Runtime Complexity: TRS Innermost pair #487112704

details

property	value
status	complete
benchmark	naiverev.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.70803 seconds
cpu usage	11.4594
user time	10.8445
system time	0.614853
max virtual memory	1.9011556E7
max residence set size	1732908.0

stage attributes

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

output

WORST_CASE(Omega(n^2), O(n^2))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^2, 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), 0 ms]
    (6) CpxTypedWeightedCompleteTrs
    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (8) CpxRNTS
    (9) CompleteCoflocoProof [FINISHED, 167 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), 266 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), 0 ms]
            (26) proven lower bound
            (27) LowerBoundPropagationProof [FINISHED, 0 ms]
            (28) BOUNDS(n^2, INF)


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

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


The TRS R consists of the following rules:

   naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil))
   app(Cons(x, xs), ys) -> Cons(x, app(xs, ys))
   notEmpty(Cons(x, xs)) -> True
   notEmpty(Nil) -> False
   naiverev(Nil) -> Nil
   app(Nil, ys) -> ys
   goal(xs) -> naiverev(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^2).


The TRS R consists of the following rules:

   naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) [1]
   app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) [1]
   notEmpty(Cons(x, xs)) -> True [1]
   notEmpty(Nil) -> False [1]
   naiverev(Nil) -> Nil [1]
   app(Nil, ys) -> ys [1]
   goal(xs) -> naiverev(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:

   naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) [1]
   app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) [1]
   notEmpty(Cons(x, xs)) -> True [1]
   notEmpty(Nil) -> False [1]
   naiverev(Nil) -> Nil [1]
   app(Nil, ys) -> ys [1]
   goal(xs) -> naiverev(xs) [1]

The TRS has the following type information:
naiverev :: Cons:Nil -> Cons:Nil

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