Runti Compl Full Rewri 10127 pair #381902674

details

property	value
status	complete
benchmark	gcd.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n049.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.910983086 seconds
cpu usage	307.485258867
max memory	5.312290816E9

stage attributes

key	value
output-size	9390
starexec-result	WORST_CASE(Omega(n^1), ?)

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^1), ?)
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^1, 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), 295 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), 85 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 25 ms]
        (16) typed CpxTrs


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


The TRS R consists of the following rules:

   min(x, 0) -> 0
   min(0, y) -> 0
   min(s(x), s(y)) -> s(min(x, y))
   max(x, 0) -> x
   max(0, y) -> y
   max(s(x), s(y)) -> s(max(x, y))
   -(x, 0) -> x
   -(s(x), s(y)) -> -(x, y)
   gcd(s(x), 0) -> s(x)
   gcd(0, s(x)) -> s(x)
   gcd(s(x), s(y)) -> gcd(-(max(x, y), min(x, y)), s(min(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^1, INF).


The TRS R consists of the following rules:

   min(x, 0') -> 0'
   min(0', y) -> 0'
   min(s(x), s(y)) -> s(min(x, y))
   max(x, 0') -> x
   max(0', y) -> y
   max(s(x), s(y)) -> s(max(x, y))
   -(x, 0') -> x
   -(s(x), s(y)) -> -(x, y)
   gcd(s(x), 0') -> s(x)
   gcd(0', s(x)) -> s(x)
   gcd(s(x), s(y)) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)))

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

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

(4)
Obligation:
TRS:
Rules:
min(x, 0') -> 0'
min(0', y) -> 0'
min(s(x), s(y)) -> s(min(x, y))
max(x, 0') -> x
max(0', y) -> y
max(s(x), s(y)) -> s(max(x, y))
-(x, 0') -> x
-(s(x), s(y)) -> -(x, y)

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