Runtime Complexity: TRS Innermost pair #487111718

details

property	value
status	complete
benchmark	thiemann26.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	17.7144 seconds
cpu usage	64.4797
user time	61.9219
system time	2.55782
max virtual memory	3.7459224E7
max residence set size	4475624.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^1).

(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), 8 ms]
    (8) CpxRNTS
    (9) CompleteCoflocoProof [FINISHED, 1084 ms]
    (10) BOUNDS(1, n^1)
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(12) TRS for Loop Detection
    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (14) BEST
        (15) proven lower bound
            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
            (17) BOUNDS(n^1, INF)
        (18) TRS for Loop Detection


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

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


The TRS R consists of the following rules:

   ge(x, 0) -> true
   ge(0, s(y)) -> false
   ge(s(x), s(y)) -> ge(x, y)
   minus(x, 0) -> x
   minus(0, y) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   id_inc(x) -> x
   id_inc(x) -> s(x)
   quot(x, y) -> div(x, y, 0)
   div(x, y, z) -> if(ge(y, s(0)), ge(x, y), x, y, z)
   if(false, b, x, y, z) -> div_by_zero
   if(true, false, x, y, z) -> z
   if(true, true, x, y, z) -> div(minus(x, y), y, id_inc(z))

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^1).


The TRS R consists of the following rules:

   ge(x, 0) -> true [1]
   ge(0, s(y)) -> false [1]
   ge(s(x), s(y)) -> ge(x, y) [1]
   minus(x, 0) -> x [1]
   minus(0, y) -> 0 [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   id_inc(x) -> x [1]
   id_inc(x) -> s(x) [1]
   quot(x, y) -> div(x, y, 0) [1]
   div(x, y, z) -> if(ge(y, s(0)), ge(x, y), x, y, z) [1]
   if(false, b, x, y, z) -> div_by_zero [1]
   if(true, false, x, y, z) -> z [1]
   if(true, true, x, y, z) -> div(minus(x, y), y, id_inc(z)) [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:

   ge(x, 0) -> true [1]
   ge(0, s(y)) -> false [1]
   ge(s(x), s(y)) -> ge(x, y) [1]
   minus(x, 0) -> x [1]
   minus(0, y) -> 0 [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   id_inc(x) -> x [1]
   id_inc(x) -> s(x) [1]

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