/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 21 ms]
(6) HASKELL
(7) LetRed [EQUIVALENT, 0 ms]
(8) HASKELL
(9) Narrow [SOUND, 0 ms]
(10) AND
    (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 66 ms]
        (13) YES
    (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES


----------------------------------------

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
group :: Eq a => [a]  ->  [[a]];
group = groupBy (==);

groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
groupBy _ [] = [];
groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
vv10 = span (eq x) xs;
ys = (\(ys,_) ->ys) vv10;
zs = (\(_,zs) ->zs) vv10;
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\(_,zs)->zs"
is transformed to
"zs0 (_,zs) = zs;
"
The following Lambda expression
"\(ys,_)->ys"
is transformed to
"ys0 (ys,_) = ys;
"
The following Lambda expression
"\(_,zs)->zs"
is transformed to
"zs1 (_,zs) = zs;
"
The following Lambda expression
"\(ys,_)->ys"
is transformed to
"ys1 (ys,_) = ys;
"

----------------------------------------

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
group :: Eq a => [a]  ->  [[a]];
group = groupBy (==);

groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
groupBy _ [] = [];
groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
vv10 = span (eq x) xs;
ys = ys1 vv10;
ys1 (ys,_) = ys;
zs = zs1 vv10;
zs1 (_,zs) = zs;
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(3) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.

Binding Reductions:
The bind variable of the following binding Pattern
"xs@(vx : vy)"
is replaced by the following term
"vx : vy"

----------------------------------------

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
group :: Eq a => [a]  ->  [[a]];
group = groupBy (==);

groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
groupBy ww [] = [];
groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
vv10 = span (eq x) xs;
ys = ys1 vv10;
ys1 (ys,wx) = ys;
zs = zs1 vv10;
zs1 (wy,zs) = zs;
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"span p [] = ([],[]);
span p (vx : vy)|p vx(vx : ys,zs)|otherwise([],vx : vy) where {
vu43  = span p vy;
;
ys  = ys0 vu43;
;
ys0 (ys,wu) = ys;
;
zs  = zs0 vu43;
;
zs0 (vz,zs) = zs;
} 
;
"
is transformed to
"span p [] = span3 p [];
span p (vx : vy) = span2 p (vx : vy);
"
"span2 p (vx : vy) = span1 p vx vy (p vx) where {
span0 p vx vy True = ([],vx : vy);
;
span1 p vx vy True = (vx : ys,zs);
span1 p vx vy False = span0 p vx vy otherwise;
;
vu43  = span p vy;
;
ys  = ys0 vu43;
;
ys0 (ys,wu) = ys;
;
zs  = zs0 vu43;
;
zs0 (vz,zs) = zs;
} 
;
"
"span3 p [] = ([],[]);
span3 xv xw = span2 xv xw;
"

----------------------------------------

(6)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
group :: Eq a => [a]  ->  [[a]];
group = groupBy (==);

groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
groupBy ww [] = [];
groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { 
vv10 = span (eq x) xs;
ys = ys1 vv10;
ys1 (ys,wx) = ys;
zs = zs1 vv10;
zs1 (wy,zs) = zs;
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(7) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"span1 p vx vy (p vx) where {
span0 p vx vy True = ([],vx : vy);
;
span1 p vx vy True = (vx : ys,zs);
span1 p vx vy False = span0 p vx vy otherwise;
;
vu43  = span p vy;
;
ys  = ys0 vu43;
;
ys0 (ys,wu) = ys;
;
zs  = zs0 vu43;
;
zs0 (vz,zs) = zs;
} 
"
are unpacked to the following functions on top level
"span2Vu43 xx xy = span xx xy;
"
"span2Zs xx xy = span2Zs0 xx xy (span2Vu43 xx xy);
"
"span2Zs0 xx xy (vz,zs) = zs;
"
"span2Span1 xx xy p vx vy True = (vx : span2Ys xx xy,span2Zs xx xy);
span2Span1 xx xy p vx vy False = span2Span0 xx xy p vx vy otherwise;
"
"span2Ys xx xy = span2Ys0 xx xy (span2Vu43 xx xy);
"
"span2Ys0 xx xy (ys,wu) = ys;
"
"span2Span0 xx xy p vx vy True = ([],vx : vy);
"
The bindings of the following Let/Where expression
"(x : ys) : groupBy eq zs where {
vv10  = span (eq x) xs;
;
ys  = ys1 vv10;
;
ys1 (ys,wx) = ys;
;
zs  = zs1 vv10;
;
zs1 (wy,zs) = zs;
} 
"
are unpacked to the following functions on top level
"groupByYs xz yu yv = groupByYs1 xz yu yv (groupByVv10 xz yu yv);
"
"groupByZs1 xz yu yv (wy,zs) = zs;
"
"groupByZs xz yu yv = groupByZs1 xz yu yv (groupByVv10 xz yu yv);
"
"groupByYs1 xz yu yv (ys,wx) = ys;
"
"groupByVv10 xz yu yv = span (xz yu) yv;
"

