11.00/4.49	MAYBE
13.20/5.14	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
13.20/5.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.20/5.14	
13.20/5.14	
13.20/5.14	H-Termination with start terms of the given HASKELL could not be shown:
13.20/5.14	
13.20/5.14	(0) HASKELL
13.20/5.14	(1) LR [EQUIVALENT, 0 ms]
13.20/5.14	(2) HASKELL
13.20/5.14	(3) BR [EQUIVALENT, 0 ms]
13.20/5.14	(4) HASKELL
13.20/5.14	(5) COR [EQUIVALENT, 0 ms]
13.20/5.14	(6) HASKELL
13.20/5.14	(7) LetRed [EQUIVALENT, 0 ms]
13.20/5.14	(8) HASKELL
13.20/5.14	(9) Narrow [SOUND, 0 ms]
13.20/5.14	(10) AND
13.20/5.14	    (11) QDP
13.20/5.14	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.20/5.14	        (13) YES
13.20/5.14	    (14) QDP
13.20/5.14	        (15) NonTerminationLoopProof [COMPLETE, 0 ms]
13.20/5.14	        (16) NO
13.20/5.14	(17) Narrow [COMPLETE, 0 ms]
13.20/5.14	(18) QDP
13.20/5.14	    (19) PisEmptyProof [EQUIVALENT, 0 ms]
13.20/5.14	    (20) YES
13.20/5.14	
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(0)
13.20/5.14	Obligation:
13.20/5.14	mainModule Main 
13.20/5.14	module Maybe where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	module List where {
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
13.20/5.14	groupBy _ [] = [];
13.20/5.14	groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
13.20/5.14	vv10 = span (eq x) xs;
13.20/5.14	ys = (\(ys,_) ->ys) vv10;
13.20/5.14	zs = (\(_,zs) ->zs) vv10;
13.20/5.14	 };
13.20/5.14	
13.20/5.14	}
13.20/5.14	module Main where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(1) LR (EQUIVALENT)
13.20/5.14	Lambda Reductions:
13.20/5.14	The following Lambda expression
13.20/5.14	"\(_,zs)->zs"
13.20/5.14	is transformed to
13.20/5.14	"zs0 (_,zs) = zs;
13.20/5.14	"
13.20/5.14	The following Lambda expression
13.20/5.14	"\(ys,_)->ys"
13.20/5.14	is transformed to
13.20/5.14	"ys0 (ys,_) = ys;
13.20/5.14	"
13.20/5.14	The following Lambda expression
13.20/5.14	"\(_,zs)->zs"
13.20/5.14	is transformed to
13.20/5.14	"zs1 (_,zs) = zs;
13.20/5.14	"
13.20/5.14	The following Lambda expression
13.20/5.14	"\(ys,_)->ys"
13.20/5.14	is transformed to
13.20/5.14	"ys1 (ys,_) = ys;
13.20/5.14	"
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(2)
13.20/5.14	Obligation:
13.20/5.14	mainModule Main 
13.20/5.14	module Maybe where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	module List where {
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
13.20/5.14	groupBy _ [] = [];
13.20/5.14	groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
13.20/5.14	vv10 = span (eq x) xs;
13.20/5.14	ys = ys1 vv10;
13.20/5.14	ys1 (ys,_) = ys;
13.20/5.14	zs = zs1 vv10;
13.20/5.14	zs1 (_,zs) = zs;
13.20/5.14	 };
13.20/5.14	
13.20/5.14	}
13.20/5.14	module Main where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(3) BR (EQUIVALENT)
13.20/5.14	Replaced joker patterns by fresh variables and removed binding patterns.
13.20/5.14	
13.20/5.14	Binding Reductions:
13.20/5.14	The bind variable of the following binding Pattern
13.20/5.14	"xs@(vy : vz)"
13.20/5.14	is replaced by the following term
13.20/5.14	"vy : vz"
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(4)
13.20/5.14	Obligation:
13.20/5.14	mainModule Main 
13.20/5.14	module Maybe where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	module List where {
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
13.20/5.14	groupBy ww [] = [];
13.20/5.14	groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
13.20/5.14	vv10 = span (eq x) xs;
13.20/5.14	ys = ys1 vv10;
13.20/5.14	ys1 (ys,wx) = ys;
13.20/5.14	zs = zs1 vv10;
13.20/5.14	zs1 (wy,zs) = zs;
13.20/5.14	 };
13.20/5.14	
13.20/5.14	}
13.20/5.14	module Main where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(5) COR (EQUIVALENT)
13.20/5.14	Cond Reductions:
13.20/5.14	The following Function with conditions
13.20/5.14	"undefined |Falseundefined;
13.20/5.14	"
13.20/5.14	is transformed to
13.20/5.14	"undefined  = undefined1;
13.20/5.14	"
13.20/5.14	"undefined0 True = undefined;
13.20/5.14	"
13.20/5.14	"undefined1  = undefined0 False;
13.20/5.14	"
13.20/5.14	The following Function with conditions
13.20/5.14	"span p [] = ([],[]);
13.20/5.14	span p (vy : vz)|p vy(vy : ys,zs)|otherwise([],vy : vz) where {
13.20/5.14	vu43  = span p vz;
13.20/5.14	;
13.20/5.14	ys  = ys0 vu43;
13.20/5.14	;
13.20/5.14	ys0 (ys,wv) = ys;
13.20/5.14	;
13.20/5.14	zs  = zs0 vu43;
13.20/5.14	;
13.20/5.14	zs0 (wu,zs) = zs;
13.20/5.14	} 
13.20/5.14	;
13.20/5.14	"
13.20/5.14	is transformed to
13.20/5.14	"span p [] = span3 p [];
13.20/5.14	span p (vy : vz) = span2 p (vy : vz);
13.20/5.14	"
13.20/5.14	"span2 p (vy : vz) = span1 p vy vz (p vy) where {
13.20/5.14	span0 p vy vz True = ([],vy : vz);
13.20/5.14	;
13.20/5.14	span1 p vy vz True = (vy : ys,zs);
13.20/5.14	span1 p vy vz False = span0 p vy vz otherwise;
13.20/5.14	;
13.20/5.14	vu43  = span p vz;
13.20/5.14	;
13.20/5.14	ys  = ys0 vu43;
13.20/5.14	;
13.20/5.14	ys0 (ys,wv) = ys;
13.20/5.14	;
13.20/5.14	zs  = zs0 vu43;
13.20/5.14	;
13.20/5.14	zs0 (wu,zs) = zs;
13.20/5.14	} 
13.20/5.14	;
