Runti Compl Full Rewri 10127 pair #381902500

details

property	value
status	complete
benchmark	factorial2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.487274885 seconds
cpu usage	321.387085613
max memory	5.666217984E9

stage attributes

key	value
output-size	16642
starexec-result	WORST_CASE(Omega(n^3), ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^3), ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF).

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) typed CpxTrs
(5) OrderProof [LOWER BOUND(ID), 0 ms]
(6) typed CpxTrs
(7) RewriteLemmaProof [LOWER BOUND(ID), 271 ms]
(8) BEST
    (9) proven lower bound
        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
        (11) BOUNDS(n^1, INF)
    (12) typed CpxTrs
        (13) RewriteLemmaProof [LOWER BOUND(ID), 50 ms]
        (14) BEST
            (15) proven lower bound
                (16) LowerBoundPropagationProof [FINISHED, 0 ms]
                (17) BOUNDS(n^2, INF)
            (18) typed CpxTrs
                (19) RewriteLemmaProof [LOWER BOUND(ID), 472 ms]
                (20) typed CpxTrs
                (21) RewriteLemmaProof [LOWER BOUND(ID), 292 ms]
                (22) proven lower bound
                (23) LowerBoundPropagationProof [FINISHED, 0 ms]
                (24) BOUNDS(n^3, INF)


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


The TRS R consists of the following rules:

   plus(0, x) -> x
   plus(s(x), y) -> s(plus(x, y))
   times(0, y) -> 0
   times(s(x), y) -> plus(y, times(x, y))
   p(s(x)) -> x
   p(0) -> 0
   minus(x, 0) -> x
   minus(0, x) -> 0
   minus(x, s(y)) -> p(minus(x, y))
   isZero(0) -> true
   isZero(s(x)) -> false
   facIter(x, y) -> if(isZero(x), minus(x, s(0)), y, times(y, x))
   if(true, x, y, z) -> y
   if(false, x, y, z) -> facIter(x, z)
   factorial(x) -> facIter(x, s(0))

S is empty.
Rewrite Strategy: FULL
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(1) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(2)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF).


The TRS R consists of the following rules:

   plus(0', x) -> x
   plus(s(x), y) -> s(plus(x, y))
   times(0', y) -> 0'
   times(s(x), y) -> plus(y, times(x, y))
   p(s(x)) -> x
   p(0') -> 0'
   minus(x, 0') -> x
   minus(0', x) -> 0'
   minus(x, s(y)) -> p(minus(x, y))
   isZero(0') -> true
   isZero(s(x)) -> false
   facIter(x, y) -> if(isZero(x), minus(x, s(0')), y, times(y, x))
   if(true, x, y, z) -> y
   if(false, x, y, z) -> facIter(x, z)
   factorial(x) -> facIter(x, s(0'))

S is empty.
Rewrite Strategy: FULL
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