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	n150.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.10185 seconds
cpu usage	16.289
user time	15.2209
system time	1.06807
max virtual memory	1.9319952E7
max residence set size	3079916.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 113 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), 261 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 nestdec0(0) -> 3 number170(0) -> 4 goal0(0) -> 5 Nil1() -> 1 Cons1(0, 0) -> 6 dec1(6) -> 1 popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost