/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(6) YES


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

data Integer = Integer MyInt ;

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

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

fromIntegerFloat :: Integer  ->  Float;
fromIntegerFloat = primIntegerToFloat;

fromIntegral = pt fromIntegerFloat toIntegerMyInt;

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

primIntegerToFloat :: Integer  ->  Float;
primIntegerToFloat (Integer x) = primIntToFloat x;

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

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

}

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

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

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

data Integer = Integer MyInt ;

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

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

fromIntegerFloat :: Integer  ->  Float;
fromIntegerFloat = primIntegerToFloat;

fromIntegral = pt fromIntegerFloat toIntegerMyInt;

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

primIntegerToFloat :: Integer  ->  Float;
primIntegerToFloat (Integer x) = primIntToFloat x;

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

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

}

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

(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 Float = Float MyInt MyInt ;

data Integer = Integer MyInt ;

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

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

fromIntegerFloat :: Integer  ->  Float;
fromIntegerFloat = primIntegerToFloat;

fromIntegral = pt fromIntegerFloat toIntegerMyInt;

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

primIntegerToFloat :: Integer  ->  Float;
primIntegerToFloat (Integer x) = primIntToFloat x;

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

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

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="fromIntegral",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fromIntegral vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="pt fromIntegerFloat toIntegerMyInt vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="fromIntegerFloat (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="primIntegerToFloat (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="primIntegerToFloat (Integer vx3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="primIntToFloat vx3",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="Float vx3 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];}

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

(6)
YES