10.16/4.34	YES
12.58/5.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.58/5.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.58/5.02	
12.58/5.02	
12.58/5.02	H-Termination with start terms of the given HASKELL could be proven:
12.58/5.02	
12.58/5.02	(0) HASKELL
12.58/5.02	(1) LR [EQUIVALENT, 0 ms]
12.58/5.02	(2) HASKELL
12.58/5.02	(3) CR [EQUIVALENT, 0 ms]
12.58/5.02	(4) HASKELL
12.58/5.02	(5) IFR [EQUIVALENT, 0 ms]
12.58/5.02	(6) HASKELL
12.58/5.02	(7) BR [EQUIVALENT, 0 ms]
12.58/5.02	(8) HASKELL
12.58/5.02	(9) COR [EQUIVALENT, 0 ms]
12.58/5.02	(10) HASKELL
12.58/5.02	(11) Narrow [SOUND, 0 ms]
12.58/5.02	(12) AND
12.58/5.02	    (13) QDP
12.58/5.02	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.58/5.02	        (15) YES
12.58/5.02	    (16) QDP
12.58/5.02	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.58/5.02	        (18) YES
12.58/5.02	
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(0)
12.58/5.02	Obligation:
12.58/5.02	mainModule Main 
12.58/5.02	module Maybe where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	module List where {
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	intersectBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
12.58/5.02	intersectBy eq xs ys = concatMap (\vv2 ->case vv2 of { 
12.58/5.02	x->  if any (eq x) ys then x : [] else []; 
12.58/5.02	_-> []; 
12.58/5.02	 } ) xs;
12.58/5.02	
12.58/5.02	}
12.58/5.02	module Main where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(1) LR (EQUIVALENT)
12.58/5.02	Lambda Reductions:
12.58/5.02	The following Lambda expression
12.58/5.02	"\vv2->case vv2 of {
12.58/5.02	x  -> if any (eq x) ys then x : [] else [];
12.58/5.02	_  -> []}
12.58/5.02	"
12.58/5.02	is transformed to
12.58/5.02	"intersectBy0 eq ys vv2 = case vv2 of {
12.58/5.02	x  -> if any (eq x) ys then x : [] else [];
12.58/5.02	_  -> []}
12.58/5.02	;
12.58/5.02	"
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(2)
12.58/5.02	Obligation:
12.58/5.02	mainModule Main 
12.58/5.02	module Maybe where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	module List where {
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	intersectBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
12.58/5.02	intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs;
12.58/5.02	
12.58/5.02	intersectBy0 eq ys vv2 = case vv2 of { 
12.58/5.02	x->  if any (eq x) ys then x : [] else []; 
12.58/5.02	_-> []; 
12.58/5.02	 } ;
12.58/5.02	
12.58/5.02	}
12.58/5.02	module Main where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(3) CR (EQUIVALENT)
12.58/5.02	Case Reductions:
12.58/5.02	The following Case expression
12.58/5.02	"case vv2 of {
12.58/5.02	x  -> if any (eq x) ys then x : [] else [];
12.58/5.02	_  -> []}
12.58/5.02	"
12.58/5.02	is transformed to
12.58/5.02	"intersectBy00 eq ys x = if any (eq x) ys then x : [] else [];
12.58/5.02	intersectBy00 eq ys _ = [];
12.58/5.02	"
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(4)
12.58/5.02	Obligation:
12.58/5.02	mainModule Main 
12.58/5.02	module Maybe where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	module List where {
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	intersectBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
12.58/5.02	intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs;
12.58/5.02	
12.58/5.02	intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2;
12.58/5.02	
12.58/5.02	intersectBy00 eq ys x =  if any (eq x) ys then x : [] else [];
12.58/5.02	intersectBy00 eq ys _ = [];
12.58/5.02	
12.58/5.02	}
12.58/5.02	module Main where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(5) IFR (EQUIVALENT)
12.58/5.02	If Reductions:
12.58/5.02	The following If expression
12.58/5.02	"if any (eq x) ys then x : [] else []"
12.58/5.02	is transformed to
12.58/5.02	"intersectBy000 x True = x : [];
12.58/5.02	intersectBy000 x False = [];
12.58/5.02	"
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(6)
12.58/5.02	Obligation:
12.58/5.02	mainModule Main 
12.58/5.02	module Maybe where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	module List where {
12.58/5.02	import qualified Main;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	intersectBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
12.58/5.02	intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs;
12.58/5.02	
12.58/5.02	intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2;
12.58/5.02	
12.58/5.02	intersectBy00 eq ys x = intersectBy000 x (any (eq x) ys);
12.58/5.02	intersectBy00 eq ys _ = [];
12.58/5.02	
12.58/5.02	intersectBy000 x True = x : [];
12.58/5.02	intersectBy000 x False = [];
12.58/5.02	
12.58/5.02	}
12.58/5.02	module Main where {
12.58/5.02	import qualified List;
12.58/5.02	import qualified Maybe;
12.58/5.02	import qualified Prelude;
12.58/5.02	}
12.58/5.02	
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(7) BR (EQUIVALENT)
12.58/5.02	Replaced joker patterns by fresh variables and removed binding patterns.
