8.12/3.48	YES
9.83/4.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.83/4.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.83/4.00	
9.83/4.00	
9.83/4.00	H-Termination with start terms of the given HASKELL could be proven:
9.83/4.00	
9.83/4.00	(0) HASKELL
9.83/4.00	(1) BR [EQUIVALENT, 0 ms]
9.83/4.00	(2) HASKELL
9.83/4.00	(3) COR [EQUIVALENT, 0 ms]
9.83/4.00	(4) HASKELL
9.83/4.00	(5) NumRed [SOUND, 0 ms]
9.83/4.00	(6) HASKELL
9.83/4.00	(7) Narrow [EQUIVALENT, 22 ms]
9.83/4.00	(8) YES
9.83/4.00	
9.83/4.00	
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(0)
9.83/4.00	Obligation:
9.83/4.00	mainModule Main 
9.83/4.00	module Main where {
9.83/4.00	import qualified Prelude;
9.83/4.00	}
9.83/4.00	
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(1) BR (EQUIVALENT)
9.83/4.00	Replaced joker patterns by fresh variables and removed binding patterns.
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(2)
9.83/4.00	Obligation:
9.83/4.00	mainModule Main 
9.83/4.00	module Main where {
9.83/4.00	import qualified Prelude;
9.83/4.00	}
9.83/4.00	
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(3) COR (EQUIVALENT)
9.83/4.00	Cond Reductions:
9.83/4.00	The following Function with conditions
9.83/4.00	"undefined |Falseundefined;
9.83/4.00	"
9.83/4.00	is transformed to
9.83/4.00	"undefined  = undefined1;
9.83/4.00	"
9.83/4.00	"undefined0 True = undefined;
9.83/4.00	"
9.83/4.00	"undefined1  = undefined0 False;
9.83/4.00	"
9.83/4.00	
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(4)
9.83/4.00	Obligation:
9.83/4.00	mainModule Main 
9.83/4.00	module Main where {
9.83/4.00	import qualified Prelude;
9.83/4.00	}
9.83/4.00	
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(5) NumRed (SOUND)
9.83/4.00	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(6)
9.83/4.00	Obligation:
9.83/4.00	mainModule Main 
9.83/4.00	module Main where {
9.83/4.00	import qualified Prelude;
9.83/4.00	}
9.83/4.00	
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(7) Narrow (EQUIVALENT)
9.83/4.00	Haskell To QDPs
9.83/4.00	
9.83/4.00	digraph dp_graph {
9.83/4.00	node [outthreshold=100, inthreshold=100];1[label="fromIntegral",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.83/4.00	3[label="fromIntegral vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.83/4.00	4[label="fromInteger . toInteger",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.83/4.00	5[label="fromInteger (toInteger vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.83/4.00	6[label="fromInteger (toInteger vx3) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];6 -> 7[label="",style="dashed", color="green", weight=3];
9.83/4.00	6 -> 8[label="",style="dashed", color="green", weight=3];
9.83/4.00	7[label="fromInteger (toInteger vx3)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.83/4.00	8[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9.83/4.00	9[label="fromInteger (Integer vx3)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
9.83/4.00	10[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];11[label="vx3",fontsize=16,color="green",shape="box"];}
9.83/4.00	
9.83/4.00	----------------------------------------
9.83/4.00	
9.83/4.00	(8)
9.83/4.00	YES
10.05/4.05	EOF