Haskell pair #487599743

details

property	value
status	complete
benchmark	FiniteMap_foldFM_LE_4.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.93540501595 seconds
cpu usage	22.669487544
max memory	1.756807168E9

stage attributes

key	value
output-size	1083625
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) CR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) IFR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) BR [EQUIVALENT, 14 ms]
(8) HASKELL
(9) COR [EQUIVALENT, 0 ms]
(10) HASKELL
(11) LetRed [EQUIVALENT, 24 ms]
(12) HASKELL
(13) NumRed [SOUND, 0 ms]
(14) HASKELL
(15) Narrow [SOUND, 0 ms]
(16) AND
    (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 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) QDPSizeChangeProof [EQUIVALENT, 226 ms]
        (36) YES
    (37) QDP
        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) QDP
        (41) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (42) YES
    (43) QDP
        (44) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (45) YES


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

(0)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;

instance (Eq a, Eq b) => Eq FiniteMap b a where { 
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2;
}
fmToList :: FiniteMap a b  ->  [(a,b)];
fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm;

foldFM :: (c  ->  a  ->  b  ->  b)  ->  b  ->  FiniteMap c a  ->  b;
foldFM k z EmptyFM = z;
foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l;

foldFM_LE :: Ord a => (a  ->  b  ->  c  ->  c)  ->  c  ->  a  ->  FiniteMap a b  ->  c;
foldFM_LE k z fr EmptyFM = z;
foldFM_LE k z fr (Branch key elt _ fm_l fm_r)  | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
 | otherwise = foldFM_LE k z fr fm_l;

sizeFM :: FiniteMap a b  ->  Int;
sizeFM EmptyFM = 0;
sizeFM (Branch _ _ size _ _) = size;

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

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