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	n049.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.755467176 seconds
cpu usage	1120.60426127
max memory	1.5356755968E10

stage attributes

key	value
output-size	4554
starexec-result	WORST_CASE(Omega(n^1), ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) a__g(0) -> s(0) a__g(s(X)) -> s(s(a__g(mark(X)))) a__sel(0, cons(X, Y)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> a__g(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__g(X) -> g(X) a__sel(X1, X2) -> sel(X1, X2) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) a__g(0) -> s(0) a__g(s(X)) -> s(s(a__g(mark(X)))) a__sel(0, cons(X, Y)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> a__g(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__g(X) -> g(X) a__sel(X1, X2) -> sel(X1, X2) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence mark(f(X)) ->^+ a__f(mark(X)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [X / f(X)]. The result substitution is [ ]. popout

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all output return to Runti Compl Inner Rewri 22807