Funct Progr 77531 pair #381920535

details

property	value
status	complete
benchmark	range_4.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n040.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.54457592964 seconds
cpu usage	11.346051802
max memory	6.01239552E8

stage attributes

key	value
output-size	126194
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 221 ms]
(6) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

data Tup2 b a = Tup2 b a ;

asAs :: MyBool  ->  MyBool  ->  MyBool;
asAs MyFalse x = MyFalse;
asAs MyTrue x = x;

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 (ltEsOrdering x y);

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

compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
compareOrdering x y = compare3 x y;

concat :: List (List a)  ->  List a;
concat = foldr psPs Nil;

concatMap :: (a  ->  List b)  ->  List a  ->  List b;
concatMap f = pt concat (map f);

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;

foldr :: (a  ->  b  ->  b)  ->  b  ->  List a  ->  b;
foldr f z Nil = z;
foldr f z (Cons x xs) = f x (foldr f z xs);

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

gtEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
gtEsOrdering x y = fsEsOrdering (compareOrdering x y) LT;

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

map :: (b  ->  a)  ->  List b  ->  List a;
map f Nil = Nil;
map f (Cons x xs) = Cons (f x) (map f xs);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

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