Runtime Complexity: TRS pair #487111044

details

property	value
status	complete
benchmark	thiemann29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.644 seconds
cpu usage	316.475
user time	314.322
system time	2.15312
max virtual memory	1.8279408E7
max residence set size	5552932.0

stage attributes

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

output

WORST_CASE(Omega(n^2), ?)
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, 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), 273 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), 28 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 30 ms]
        (16) BEST
            (17) proven lower bound
                (18) LowerBoundPropagationProof [FINISHED, 0 ms]
                (19) BOUNDS(n^2, INF)
            (20) typed CpxTrs


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

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


The TRS R consists of the following rules:

   le(s(x), 0) -> false
   le(0, y) -> true
   le(s(x), s(y)) -> le(x, y)
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(0, y) -> 0
   times(s(x), y) -> plus(y, times(x, y))
   log(x, 0) -> baseError
   log(x, s(0)) -> baseError
   log(0, s(s(b))) -> logZeroError
   log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0), 0)
   loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z)
   if(true, x, b, y, z) -> z
   if(false, x, b, y, z) -> loop(x, b, times(b, y), s(z))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(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^2, INF).


The TRS R consists of the following rules:

   le(s(x), 0') -> false
   le(0', y) -> true
   le(s(x), s(y)) -> le(x, y)
   plus(0', y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(0', y) -> 0'
   times(s(x), y) -> plus(y, times(x, y))
   log(x, 0') -> baseError
   log(x, s(0')) -> baseError
   log(0', s(s(b))) -> logZeroError
   log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0'), 0')
   loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z)
   if(true, x, b, y, z) -> z
   if(false, x, b, y, z) -> loop(x, b, times(b, y), s(z))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

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

(4)
Obligation:
TRS:
Rules:
le(s(x), 0') -> false
le(0', y) -> true
le(s(x), s(y)) -> le(x, y)
plus(0', y) -> y

popout

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

job log

popout

actions all output return to Runtime Complexity: TRS