/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 29 ms]
(6) YES


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(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

data Main.Maybe a = Nothing  | Just a ;

data MyBool = MyTrue  | MyFalse ;

data Tup0 = Tup0 ;

data Tup2 a b = Tup2 a b ;

esEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
esEsTup0 Tup0 Tup0 = MyTrue;

lookup k Nil = lookup3 k Nil;
lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);

lookup0 k x y xys MyTrue = lookup k xys;

lookup1 k x y xys MyTrue = Main.Just y;
lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;

lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsTup0 k x);

lookup3 k Nil = Main.Nothing;
lookup3 vy vz = lookup2 vy vz;

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 List a = Cons a (List a)  | Nil ;

data Main.Maybe a = Nothing  | Just a ;

data MyBool = MyTrue  | MyFalse ;

data Tup0 = Tup0 ;

data Tup2 b a = Tup2 b a ;

esEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
esEsTup0 Tup0 Tup0 = MyTrue;

lookup k Nil = lookup3 k Nil;
lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);

lookup0 k x y xys MyTrue = lookup k xys;

lookup1 k x y xys MyTrue = Main.Just y;
lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;

lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsTup0 k x);

lookup3 k Nil = Main.Nothing;
lookup3 vy vz = lookup2 vy vz;

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 List a = Cons a (List a)  | Nil ;

data Main.Maybe a = Nothing  | Just a ;

data MyBool = MyTrue  | MyFalse ;

data Tup0 = Tup0 ;

data Tup2 a b = Tup2 a b ;

esEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
esEsTup0 Tup0 Tup0 = MyTrue;

lookup k Nil = lookup3 k Nil;
lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);

lookup0 k x y xys MyTrue = lookup k xys;

lookup1 k x y xys MyTrue = Main.Just y;
lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;

lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsTup0 k x);

lookup3 k Nil = Main.Nothing;
lookup3 vy vz = lookup2 vy vz;

otherwise :: MyBool;
otherwise = MyTrue;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="lookup",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="lookup vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="lookup vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];16[label="vx4/Cons vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 5[label="",style="solid", color="burlywood", weight=3];
17[label="vx4/Nil",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9];
17 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="lookup vx3 (Cons vx40 vx41)",fontsize=16,color="burlywood",shape="box"];18[label="vx40/Tup2 vx400 vx401",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
18 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="lookup vx3 Nil",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="lookup vx3 (Cons (Tup2 vx400 vx401) vx41)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookup3 vx3 Nil",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="lookup2 vx3 (Cons (Tup2 vx400 vx401) vx41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="lookup1 vx3 vx400 vx401 vx41 (esEsTup0 vx3 vx400)",fontsize=16,color="burlywood",shape="box"];19[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];11 -> 19[label="",style="solid", color="burlywood", weight=9];
19 -> 12[label="",style="solid", color="burlywood", weight=3];
12[label="lookup1 Tup0 vx400 vx401 vx41 (esEsTup0 Tup0 vx400)",fontsize=16,color="burlywood",shape="box"];20[label="vx400/Tup0",fontsize=10,color="white",style="solid",shape="box"];12 -> 20[label="",style="solid", color="burlywood", weight=9];
20 -> 13[label="",style="solid", color="burlywood", weight=3];
13[label="lookup1 Tup0 Tup0 vx401 vx41 (esEsTup0 Tup0 Tup0)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="lookup1 Tup0 Tup0 vx401 vx41 MyTrue",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="Just vx401",fontsize=16,color="green",shape="box"];}

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

(6)
YES