7.33/3.39	YES
8.81/3.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.81/3.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.81/3.84	
8.81/3.84	
8.81/3.84	H-Termination with start terms of the given HASKELL could be proven:
8.81/3.84	
8.81/3.84	(0) HASKELL
8.81/3.84	(1) BR [EQUIVALENT, 0 ms]
8.81/3.84	(2) HASKELL
8.81/3.84	(3) COR [EQUIVALENT, 0 ms]
8.81/3.84	(4) HASKELL
8.81/3.84	(5) Narrow [EQUIVALENT, 0 ms]
8.81/3.84	(6) YES
8.81/3.84	
8.81/3.84	
8.81/3.84	----------------------------------------
8.81/3.84	
8.81/3.84	(0)
8.81/3.84	Obligation:
8.81/3.84	mainModule Main 
8.81/3.84	module Main where {
8.81/3.84	import qualified Prelude;
8.81/3.84	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.81/3.84	
8.81/3.84	data Main.Nat = Succ Main.Nat  | Zero ;
8.81/3.84	
8.81/3.84	data Ratio a = CnPc a a ;
8.81/3.84	
8.81/3.84	denominator (CnPc x y) = y;
8.81/3.84	
8.81/3.84	}
8.81/3.84	
8.81/3.84	----------------------------------------
8.81/3.84	
8.81/3.84	(1) BR (EQUIVALENT)
8.81/3.84	Replaced joker patterns by fresh variables and removed binding patterns.
8.81/3.84	----------------------------------------
8.81/3.84	
8.81/3.84	(2)
8.81/3.84	Obligation:
8.81/3.84	mainModule Main 
8.81/3.84	module Main where {
8.81/3.84	import qualified Prelude;
8.81/3.84	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.81/3.84	
8.81/3.84	data Main.Nat = Succ Main.Nat  | Zero ;
8.81/3.84	
8.81/3.84	data Ratio a = CnPc a a ;
8.81/3.84	
8.81/3.84	denominator (CnPc x y) = y;
8.81/3.84	
8.81/3.84	}
8.81/3.84	
8.81/3.84	----------------------------------------
8.81/3.84	
8.81/3.84	(3) COR (EQUIVALENT)
8.81/3.84	Cond Reductions:
8.81/3.84	The following Function with conditions
8.81/3.84	"undefined |Falseundefined;
8.81/3.84	"
8.81/3.84	is transformed to
8.81/3.84	"undefined  = undefined1;
8.81/3.84	"
8.81/3.84	"undefined0 True = undefined;
8.81/3.84	"
8.81/3.84	"undefined1  = undefined0 False;
8.81/3.84	"
8.81/3.84	
8.81/3.84	----------------------------------------
8.81/3.84	
8.81/3.84	(4)
8.81/3.84	Obligation:
8.81/3.84	mainModule Main 
8.81/3.84	module Main where {
8.81/3.84	import qualified Prelude;
8.81/3.84	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.81/3.84	
8.81/3.84	data Main.Nat = Succ Main.Nat  | Zero ;
8.81/3.84	
8.81/3.84	data Ratio a = CnPc a a ;
8.81/3.84	
8.81/3.84	denominator (CnPc x y) = y;
8.81/3.84	
8.81/3.84	}
8.81/3.84	
8.81/3.84	----------------------------------------
8.81/3.84	
8.81/3.84	(5) Narrow (EQUIVALENT)
8.81/3.84	Haskell To QDPs
8.81/3.84	
8.81/3.84	digraph dp_graph {
8.81/3.84	node [outthreshold=100, inthreshold=100];1[label="denominator",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.81/3.84	3[label="denominator 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];
8.81/3.84	6 -> 4[label="",style="solid", color="burlywood", weight=3];
8.81/3.84	4[label="denominator (CnPc vx30 vx31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
8.81/3.84	5[label="vx31",fontsize=16,color="green",shape="box"];}
8.81/3.84	
8.81/3.84	----------------------------------------
8.81/3.84	
8.81/3.84	(6)
8.81/3.84	YES
9.07/3.88	EOF