Runti Compl Full Rewri 10127 pair #381902452

details

property	value
status	complete
benchmark	maxsortcondition.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.034567118 seconds
cpu usage	313.150065927
max memory	5.328130048E9

stage attributes

key	value
output-size	18355
starexec-result	WORST_CASE(Omega(n^2), ?)

output

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


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WORST_CASE(Omega(n^2), ?)
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^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), 275 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), 21 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 62 ms]
        (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 78 ms]
        (18) proven lower bound
        (19) LowerBoundPropagationProof [FINISHED, 0 ms]
        (20) BOUNDS(n^2, INF)


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(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:

   max(nil) -> 0
   max(cons(x, nil)) -> x
   max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs)
   if1(true, x, y, xs) -> max(cons(x, xs))
   if1(false, x, y, xs) -> max(cons(y, xs))
   del(x, nil) -> nil
   del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
   if2(true, x, y, xs) -> xs
   if2(false, x, y, xs) -> cons(y, del(x, xs))
   eq(0, 0) -> true
   eq(0, s(y)) -> false
   eq(s(x), 0) -> false
   eq(s(x), s(y)) -> eq(x, y)
   sort(xs) -> if3(empty(xs), xs)
   if3(true, xs) -> nil
   if3(false, xs) -> sort(del(max(xs), xs))
   empty(nil) -> true
   empty(cons(x, xs)) -> false
   ge(x, 0) -> true
   ge(0, s(x)) -> false
   ge(s(x), s(y)) -> ge(x, y)

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:

   max(nil) -> 0'
   max(cons(x, nil)) -> x
   max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs)
   if1(true, x, y, xs) -> max(cons(x, xs))
   if1(false, x, y, xs) -> max(cons(y, xs))
   del(x, nil) -> nil
   del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
   if2(true, x, y, xs) -> xs
   if2(false, x, y, xs) -> cons(y, del(x, xs))
   eq(0', 0') -> true
   eq(0', s(y)) -> false
   eq(s(x), 0') -> false
   eq(s(x), s(y)) -> eq(x, y)
   sort(xs) -> if3(empty(xs), xs)
   if3(true, xs) -> nil
   if3(false, xs) -> sort(del(max(xs), xs))
   empty(nil) -> true
   empty(cons(x, xs)) -> false

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