Runtime Complexity: TRS pair #487111026

details

property	value
status	complete
benchmark	otto01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.666 seconds
cpu usage	1030.0
user time	1018.74
system time	11.2605
max virtual memory	3.8041364E7
max residence set size	1.4782464E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).

(0) CpxTRS
(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 14 ms]
(2) CpxTRS
    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxWeightedTrs
    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxTypedWeightedTrs
    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (10) CpxRNTS
    (11) CompleteCoflocoProof [FINISHED, 4066 ms]
    (12) BOUNDS(1, n^1)
(13) RenamingProof [BOTH BOUNDS(ID, 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), 293 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), 41 ms]
            (26) typed CpxTrs
            (27) RewriteLemmaProof [LOWER BOUND(ID), 22 ms]
            (28) typed CpxTrs
            (29) RewriteLemmaProof [LOWER BOUND(ID), 13 ms]
            (30) typed CpxTrs
            (31) RewriteLemmaProof [LOWER BOUND(ID), 10 ms]
            (32) typed CpxTrs


----------------------------------------

(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).


The TRS R consists of the following rules:

   min(0, y) -> 0
   min(s(x), 0) -> 0
   min(s(x), s(y)) -> min(x, y)
   len(nil) -> 0
   len(cons(x, xs)) -> s(len(xs))
   sum(x, 0) -> x
   sum(x, s(y)) -> s(sum(x, y))
   le(0, x) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   take(0, cons(y, ys)) -> y
   take(s(x), cons(y, ys)) -> take(x, ys)
   addList(x, y) -> if(le(0, min(len(x), len(y))), 0, x, y, nil)
   if(false, c, x, y, z) -> z
   if(true, c, xs, ys, z) -> if(le(s(c), min(len(xs), len(ys))), s(c), xs, ys, cons(sum(take(c, xs), take(c, ys)), z))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
Converted rc-obligation to irc-obligation.

The duplicating contexts are:
addList([], y)
addList(x, [])
if(true, [], xs, ys, z)
if(true, c, [], ys, z)
if(true, c, xs, [], z)


The defined contexts are:
if([], s(x1), x2, x3, cons(x4, x5))
le(s(x0), [])
min([], x1)
min(x0, [])
if(x0, s(x1), x2, x3, cons([], x5))
sum([], x1)
sum(x0, [])
if([], 0, x1, x2, nil)
le(0, [])
le(x0, [])
if(x0, s(x1), x2, x3, cons(x4, []))


[] just represents basic- or constructor-terms in the following defined contexts:
sum([], x1)
sum(x0, [])

popout

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

job log

popout

actions all output return to Runtime Complexity: TRS