Haskell pair #487599643

details

property	value
status	complete
benchmark	List_sort_4.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n080.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	19.4174370766 seconds
cpu usage	39.804791472
max memory	4.051341312E9

stage attributes

key	value
output-size	1116791
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) CR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) IFR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) BR [EQUIVALENT, 3 ms]
(6) HASKELL
(7) COR [EQUIVALENT, 0 ms]
(8) HASKELL
(9) LetRed [EQUIVALENT, 0 ms]
(10) HASKELL
(11) NumRed [SOUND, 0 ms]
(12) HASKELL
(13) Narrow [SOUND, 0 ms]
(14) AND
    (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) QDPOrderProof [EQUIVALENT, 647 ms]
        (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 9 ms]
        (28) YES
    (29) QDP
        (30) QDPSizeChangeProof [EQUIVALENT, 84 ms]
        (31) YES
    (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) QDP
        (36) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (37) YES
    (38) QDP
        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (42) YES
    (43) QDP
        (44) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (45) YES
    (46) QDP
        (47) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (48) YES


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
merge cmp xs [] = xs;
merge cmp [] ys = ys;
merge cmp (x : xs) (y : ys) = case x `cmp` y of { 
GT-> y : merge cmp (x : xs) ys; 
_-> x : merge cmp xs (y : ys); 
 } ;

merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
merge_pairs cmp [] = [];
merge_pairs cmp (xs : []) = xs : [];
merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;

mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
mergesort cmp = mergesort' cmp . map wrap;

mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
mergesort' cmp [] = [];
mergesort' cmp (xs : []) = xs;
mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);

sort :: Ord a => [a]  ->  [a];

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