/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 27 ms]
(6) YES


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(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Integer = Integer MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

data Ratio a = CnPc a a ;

fromIntegerMyInt :: Integer  ->  MyInt;
fromIntegerMyInt (Integer x) = x;

fromRational (CnPc x y) = CnPc (fromIntegerMyInt x) (fromIntegerMyInt y);

pt :: (c  ->  a)  ->  (b  ->  c)  ->  b  ->  a;
pt f g x = f (g x);

realToFrac = pt fromRational toRational;

toIntegerMyInt :: MyInt  ->  Integer;
toIntegerMyInt x = Integer x;

toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Integer = Integer MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

data Ratio a = CnPc a a ;

fromIntegerMyInt :: Integer  ->  MyInt;
fromIntegerMyInt (Integer x) = x;

fromRational (CnPc x y) = CnPc (fromIntegerMyInt x) (fromIntegerMyInt y);

pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
pt f g x = f (g x);

realToFrac = pt fromRational toRational;

toIntegerMyInt :: MyInt  ->  Integer;
toIntegerMyInt x = Integer x;

toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);

}

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

(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 Integer = Integer MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

data Ratio a = CnPc a a ;

fromIntegerMyInt :: Integer  ->  MyInt;
fromIntegerMyInt (Integer x) = x;

fromRational (CnPc x y) = CnPc (fromIntegerMyInt x) (fromIntegerMyInt y);

pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
pt f g x = f (g x);

realToFrac = pt fromRational toRational;

toIntegerMyInt :: MyInt  ->  Integer;
toIntegerMyInt x = Integer x;

toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="realToFrac",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="realToFrac vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="pt fromRational toRational vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="fromRational (toRational vx3)",fontsize=16,color="burlywood",shape="box"];14[label="vx3/CnPc vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 14[label="",style="solid", color="burlywood", weight=9];
14 -> 6[label="",style="solid", color="burlywood", weight=3];
6[label="fromRational (toRational (CnPc vx30 vx31))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="fromRational (CnPc (toIntegerMyInt vx30) (toIntegerMyInt vx31))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="CnPc (fromIntegerMyInt (toIntegerMyInt vx30)) (fromIntegerMyInt (toIntegerMyInt vx31))",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3];
8 -> 10[label="",style="dashed", color="green", weight=3];
9[label="fromIntegerMyInt (toIntegerMyInt vx30)",fontsize=16,color="black",shape="triangle"];9 -> 11[label="",style="solid", color="black", weight=3];
10 -> 9[label="",style="dashed", color="red", weight=0];
10[label="fromIntegerMyInt (toIntegerMyInt vx31)",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3];
11[label="fromIntegerMyInt (Integer vx30)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="vx31",fontsize=16,color="green",shape="box"];13[label="vx30",fontsize=16,color="green",shape="box"];}

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

(6)
YES