Haskell pair #487599558

details

property	value
status	complete
benchmark	FiniteMap_keysFM_LE_12.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.19483995438 seconds
cpu usage	18.712403932
max memory	1.286180864E9

stage attributes

key	value
output-size	616716
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 15 ms]
(8) HASKELL
(9) COR [EQUIVALENT, 0 ms]
(10) HASKELL
(11) LetRed [EQUIVALENT, 0 ms]
(12) HASKELL
(13) NumRed [SOUND, 2 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) DependencyGraphProof [EQUIVALENT, 3 ms]
        (28) QDP
        (29) QDPSizeChangeProof [EQUIVALENT, 97 ms]
        (30) YES
    (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (39) 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 a b where { 
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2;
}
fmToList :: FiniteMap b a  ->  [(b,a)];
fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm;

foldFM :: (a  ->  b  ->  c  ->  c)  ->  c  ->  FiniteMap a b  ->  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 c => (c  ->  b  ->  a  ->  a)  ->  a  ->  c  ->  FiniteMap c b  ->  a;
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;

keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b];
keysFM_LE fm fr = foldFM_LE (\key elt rest ->key : rest) [] fr fm;

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;
import qualified Prelude;
}

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