Haskell pair #487598094

details

property	value
status	complete
benchmark	notElem_2.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.18248009682 seconds
cpu usage	10.066731075
max memory	5.97200896E8

stage attributes

key	value
output-size	11089
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [SOUND, 0 ms]
(6) QDP
(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(8) YES


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

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

data MyBool = MyTrue  | MyFalse ;

all :: (a  ->  MyBool)  ->  List a  ->  MyBool;
all p = pt and (map p);

and :: List MyBool  ->  MyBool;
and = foldr asAs MyTrue;

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

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

fsEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
fsEsMyBool x y = not (esEsMyBool x y);

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;

notElemMyBool :: MyBool  ->  List MyBool  ->  MyBool;
notElemMyBool = pt all fsEsMyBool;

pt :: (c  ->  a)  ->  (b  ->  c)  ->  b  ->  a;
pt f g x = f (g x);

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

data MyBool = MyTrue  | MyFalse ;

all :: (a  ->  MyBool)  ->  List a  ->  MyBool;
all p = pt and (map p);

and :: List MyBool  ->  MyBool;
and = foldr asAs MyTrue;

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

esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;

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