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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313533
details
property
value
status
complete
benchmark
Ex4_Zan97_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.608 seconds
cpu usage
1115.29
user time
1102.99
system time
12.3073
max virtual memory
3.7112632E7
max residence set size
1.4861444E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1115.05/291.53 WORST_CASE(Omega(n^1), ?) 1115.05/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1115.05/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1115.05/291.54 1115.05/291.54 1115.05/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1115.05/291.54 1115.05/291.54 (0) CpxTRS 1115.05/291.54 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1115.05/291.54 (2) TRS for Loop Detection 1115.05/291.54 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1115.05/291.54 (4) BEST 1115.05/291.54 (5) proven lower bound 1115.05/291.54 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1115.05/291.54 (7) BOUNDS(n^1, INF) 1115.05/291.54 (8) TRS for Loop Detection 1115.05/291.54 1115.05/291.54 1115.05/291.54 ---------------------------------------- 1115.05/291.54 1115.05/291.54 (0) 1115.05/291.54 Obligation: 1115.05/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1115.05/291.54 1115.05/291.54 1115.05/291.54 The TRS R consists of the following rules: 1115.05/291.54 1115.05/291.54 a__f(X) -> cons(mark(X), f(g(X))) 1115.05/291.54 a__g(0) -> s(0) 1115.05/291.54 a__g(s(X)) -> s(s(a__g(mark(X)))) 1115.05/291.54 a__sel(0, cons(X, Y)) -> mark(X) 1115.05/291.54 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 1115.05/291.54 mark(f(X)) -> a__f(mark(X)) 1115.05/291.54 mark(g(X)) -> a__g(mark(X)) 1115.05/291.54 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1115.05/291.54 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1115.05/291.54 mark(0) -> 0 1115.05/291.54 mark(s(X)) -> s(mark(X)) 1115.05/291.54 a__f(X) -> f(X) 1115.05/291.54 a__g(X) -> g(X) 1115.05/291.54 a__sel(X1, X2) -> sel(X1, X2) 1115.05/291.54 1115.05/291.54 S is empty. 1115.05/291.54 Rewrite Strategy: INNERMOST 1115.05/291.54 ---------------------------------------- 1115.05/291.54 1115.05/291.54 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1115.05/291.54 Transformed a relative TRS into a decreasing-loop problem. 1115.05/291.54 ---------------------------------------- 1115.05/291.54 1115.05/291.54 (2) 1115.05/291.54 Obligation: 1115.05/291.54 Analyzing the following TRS for decreasing loops: 1115.05/291.54 1115.05/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1115.05/291.54 1115.05/291.54 1115.05/291.54 The TRS R consists of the following rules: 1115.05/291.54 1115.05/291.54 a__f(X) -> cons(mark(X), f(g(X))) 1115.05/291.54 a__g(0) -> s(0) 1115.05/291.54 a__g(s(X)) -> s(s(a__g(mark(X)))) 1115.05/291.54 a__sel(0, cons(X, Y)) -> mark(X) 1115.05/291.54 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 1115.05/291.54 mark(f(X)) -> a__f(mark(X)) 1115.05/291.54 mark(g(X)) -> a__g(mark(X)) 1115.05/291.54 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1115.05/291.54 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1115.05/291.54 mark(0) -> 0 1115.05/291.54 mark(s(X)) -> s(mark(X)) 1115.05/291.54 a__f(X) -> f(X) 1115.05/291.54 a__g(X) -> g(X) 1115.05/291.54 a__sel(X1, X2) -> sel(X1, X2) 1115.05/291.54 1115.05/291.54 S is empty. 1115.05/291.54 Rewrite Strategy: INNERMOST 1115.05/291.54 ---------------------------------------- 1115.05/291.54 1115.05/291.54 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1115.05/291.54 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1115.05/291.54 1115.05/291.54 The rewrite sequence 1115.05/291.54 1115.05/291.54 mark(f(X)) ->^+ a__f(mark(X)) 1115.05/291.54 1115.05/291.54 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1115.05/291.54 1115.05/291.54 The pumping substitution is [X / f(X)]. 1115.05/291.54 1115.05/291.54 The result substitution is [ ]. 1115.05/291.54 1115.05/291.54 1115.05/291.54 1115.05/291.54 1115.05/291.54 ---------------------------------------- 1115.05/291.54 1115.05/291.54 (4) 1115.05/291.54 Complex Obligation (BEST) 1115.05/291.54 1115.05/291.54 ----------------------------------------
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