Haskell pair #487598163

details

property	value
status	complete
benchmark	mapM__1.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n083.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.26676607132 seconds
cpu usage	10.070555931
max memory	6.4028672E8

stage attributes

key	value
output-size	8964
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 Main.Maybe a = Nothing  | Just a ;

data Tup0 = Tup0 ;

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);

gtGt0 q vv = q;

gtGtEsMaybe :: Main.Maybe b  ->  (b  ->  Main.Maybe a)  ->  Main.Maybe a;
gtGtEsMaybe (Main.Just x) k = k x;
gtGtEsMaybe Main.Nothing k = Main.Nothing;

gtGtMaybe :: Main.Maybe a  ->  Main.Maybe b  ->  Main.Maybe b;
gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q);

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

mapM_ f = pt sequence_Maybe (map f);

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

returnMaybe :: a  ->  Main.Maybe a;
returnMaybe = Main.Just;

sequence_Maybe :: List (Main.Maybe a)  ->  Main.Maybe Tup0;
sequence_Maybe = foldr gtGtMaybe (returnMaybe Tup0);

}

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

(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 Main.Maybe a = Nothing  | Just a ;

data Tup0 = Tup0 ;

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

gtGt0 q vv = q;

gtGtEsMaybe :: Main.Maybe b  ->  (b  ->  Main.Maybe a)  ->  Main.Maybe a;
gtGtEsMaybe (Main.Just x) k = k x;
gtGtEsMaybe Main.Nothing k = Main.Nothing;

gtGtMaybe :: Main.Maybe b  ->  Main.Maybe a  ->  Main.Maybe a;
gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q);

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

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