13.20/5.14	"
13.20/5.14	"span3 p [] = ([],[]);
13.20/5.14	span3 xv xw = span2 xv xw;
13.20/5.14	"
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(6)
13.20/5.14	Obligation:
13.20/5.14	mainModule Main 
13.20/5.14	module Maybe where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	module List where {
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
13.20/5.14	groupBy ww [] = [];
13.20/5.14	groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
13.20/5.14	vv10 = span (eq x) xs;
13.20/5.14	ys = ys1 vv10;
13.20/5.14	ys1 (ys,wx) = ys;
13.20/5.14	zs = zs1 vv10;
13.20/5.14	zs1 (wy,zs) = zs;
13.20/5.14	 };
13.20/5.14	
13.20/5.14	}
13.20/5.14	module Main where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(7) LetRed (EQUIVALENT)
13.20/5.14	Let/Where Reductions:
13.20/5.14	The bindings of the following Let/Where expression
13.20/5.14	"span1 p vy vz (p vy) where {
13.20/5.14	span0 p vy vz True = ([],vy : vz);
13.20/5.14	;
13.20/5.14	span1 p vy vz True = (vy : ys,zs);
13.20/5.14	span1 p vy vz False = span0 p vy vz otherwise;
13.20/5.14	;
13.20/5.14	vu43  = span p vz;
13.20/5.14	;
13.20/5.14	ys  = ys0 vu43;
13.20/5.14	;
13.20/5.14	ys0 (ys,wv) = ys;
13.20/5.14	;
13.20/5.14	zs  = zs0 vu43;
13.20/5.14	;
13.20/5.14	zs0 (wu,zs) = zs;
13.20/5.14	} 
13.20/5.14	"
13.20/5.14	are unpacked to the following functions on top level
13.20/5.14	"span2Vu43 xx xy = span xx xy;
13.20/5.14	"
13.20/5.14	"span2Zs0 xx xy (wu,zs) = zs;
13.20/5.14	"
13.20/5.14	"span2Ys0 xx xy (ys,wv) = ys;
13.20/5.14	"
13.20/5.14	"span2Ys xx xy = span2Ys0 xx xy (span2Vu43 xx xy);
13.20/5.14	"
13.20/5.14	"span2Span0 xx xy p vy vz True = ([],vy : vz);
13.20/5.14	"
13.20/5.14	"span2Zs xx xy = span2Zs0 xx xy (span2Vu43 xx xy);
13.20/5.14	"
13.20/5.14	"span2Span1 xx xy p vy vz True = (vy : span2Ys xx xy,span2Zs xx xy);
13.20/5.14	span2Span1 xx xy p vy vz False = span2Span0 xx xy p vy vz otherwise;
13.20/5.14	"
13.20/5.14	The bindings of the following Let/Where expression
13.20/5.14	"(x : ys) : groupBy eq zs where {
13.20/5.14	vv10  = span (eq x) xs;
13.20/5.14	;
13.20/5.14	ys  = ys1 vv10;
13.20/5.14	;
13.20/5.14	ys1 (ys,wx) = ys;
13.20/5.14	;
13.20/5.14	zs  = zs1 vv10;
13.20/5.14	;
13.20/5.14	zs1 (wy,zs) = zs;
13.20/5.14	} 
13.20/5.14	"
13.20/5.14	are unpacked to the following functions on top level
13.20/5.14	"groupByZs xz yu yv = groupByZs1 xz yu yv (groupByVv10 xz yu yv);
13.20/5.14	"
13.20/5.14	"groupByYs1 xz yu yv (ys,wx) = ys;
13.20/5.14	"
13.20/5.14	"groupByZs1 xz yu yv (wy,zs) = zs;
13.20/5.14	"
13.20/5.14	"groupByYs xz yu yv = groupByYs1 xz yu yv (groupByVv10 xz yu yv);
13.20/5.14	"
13.20/5.14	"groupByVv10 xz yu yv = span (xz yu) yv;
13.20/5.14	"
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(8)
13.20/5.14	Obligation:
13.20/5.14	mainModule Main 
13.20/5.14	module Maybe where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	module List where {
13.20/5.14	import qualified Main;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
13.20/5.14	groupBy ww [] = [];
13.20/5.14	groupBy eq (x : xs) = (x : groupByYs eq x xs) : groupBy eq (groupByZs eq x xs);
13.20/5.14	
13.20/5.14	groupByVv10 xz yu yv = span (xz yu) yv;
13.20/5.14	
13.20/5.14	groupByYs xz yu yv = groupByYs1 xz yu yv (groupByVv10 xz yu yv);
13.20/5.14	
13.20/5.14	groupByYs1 xz yu yv (ys,wx) = ys;
13.20/5.14	
13.20/5.14	groupByZs xz yu yv = groupByZs1 xz yu yv (groupByVv10 xz yu yv);
13.20/5.14	
13.20/5.14	groupByZs1 xz yu yv (wy,zs) = zs;
13.20/5.14	
13.20/5.14	}
13.20/5.14	module Main where {
13.20/5.14	import qualified List;
13.20/5.14	import qualified Maybe;
13.20/5.14	import qualified Prelude;
13.20/5.14	}
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(9) Narrow (SOUND)
13.20/5.14	Haskell To QDPs
13.20/5.14	
13.20/5.14	digraph dp_graph {
13.20/5.14	node [outthreshold=100, inthreshold=100];1[label="List.groupBy",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.20/5.14	3[label="List.groupBy yw3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
13.20/5.14	4[label="List.groupBy yw3 yw4",fontsize=16,color="burlywood",shape="triangle"];113[label="yw4/yw40 : yw41",fontsize=10,color="white",style="solid",shape="box"];4 -> 113[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	113 -> 5[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	114[label="yw4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 114[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	114 -> 6[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	5[label="List.groupBy yw3 (yw40 : yw41)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
13.20/5.14	6[label="List.groupBy yw3 []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
13.20/5.14	7[label="(yw40 : List.groupByYs yw3 yw40 yw41) : List.groupBy yw3 (List.groupByZs yw3 yw40 yw41)",fontsize=16,color="green",shape="box"];7 -> 9[label="",style="dashed", color="green", weight=3];
13.20/5.14	7 -> 10[label="",style="dashed", color="green", weight=3];
13.20/5.14	8[label="[]",fontsize=16,color="green",shape="box"];9[label="List.groupByYs yw3 yw40 yw41",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
