Runtime Complexity: TRS Innermost pair #487111840

details

property	value
status	complete
benchmark	log.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	12.7604 seconds
cpu usage	43.63
user time	41.7664
system time	1.86354
max virtual memory	3.690814E7
max residence set size	3992836.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^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), 2 ms]
    (8) CpxRNTS
    (9) CompleteCoflocoProof [FINISHED, 310 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:

   half(x) -> if(ge(x, s(s(0))), x)
   if(false, x) -> 0
   if(true, x) -> s(half(p(p(x))))
   p(0) -> 0
   p(s(x)) -> x
   ge(x, 0) -> true
   ge(0, s(x)) -> false
   ge(s(x), s(y)) -> ge(x, y)
   log(0) -> 0
   log(s(x)) -> s(log(half(s(x))))

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:

   half(x) -> if(ge(x, s(s(0))), x) [1]
   if(false, x) -> 0 [1]
   if(true, x) -> s(half(p(p(x)))) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   ge(x, 0) -> true [1]
   ge(0, s(x)) -> false [1]
   ge(s(x), s(y)) -> ge(x, y) [1]
   log(0) -> 0 [1]
   log(s(x)) -> s(log(half(s(x)))) [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:

   half(x) -> if(ge(x, s(s(0))), x) [1]
   if(false, x) -> 0 [1]
   if(true, x) -> s(half(p(p(x)))) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   ge(x, 0) -> true [1]
   ge(0, s(x)) -> false [1]
   ge(s(x), s(y)) -> ge(x, y) [1]
   log(0) -> 0 [1]
   log(s(x)) -> s(log(half(s(x)))) [1]

The TRS has the following type information:
half :: 0:s -> 0:s
if :: false:true -> 0:s -> 0:s

popout

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

job log

popout

actions all output return to Runtime Complexity: TRS Innermost