Haskell pair #487598695

details

property	value
status	complete
benchmark	List_union_11.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.2431659698 seconds
cpu usage	19.430620363
max memory	1.782566912E9

stage attributes

key	value
output-size	394230
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) IFR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 8 ms]
(6) HASKELL
(7) LetRed [EQUIVALENT, 0 ms]
(8) HASKELL
(9) Narrow [SOUND, 0 ms]
(10) AND
    (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 22 ms]
        (19) YES
    (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) DependencyGraphProof [EQUIVALENT, 0 ms]
        (25) AND
            (26) QDP
                (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (28) YES
            (29) QDP
                (30) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (31) YES
    (32) QDP
        (33) DependencyGraphProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) TransformationProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (38) YES
    (39) QDP
        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (41) YES
    (42) QDP
        (43) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (44) 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;
deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
deleteBy _ _ [] = [];
deleteBy eq x (y : ys) =  if x `eq` y then ys else y : deleteBy eq x ys;

elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
elem_by _ _ [] = False;
elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;

nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
nubBy eq l = nubBy' l [] where { 
nubBy' [] _ = [];
nubBy' (y : ys) xs  | elem_by eq y xs = nubBy' ys xs
 | otherwise = y : nubBy' ys (y : xs);
 };

union :: Eq a => [a]  ->  [a]  ->  [a];
union = unionBy (==);

unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;

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