7.35/3.50	YES
8.95/3.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.95/3.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.95/3.95	
8.95/3.95	
8.95/3.95	H-Termination with start terms of the given HASKELL could be proven:
8.95/3.95	
8.95/3.95	(0) HASKELL
8.95/3.95	(1) BR [EQUIVALENT, 0 ms]
8.95/3.95	(2) HASKELL
8.95/3.95	(3) COR [EQUIVALENT, 0 ms]
8.95/3.95	(4) HASKELL
8.95/3.95	(5) Narrow [EQUIVALENT, 0 ms]
8.95/3.95	(6) YES
8.95/3.95	
8.95/3.95	
8.95/3.95	----------------------------------------
8.95/3.95	
8.95/3.95	(0)
8.95/3.95	Obligation:
8.95/3.95	mainModule Main 
8.95/3.95	module Main where {
8.95/3.95	import qualified Prelude;
8.95/3.95	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.95/3.95	
8.95/3.95	data Main.Nat = Succ Main.Nat  | Zero ;
8.95/3.95	
8.95/3.95	data Ratio a = CnPc a a ;
8.95/3.95	
8.95/3.95	numerator (CnPc x y) = x;
8.95/3.95	
8.95/3.95	}
8.95/3.95	
8.95/3.95	----------------------------------------
8.95/3.95	
8.95/3.95	(1) BR (EQUIVALENT)
8.95/3.95	Replaced joker patterns by fresh variables and removed binding patterns.
8.95/3.95	----------------------------------------
8.95/3.95	
8.95/3.95	(2)
8.95/3.95	Obligation:
8.95/3.95	mainModule Main 
8.95/3.95	module Main where {
8.95/3.95	import qualified Prelude;
8.95/3.95	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.95/3.95	
8.95/3.95	data Main.Nat = Succ Main.Nat  | Zero ;
8.95/3.95	
8.95/3.95	data Ratio a = CnPc a a ;
8.95/3.95	
8.95/3.95	numerator (CnPc x y) = x;
8.95/3.95	
8.95/3.95	}
8.95/3.95	
8.95/3.95	----------------------------------------
8.95/3.95	
8.95/3.95	(3) COR (EQUIVALENT)
8.95/3.95	Cond Reductions:
8.95/3.95	The following Function with conditions
8.95/3.95	"undefined |Falseundefined;
8.95/3.95	"
8.95/3.95	is transformed to
8.95/3.95	"undefined  = undefined1;
8.95/3.95	"
8.95/3.95	"undefined0 True = undefined;
8.95/3.95	"
8.95/3.95	"undefined1  = undefined0 False;
8.95/3.95	"
8.95/3.95	
8.95/3.95	----------------------------------------
8.95/3.95	
8.95/3.95	(4)
8.95/3.95	Obligation:
8.95/3.95	mainModule Main 
8.95/3.95	module Main where {
8.95/3.95	import qualified Prelude;
8.95/3.95	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.95/3.95	
8.95/3.95	data Main.Nat = Succ Main.Nat  | Zero ;
8.95/3.95	
8.95/3.95	data Ratio a = CnPc a a ;
8.95/3.95	
8.95/3.95	numerator (CnPc x y) = x;
8.95/3.95	
8.95/3.95	}
8.95/3.95	
8.95/3.95	----------------------------------------
8.95/3.95	
8.95/3.95	(5) Narrow (EQUIVALENT)
8.95/3.95	Haskell To QDPs
8.95/3.95	
8.95/3.95	digraph dp_graph {
8.95/3.95	node [outthreshold=100, inthreshold=100];1[label="numerator",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.95/3.95	3[label="numerator vx3",fontsize=16,color="burlywood",shape="triangle"];6[label="vx3/CnPc vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];3 -> 6[label="",style="solid", color="burlywood", weight=9];
8.95/3.95	6 -> 4[label="",style="solid", color="burlywood", weight=3];
8.95/3.95	4[label="numerator (CnPc vx30 vx31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
8.95/3.95	5[label="vx30",fontsize=16,color="green",shape="box"];}
8.95/3.95	
8.95/3.95	----------------------------------------
8.95/3.95	
8.95/3.95	(6)
8.95/3.95	YES
9.18/3.99	EOF