details

property	value
status	complete
benchmark	AAECC.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	AProVE_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.614 seconds
cpu usage	1146.87
user time	1139.84
system time	7.03158
max virtual memory	3.8053356E7
max residence set size	5794600.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 1 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 1137 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 326 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 26 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 46 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 2636 ms] (34) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: fstsplit(0, x) -> nil fstsplit(s(n), nil) -> nil fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) sndsplit(0, x) -> x sndsplit(s(n), nil) -> nil sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) empty(nil) -> true empty(cons(h, t)) -> false leq(0, m) -> true leq(s(n), 0) -> false leq(s(n), s(m)) -> leq(n, m) length(nil) -> 0 length(cons(h, t)) -> s(length(t)) app(nil, x) -> x app(cons(h, t), x) -> cons(h, app(t, x)) map_f(pid, nil) -> nil map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) process(store, m) -> if1(store, m, leq(m, length(store))) if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store))) if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store)))) if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m) if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: fstsplit(0, x) -> nil [1] fstsplit(s(n), nil) -> nil [1] fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) [1] sndsplit(0, x) -> x [1] sndsplit(s(n), nil) -> nil [1] sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) [1] empty(nil) -> true [1] empty(cons(h, t)) -> false [1] leq(0, m) -> true [1] popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost