9.83/4.40	YES
11.56/4.92	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.56/4.92	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.56/4.92	
11.56/4.92	
11.56/4.92	H-Termination with start terms of the given HASKELL could be proven:
11.56/4.92	
11.56/4.92	(0) HASKELL
11.56/4.92	(1) BR [EQUIVALENT, 0 ms]
11.56/4.92	(2) HASKELL
11.56/4.92	(3) COR [EQUIVALENT, 0 ms]
11.56/4.92	(4) HASKELL
11.56/4.92	(5) NumRed [SOUND, 0 ms]
11.56/4.92	(6) HASKELL
11.56/4.92	(7) Narrow [EQUIVALENT, 16 ms]
11.56/4.92	(8) YES
11.56/4.92	
11.56/4.92	
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(0)
11.56/4.92	Obligation:
11.56/4.92	mainModule Main 
11.56/4.92	module FiniteMap where {
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
11.56/4.92	
11.56/4.92	emptyFM :: FiniteMap b a;
11.56/4.92	emptyFM = EmptyFM;
11.56/4.92	
11.56/4.92	unitFM :: a  ->  b  ->  FiniteMap a b;
11.56/4.92	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
11.56/4.92	
11.56/4.92	}
11.56/4.92	module Maybe where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	module Main where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(1) BR (EQUIVALENT)
11.56/4.92	Replaced joker patterns by fresh variables and removed binding patterns.
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(2)
11.56/4.92	Obligation:
11.56/4.92	mainModule Main 
11.56/4.92	module FiniteMap where {
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
11.56/4.92	
11.56/4.92	emptyFM :: FiniteMap a b;
11.56/4.92	emptyFM = EmptyFM;
11.56/4.92	
11.56/4.92	unitFM :: a  ->  b  ->  FiniteMap a b;
11.56/4.92	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
11.56/4.92	
11.56/4.92	}
11.56/4.92	module Maybe where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	module Main where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(3) COR (EQUIVALENT)
11.56/4.92	Cond Reductions:
11.56/4.92	The following Function with conditions
11.56/4.92	"undefined |Falseundefined;
11.56/4.92	"
11.56/4.92	is transformed to
11.56/4.92	"undefined  = undefined1;
11.56/4.92	"
11.56/4.92	"undefined0 True = undefined;
11.56/4.92	"
11.56/4.92	"undefined1  = undefined0 False;
11.56/4.92	"
11.56/4.92	
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(4)
11.56/4.92	Obligation:
11.56/4.92	mainModule Main 
11.56/4.92	module FiniteMap where {
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
11.56/4.92	
11.56/4.92	emptyFM :: FiniteMap b a;
11.56/4.92	emptyFM = EmptyFM;
11.56/4.92	
11.56/4.92	unitFM :: a  ->  b  ->  FiniteMap a b;
11.56/4.92	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
11.56/4.92	
11.56/4.92	}
11.56/4.92	module Maybe where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	module Main where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(5) NumRed (SOUND)
11.56/4.92	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(6)
11.56/4.92	Obligation:
11.56/4.92	mainModule Main 
11.56/4.92	module FiniteMap where {
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
11.56/4.92	
11.56/4.92	emptyFM :: FiniteMap a b;
11.56/4.92	emptyFM = EmptyFM;
11.56/4.92	
11.56/4.92	unitFM :: b  ->  a  ->  FiniteMap b a;
11.56/4.92	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
11.56/4.92	
11.56/4.92	}
11.56/4.92	module Maybe where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Main;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	module Main where {
11.56/4.92	import qualified FiniteMap;
11.56/4.92	import qualified Maybe;
11.56/4.92	import qualified Prelude;
11.56/4.92	}
11.56/4.92	
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(7) Narrow (EQUIVALENT)
11.56/4.92	Haskell To QDPs
11.56/4.92	
11.56/4.92	digraph dp_graph {
11.56/4.92	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.unitFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.56/4.92	3[label="FiniteMap.unitFM vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.56/4.92	4[label="FiniteMap.unitFM vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
11.56/4.92	5[label="FiniteMap.Branch vy3 vy4 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
11.56/4.92	5 -> 7[label="",style="dashed", color="green", weight=3];
11.56/4.92	6[label="FiniteMap.emptyFM",fontsize=16,color="black",shape="triangle"];6 -> 8[label="",style="solid", color="black", weight=3];
11.56/4.92	7 -> 6[label="",style="dashed", color="red", weight=0];
11.56/4.92	7[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];8[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];}
11.56/4.92	
11.56/4.92	----------------------------------------
11.56/4.92	
11.56/4.92	(8)
11.56/4.92	YES
11.90/4.96	EOF