details

property	value
status	complete
benchmark	nestdec.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.73072504997 seconds
cpu usage	15.470730898
max memory	2.896699392E9

stage attributes

key	value
output-size	13871
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsTAProof [FINISHED, 127 ms] (4) BOUNDS(1, n^1) (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTRS (7) SlicingProof [LOWER BOUND(ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 221 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: dec(Cons(Nil, Nil)) -> Nil dec(Cons(Nil, Cons(x, xs))) -> dec(Cons(x, xs)) dec(Cons(Cons(x, xs), Nil)) -> dec(Nil) dec(Cons(Cons(x', xs'), Cons(x, xs))) -> dec(Cons(x, xs)) isNilNil(Cons(Nil, Nil)) -> True isNilNil(Cons(Nil, Cons(x, xs))) -> False isNilNil(Cons(Cons(x, xs), Nil)) -> False isNilNil(Cons(Cons(x', xs'), Cons(x, xs))) -> False nestdec(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, Cons(Nil, Nil))))))))))))))))) nestdec(Cons(x, xs)) -> nestdec(dec(Cons(x, xs))) number17(n) -> 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) -> nestdec(x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: dec(Cons(Nil, Nil)) -> Nil dec(Cons(Nil, Cons(x, xs))) -> dec(Cons(x, xs)) dec(Cons(Cons(x, xs), Nil)) -> dec(Nil) dec(Cons(Cons(x', xs'), Cons(x, xs))) -> dec(Cons(x, xs)) isNilNil(Cons(Nil, Nil)) -> True isNilNil(Cons(Nil, Cons(x, xs))) -> False isNilNil(Cons(Cons(x, xs), Nil)) -> False isNilNil(Cons(Cons(x', xs'), Cons(x, xs))) -> False nestdec(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, Cons(Nil, Nil))))))))))))))))) nestdec(Cons(x, xs)) -> nestdec(dec(Cons(x, xs))) number17(n) -> 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) -> nestdec(x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsTAProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2, 3, 4, 5] transitions: Cons0(0, 0) -> 0 Nil0() -> 0 True0() -> 0 False0() -> 0 dec0(0) -> 1 isNilNil0(0) -> 2 popout

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actions

all output return to Runti Compl Inner Rewri 22807