details

property	value
status	complete
benchmark	nestinc.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.58337903023 seconds
cpu usage	3.436314479
max memory	2.2052864E8

stage attributes

key	value
output-size	4933
starexec-result	WORST_CASE(NON_POLY, ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).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 (9) InfiniteLowerBoundProof [FINISHED, 0 ms] (10) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: inc(Cons(x, xs)) -> Cons(Cons(Nil, Nil), inc(xs)) nestinc(Nil) -> number17(Nil) nestinc(Cons(x, xs)) -> nestinc(inc(Cons(x, xs))) inc(Nil) -> Cons(Nil, Nil) number17(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))) goal(x) -> nestinc(x) 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(INF, INF). The TRS R consists of the following rules: inc(Cons(x, xs)) -> Cons(Cons(Nil, Nil), inc(xs)) nestinc(Nil) -> number17(Nil) nestinc(Cons(x, xs)) -> nestinc(inc(Cons(x, xs))) inc(Nil) -> Cons(Nil, Nil) number17(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))) goal(x) -> nestinc(x) 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 inc(Cons(x, xs)) ->^+ Cons(Cons(Nil, Nil), inc(xs)) gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. The pumping substitution is [xs / Cons(x, xs)]. The result substitution is [ ]. ---------------------------------------- (4) Complex Obligation (BEST) ---------------------------------------- (5) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). popout

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actions

all output return to Runti Compl Inner Rewri 22807