/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) Narrow [EQUIVALENT, 31 ms]
(8) YES


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Prelude;
fromMaybe :: a  ->  Maybe a  ->  a;
fromMaybe d x = case x of { 
Nothing-> d; 
Just v-> v; 
 } ;

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

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

(1) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case x of {
Nothing  -> d;
Just v  -> v}
"
is transformed to
"fromMaybe0 d Nothing = d;
fromMaybe0 d (Just v) = v;
"

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Prelude;
fromMaybe :: a  ->  Maybe a  ->  a;
fromMaybe d x = fromMaybe0 d x;

fromMaybe0 d Nothing = d;
fromMaybe0 d (Just v) = v;

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

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

(3) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Prelude;
fromMaybe :: a  ->  Maybe a  ->  a;
fromMaybe d x = fromMaybe0 d x;

fromMaybe0 d Nothing = d;
fromMaybe0 d (Just v) = v;

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

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

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

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

(6)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Prelude;
fromMaybe :: a  ->  Maybe a  ->  a;
fromMaybe d x = fromMaybe0 d x;

fromMaybe0 d Nothing = d;
fromMaybe0 d (Just v) = v;

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

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

(7) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="Maybe.fromMaybe",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="Maybe.fromMaybe vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="Maybe.fromMaybe vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="Maybe.fromMaybe0 vy3 vy4",fontsize=16,color="burlywood",shape="box"];10[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];5 -> 10[label="",style="solid", color="burlywood", weight=9];
10 -> 6[label="",style="solid", color="burlywood", weight=3];
11[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9];
11 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="Maybe.fromMaybe0 vy3 Nothing",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="Maybe.fromMaybe0 vy3 (Just vy40)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="vy3",fontsize=16,color="green",shape="box"];9[label="vy40",fontsize=16,color="green",shape="box"];}

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

(8)
YES