Funct Progr 77531 pair #381920848

details

property	value
status	complete
benchmark	List_sort_9.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	18.9148631096 seconds
cpu usage	40.015513539
max memory	4.032434176E9

stage attributes

key	value
output-size	1042993
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) CR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) IFR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) BR [EQUIVALENT, 0 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) QDPOrderProof [EQUIVALENT, 576 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) DependencyGraphProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) DependencyGraphProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) QDPSizeChangeProof [EQUIVALENT, 83 ms]
        (41) YES
    (42) QDP
        (43) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (44) YES
    (45) QDP
        (46) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (47) YES
    (48) QDP
        (49) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (50) 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);

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