13.20/5.14	10 -> 4[label="",style="dashed", color="red", weight=0];
13.20/5.14	10[label="List.groupBy yw3 (List.groupByZs yw3 yw40 yw41)",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	11[label="List.groupByYs1 yw3 yw40 yw41 (List.groupByVv10 yw3 yw40 yw41)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
13.20/5.14	12[label="List.groupByZs yw3 yw40 yw41",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13.20/5.14	13[label="List.groupByYs1 yw3 yw40 yw41 (span (yw3 yw40) yw41)",fontsize=16,color="burlywood",shape="box"];115[label="yw41/yw410 : yw411",fontsize=10,color="white",style="solid",shape="box"];13 -> 115[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	115 -> 15[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	116[label="yw41/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 116[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	116 -> 16[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	14[label="List.groupByZs1 yw3 yw40 yw41 (List.groupByVv10 yw3 yw40 yw41)",fontsize=16,color="black",shape="box"];14 -> 17[label="",style="solid", color="black", weight=3];
13.20/5.14	15[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span (yw3 yw40) (yw410 : yw411))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
13.20/5.14	16[label="List.groupByYs1 yw3 yw40 [] (span (yw3 yw40) [])",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
13.20/5.14	17[label="List.groupByZs1 yw3 yw40 yw41 (span (yw3 yw40) yw41)",fontsize=16,color="burlywood",shape="box"];117[label="yw41/yw410 : yw411",fontsize=10,color="white",style="solid",shape="box"];17 -> 117[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	117 -> 20[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	118[label="yw41/[]",fontsize=10,color="white",style="solid",shape="box"];17 -> 118[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	118 -> 21[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	18[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2 (yw3 yw40) (yw410 : yw411))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
13.20/5.14	19[label="List.groupByYs1 yw3 yw40 [] (span3 (yw3 yw40) [])",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
13.20/5.14	20[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span (yw3 yw40) (yw410 : yw411))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
13.20/5.14	21[label="List.groupByZs1 yw3 yw40 [] (span (yw3 yw40) [])",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
13.20/5.14	22 -> 26[label="",style="dashed", color="red", weight=0];
13.20/5.14	22[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 (yw3 yw40 yw410))",fontsize=16,color="magenta"];22 -> 27[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	23[label="List.groupByYs1 yw3 yw40 [] ([],[])",fontsize=16,color="black",shape="box"];23 -> 28[label="",style="solid", color="black", weight=3];
13.20/5.14	24[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2 (yw3 yw40) (yw410 : yw411))",fontsize=16,color="black",shape="box"];24 -> 29[label="",style="solid", color="black", weight=3];
13.20/5.14	25[label="List.groupByZs1 yw3 yw40 [] (span3 (yw3 yw40) [])",fontsize=16,color="black",shape="box"];25 -> 30[label="",style="solid", color="black", weight=3];
13.20/5.14	27[label="yw3 yw40 yw410",fontsize=16,color="green",shape="box"];27 -> 35[label="",style="dashed", color="green", weight=3];
13.20/5.14	27 -> 36[label="",style="dashed", color="green", weight=3];
13.20/5.14	26[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 yw5)",fontsize=16,color="burlywood",shape="triangle"];119[label="yw5/False",fontsize=10,color="white",style="solid",shape="box"];26 -> 119[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	119 -> 33[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	120[label="yw5/True",fontsize=10,color="white",style="solid",shape="box"];26 -> 120[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	120 -> 34[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	28[label="[]",fontsize=16,color="green",shape="box"];29 -> 37[label="",style="dashed", color="red", weight=0];
13.20/5.14	29[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 (yw3 yw40 yw410))",fontsize=16,color="magenta"];29 -> 38[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	30[label="List.groupByZs1 yw3 yw40 [] ([],[])",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
13.20/5.14	35[label="yw40",fontsize=16,color="green",shape="box"];36[label="yw410",fontsize=16,color="green",shape="box"];33[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 False)",fontsize=16,color="black",shape="box"];33 -> 40[label="",style="solid", color="black", weight=3];
13.20/5.14	34[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 True)",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3];
13.20/5.14	38[label="yw3 yw40 yw410",fontsize=16,color="green",shape="box"];38 -> 46[label="",style="dashed", color="green", weight=3];
13.20/5.14	38 -> 47[label="",style="dashed", color="green", weight=3];
13.20/5.14	37[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 yw6)",fontsize=16,color="burlywood",shape="triangle"];121[label="yw6/False",fontsize=10,color="white",style="solid",shape="box"];37 -> 121[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	121 -> 44[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	122[label="yw6/True",fontsize=10,color="white",style="solid",shape="box"];37 -> 122[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	122 -> 45[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	39[label="[]",fontsize=16,color="green",shape="box"];40[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span0 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 otherwise)",fontsize=16,color="black",shape="box"];40 -> 48[label="",style="solid", color="black", weight=3];
13.20/5.14	41[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (yw410 : span2Ys (yw3 yw40) yw411,span2Zs (yw3 yw40) yw411)",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3];
13.20/5.14	46[label="yw40",fontsize=16,color="green",shape="box"];47[label="yw410",fontsize=16,color="green",shape="box"];44[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 False)",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
13.20/5.14	45[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 True)",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3];
13.20/5.14	48[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span0 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 True)",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3];
13.20/5.14	49[label="yw410 : span2Ys (yw3 yw40) yw411",fontsize=16,color="green",shape="box"];49 -> 53[label="",style="dashed", color="green", weight=3];
13.20/5.14	50[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span0 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 otherwise)",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
13.20/5.14	51[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (yw410 : span2Ys (yw3 yw40) yw411,span2Zs (yw3 yw40) yw411)",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3];
13.20/5.14	52[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) ([],yw410 : yw411)",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3];
13.20/5.14	53[label="span2Ys (yw3 yw40) yw411",fontsize=16,color="black",shape="triangle"];53 -> 57[label="",style="solid", color="black", weight=3];
13.20/5.14	54[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span0 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 True)",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
13.20/5.14	55[label="span2Zs (yw3 yw40) yw411",fontsize=16,color="black",shape="triangle"];55 -> 59[label="",style="solid", color="black", weight=3];
13.20/5.14	56[label="[]",fontsize=16,color="green",shape="box"];57[label="span2Ys0 (yw3 yw40) yw411 (span2Vu43 (yw3 yw40) yw411)",fontsize=16,color="black",shape="box"];57 -> 60[label="",style="solid", color="black", weight=3];
13.20/5.14	58[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) ([],yw410 : yw411)",fontsize=16,color="black",shape="box"];58 -> 61[label="",style="solid", color="black", weight=3];
13.20/5.14	59[label="span2Zs0 (yw3 yw40) yw411 (span2Vu43 (yw3 yw40) yw411)",fontsize=16,color="black",shape="box"];59 -> 62[label="",style="solid", color="black", weight=3];
13.20/5.14	60[label="span2Ys0 (yw3 yw40) yw411 (span (yw3 yw40) yw411)",fontsize=16,color="burlywood",shape="box"];123[label="yw411/yw4110 : yw4111",fontsize=10,color="white",style="solid",shape="box"];60 -> 123[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	123 -> 63[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	124[label="yw411/[]",fontsize=10,color="white",style="solid",shape="box"];60 -> 124[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	124 -> 64[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	61[label="yw410 : yw411",fontsize=16,color="green",shape="box"];62[label="span2Zs0 (yw3 yw40) yw411 (span (yw3 yw40) yw411)",fontsize=16,color="burlywood",shape="box"];125[label="yw411/yw4110 : yw4111",fontsize=10,color="white",style="solid",shape="box"];62 -> 125[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	125 -> 65[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	126[label="yw411/[]",fontsize=10,color="white",style="solid",shape="box"];62 -> 126[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	126 -> 66[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	63[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span (yw3 yw40) (yw4110 : yw4111))",fontsize=16,color="black",shape="box"];63 -> 67[label="",style="solid", color="black", weight=3];
13.20/5.14	64[label="span2Ys0 (yw3 yw40) [] (span (yw3 yw40) [])",fontsize=16,color="black",shape="box"];64 -> 68[label="",style="solid", color="black", weight=3];
13.20/5.14	65[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span (yw3 yw40) (yw4110 : yw4111))",fontsize=16,color="black",shape="box"];65 -> 69[label="",style="solid", color="black", weight=3];
