Runtime Complexity: TRS Innermost pair #487112658

details

property	value
status	complete
benchmark	shuffle.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.1327 seconds
cpu usage	13.4554
user time	12.7539
system time	0.701476
max virtual memory	3.8039712E7
max residence set size	1791244.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^3), O(n^3))

output

WORST_CASE(Omega(n^3), O(n^3))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^3, n^3).

(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), 0 ms]
    (6) CpxTypedWeightedCompleteTrs
    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (8) CpxRNTS
    (9) CompleteCoflocoProof [FINISHED, 206 ms]
    (10) BOUNDS(1, n^3)
(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), 287 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), 18 ms]
            (26) BEST
                (27) proven lower bound
                    (28) LowerBoundPropagationProof [FINISHED, 0 ms]
                    (29) BOUNDS(n^2, INF)
                (30) typed CpxTrs
                    (31) RewriteLemmaProof [LOWER BOUND(ID), 18 ms]
                    (32) proven lower bound
                    (33) LowerBoundPropagationProof [FINISHED, 0 ms]
                    (34) BOUNDS(n^3, INF)


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

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3).


The TRS R consists of the following rules:

   shuffle(Cons(x, xs)) -> Cons(x, shuffle(reverse(xs)))
   reverse(Cons(x, xs)) -> append(reverse(xs), Cons(x, Nil))
   append(Cons(x, xs), ys) -> Cons(x, append(xs, ys))
   shuffle(Nil) -> Nil
   reverse(Nil) -> Nil
   append(Nil, ys) -> ys
   goal(xs) -> shuffle(xs)

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^3).


The TRS R consists of the following rules:

   shuffle(Cons(x, xs)) -> Cons(x, shuffle(reverse(xs))) [1]
   reverse(Cons(x, xs)) -> append(reverse(xs), Cons(x, Nil)) [1]
   append(Cons(x, xs), ys) -> Cons(x, append(xs, ys)) [1]
   shuffle(Nil) -> Nil [1]
   reverse(Nil) -> Nil [1]
   append(Nil, ys) -> ys [1]
   goal(xs) -> shuffle(xs) [1]

Rewrite Strategy: INNERMOST
----------------------------------------

(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(4)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   shuffle(Cons(x, xs)) -> Cons(x, shuffle(reverse(xs))) [1]
   reverse(Cons(x, xs)) -> append(reverse(xs), Cons(x, Nil)) [1]
   append(Cons(x, xs), ys) -> Cons(x, append(xs, ys)) [1]
   shuffle(Nil) -> Nil [1]

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