Funct Progr 77531 pair #381920541

details

property	value
status	complete
benchmark	GT_3.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.34631991386 seconds
cpu usage	9.889323072
max memory	5.53099264E8

stage attributes

key	value
output-size	10462
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [EQUIVALENT, 20 ms]
(6) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

compare0 x y MyTrue = GT;

compare1 x y MyTrue = LT;
compare1 x y MyFalse = compare0 x y otherwise;

compare2 x y MyTrue = EQ;
compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);

compare3 x y = compare2 x y (esEsMyBool x y);

compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
compareMyBool x y = compare3 x y;

esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
esEsMyBool MyFalse MyFalse = MyTrue;
esEsMyBool MyFalse MyTrue = MyFalse;
esEsMyBool MyTrue MyFalse = MyFalse;
esEsMyBool MyTrue MyTrue = MyTrue;

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

gtMyBool :: MyBool  ->  MyBool  ->  MyBool;
gtMyBool x y = esEsOrdering (compareMyBool x y) GT;

ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltEsMyBool MyFalse MyFalse = MyTrue;
ltEsMyBool MyFalse MyTrue = MyTrue;
ltEsMyBool MyTrue MyFalse = MyFalse;
ltEsMyBool MyTrue MyTrue = MyTrue;

otherwise :: MyBool;
otherwise = MyTrue;

}

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

(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

compare0 x y MyTrue = GT;

compare1 x y MyTrue = LT;
compare1 x y MyFalse = compare0 x y otherwise;

compare2 x y MyTrue = EQ;
compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);

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