----------------------------------------

(8)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
group :: Eq a => [a]  ->  [[a]];
group = groupBy (==);

groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]];
groupBy ww [] = [];
groupBy eq (x : xs) = (x : groupByYs eq x xs) : groupBy eq (groupByZs eq x xs);

groupByVv10 xz yu yv = span (xz yu) yv;

groupByYs xz yu yv = groupByYs1 xz yu yv (groupByVv10 xz yu yv);

groupByYs1 xz yu yv (ys,wx) = ys;

groupByZs xz yu yv = groupByZs1 xz yu yv (groupByVv10 xz yu yv);

groupByZs1 xz yu yv (wy,zs) = zs;

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(9) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="List.group",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="List.group yw3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="List.groupBy (==) yw3",fontsize=16,color="burlywood",shape="triangle"];315[label="yw3/yw30 : yw31",fontsize=10,color="white",style="solid",shape="box"];4 -> 315[label="",style="solid", color="burlywood", weight=9];
315 -> 5[label="",style="solid", color="burlywood", weight=3];
316[label="yw3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 316[label="",style="solid", color="burlywood", weight=9];
316 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="List.groupBy (==) (yw30 : yw31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="List.groupBy (==) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="(yw30 : List.groupByYs (==) yw30 yw31) : List.groupBy (==) (List.groupByZs (==) yw30 yw31)",fontsize=16,color="green",shape="box"];7 -> 9[label="",style="dashed", color="green", weight=3];
7 -> 10[label="",style="dashed", color="green", weight=3];
8[label="[]",fontsize=16,color="green",shape="box"];9[label="List.groupByYs (==) yw30 yw31",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10 -> 4[label="",style="dashed", color="red", weight=0];
10[label="List.groupBy (==) (List.groupByZs (==) yw30 yw31)",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3];
11[label="List.groupByYs1 (==) yw30 yw31 (List.groupByVv10 (==) yw30 yw31)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="List.groupByZs (==) yw30 yw31",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="List.groupByYs1 (==) yw30 yw31 (span ((==) yw30) yw31)",fontsize=16,color="burlywood",shape="box"];317[label="yw31/yw310 : yw311",fontsize=10,color="white",style="solid",shape="box"];13 -> 317[label="",style="solid", color="burlywood", weight=9];
317 -> 15[label="",style="solid", color="burlywood", weight=3];
318[label="yw31/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 318[label="",style="solid", color="burlywood", weight=9];
318 -> 16[label="",style="solid", color="burlywood", weight=3];
14[label="List.groupByZs1 (==) yw30 yw31 (List.groupByVv10 (==) yw30 yw31)",fontsize=16,color="black",shape="box"];14 -> 17[label="",style="solid", color="black", weight=3];
15[label="List.groupByYs1 (==) yw30 (yw310 : yw311) (span ((==) yw30) (yw310 : yw311))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
16[label="List.groupByYs1 (==) yw30 [] (span ((==) yw30) [])",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
17[label="List.groupByZs1 (==) yw30 yw31 (span ((==) yw30) yw31)",fontsize=16,color="burlywood",shape="box"];319[label="yw31/yw310 : yw311",fontsize=10,color="white",style="solid",shape="box"];17 -> 319[label="",style="solid", color="burlywood", weight=9];
319 -> 20[label="",style="solid", color="burlywood", weight=3];
320[label="yw31/[]",fontsize=10,color="white",style="solid",shape="box"];17 -> 320[label="",style="solid", color="burlywood", weight=9];
320 -> 21[label="",style="solid", color="burlywood", weight=3];
18[label="List.groupByYs1 (==) yw30 (yw310 : yw311) (span2 ((==) yw30) (yw310 : yw311))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="List.groupByYs1 (==) yw30 [] (span3 ((==) yw30) [])",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="List.groupByZs1 (==) yw30 (yw310 : yw311) (span ((==) yw30) (yw310 : yw311))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="List.groupByZs1 (==) yw30 [] (span ((==) yw30) [])",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="List.groupByYs1 (==) yw30 (yw310 : yw311) (span2Span1 ((==) yw30) yw311 ((==) yw30) yw310 yw311 ((==) yw30 yw310))",fontsize=16,color="burlywood",shape="box"];321[label="yw30/LT",fontsize=10,color="white",style="solid",shape="box"];22 -> 321[label="",style="solid", color="burlywood", weight=9];
321 -> 26[label="",style="solid", color="burlywood", weight=3];
322[label="yw30/EQ",fontsize=10,color="white",style="solid",shape="box"];22 -> 322[label="",style="solid", color="burlywood", weight=9];
322 -> 27[label="",style="solid", color="burlywood", weight=3];
323[label="yw30/GT",fontsize=10,color="white",style="solid",shape="box"];22 -> 323[label="",style="solid", color="burlywood", weight=9];
323 -> 28[label="",style="solid", color="burlywood", weight=3];
23[label="List.groupByYs1 (==) yw30 [] ([],[])",fontsize=16,color="black",shape="box"];23 -> 29[label="",style="solid", color="black", weight=3];
24[label="List.groupByZs1 (==) yw30 (yw310 : yw311) (span2 ((==) yw30) (yw310 : yw311))",fontsize=16,color="black",shape="box"];24 -> 30[label="",style="solid", color="black", weight=3];
25[label="List.groupByZs1 (==) yw30 [] (span3 ((==) yw30) [])",fontsize=16,color="black",shape="box"];25 -> 31[label="",style="solid", color="black", weight=3];
26[label="List.groupByYs1 (==) LT (yw310 : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) yw310 yw311 ((==) LT yw310))",fontsize=16,color="burlywood",shape="box"];324[label="yw310/LT",fontsize=10,color="white",style="solid",shape="box"];26 -> 324[label="",style="solid", color="burlywood", weight=9];
324 -> 32[label="",style="solid", color="burlywood", weight=3];
325[label="yw310/EQ",fontsize=10,color="white",style="solid",shape="box"];26 -> 325[label="",style="solid", color="burlywood", weight=9];
325 -> 33[label="",style="solid", color="burlywood", weight=3];
326[label="yw310/GT",fontsize=10,color="white",style="solid",shape="box"];26 -> 326[label="",style="solid", color="burlywood", weight=9];
326 -> 34[label="",style="solid", color="burlywood", weight=3];
27[label="List.groupByYs1 (==) EQ (yw310 : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) yw310 yw311 ((==) EQ yw310))",fontsize=16,color="burlywood",shape="box"];327[label="yw310/LT",fontsize=10,color="white",style="solid",shape="box"];27 -> 327[label="",style="solid", color="burlywood", weight=9];
327 -> 35[label="",style="solid", color="burlywood", weight=3];
328[label="yw310/EQ",fontsize=10,color="white",style="solid",shape="box"];27 -> 328[label="",style="solid", color="burlywood", weight=9];
328 -> 36[label="",style="solid", color="burlywood", weight=3];
329[label="yw310/GT",fontsize=10,color="white",style="solid",shape="box"];27 -> 329[label="",style="solid", color="burlywood", weight=9];
329 -> 37[label="",style="solid", color="burlywood", weight=3];
28[label="List.groupByYs1 (==) GT (yw310 : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) yw310 yw311 ((==) GT yw310))",fontsize=16,color="burlywood",shape="box"];330[label="yw310/LT",fontsize=10,color="white",style="solid",shape="box"];28 -> 330[label="",style="solid", color="burlywood", weight=9];
330 -> 38[label="",style="solid", color="burlywood", weight=3];
331[label="yw310/EQ",fontsize=10,color="white",style="solid",shape="box"];28 -> 331[label="",style="solid", color="burlywood", weight=9];
331 -> 39[label="",style="solid", color="burlywood", weight=3];
332[label="yw310/GT",fontsize=10,color="white",style="solid",shape="box"];28 -> 332[label="",style="solid", color="burlywood", weight=9];
332 -> 40[label="",style="solid", color="burlywood", weight=3];
29[label="[]",fontsize=16,color="green",shape="box"];30[label="List.groupByZs1 (==) yw30 (yw310 : yw311) (span2Span1 ((==) yw30) yw311 ((==) yw30) yw310 yw311 ((==) yw30 yw310))",fontsize=16,color="burlywood",shape="box"];333[label="yw30/LT",fontsize=10,color="white",style="solid",shape="box"];30 -> 333[label="",style="solid", color="burlywood", weight=9];
333 -> 41[label="",style="solid", color="burlywood", weight=3];
334[label="yw30/EQ",fontsize=10,color="white",style="solid",shape="box"];30 -> 334[label="",style="solid", color="burlywood", weight=9];
334 -> 42[label="",style="solid", color="burlywood", weight=3];
335[label="yw30/GT",fontsize=10,color="white",style="solid",shape="box"];30 -> 335[label="",style="solid", color="burlywood", weight=9];
335 -> 43[label="",style="solid", color="burlywood", weight=3];
31[label="List.groupByZs1 (==) yw30 [] ([],[])",fontsize=16,color="black",shape="box"];31 -> 44[label="",style="solid", color="black", weight=3];
32[label="List.groupByYs1 (==) LT (LT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) LT yw311 ((==) LT LT))",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3];
33[label="List.groupByYs1 (==) LT (EQ : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) EQ yw311 ((==) LT EQ))",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3];
34[label="List.groupByYs1 (==) LT (GT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) GT yw311 ((==) LT GT))",fontsize=16,color="black",shape="box"];34 -> 47[label="",style="solid", color="black", weight=3];
35[label="List.groupByYs1 (==) EQ (LT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) LT yw311 ((==) EQ LT))",fontsize=16,color="black",shape="box"];35 -> 48[label="",style="solid", color="black", weight=3];
36[label="List.groupByYs1 (==) EQ (EQ : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) EQ yw311 ((==) EQ EQ))",fontsize=16,color="black",shape="box"];36 -> 49[label="",style="solid", color="black", weight=3];
37[label="List.groupByYs1 (==) EQ (GT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) GT yw311 ((==) EQ GT))",fontsize=16,color="black",shape="box"];37 -> 50[label="",style="solid", color="black", weight=3];
38[label="List.groupByYs1 (==) GT (LT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) LT yw311 ((==) GT LT))",fontsize=16,color="black",shape="box"];38 -> 51[label="",style="solid", color="black", weight=3];
39[label="List.groupByYs1 (==) GT (EQ : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) EQ yw311 ((==) GT EQ))",fontsize=16,color="black",shape="box"];39 -> 52[label="",style="solid", color="black", weight=3];
40[label="List.groupByYs1 (==) GT (GT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) GT yw311 ((==) GT GT))",fontsize=16,color="black",shape="box"];40 -> 53[label="",style="solid", color="black", weight=3];
41[label="List.groupByZs1 (==) LT (yw310 : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) yw310 yw311 ((==) LT yw310))",fontsize=16,color="burlywood",shape="box"];336[label="yw310/LT",fontsize=10,color="white",style="solid",shape="box"];41 -> 336[label="",style="solid", color="burlywood", weight=9];
336 -> 54[label="",style="solid", color="burlywood", weight=3];
337[label="yw310/EQ",fontsize=10,color="white",style="solid",shape="box"];41 -> 337[label="",style="solid", color="burlywood", weight=9];
337 -> 55[label="",style="solid", color="burlywood", weight=3];
338[label="yw310/GT",fontsize=10,color="white",style="solid",shape="box"];41 -> 338[label="",style="solid", color="burlywood", weight=9];
338 -> 56[label="",style="solid", color="burlywood", weight=3];
