7.46/3.47	YES
8.80/3.91	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.80/3.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.80/3.91	
8.80/3.91	
8.80/3.91	H-Termination with start terms of the given HASKELL could be proven:
8.80/3.91	
8.80/3.91	(0) HASKELL
8.80/3.91	(1) BR [EQUIVALENT, 0 ms]
8.80/3.91	(2) HASKELL
8.80/3.91	(3) COR [EQUIVALENT, 0 ms]
8.80/3.91	(4) HASKELL
8.80/3.91	(5) Narrow [EQUIVALENT, 0 ms]
8.80/3.91	(6) YES
8.80/3.91	
8.80/3.91	
8.80/3.91	----------------------------------------
8.80/3.91	
8.80/3.91	(0)
8.80/3.91	Obligation:
8.80/3.91	mainModule Main 
8.80/3.91	module Main where {
8.80/3.91	import qualified Prelude;
8.80/3.91	data List a = Cons a (List a)  | Nil ;
8.80/3.91	
8.80/3.91	data MyBool = MyTrue  | MyFalse ;
8.80/3.91	
8.80/3.91	null :: List a  ->  MyBool;
8.80/3.91	null Nil = MyTrue;
8.80/3.91	null (Cons vv vw) = MyFalse;
8.80/3.91	
8.80/3.91	}
8.80/3.91	
8.80/3.91	----------------------------------------
8.80/3.91	
8.80/3.91	(1) BR (EQUIVALENT)
8.80/3.91	Replaced joker patterns by fresh variables and removed binding patterns.
8.80/3.91	----------------------------------------
8.80/3.91	
8.80/3.91	(2)
8.80/3.91	Obligation:
8.80/3.91	mainModule Main 
8.80/3.91	module Main where {
8.80/3.91	import qualified Prelude;
8.80/3.91	data List a = Cons a (List a)  | Nil ;
8.80/3.91	
8.80/3.91	data MyBool = MyTrue  | MyFalse ;
8.80/3.91	
8.80/3.91	null :: List a  ->  MyBool;
8.80/3.91	null Nil = MyTrue;
8.80/3.91	null (Cons vv vw) = MyFalse;
8.80/3.91	
8.80/3.91	}
8.80/3.91	
8.80/3.91	----------------------------------------
8.80/3.91	
8.80/3.91	(3) COR (EQUIVALENT)
8.80/3.91	Cond Reductions:
8.80/3.91	The following Function with conditions
8.80/3.91	"undefined |Falseundefined;
8.80/3.91	"
8.80/3.91	is transformed to
8.80/3.91	"undefined  = undefined1;
8.80/3.91	"
8.80/3.91	"undefined0 True = undefined;
8.80/3.91	"
8.80/3.91	"undefined1  = undefined0 False;
8.80/3.91	"
8.80/3.91	
8.80/3.91	----------------------------------------
8.80/3.91	
8.80/3.91	(4)
8.80/3.91	Obligation:
8.80/3.91	mainModule Main 
8.80/3.91	module Main where {
8.80/3.91	import qualified Prelude;
8.80/3.91	data List a = Cons a (List a)  | Nil ;
8.80/3.91	
8.80/3.91	data MyBool = MyTrue  | MyFalse ;
8.80/3.91	
8.80/3.91	null :: List a  ->  MyBool;
8.80/3.91	null Nil = MyTrue;
8.80/3.91	null (Cons vv vw) = MyFalse;
8.80/3.91	
8.80/3.91	}
8.80/3.91	
8.80/3.91	----------------------------------------
8.80/3.91	
8.80/3.91	(5) Narrow (EQUIVALENT)
8.80/3.91	Haskell To QDPs
8.80/3.91	
8.80/3.91	digraph dp_graph {
8.80/3.91	node [outthreshold=100, inthreshold=100];1[label="null",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.80/3.91	3[label="null vz3",fontsize=16,color="burlywood",shape="triangle"];8[label="vz3/Cons vz30 vz31",fontsize=10,color="white",style="solid",shape="box"];3 -> 8[label="",style="solid", color="burlywood", weight=9];
8.80/3.91	8 -> 4[label="",style="solid", color="burlywood", weight=3];
8.80/3.91	9[label="vz3/Nil",fontsize=10,color="white",style="solid",shape="box"];3 -> 9[label="",style="solid", color="burlywood", weight=9];
8.80/3.91	9 -> 5[label="",style="solid", color="burlywood", weight=3];
8.80/3.91	4[label="null (Cons vz30 vz31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
8.80/3.91	5[label="null Nil",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
8.80/3.91	6[label="MyFalse",fontsize=16,color="green",shape="box"];7[label="MyTrue",fontsize=16,color="green",shape="box"];}
8.80/3.91	
8.80/3.91	----------------------------------------
8.80/3.91	
8.80/3.91	(6)
8.80/3.91	YES
9.08/3.99	EOF