Haskell pair #487598202

details

property	value
status	complete
benchmark	concatMap_1.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.10236287117 seconds
cpu usage	10.022613733
max memory	5.56347392E8

stage attributes

key	value
output-size	8585
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) AND
    (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (12) YES


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

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

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

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

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);

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

psPs :: List a  ->  List a  ->  List a;
psPs Nil ys = ys;
psPs (Cons x xs) ys = Cons x (psPs xs ys);

pt :: (c  ->  b)  ->  (a  ->  c)  ->  a  ->  b;
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 ;

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

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

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);

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

psPs :: List a  ->  List a  ->  List a;
psPs Nil ys = ys;
psPs (Cons x xs) ys = Cons x (psPs xs ys);

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

}

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

(3) COR (EQUIVALENT)
Cond Reductions:

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