42[label="List.groupByZs1 (==) EQ (yw310 : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) yw310 yw311 ((==) EQ yw310))",fontsize=16,color="burlywood",shape="box"];339[label="yw310/LT",fontsize=10,color="white",style="solid",shape="box"];42 -> 339[label="",style="solid", color="burlywood", weight=9];
339 -> 57[label="",style="solid", color="burlywood", weight=3];
340[label="yw310/EQ",fontsize=10,color="white",style="solid",shape="box"];42 -> 340[label="",style="solid", color="burlywood", weight=9];
340 -> 58[label="",style="solid", color="burlywood", weight=3];
341[label="yw310/GT",fontsize=10,color="white",style="solid",shape="box"];42 -> 341[label="",style="solid", color="burlywood", weight=9];
341 -> 59[label="",style="solid", color="burlywood", weight=3];
43[label="List.groupByZs1 (==) GT (yw310 : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) yw310 yw311 ((==) GT yw310))",fontsize=16,color="burlywood",shape="box"];342[label="yw310/LT",fontsize=10,color="white",style="solid",shape="box"];43 -> 342[label="",style="solid", color="burlywood", weight=9];
342 -> 60[label="",style="solid", color="burlywood", weight=3];
343[label="yw310/EQ",fontsize=10,color="white",style="solid",shape="box"];43 -> 343[label="",style="solid", color="burlywood", weight=9];
343 -> 61[label="",style="solid", color="burlywood", weight=3];
344[label="yw310/GT",fontsize=10,color="white",style="solid",shape="box"];43 -> 344[label="",style="solid", color="burlywood", weight=9];
344 -> 62[label="",style="solid", color="burlywood", weight=3];
44[label="[]",fontsize=16,color="green",shape="box"];45[label="List.groupByYs1 (==) LT (LT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) LT yw311 True)",fontsize=16,color="black",shape="box"];45 -> 63[label="",style="solid", color="black", weight=3];
46[label="List.groupByYs1 (==) LT (EQ : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) EQ yw311 False)",fontsize=16,color="black",shape="box"];46 -> 64[label="",style="solid", color="black", weight=3];
47[label="List.groupByYs1 (==) LT (GT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) GT yw311 False)",fontsize=16,color="black",shape="box"];47 -> 65[label="",style="solid", color="black", weight=3];
48[label="List.groupByYs1 (==) EQ (LT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) LT yw311 False)",fontsize=16,color="black",shape="box"];48 -> 66[label="",style="solid", color="black", weight=3];
49[label="List.groupByYs1 (==) EQ (EQ : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) EQ yw311 True)",fontsize=16,color="black",shape="box"];49 -> 67[label="",style="solid", color="black", weight=3];
50[label="List.groupByYs1 (==) EQ (GT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) GT yw311 False)",fontsize=16,color="black",shape="box"];50 -> 68[label="",style="solid", color="black", weight=3];
51[label="List.groupByYs1 (==) GT (LT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) LT yw311 False)",fontsize=16,color="black",shape="box"];51 -> 69[label="",style="solid", color="black", weight=3];
52[label="List.groupByYs1 (==) GT (EQ : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) EQ yw311 False)",fontsize=16,color="black",shape="box"];52 -> 70[label="",style="solid", color="black", weight=3];
53[label="List.groupByYs1 (==) GT (GT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) GT yw311 True)",fontsize=16,color="black",shape="box"];53 -> 71[label="",style="solid", color="black", weight=3];
54[label="List.groupByZs1 (==) LT (LT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) LT yw311 ((==) LT LT))",fontsize=16,color="black",shape="box"];54 -> 72[label="",style="solid", color="black", weight=3];
55[label="List.groupByZs1 (==) LT (EQ : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) EQ yw311 ((==) LT EQ))",fontsize=16,color="black",shape="box"];55 -> 73[label="",style="solid", color="black", weight=3];
