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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 24 ms]
(6) YES


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

(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 (ltEsOrdering x y);

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

compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
compareOrdering x y = compare3 x y;

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);

gtEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
gtEsOrdering x y = fsEsOrdering (compareOrdering x y) LT;

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

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = 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 (ltEsOrdering x y);

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

compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
compareOrdering x y = compare3 x y;

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);

gtEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
gtEsOrdering x y = fsEsOrdering (compareOrdering x y) LT;

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

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = 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 (ltEsOrdering x y);

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

compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
compareOrdering x y = compare3 x y;

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);

gtEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
gtEsOrdering x y = fsEsOrdering (compareOrdering x y) LT;

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

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

otherwise :: MyBool;
otherwise = MyTrue;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="gtEsOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="gtEsOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="gtEsOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="fsEsOrdering (compareOrdering vx3 vx4) LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="not (esEsOrdering (compareOrdering vx3 vx4) LT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="not (esEsOrdering (compare3 vx3 vx4) LT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="not (esEsOrdering (compare2 vx3 vx4 (esEsOrdering vx3 vx4)) LT)",fontsize=16,color="burlywood",shape="box"];62[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 62[label="",style="solid", color="burlywood", weight=9];
62 -> 9[label="",style="solid", color="burlywood", weight=3];
63[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 63[label="",style="solid", color="burlywood", weight=9];
63 -> 10[label="",style="solid", color="burlywood", weight=3];
64[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 64[label="",style="solid", color="burlywood", weight=9];
64 -> 11[label="",style="solid", color="burlywood", weight=3];
9[label="not (esEsOrdering (compare2 LT vx4 (esEsOrdering LT vx4)) LT)",fontsize=16,color="burlywood",shape="box"];65[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 65[label="",style="solid", color="burlywood", weight=9];
65 -> 12[label="",style="solid", color="burlywood", weight=3];
66[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 66[label="",style="solid", color="burlywood", weight=9];
66 -> 13[label="",style="solid", color="burlywood", weight=3];
67[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 67[label="",style="solid", color="burlywood", weight=9];
67 -> 14[label="",style="solid", color="burlywood", weight=3];
10[label="not (esEsOrdering (compare2 EQ vx4 (esEsOrdering EQ vx4)) LT)",fontsize=16,color="burlywood",shape="box"];68[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];10 -> 68[label="",style="solid", color="burlywood", weight=9];
68 -> 15[label="",style="solid", color="burlywood", weight=3];
69[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];10 -> 69[label="",style="solid", color="burlywood", weight=9];
69 -> 16[label="",style="solid", color="burlywood", weight=3];
70[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];10 -> 70[label="",style="solid", color="burlywood", weight=9];
70 -> 17[label="",style="solid", color="burlywood", weight=3];
11[label="not (esEsOrdering (compare2 GT vx4 (esEsOrdering GT vx4)) LT)",fontsize=16,color="burlywood",shape="box"];71[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];11 -> 71[label="",style="solid", color="burlywood", weight=9];
71 -> 18[label="",style="solid", color="burlywood", weight=3];
72[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];11 -> 72[label="",style="solid", color="burlywood", weight=9];
72 -> 19[label="",style="solid", color="burlywood", weight=3];
73[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];11 -> 73[label="",style="solid", color="burlywood", weight=9];
73 -> 20[label="",style="solid", color="burlywood", weight=3];
12[label="not (esEsOrdering (compare2 LT LT (esEsOrdering LT LT)) LT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
13[label="not (esEsOrdering (compare2 LT EQ (esEsOrdering LT EQ)) LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
14[label="not (esEsOrdering (compare2 LT GT (esEsOrdering LT GT)) LT)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
15[label="not (esEsOrdering (compare2 EQ LT (esEsOrdering EQ LT)) LT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
16[label="not (esEsOrdering (compare2 EQ EQ (esEsOrdering EQ EQ)) LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