13.20/5.14	66[label="span2Zs0 (yw3 yw40) [] (span (yw3 yw40) [])",fontsize=16,color="black",shape="box"];66 -> 70[label="",style="solid", color="black", weight=3];
13.20/5.14	67[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2 (yw3 yw40) (yw4110 : yw4111))",fontsize=16,color="black",shape="box"];67 -> 71[label="",style="solid", color="black", weight=3];
13.20/5.14	68[label="span2Ys0 (yw3 yw40) [] (span3 (yw3 yw40) [])",fontsize=16,color="black",shape="box"];68 -> 72[label="",style="solid", color="black", weight=3];
13.20/5.14	69[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2 (yw3 yw40) (yw4110 : yw4111))",fontsize=16,color="black",shape="box"];69 -> 73[label="",style="solid", color="black", weight=3];
13.20/5.14	70[label="span2Zs0 (yw3 yw40) [] (span3 (yw3 yw40) [])",fontsize=16,color="black",shape="box"];70 -> 74[label="",style="solid", color="black", weight=3];
13.20/5.14	71 -> 75[label="",style="dashed", color="red", weight=0];
13.20/5.14	71[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 (yw3 yw40 yw4110))",fontsize=16,color="magenta"];71 -> 76[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	72[label="span2Ys0 (yw3 yw40) [] ([],[])",fontsize=16,color="black",shape="box"];72 -> 77[label="",style="solid", color="black", weight=3];
13.20/5.14	73 -> 78[label="",style="dashed", color="red", weight=0];
13.20/5.14	73[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 (yw3 yw40 yw4110))",fontsize=16,color="magenta"];73 -> 79[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	74[label="span2Zs0 (yw3 yw40) [] ([],[])",fontsize=16,color="black",shape="box"];74 -> 80[label="",style="solid", color="black", weight=3];
13.20/5.14	76[label="yw3 yw40 yw4110",fontsize=16,color="green",shape="box"];76 -> 81[label="",style="dashed", color="green", weight=3];
13.20/5.14	76 -> 82[label="",style="dashed", color="green", weight=3];
13.20/5.14	75[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 yw7)",fontsize=16,color="burlywood",shape="triangle"];127[label="yw7/False",fontsize=10,color="white",style="solid",shape="box"];75 -> 127[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	127 -> 83[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	128[label="yw7/True",fontsize=10,color="white",style="solid",shape="box"];75 -> 128[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	128 -> 84[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	77[label="[]",fontsize=16,color="green",shape="box"];79[label="yw3 yw40 yw4110",fontsize=16,color="green",shape="box"];79 -> 89[label="",style="dashed", color="green", weight=3];
13.20/5.14	79 -> 90[label="",style="dashed", color="green", weight=3];
13.20/5.14	78[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 yw8)",fontsize=16,color="burlywood",shape="triangle"];129[label="yw8/False",fontsize=10,color="white",style="solid",shape="box"];78 -> 129[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	129 -> 87[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	130[label="yw8/True",fontsize=10,color="white",style="solid",shape="box"];78 -> 130[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	130 -> 88[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	80[label="[]",fontsize=16,color="green",shape="box"];81[label="yw40",fontsize=16,color="green",shape="box"];82[label="yw4110",fontsize=16,color="green",shape="box"];83[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 False)",fontsize=16,color="black",shape="box"];83 -> 91[label="",style="solid", color="black", weight=3];
13.20/5.14	84[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];84 -> 92[label="",style="solid", color="black", weight=3];
13.20/5.14	89[label="yw40",fontsize=16,color="green",shape="box"];90[label="yw4110",fontsize=16,color="green",shape="box"];87[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 False)",fontsize=16,color="black",shape="box"];87 -> 93[label="",style="solid", color="black", weight=3];
13.20/5.14	88[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];88 -> 94[label="",style="solid", color="black", weight=3];
13.20/5.14	91[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 otherwise)",fontsize=16,color="black",shape="box"];91 -> 95[label="",style="solid", color="black", weight=3];
13.20/5.14	92 -> 96[label="",style="dashed", color="red", weight=0];
13.20/5.14	92[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : span2Ys (yw3 yw40) yw4111,span2Zs (yw3 yw40) yw4111)",fontsize=16,color="magenta"];92 -> 97[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	92 -> 98[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	93[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 otherwise)",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
13.20/5.14	94 -> 100[label="",style="dashed", color="red", weight=0];
13.20/5.14	94[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : span2Ys (yw3 yw40) yw4111,span2Zs (yw3 yw40) yw4111)",fontsize=16,color="magenta"];94 -> 101[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	94 -> 102[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	95[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];95 -> 103[label="",style="solid", color="black", weight=3];
