRS into a decreasing-loop problem. 1155.12/300.02 ---------------------------------------- 1155.12/300.02 1155.12/300.02 (2) 1155.12/300.02 Obligation: 1155.12/300.02 Analyzing the following TRS for decreasing loops: 1155.12/300.02 1155.12/300.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1155.12/300.02 1155.12/300.02 1155.12/300.02 The TRS R consists of the following rules: 1155.12/300.02 1155.12/300.02 a__from(X) -> cons(mark(X), from(s(X))) 1155.12/300.02 a__head(cons(X, XS)) -> mark(X) 1155.12/300.02 a__2nd(cons(X, XS)) -> a__head(mark(XS)) 1155.12/300.02 a__take(0, XS) -> nil 1155.12/300.02 a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) 1155.12/300.02 a__sel(0, cons(X, XS)) -> mark(X) 1155.12/300.02 a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1155.12/300.02 mark(from(X)) -> a__from(mark(X)) 1155.12/300.02 mark(head(X)) -> a__head(mark(X)) 1155.12/300.02 mark(2nd(X)) -> a__2nd(mark(X)) 1155.12/300.02 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1155.12/300.02 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1155.12/300.02 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1155.12/300.02 mark(s(X)) -> s(mark(X)) 1155.12/300.02 mark(0) -> 0 1155.12/300.02 mark(nil) -> nil 1155.12/300.02 a__from(X) -> from(X) 1155.12/300.02 a__head(X) -> head(X) 1155.12/300.02 a__2nd(X) -> 2nd(X) 1155.12/300.02 a__take(X1, X2) -> take(X1, X2) 1155.12/300.02 a__sel(X1, X2) -> sel(X1, X2) 1155.12/300.02 1155.12/300.02 S is empty. 1155.12/300.02 Rewrite Strategy: INNERMOST 1155.12/300.02 ---------------------------------------- 1155.12/300.02 1155.12/300.02 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1155.12/300.02 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1155.12/300.02 1155.12/300.02 The rewrite sequence 1155.12/300.02 1155.12/300.02 mark(from(X)) ->^+ a__from(mark(X)) 1155.12/300.02 1155.12/300.02 gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
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