17[label="not (esEsOrdering (compare2 EQ GT (esEsOrdering EQ GT)) LT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
18[label="not (esEsOrdering (compare2 GT LT (esEsOrdering GT LT)) LT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
19[label="not (esEsOrdering (compare2 GT EQ (esEsOrdering GT EQ)) LT)",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
20[label="not (esEsOrdering (compare2 GT GT (esEsOrdering GT GT)) LT)",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
21[label="not (esEsOrdering (compare2 LT LT MyTrue) LT)",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
22[label="not (esEsOrdering (compare2 LT EQ MyFalse) LT)",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
23[label="not (esEsOrdering (compare2 LT GT MyFalse) LT)",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
24[label="not (esEsOrdering (compare2 EQ LT MyFalse) LT)",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
25[label="not (esEsOrdering (compare2 EQ EQ MyTrue) LT)",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
26[label="not (esEsOrdering (compare2 EQ GT MyFalse) LT)",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
27[label="not (esEsOrdering (compare2 GT LT MyFalse) LT)",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
28[label="not (esEsOrdering (compare2 GT EQ MyFalse) LT)",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
29[label="not (esEsOrdering (compare2 GT GT MyTrue) LT)",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
30[label="not (esEsOrdering EQ LT)",fontsize=16,color="black",shape="triangle"];30 -> 39[label="",style="solid", color="black", weight=3];
31[label="not (esEsOrdering (compare1 LT EQ (ltEsOrdering LT EQ)) LT)",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
32[label="not (esEsOrdering (compare1 LT GT (ltEsOrdering LT GT)) LT)",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
33[label="not (esEsOrdering (compare1 EQ LT (ltEsOrdering EQ LT)) LT)",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
34 -> 30[label="",style="dashed", color="red", weight=0];
34[label="not (esEsOrdering EQ LT)",fontsize=16,color="magenta"];35[label="not (esEsOrdering (compare1 EQ GT (ltEsOrdering EQ GT)) LT)",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
36[label="not (esEsOrdering (compare1 GT LT (ltEsOrdering GT LT)) LT)",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
37[label="not (esEsOrdering (compare1 GT EQ (ltEsOrdering GT EQ)) LT)",fontsize=16,color="black",shape="box"];37 -> 45[label="",style="solid", color="black", weight=3];
38 -> 30[label="",style="dashed", color="red", weight=0];
38[label="not (esEsOrdering EQ LT)",fontsize=16,color="magenta"];39[label="not MyFalse",fontsize=16,color="black",shape="triangle"];39 -> 46[label="",style="solid", color="black", weight=3];
40[label="not (esEsOrdering (compare1 LT EQ MyTrue) LT)",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3];
41[label="not (esEsOrdering (compare1 LT GT MyTrue) LT)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3];
42[label="not (esEsOrdering (compare1 EQ LT MyFalse) LT)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
43[label="not (esEsOrdering (compare1 EQ GT MyTrue) LT)",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3];
44[label="not (esEsOrdering (compare1 GT LT MyFalse) LT)",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3];
45[label="not (esEsOrdering (compare1 GT EQ MyFalse) LT)",fontsize=16,color="black",shape="box"];45 -> 52[label="",style="solid", color="black", weight=3];
46[label="MyTrue",fontsize=16,color="green",shape="box"];47[label="not (esEsOrdering LT LT)",fontsize=16,color="black",shape="triangle"];47 -> 53[label="",style="solid", color="black", weight=3];
48 -> 47[label="",style="dashed", color="red", weight=0];
48[label="not (esEsOrdering LT LT)",fontsize=16,color="magenta"];49[label="not (esEsOrdering (compare0 EQ LT otherwise) LT)",fontsize=16,color="black",shape="box"];49 -> 54[label="",style="solid", color="black", weight=3];
50 -> 47[label="",style="dashed", color="red", weight=0];
50[label="not (esEsOrdering LT LT)",fontsize=16,color="magenta"];51[label="not (esEsOrdering (compare0 GT LT otherwise) LT)",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3];
52[label="not (esEsOrdering (compare0 GT EQ otherwise) LT)",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3];
53[label="not MyTrue",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
54[label="not (esEsOrdering (compare0 EQ LT MyTrue) LT)",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
55[label="not (esEsOrdering (compare0 GT LT MyTrue) LT)",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
56[label="not (esEsOrdering (compare0 GT EQ MyTrue) LT)",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
57[label="MyFalse",fontsize=16,color="green",shape="box"];58[label="not (esEsOrdering GT LT)",fontsize=16,color="black",shape="triangle"];58 -> 61[label="",style="solid", color="black", weight=3];
59 -> 58[label="",style="dashed", color="red", weight=0];
59[label="not (esEsOrdering GT LT)",fontsize=16,color="magenta"];60 -> 58[label="",style="dashed", color="red", weight=0];
60[label="not (esEsOrdering GT LT)",fontsize=16,color="magenta"];61 -> 39[label="",style="dashed", color="red", weight=0];
61[label="not MyFalse",fontsize=16,color="magenta"];}

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

(6)
YES