13.20/5.14	97 -> 55[label="",style="dashed", color="red", weight=0];
13.20/5.14	97[label="span2Zs (yw3 yw40) yw4111",fontsize=16,color="magenta"];97 -> 104[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	98 -> 53[label="",style="dashed", color="red", weight=0];
13.20/5.14	98[label="span2Ys (yw3 yw40) yw4111",fontsize=16,color="magenta"];98 -> 105[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	96[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : yw10,yw9)",fontsize=16,color="black",shape="triangle"];96 -> 106[label="",style="solid", color="black", weight=3];
13.20/5.14	99[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];99 -> 107[label="",style="solid", color="black", weight=3];
13.20/5.14	101 -> 55[label="",style="dashed", color="red", weight=0];
13.20/5.14	101[label="span2Zs (yw3 yw40) yw4111",fontsize=16,color="magenta"];101 -> 108[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	102 -> 53[label="",style="dashed", color="red", weight=0];
13.20/5.14	102[label="span2Ys (yw3 yw40) yw4111",fontsize=16,color="magenta"];102 -> 109[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	100[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : yw12,yw11)",fontsize=16,color="black",shape="triangle"];100 -> 110[label="",style="solid", color="black", weight=3];
13.20/5.14	103[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) ([],yw4110 : yw4111)",fontsize=16,color="black",shape="box"];103 -> 111[label="",style="solid", color="black", weight=3];
13.20/5.14	104[label="yw4111",fontsize=16,color="green",shape="box"];105[label="yw4111",fontsize=16,color="green",shape="box"];106[label="yw4110 : yw10",fontsize=16,color="green",shape="box"];107[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) ([],yw4110 : yw4111)",fontsize=16,color="black",shape="box"];107 -> 112[label="",style="solid", color="black", weight=3];
13.20/5.14	108[label="yw4111",fontsize=16,color="green",shape="box"];109[label="yw4111",fontsize=16,color="green",shape="box"];110[label="yw11",fontsize=16,color="green",shape="box"];111[label="[]",fontsize=16,color="green",shape="box"];112[label="yw4110 : yw4111",fontsize=16,color="green",shape="box"];}
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(10)
13.20/5.14	Complex Obligation (AND)
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(11)
13.20/5.14	Obligation:
13.20/5.14	Q DP problem:
13.20/5.14	The TRS P consists of the following rules:
13.20/5.14	
13.20/5.14	   new_span2Zs0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Ys(yw3, yw40, yw4111, ba)
13.20/5.14	   new_span2Ys0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Ys(yw3, yw40, yw4111, ba)
13.20/5.14	   new_span2Zs(yw3, yw40, :(yw4110, yw4111), ba) -> new_span2Zs0(yw3, yw40, yw4110, yw4111, ba)
13.20/5.14	   new_span2Zs0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Zs(yw3, yw40, yw4111, ba)
13.20/5.14	   new_span2Ys0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Zs(yw3, yw40, yw4111, ba)
13.20/5.14	   new_span2Ys(yw3, yw40, :(yw4110, yw4111), ba) -> new_span2Ys0(yw3, yw40, yw4110, yw4111, ba)
13.20/5.14	
13.20/5.14	R is empty.
13.20/5.14	Q is empty.
13.20/5.14	We have to consider all minimal (P,Q,R)-chains.
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(12) QDPSizeChangeProof (EQUIVALENT)
13.20/5.14	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. 
13.20/5.14	
13.20/5.14	From the DPs we obtained the following set of size-change graphs:
13.20/5.14	*new_span2Ys(yw3, yw40, :(yw4110, yw4111), ba) -> new_span2Ys0(yw3, yw40, yw4110, yw4111, ba)
13.20/5.14	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 4 >= 5
13.20/5.14	
13.20/5.14	
13.20/5.14	*new_span2Zs(yw3, yw40, :(yw4110, yw4111), ba) -> new_span2Zs0(yw3, yw40, yw4110, yw4111, ba)
13.20/5.14	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 4 >= 5
13.20/5.14	
13.20/5.14	
13.20/5.14	*new_span2Zs0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Zs(yw3, yw40, yw4111, ba)
13.20/5.14	The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
13.20/5.14	
13.20/5.14	
13.20/5.14	*new_span2Zs0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Ys(yw3, yw40, yw4111, ba)
13.20/5.14	The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
13.20/5.14	
13.20/5.14	
13.20/5.14	*new_span2Ys0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Zs(yw3, yw40, yw4111, ba)
13.20/5.14	The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
13.20/5.14	
13.20/5.14	
13.20/5.14	*new_span2Ys0(yw3, yw40, yw4110, yw4111, ba) -> new_span2Ys(yw3, yw40, yw4111, ba)
13.20/5.14	The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
13.20/5.14	
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(13)
13.20/5.14	YES
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(14)
13.20/5.14	Obligation:
13.20/5.14	Q DP problem:
13.20/5.14	The TRS P consists of the following rules:
13.20/5.14	
13.20/5.14	   new_groupBy(yw3, ba) -> new_groupBy(yw3, ba)
13.20/5.14	
13.20/5.14	R is empty.
13.20/5.14	Q is empty.
