Haskell pair #487599158

details

property	value
status	complete
benchmark	FiniteMap_foldFM_LE_9.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	18.5300838947 seconds
cpu usage	37.132064701
max memory	4.047798272E9

stage attributes

key	value
output-size	650295
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(12) HASKELL
(13) NumRed [SOUND, 5 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 70 ms]
        (28) YES
    (29) QDP
        (30) DependencyGraphProof [EQUIVALENT, 0 ms]
        (31) AND
            (32) QDP
                (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (34) YES
            (35) QDP
                (36) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (37) YES
    (38) QDP
        (39) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (40) YES
    (41) QDP
        (42) TransformationProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) TransformationProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) UsableRulesProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) QReductionProof [EQUIVALENT, 5 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 149 ms]
        (51) QDP
        (52) DependencyGraphProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (55) YES
    (56) QDP
        (57) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (58) YES
    (59) QDP
        (60) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (61) YES


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

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

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 :: (b  ->  a  ->  c  ->  c)  ->  c  ->  FiniteMap b a  ->  c;
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  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b;
foldFM_LE k z fr EmptyFM = z;

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