/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [EQUIVALENT, 23 ms]
(6) YES


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(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

compare0 x y MyTrue = GT;

compare1 x y MyTrue = LT;
compare1 x y MyFalse = compare0 x y otherwise;

compare2 x y MyTrue = EQ;
compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);

compare3 x y = compare2 x y (esEsMyBool x y);

compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
compareMyBool x y = compare3 x y;

esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
esEsMyBool MyFalse MyFalse = MyTrue;
esEsMyBool MyFalse MyTrue = MyFalse;
esEsMyBool MyTrue MyFalse = MyFalse;
esEsMyBool MyTrue MyTrue = MyTrue;

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltEsMyBool MyFalse MyFalse = MyTrue;
ltEsMyBool MyFalse MyTrue = MyTrue;
ltEsMyBool MyTrue MyFalse = MyFalse;
ltEsMyBool MyTrue MyTrue = MyTrue;

ltMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltMyBool x y = esEsOrdering (compareMyBool x y) LT;

otherwise :: MyBool;
otherwise = MyTrue;

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

compare0 x y MyTrue = GT;

compare1 x y MyTrue = LT;
compare1 x y MyFalse = compare0 x y otherwise;

compare2 x y MyTrue = EQ;
compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);

compare3 x y = compare2 x y (esEsMyBool x y);

compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
compareMyBool x y = compare3 x y;

esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
esEsMyBool MyFalse MyFalse = MyTrue;
esEsMyBool MyFalse MyTrue = MyFalse;
esEsMyBool MyTrue MyFalse = MyFalse;
esEsMyBool MyTrue MyTrue = MyTrue;

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltEsMyBool MyFalse MyFalse = MyTrue;
ltEsMyBool MyFalse MyTrue = MyTrue;
ltEsMyBool MyTrue MyFalse = MyFalse;
ltEsMyBool MyTrue MyTrue = MyTrue;

ltMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltMyBool x y = esEsOrdering (compareMyBool x y) LT;

otherwise :: MyBool;
otherwise = MyTrue;

}

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

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

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

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

compare0 x y MyTrue = GT;

compare1 x y MyTrue = LT;
compare1 x y MyFalse = compare0 x y otherwise;

compare2 x y MyTrue = EQ;
compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);

compare3 x y = compare2 x y (esEsMyBool x y);

compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
compareMyBool x y = compare3 x y;

esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
esEsMyBool MyFalse MyFalse = MyTrue;
esEsMyBool MyFalse MyTrue = MyFalse;
esEsMyBool MyTrue MyFalse = MyFalse;
esEsMyBool MyTrue MyTrue = MyTrue;

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltEsMyBool MyFalse MyFalse = MyTrue;
ltEsMyBool MyFalse MyTrue = MyTrue;
ltEsMyBool MyTrue MyFalse = MyFalse;
ltEsMyBool MyTrue MyTrue = MyTrue;

ltMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltMyBool x y = esEsOrdering (compareMyBool x y) LT;

otherwise :: MyBool;
otherwise = MyTrue;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="ltMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="ltMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="ltMyBool vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="esEsOrdering (compareMyBool vx3 vx4) LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="esEsOrdering (compare3 vx3 vx4) LT",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="esEsOrdering (compare2 vx3 vx4 (esEsMyBool vx3 vx4)) LT",fontsize=16,color="burlywood",shape="box"];31[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];7 -> 31[label="",style="solid", color="burlywood", weight=9];
31 -> 8[label="",style="solid", color="burlywood", weight=3];
32[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];7 -> 32[label="",style="solid", color="burlywood", weight=9];
32 -> 9[label="",style="solid", color="burlywood", weight=3];
8[label="esEsOrdering (compare2 MyTrue vx4 (esEsMyBool MyTrue vx4)) LT",fontsize=16,color="burlywood",shape="box"];33[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];8 -> 33[label="",style="solid", color="burlywood", weight=9];
33 -> 10[label="",style="solid", color="burlywood", weight=3];
34[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];8 -> 34[label="",style="solid", color="burlywood", weight=9];
34 -> 11[label="",style="solid", color="burlywood", weight=3];
9[label="esEsOrdering (compare2 MyFalse vx4 (esEsMyBool MyFalse vx4)) LT",fontsize=16,color="burlywood",shape="box"];35[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];9 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 12[label="",style="solid", color="burlywood", weight=3];
36[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];9 -> 36[label="",style="solid", color="burlywood", weight=9];
36 -> 13[label="",style="solid", color="burlywood", weight=3];
10[label="esEsOrdering (compare2 MyTrue MyTrue (esEsMyBool MyTrue MyTrue)) LT",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="esEsOrdering (compare2 MyTrue MyFalse (esEsMyBool MyTrue MyFalse)) LT",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="esEsOrdering (compare2 MyFalse MyTrue (esEsMyBool MyFalse MyTrue)) LT",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="esEsOrdering (compare2 MyFalse MyFalse (esEsMyBool MyFalse MyFalse)) LT",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="esEsOrdering (compare2 MyTrue MyTrue MyTrue) LT",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="esEsOrdering (compare2 MyTrue MyFalse MyFalse) LT",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="esEsOrdering (compare2 MyFalse MyTrue MyFalse) LT",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="esEsOrdering (compare2 MyFalse MyFalse MyTrue) LT",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="esEsOrdering EQ LT",fontsize=16,color="black",shape="triangle"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="esEsOrdering (compare1 MyTrue MyFalse (ltEsMyBool MyTrue MyFalse)) LT",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="esEsOrdering (compare1 MyFalse MyTrue (ltEsMyBool MyFalse MyTrue)) LT",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21 -> 18[label="",style="dashed", color="red", weight=0];
21[label="esEsOrdering EQ LT",fontsize=16,color="magenta"];22[label="MyFalse",fontsize=16,color="green",shape="box"];23[label="esEsOrdering (compare1 MyTrue MyFalse MyFalse) LT",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
24[label="esEsOrdering (compare1 MyFalse MyTrue MyTrue) LT",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
25[label="esEsOrdering (compare0 MyTrue MyFalse otherwise) LT",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
26[label="esEsOrdering LT LT",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
27[label="esEsOrdering (compare0 MyTrue MyFalse MyTrue) LT",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
28[label="MyTrue",fontsize=16,color="green",shape="box"];29[label="esEsOrdering GT LT",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3];
30[label="MyFalse",fontsize=16,color="green",shape="box"];}

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

(6)
YES