details

property	value
status	complete
benchmark	permute.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n058.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.49457597733 seconds
cpu usage	7.183440683
max memory	1.1758592E9

stage attributes

key	value
output-size	6055
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).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) DecreasingLoopProof [FINISHED, 565 ms] (10) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs)) revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) permute(Cons(x, xs)) -> select(x, Nil, xs) mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil) revapp(Nil, rest) -> rest permute(Nil) -> Cons(Nil, Nil) mapconsapp(x, Nil, rest) -> rest goal(xs) -> permute(xs) 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(EXP, INF). The TRS R consists of the following rules: select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs)) revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) permute(Cons(x, xs)) -> select(x, Nil, xs) mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil) revapp(Nil, rest) -> rest permute(Nil) -> Cons(Nil, Nil) mapconsapp(x, Nil, rest) -> rest goal(xs) -> permute(xs) 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 revapp(Cons(x, xs), rest) ->^+ revapp(xs, Cons(x, rest)) gives rise to a decreasing loop by considering the right hand sides subterm at position []. The pumping substitution is [xs / Cons(x, xs)]. The result substitution is [rest / Cons(x, rest)]. ---------------------------------------- (4) Complex Obligation (BEST) ---------------------------------------- (5) popout

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actions

all output return to Runti Compl Inner Rewri 22807