Runtime Complexity: TRS pair #487111258

details

property	value
status	complete
benchmark	zerolist.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.645 seconds
cpu usage	911.86
user time	903.831
system time	8.02919
max virtual memory	1.10703388E8
max residence set size	6753972.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxTRS
(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 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, 270 ms]
    (12) BOUNDS(1, n^2)
(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), 330 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), 40 ms]
            (26) BOUNDS(1, INF)


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

(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   sub(0, 0) -> 0
   sub(s(x), 0) -> s(x)
   sub(0, s(x)) -> 0
   sub(s(x), s(y)) -> sub(x, y)
   zero(nil) -> zero2(0, nil)
   zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs))
   zero2(0, nil) -> nil
   zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs))
   zero2(s(y), nil) -> zero(nil)
   zero2(s(y), cons(x, xs)) -> zero(cons(x, xs))

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

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

The duplicating contexts are:
zero(cons([], xs))
zero2(0, cons([], xs))


The defined contexts are:
zero2([], cons(x1, x2))


[] just represents basic- or constructor-terms in the following defined contexts:
zero2([], cons(x1, x2))


As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   sub(0, 0) -> 0
   sub(s(x), 0) -> s(x)
   sub(0, s(x)) -> 0
   sub(s(x), s(y)) -> sub(x, y)
   zero(nil) -> zero2(0, nil)
   zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs))
   zero2(0, nil) -> nil
   zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs))
   zero2(s(y), nil) -> zero(nil)
   zero2(s(y), cons(x, xs)) -> zero(cons(x, xs))

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

popout

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

job log

popout

actions all output return to Runtime Complexity: TRS