9.39/4.36	YES
11.72/4.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.72/4.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.72/4.94	
11.72/4.94	
11.72/4.94	H-Termination with start terms of the given HASKELL could be proven:
11.72/4.94	
11.72/4.94	(0) HASKELL
11.72/4.94	(1) BR [EQUIVALENT, 0 ms]
11.72/4.94	(2) HASKELL
11.72/4.94	(3) COR [EQUIVALENT, 0 ms]
11.72/4.94	(4) HASKELL
11.72/4.94	(5) NumRed [SOUND, 0 ms]
11.72/4.94	(6) HASKELL
11.72/4.94	(7) Narrow [EQUIVALENT, 13 ms]
11.72/4.94	(8) YES
11.72/4.94	
11.72/4.94	
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(0)
11.72/4.94	Obligation:
11.72/4.94	mainModule Main 
11.72/4.94	module FiniteMap where {
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
11.72/4.94	
11.72/4.94	sizeFM :: FiniteMap a b  ->  Int;
11.72/4.94	sizeFM EmptyFM = 0;
11.72/4.94	sizeFM (Branch _ _ size _ _) = size;
11.72/4.94	
11.72/4.94	}
11.72/4.94	module Maybe where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	module Main where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(1) BR (EQUIVALENT)
11.72/4.94	Replaced joker patterns by fresh variables and removed binding patterns.
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(2)
11.72/4.94	Obligation:
11.72/4.94	mainModule Main 
11.72/4.94	module FiniteMap where {
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
11.72/4.94	
11.72/4.94	sizeFM :: FiniteMap a b  ->  Int;
11.72/4.94	sizeFM EmptyFM = 0;
11.72/4.94	sizeFM (Branch vy vz size wu wv) = size;
11.72/4.94	
11.72/4.94	}
11.72/4.94	module Maybe where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	module Main where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(3) COR (EQUIVALENT)
11.72/4.94	Cond Reductions:
11.72/4.94	The following Function with conditions
11.72/4.94	"undefined |Falseundefined;
11.72/4.94	"
11.72/4.94	is transformed to
11.72/4.94	"undefined  = undefined1;
11.72/4.94	"
11.72/4.94	"undefined0 True = undefined;
11.72/4.94	"
11.72/4.94	"undefined1  = undefined0 False;
11.72/4.94	"
11.72/4.94	
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(4)
11.72/4.94	Obligation:
11.72/4.94	mainModule Main 
11.72/4.94	module FiniteMap where {
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
11.72/4.94	
11.72/4.94	sizeFM :: FiniteMap b a  ->  Int;
11.72/4.94	sizeFM EmptyFM = 0;
11.72/4.94	sizeFM (Branch vy vz size wu wv) = size;
11.72/4.94	
11.72/4.94	}
11.72/4.94	module Maybe where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	module Main where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(5) NumRed (SOUND)
11.72/4.94	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(6)
11.72/4.94	Obligation:
11.72/4.94	mainModule Main 
11.72/4.94	module FiniteMap where {
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
11.72/4.94	
11.72/4.94	sizeFM :: FiniteMap a b  ->  Int;
11.72/4.94	sizeFM EmptyFM = Pos Zero;
11.72/4.94	sizeFM (Branch vy vz size wu wv) = size;
11.72/4.94	
11.72/4.94	}
11.72/4.94	module Maybe where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Main;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	module Main where {
11.72/4.94	import qualified FiniteMap;
11.72/4.94	import qualified Maybe;
11.72/4.94	import qualified Prelude;
11.72/4.94	}
11.72/4.94	
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(7) Narrow (EQUIVALENT)
11.72/4.94	Haskell To QDPs
11.72/4.94	
11.72/4.94	digraph dp_graph {
11.72/4.94	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.sizeFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.72/4.94	3[label="FiniteMap.sizeFM ww3",fontsize=16,color="burlywood",shape="triangle"];8[label="ww3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];3 -> 8[label="",style="solid", color="burlywood", weight=9];
11.72/4.94	8 -> 4[label="",style="solid", color="burlywood", weight=3];
11.72/4.94	9[label="ww3/FiniteMap.Branch ww30 ww31 ww32 ww33 ww34",fontsize=10,color="white",style="solid",shape="box"];3 -> 9[label="",style="solid", color="burlywood", weight=9];
11.72/4.94	9 -> 5[label="",style="solid", color="burlywood", weight=3];
11.72/4.94	4[label="FiniteMap.sizeFM FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
11.72/4.94	5[label="FiniteMap.sizeFM (FiniteMap.Branch ww30 ww31 ww32 ww33 ww34)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
11.72/4.94	6[label="Pos Zero",fontsize=16,color="green",shape="box"];7[label="ww32",fontsize=16,color="green",shape="box"];}
11.72/4.94	
11.72/4.94	----------------------------------------
11.72/4.94	
11.72/4.94	(8)
11.72/4.94	YES
11.72/4.98	EOF