13.20/5.14	We have to consider all minimal (P,Q,R)-chains.
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(15) NonTerminationLoopProof (COMPLETE)
13.20/5.14	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
13.20/5.14	Found a loop by semiunifying a rule from P directly.
13.20/5.14	
13.20/5.14	s = new_groupBy(yw3, ba) evaluates to  t =new_groupBy(yw3, ba)
13.20/5.14	
13.20/5.14	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
13.20/5.14	* Matcher: [ ]
13.20/5.14	* Semiunifier: [ ]
13.20/5.14	
13.20/5.14	--------------------------------------------------------------------------------
13.20/5.14	Rewriting sequence
13.20/5.14	
13.20/5.14	The DP semiunifies directly so there is only one rewrite step from new_groupBy(yw3, ba) to new_groupBy(yw3, ba).
13.20/5.14	
13.20/5.14	
13.20/5.14	
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(16)
13.20/5.14	NO
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(17) Narrow (COMPLETE)
13.20/5.14	Haskell To QDPs
13.20/5.14	
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13.20/5.14	113 -> 5[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	114[label="yw4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 114[label="",style="solid", color="burlywood", weight=9];
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13.20/5.14	10 -> 4[label="",style="dashed", color="red", weight=0];
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13.20/5.14	12[label="List.groupByZs yw3 yw40 yw41",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
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13.20/5.14	115 -> 15[label="",style="solid", color="burlywood", weight=3];
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13.20/5.14	15[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span (yw3 yw40) (yw410 : yw411))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
13.20/5.14	16[label="List.groupByYs1 yw3 yw40 [] (span (yw3 yw40) [])",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
13.20/5.14	17[label="List.groupByZs1 yw3 yw40 yw41 (span (yw3 yw40) yw41)",fontsize=16,color="burlywood",shape="box"];117[label="yw41/yw410 : yw411",fontsize=10,color="white",style="solid",shape="box"];17 -> 117[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	117 -> 20[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	118[label="yw41/[]",fontsize=10,color="white",style="solid",shape="box"];17 -> 118[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	118 -> 21[label="",style="solid", color="burlywood", weight=3];
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13.20/5.14	20[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span (yw3 yw40) (yw410 : yw411))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
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13.20/5.14	27[label="yw3 yw40 yw410",fontsize=16,color="green",shape="box"];27 -> 35[label="",style="dashed", color="green", weight=3];
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13.20/5.14	26[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 yw5)",fontsize=16,color="burlywood",shape="triangle"];119[label="yw5/False",fontsize=10,color="white",style="solid",shape="box"];26 -> 119[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	119 -> 33[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	120[label="yw5/True",fontsize=10,color="white",style="solid",shape="box"];26 -> 120[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	120 -> 34[label="",style="solid", color="burlywood", weight=3];
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13.20/5.14	30[label="List.groupByZs1 yw3 yw40 [] ([],[])",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
13.20/5.14	35[label="yw40",fontsize=16,color="green",shape="box"];36[label="yw410",fontsize=16,color="green",shape="box"];33[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 False)",fontsize=16,color="black",shape="box"];33 -> 40[label="",style="solid", color="black", weight=3];
13.20/5.14	34[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 True)",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3];
13.20/5.14	38[label="yw3 yw40 yw410",fontsize=16,color="green",shape="box"];38 -> 46[label="",style="dashed", color="green", weight=3];
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13.20/5.14	37[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 yw6)",fontsize=16,color="burlywood",shape="triangle"];121[label="yw6/False",fontsize=10,color="white",style="solid",shape="box"];37 -> 121[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	121 -> 44[label="",style="solid", color="burlywood", weight=3];
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13.20/5.14	41[label="List.groupByYs1 yw3 yw40 (yw410 : yw411) (yw410 : span2Ys (yw3 yw40) yw411,span2Zs (yw3 yw40) yw411)",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3];
13.20/5.14	46[label="yw40",fontsize=16,color="green",shape="box"];47[label="yw410",fontsize=16,color="green",shape="box"];44[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span1 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 False)",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
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13.20/5.14	50[label="List.groupByZs1 yw3 yw40 (yw410 : yw411) (span2Span0 (yw3 yw40) yw411 (yw3 yw40) yw410 yw411 otherwise)",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
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13.20/5.14	59[label="span2Zs0 (yw3 yw40) yw411 (span2Vu43 (yw3 yw40) yw411)",fontsize=16,color="black",shape="box"];59 -> 62[label="",style="solid", color="black", weight=3];
13.20/5.14	60[label="span2Ys0 (yw3 yw40) yw411 (span (yw3 yw40) yw411)",fontsize=16,color="burlywood",shape="box"];123[label="yw411/yw4110 : yw4111",fontsize=10,color="white",style="solid",shape="box"];60 -> 123[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	123 -> 63[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	124[label="yw411/[]",fontsize=10,color="white",style="solid",shape="box"];60 -> 124[label="",style="solid", color="burlywood", weight=9];