12.58/5.02	----------------------------------------
12.58/5.02	
12.58/5.02	(8)
12.58/5.02	Obligation:
12.58/5.02	mainModule Main 
12.58/5.03	module Maybe where {
12.58/5.03	import qualified List;
12.58/5.03	import qualified Main;
12.58/5.03	import qualified Prelude;
12.58/5.03	}
12.58/5.03	module List where {
12.58/5.03	import qualified Main;
12.58/5.03	import qualified Maybe;
12.58/5.03	import qualified Prelude;
12.58/5.03	intersectBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
12.58/5.03	intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs;
12.58/5.03	
12.58/5.03	intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2;
12.58/5.03	
12.58/5.03	intersectBy00 eq ys x = intersectBy000 x (any (eq x) ys);
12.58/5.03	intersectBy00 eq ys vy = [];
12.58/5.03	
12.58/5.03	intersectBy000 x True = x : [];
12.58/5.03	intersectBy000 x False = [];
12.58/5.03	
12.58/5.03	}
12.58/5.03	module Main where {
12.58/5.03	import qualified List;
12.58/5.03	import qualified Maybe;
12.58/5.03	import qualified Prelude;
12.58/5.03	}
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(9) COR (EQUIVALENT)
12.58/5.03	Cond Reductions:
12.58/5.03	The following Function with conditions
12.58/5.03	"undefined |Falseundefined;
12.58/5.03	"
12.58/5.03	is transformed to
12.58/5.03	"undefined  = undefined1;
12.58/5.03	"
12.58/5.03	"undefined0 True = undefined;
12.58/5.03	"
12.58/5.03	"undefined1  = undefined0 False;
12.58/5.03	"
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(10)
12.58/5.03	Obligation:
12.58/5.03	mainModule Main 
12.58/5.03	module Maybe where {
12.58/5.03	import qualified List;
12.58/5.03	import qualified Main;
12.58/5.03	import qualified Prelude;
12.58/5.03	}
12.58/5.03	module List where {
12.58/5.03	import qualified Main;
12.58/5.03	import qualified Maybe;
12.58/5.03	import qualified Prelude;
12.58/5.03	intersectBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
12.58/5.03	intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs;
12.58/5.03	
12.58/5.03	intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2;
12.58/5.03	
12.58/5.03	intersectBy00 eq ys x = intersectBy000 x (any (eq x) ys);
12.58/5.03	intersectBy00 eq ys vy = [];
12.58/5.03	
12.58/5.03	intersectBy000 x True = x : [];
12.58/5.03	intersectBy000 x False = [];
12.58/5.03	
12.58/5.03	}
12.58/5.03	module Main where {
12.58/5.03	import qualified List;
12.58/5.03	import qualified Maybe;
12.58/5.03	import qualified Prelude;
12.58/5.03	}
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(11) Narrow (SOUND)
12.58/5.03	Haskell To QDPs
12.58/5.03	
12.58/5.03	digraph dp_graph {
12.58/5.03	node [outthreshold=100, inthreshold=100];1[label="List.intersectBy",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.58/5.03	3[label="List.intersectBy vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.58/5.03	4[label="List.intersectBy vz3 vz4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
12.58/5.03	5[label="List.intersectBy vz3 vz4 vz5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
12.58/5.03	6[label="concatMap (List.intersectBy0 vz3 vz5) vz4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
12.58/5.03	7[label="concat . map (List.intersectBy0 vz3 vz5)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
12.58/5.03	8[label="concat (map (List.intersectBy0 vz3 vz5) vz4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
12.58/5.03	9[label="foldr (++) [] (map (List.intersectBy0 vz3 vz5) vz4)",fontsize=16,color="burlywood",shape="triangle"];46[label="vz4/vz40 : vz41",fontsize=10,color="white",style="solid",shape="box"];9 -> 46[label="",style="solid", color="burlywood", weight=9];
12.58/5.03	46 -> 10[label="",style="solid", color="burlywood", weight=3];
12.58/5.03	47[label="vz4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 47[label="",style="solid", color="burlywood", weight=9];
12.58/5.03	47 -> 11[label="",style="solid", color="burlywood", weight=3];
