7.86/3.51	YES
9.33/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.33/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.33/3.98	
9.33/3.98	
9.33/3.98	H-Termination with start terms of the given HASKELL could be proven:
9.33/3.98	
9.33/3.98	(0) HASKELL
9.33/3.98	(1) BR [EQUIVALENT, 0 ms]
9.33/3.98	(2) HASKELL
9.33/3.98	(3) COR [EQUIVALENT, 0 ms]
9.33/3.98	(4) HASKELL
9.33/3.98	(5) Narrow [EQUIVALENT, 0 ms]
9.33/3.98	(6) YES
9.33/3.98	
9.33/3.98	
9.33/3.98	----------------------------------------
9.33/3.98	
9.33/3.98	(0)
9.33/3.98	Obligation:
9.33/3.98	mainModule Main 
9.33/3.98	module Main where {
9.33/3.98	import qualified Prelude;
9.33/3.98	data Main.Maybe a = Nothing  | Just a ;
9.33/3.98	
9.33/3.98	gtGt0 q vv = q;
9.33/3.98	
9.33/3.98	gtGtEsMaybe :: Main.Maybe a  ->  (a  ->  Main.Maybe b)  ->  Main.Maybe b;
9.33/3.98	gtGtEsMaybe (Main.Just x) k = k x;
9.33/3.98	gtGtEsMaybe Main.Nothing k = Main.Nothing;
9.33/3.98	
9.33/3.98	gtGtMaybe :: Main.Maybe b  ->  Main.Maybe a  ->  Main.Maybe a;
9.33/3.98	gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q);
9.33/3.98	
9.33/3.98	}
9.33/3.98	
9.33/3.98	----------------------------------------
9.33/3.98	
9.33/3.98	(1) BR (EQUIVALENT)
9.33/3.98	Replaced joker patterns by fresh variables and removed binding patterns.
9.33/3.98	----------------------------------------
9.33/3.98	
9.33/3.98	(2)
9.33/3.98	Obligation:
9.33/3.98	mainModule Main 
9.33/3.98	module Main where {
9.33/3.98	import qualified Prelude;
9.33/3.98	data Main.Maybe a = Nothing  | Just a ;
9.33/3.98	
9.33/3.98	gtGt0 q vv = q;
9.33/3.98	
9.33/3.98	gtGtEsMaybe :: Main.Maybe a  ->  (a  ->  Main.Maybe b)  ->  Main.Maybe b;
9.33/3.98	gtGtEsMaybe (Main.Just x) k = k x;
9.33/3.98	gtGtEsMaybe Main.Nothing k = Main.Nothing;
9.33/3.98	
9.33/3.98	gtGtMaybe :: Main.Maybe b  ->  Main.Maybe a  ->  Main.Maybe a;
9.33/3.98	gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q);
9.33/3.98	
9.33/3.98	}
9.33/3.98	
9.33/3.98	----------------------------------------
9.33/3.98	
9.33/3.98	(3) COR (EQUIVALENT)
9.33/3.98	Cond Reductions:
9.33/3.98	The following Function with conditions
9.33/3.98	"undefined |Falseundefined;
9.33/3.98	"
9.33/3.98	is transformed to
9.33/3.98	"undefined  = undefined1;
9.33/3.98	"
9.33/3.98	"undefined0 True = undefined;
9.33/3.98	"
9.33/3.98	"undefined1  = undefined0 False;
9.33/3.98	"
9.33/3.98	
9.33/3.98	----------------------------------------
9.33/3.98	
9.33/3.98	(4)
9.33/3.98	Obligation:
9.33/3.98	mainModule Main 
9.33/3.98	module Main where {
9.33/3.98	import qualified Prelude;
9.33/3.98	data Main.Maybe a = Nothing  | Just a ;
9.33/3.98	
9.33/3.98	gtGt0 q vv = q;
9.33/3.98	
9.33/3.98	gtGtEsMaybe :: Main.Maybe b  ->  (b  ->  Main.Maybe a)  ->  Main.Maybe a;
9.33/3.98	gtGtEsMaybe (Main.Just x) k = k x;
9.33/3.98	gtGtEsMaybe Main.Nothing k = Main.Nothing;
9.33/3.98	
9.33/3.98	gtGtMaybe :: Main.Maybe a  ->  Main.Maybe b  ->  Main.Maybe b;
9.33/3.98	gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q);
9.33/3.98	
9.33/3.98	}
9.33/3.98	
9.33/3.98	----------------------------------------
9.33/3.98	
9.33/3.98	(5) Narrow (EQUIVALENT)
9.33/3.98	Haskell To QDPs
9.33/3.98	
9.33/3.98	digraph dp_graph {
9.33/3.98	node [outthreshold=100, inthreshold=100];1[label="gtGtMaybe",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.33/3.98	3[label="gtGtMaybe vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.33/3.98	4[label="gtGtMaybe vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.33/3.98	5[label="gtGtEsMaybe vy3 (gtGt0 vy4)",fontsize=16,color="burlywood",shape="box"];11[label="vy3/Nothing",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9];
9.33/3.98	11 -> 6[label="",style="solid", color="burlywood", weight=3];
9.33/3.98	12[label="vy3/Just vy30",fontsize=10,color="white",style="solid",shape="box"];5 -> 12[label="",style="solid", color="burlywood", weight=9];
9.33/3.98	12 -> 7[label="",style="solid", color="burlywood", weight=3];
9.33/3.98	6[label="gtGtEsMaybe Nothing (gtGt0 vy4)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.33/3.98	7[label="gtGtEsMaybe (Just vy30) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.33/3.98	8[label="Nothing",fontsize=16,color="green",shape="box"];9[label="gtGt0 vy4 vy30",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.33/3.98	10[label="vy4",fontsize=16,color="green",shape="box"];}
9.33/3.98	
9.33/3.98	----------------------------------------
9.33/3.98	
9.33/3.98	(6)
9.33/3.98	YES
9.67/4.05	EOF