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13.20/5.14	77[label="[]",fontsize=16,color="green",shape="box"];79[label="yw3 yw40 yw4110",fontsize=16,color="green",shape="box"];79 -> 89[label="",style="dashed", color="green", weight=3];
13.20/5.14	79 -> 90[label="",style="dashed", color="green", weight=3];
13.20/5.14	78[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 yw8)",fontsize=16,color="burlywood",shape="triangle"];129[label="yw8/False",fontsize=10,color="white",style="solid",shape="box"];78 -> 129[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	129 -> 87[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	130[label="yw8/True",fontsize=10,color="white",style="solid",shape="box"];78 -> 130[label="",style="solid", color="burlywood", weight=9];
13.20/5.14	130 -> 88[label="",style="solid", color="burlywood", weight=3];
13.20/5.14	80[label="[]",fontsize=16,color="green",shape="box"];81[label="yw40",fontsize=16,color="green",shape="box"];82[label="yw4110",fontsize=16,color="green",shape="box"];83[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 False)",fontsize=16,color="black",shape="box"];83 -> 91[label="",style="solid", color="black", weight=3];
13.20/5.14	84[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];84 -> 92[label="",style="solid", color="black", weight=3];
13.20/5.14	89[label="yw40",fontsize=16,color="green",shape="box"];90[label="yw4110",fontsize=16,color="green",shape="box"];87[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 False)",fontsize=16,color="black",shape="box"];87 -> 93[label="",style="solid", color="black", weight=3];
13.20/5.14	88[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span1 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];88 -> 94[label="",style="solid", color="black", weight=3];
13.20/5.14	91[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 otherwise)",fontsize=16,color="black",shape="box"];91 -> 95[label="",style="solid", color="black", weight=3];
13.20/5.14	92 -> 96[label="",style="dashed", color="red", weight=0];
13.20/5.14	92[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : span2Ys (yw3 yw40) yw4111,span2Zs (yw3 yw40) yw4111)",fontsize=16,color="magenta"];92 -> 97[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	92 -> 98[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	93[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 otherwise)",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
13.20/5.14	94 -> 100[label="",style="dashed", color="red", weight=0];
13.20/5.14	94[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : span2Ys (yw3 yw40) yw4111,span2Zs (yw3 yw40) yw4111)",fontsize=16,color="magenta"];94 -> 101[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	94 -> 102[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	95[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];95 -> 103[label="",style="solid", color="black", weight=3];
13.20/5.14	97 -> 55[label="",style="dashed", color="red", weight=0];
13.20/5.14	97[label="span2Zs (yw3 yw40) yw4111",fontsize=16,color="magenta"];97 -> 104[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	98 -> 53[label="",style="dashed", color="red", weight=0];
13.20/5.14	98[label="span2Ys (yw3 yw40) yw4111",fontsize=16,color="magenta"];98 -> 105[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	96[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : yw10,yw9)",fontsize=16,color="black",shape="triangle"];96 -> 106[label="",style="solid", color="black", weight=3];
13.20/5.14	99[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (span2Span0 (yw3 yw40) yw4111 (yw3 yw40) yw4110 yw4111 True)",fontsize=16,color="black",shape="box"];99 -> 107[label="",style="solid", color="black", weight=3];
13.20/5.14	101 -> 55[label="",style="dashed", color="red", weight=0];
13.20/5.14	101[label="span2Zs (yw3 yw40) yw4111",fontsize=16,color="magenta"];101 -> 108[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	102 -> 53[label="",style="dashed", color="red", weight=0];
13.20/5.14	102[label="span2Ys (yw3 yw40) yw4111",fontsize=16,color="magenta"];102 -> 109[label="",style="dashed", color="magenta", weight=3];
13.20/5.14	100[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) (yw4110 : yw12,yw11)",fontsize=16,color="black",shape="triangle"];100 -> 110[label="",style="solid", color="black", weight=3];
13.20/5.14	103[label="span2Ys0 (yw3 yw40) (yw4110 : yw4111) ([],yw4110 : yw4111)",fontsize=16,color="black",shape="box"];103 -> 111[label="",style="solid", color="black", weight=3];
13.20/5.14	104[label="yw4111",fontsize=16,color="green",shape="box"];105[label="yw4111",fontsize=16,color="green",shape="box"];106[label="yw4110 : yw10",fontsize=16,color="green",shape="box"];107[label="span2Zs0 (yw3 yw40) (yw4110 : yw4111) ([],yw4110 : yw4111)",fontsize=16,color="black",shape="box"];107 -> 112[label="",style="solid", color="black", weight=3];
13.20/5.14	108[label="yw4111",fontsize=16,color="green",shape="box"];109[label="yw4111",fontsize=16,color="green",shape="box"];110[label="yw11",fontsize=16,color="green",shape="box"];111[label="[]",fontsize=16,color="green",shape="box"];112[label="yw4110 : yw4111",fontsize=16,color="green",shape="box"];}
13.20/5.14	
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(18)
13.20/5.14	Obligation:
13.20/5.14	Q DP problem:
13.20/5.14	P is empty.
13.20/5.14	R is empty.
13.20/5.14	Q is empty.
13.20/5.14	We have to consider all (P,Q,R)-chains.
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(19) PisEmptyProof (EQUIVALENT)
13.20/5.14	The TRS P is empty. Hence, there is no (P,Q,R) chain.
13.20/5.14	----------------------------------------
13.20/5.14	
13.20/5.14	(20)
13.20/5.14	YES
13.42/5.18	EOF