12.58/5.03	10[label="foldr (++) [] (map (List.intersectBy0 vz3 vz5) (vz40 : vz41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
12.58/5.03	11[label="foldr (++) [] (map (List.intersectBy0 vz3 vz5) [])",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12.58/5.03	12[label="foldr (++) [] (List.intersectBy0 vz3 vz5 vz40 : map (List.intersectBy0 vz3 vz5) vz41)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
12.58/5.03	13[label="foldr (++) [] []",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
12.58/5.03	14 -> 16[label="",style="dashed", color="red", weight=0];
12.58/5.03	14[label="(++) List.intersectBy0 vz3 vz5 vz40 foldr (++) [] (map (List.intersectBy0 vz3 vz5) vz41)",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
12.58/5.03	15[label="[]",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0];
12.58/5.03	17[label="foldr (++) [] (map (List.intersectBy0 vz3 vz5) vz41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3];
12.58/5.03	16[label="(++) List.intersectBy0 vz3 vz5 vz40 vz6",fontsize=16,color="black",shape="triangle"];16 -> 19[label="",style="solid", color="black", weight=3];
12.58/5.03	18[label="vz41",fontsize=16,color="green",shape="box"];19[label="(++) List.intersectBy00 vz3 vz5 vz40 vz6",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
12.58/5.03	20[label="(++) List.intersectBy000 vz40 (any (vz3 vz40) vz5) vz6",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
12.58/5.03	21[label="(++) List.intersectBy000 vz40 (or . map (vz3 vz40)) vz6",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
12.58/5.03	22[label="(++) List.intersectBy000 vz40 (or (map (vz3 vz40) vz5)) vz6",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
12.58/5.03	23[label="(++) List.intersectBy000 vz40 (foldr (||) False (map (vz3 vz40) vz5)) vz6",fontsize=16,color="burlywood",shape="triangle"];48[label="vz5/vz50 : vz51",fontsize=10,color="white",style="solid",shape="box"];23 -> 48[label="",style="solid", color="burlywood", weight=9];
12.58/5.03	48 -> 24[label="",style="solid", color="burlywood", weight=3];
12.58/5.03	49[label="vz5/[]",fontsize=10,color="white",style="solid",shape="box"];23 -> 49[label="",style="solid", color="burlywood", weight=9];
12.58/5.03	49 -> 25[label="",style="solid", color="burlywood", weight=3];
12.58/5.03	24[label="(++) List.intersectBy000 vz40 (foldr (||) False (map (vz3 vz40) (vz50 : vz51))) vz6",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
12.58/5.03	25[label="(++) List.intersectBy000 vz40 (foldr (||) False (map (vz3 vz40) [])) vz6",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
12.58/5.03	26[label="(++) List.intersectBy000 vz40 (foldr (||) False (vz3 vz40 vz50 : map (vz3 vz40) vz51)) vz6",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
12.58/5.03	27[label="(++) List.intersectBy000 vz40 (foldr (||) False []) vz6",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
12.58/5.03	28 -> 30[label="",style="dashed", color="red", weight=0];
12.58/5.03	28[label="(++) List.intersectBy000 vz40 ((||) vz3 vz40 vz50 foldr (||) False (map (vz3 vz40) vz51)) vz6",fontsize=16,color="magenta"];28 -> 31[label="",style="dashed", color="magenta", weight=3];
12.58/5.03	29[label="(++) List.intersectBy000 vz40 False vz6",fontsize=16,color="black",shape="box"];29 -> 32[label="",style="solid", color="black", weight=3];
12.58/5.03	31[label="vz3 vz40 vz50",fontsize=16,color="green",shape="box"];31 -> 37[label="",style="dashed", color="green", weight=3];
12.58/5.03	31 -> 38[label="",style="dashed", color="green", weight=3];
12.58/5.03	30[label="(++) List.intersectBy000 vz40 ((||) vz7 foldr (||) False (map (vz3 vz40) vz51)) vz6",fontsize=16,color="burlywood",shape="triangle"];50[label="vz7/False",fontsize=10,color="white",style="solid",shape="box"];30 -> 50[label="",style="solid", color="burlywood", weight=9];
12.58/5.03	50 -> 35[label="",style="solid", color="burlywood", weight=3];
