/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 30 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;

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

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;

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

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;

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

otherwise :: MyBool;
otherwise = MyTrue;

}

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(5) Narrow (EQUIVALENT)
Haskell To QDPs

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

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(6)
YES