/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 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 ;

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;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = 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 ;

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;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = 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 ;

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;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="fsEsOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fsEsOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="fsEsOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="not (esEsOrdering vx3 vx4)",fontsize=16,color="burlywood",shape="box"];29[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];5 -> 29[label="",style="solid", color="burlywood", weight=9];
29 -> 6[label="",style="solid", color="burlywood", weight=3];
30[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];5 -> 30[label="",style="solid", color="burlywood", weight=9];
30 -> 7[label="",style="solid", color="burlywood", weight=3];
31[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];5 -> 31[label="",style="solid", color="burlywood", weight=9];
31 -> 8[label="",style="solid", color="burlywood", weight=3];
6[label="not (esEsOrdering LT vx4)",fontsize=16,color="burlywood",shape="box"];32[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 32[label="",style="solid", color="burlywood", weight=9];
32 -> 9[label="",style="solid", color="burlywood", weight=3];
33[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 33[label="",style="solid", color="burlywood", weight=9];
33 -> 10[label="",style="solid", color="burlywood", weight=3];
34[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9];
34 -> 11[label="",style="solid", color="burlywood", weight=3];
7[label="not (esEsOrdering EQ vx4)",fontsize=16,color="burlywood",shape="box"];35[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 12[label="",style="solid", color="burlywood", weight=3];
36[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9];
36 -> 13[label="",style="solid", color="burlywood", weight=3];
37[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9];
37 -> 14[label="",style="solid", color="burlywood", weight=3];
8[label="not (esEsOrdering GT vx4)",fontsize=16,color="burlywood",shape="box"];38[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 38[label="",style="solid", color="burlywood", weight=9];
38 -> 15[label="",style="solid", color="burlywood", weight=3];
39[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 39[label="",style="solid", color="burlywood", weight=9];
39 -> 16[label="",style="solid", color="burlywood", weight=3];
40[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 40[label="",style="solid", color="burlywood", weight=9];
40 -> 17[label="",style="solid", color="burlywood", weight=3];
9[label="not (esEsOrdering LT LT)",fontsize=16,color="black",shape="box"];9 -> 18[label="",style="solid", color="black", weight=3];
10[label="not (esEsOrdering LT EQ)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
11[label="not (esEsOrdering LT GT)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
12[label="not (esEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
13[label="not (esEsOrdering EQ EQ)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
14[label="not (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
15[label="not (esEsOrdering GT LT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
16[label="not (esEsOrdering GT EQ)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
17[label="not (esEsOrdering GT GT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
18[label="not MyTrue",fontsize=16,color="black",shape="triangle"];18 -> 27[label="",style="solid", color="black", weight=3];
19[label="not MyFalse",fontsize=16,color="black",shape="triangle"];19 -> 28[label="",style="solid", color="black", weight=3];
20 -> 19[label="",style="dashed", color="red", weight=0];
20[label="not MyFalse",fontsize=16,color="magenta"];21 -> 19[label="",style="dashed", color="red", weight=0];
21[label="not MyFalse",fontsize=16,color="magenta"];22 -> 18[label="",style="dashed", color="red", weight=0];
22[label="not MyTrue",fontsize=16,color="magenta"];23 -> 19[label="",style="dashed", color="red", weight=0];
23[label="not MyFalse",fontsize=16,color="magenta"];24 -> 19[label="",style="dashed", color="red", weight=0];
24[label="not MyFalse",fontsize=16,color="magenta"];25 -> 19[label="",style="dashed", color="red", weight=0];
25[label="not MyFalse",fontsize=16,color="magenta"];26 -> 18[label="",style="dashed", color="red", weight=0];
26[label="not MyTrue",fontsize=16,color="magenta"];27[label="MyFalse",fontsize=16,color="green",shape="box"];28[label="MyTrue",fontsize=16,color="green",shape="box"];}

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(6)
YES