12.58/5.03	51[label="vz7/True",fontsize=10,color="white",style="solid",shape="box"];30 -> 51[label="",style="solid", color="burlywood", weight=9];
12.58/5.03	51 -> 36[label="",style="solid", color="burlywood", weight=3];
12.58/5.03	32[label="(++) [] vz6",fontsize=16,color="black",shape="triangle"];32 -> 39[label="",style="solid", color="black", weight=3];
12.58/5.03	37[label="vz40",fontsize=16,color="green",shape="box"];38[label="vz50",fontsize=16,color="green",shape="box"];35[label="(++) List.intersectBy000 vz40 ((||) False foldr (||) False (map (vz3 vz40) vz51)) vz6",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3];
12.58/5.03	36[label="(++) List.intersectBy000 vz40 ((||) True foldr (||) False (map (vz3 vz40) vz51)) vz6",fontsize=16,color="black",shape="box"];36 -> 41[label="",style="solid", color="black", weight=3];
12.58/5.03	39[label="vz6",fontsize=16,color="green",shape="box"];40 -> 23[label="",style="dashed", color="red", weight=0];
12.58/5.03	40[label="(++) List.intersectBy000 vz40 (foldr (||) False (map (vz3 vz40) vz51)) vz6",fontsize=16,color="magenta"];40 -> 42[label="",style="dashed", color="magenta", weight=3];
12.58/5.03	41[label="(++) List.intersectBy000 vz40 True vz6",fontsize=16,color="black",shape="box"];41 -> 43[label="",style="solid", color="black", weight=3];
12.58/5.03	42[label="vz51",fontsize=16,color="green",shape="box"];43[label="(++) (vz40 : []) vz6",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3];
12.58/5.03	44[label="vz40 : [] ++ vz6",fontsize=16,color="green",shape="box"];44 -> 45[label="",style="dashed", color="green", weight=3];
12.58/5.03	45 -> 32[label="",style="dashed", color="red", weight=0];
12.58/5.03	45[label="[] ++ vz6",fontsize=16,color="magenta"];}
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(12)
12.58/5.03	Complex Obligation (AND)
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(13)
12.58/5.03	Obligation:
12.58/5.03	Q DP problem:
12.58/5.03	The TRS P consists of the following rules:
12.58/5.03	
12.58/5.03	   new_psPs0(vz40, vz3, :(vz50, vz51), vz6, ba) -> new_psPs(vz40, vz3, vz51, vz6, ba)
12.58/5.03	   new_psPs(vz40, vz3, vz51, vz6, ba) -> new_psPs0(vz40, vz3, vz51, vz6, ba)
12.58/5.03	
12.58/5.03	R is empty.
12.58/5.03	Q is empty.
12.58/5.03	We have to consider all minimal (P,Q,R)-chains.
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(14) QDPSizeChangeProof (EQUIVALENT)
12.58/5.03	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.58/5.03	
12.58/5.03	From the DPs we obtained the following set of size-change graphs:
12.58/5.03	*new_psPs(vz40, vz3, vz51, vz6, ba) -> new_psPs0(vz40, vz3, vz51, vz6, ba)
12.58/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
12.58/5.03	
12.58/5.03	
12.58/5.03	*new_psPs0(vz40, vz3, :(vz50, vz51), vz6, ba) -> new_psPs(vz40, vz3, vz51, vz6, ba)
12.58/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.58/5.03	
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(15)
12.58/5.03	YES
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(16)
12.58/5.03	Obligation:
12.58/5.03	Q DP problem:
12.58/5.03	The TRS P consists of the following rules:
12.58/5.03	
12.58/5.03	   new_foldr(vz3, vz5, :(vz40, vz41), ba) -> new_foldr(vz3, vz5, vz41, ba)
12.58/5.03	
12.58/5.03	R is empty.
12.58/5.03	Q is empty.
12.58/5.03	We have to consider all minimal (P,Q,R)-chains.
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(17) QDPSizeChangeProof (EQUIVALENT)
12.58/5.03	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.58/5.03	
12.58/5.03	From the DPs we obtained the following set of size-change graphs:
12.58/5.03	*new_foldr(vz3, vz5, :(vz40, vz41), ba) -> new_foldr(vz3, vz5, vz41, ba)
12.58/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4
12.58/5.03	
12.58/5.03	
12.58/5.03	----------------------------------------
12.58/5.03	
12.58/5.03	(18)
12.58/5.03	YES
12.78/5.07	EOF