56[label="List.groupByZs1 (==) LT (GT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) GT yw311 ((==) LT GT))",fontsize=16,color="black",shape="box"];56 -> 74[label="",style="solid", color="black", weight=3];
57[label="List.groupByZs1 (==) EQ (LT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) LT yw311 ((==) EQ LT))",fontsize=16,color="black",shape="box"];57 -> 75[label="",style="solid", color="black", weight=3];
58[label="List.groupByZs1 (==) EQ (EQ : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) EQ yw311 ((==) EQ EQ))",fontsize=16,color="black",shape="box"];58 -> 76[label="",style="solid", color="black", weight=3];
59[label="List.groupByZs1 (==) EQ (GT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) GT yw311 ((==) EQ GT))",fontsize=16,color="black",shape="box"];59 -> 77[label="",style="solid", color="black", weight=3];
60[label="List.groupByZs1 (==) GT (LT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) LT yw311 ((==) GT LT))",fontsize=16,color="black",shape="box"];60 -> 78[label="",style="solid", color="black", weight=3];
61[label="List.groupByZs1 (==) GT (EQ : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) EQ yw311 ((==) GT EQ))",fontsize=16,color="black",shape="box"];61 -> 79[label="",style="solid", color="black", weight=3];
62[label="List.groupByZs1 (==) GT (GT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) GT yw311 ((==) GT GT))",fontsize=16,color="black",shape="box"];62 -> 80[label="",style="solid", color="black", weight=3];
63[label="List.groupByYs1 (==) LT (LT : yw311) (LT : span2Ys ((==) LT) yw311,span2Zs ((==) LT) yw311)",fontsize=16,color="black",shape="box"];63 -> 81[label="",style="solid", color="black", weight=3];
64[label="List.groupByYs1 (==) LT (EQ : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) EQ yw311 otherwise)",fontsize=16,color="black",shape="box"];64 -> 82[label="",style="solid", color="black", weight=3];
65[label="List.groupByYs1 (==) LT (GT : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) GT yw311 otherwise)",fontsize=16,color="black",shape="box"];65 -> 83[label="",style="solid", color="black", weight=3];
66[label="List.groupByYs1 (==) EQ (LT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) LT yw311 otherwise)",fontsize=16,color="black",shape="box"];66 -> 84[label="",style="solid", color="black", weight=3];
67[label="List.groupByYs1 (==) EQ (EQ : yw311) (EQ : span2Ys ((==) EQ) yw311,span2Zs ((==) EQ) yw311)",fontsize=16,color="black",shape="box"];67 -> 85[label="",style="solid", color="black", weight=3];
68[label="List.groupByYs1 (==) EQ (GT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) GT yw311 otherwise)",fontsize=16,color="black",shape="box"];68 -> 86[label="",style="solid", color="black", weight=3];
69[label="List.groupByYs1 (==) GT (LT : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) LT yw311 otherwise)",fontsize=16,color="black",shape="box"];69 -> 87[label="",style="solid", color="black", weight=3];
70[label="List.groupByYs1 (==) GT (EQ : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) EQ yw311 otherwise)",fontsize=16,color="black",shape="box"];70 -> 88[label="",style="solid", color="black", weight=3];
71[label="List.groupByYs1 (==) GT (GT : yw311) (GT : span2Ys ((==) GT) yw311,span2Zs ((==) GT) yw311)",fontsize=16,color="black",shape="box"];71 -> 89[label="",style="solid", color="black", weight=3];
72[label="List.groupByZs1 (==) LT (LT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) LT yw311 True)",fontsize=16,color="black",shape="box"];72 -> 90[label="",style="solid", color="black", weight=3];
73[label="List.groupByZs1 (==) LT (EQ : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) EQ yw311 False)",fontsize=16,color="black",shape="box"];73 -> 91[label="",style="solid", color="black", weight=3];
74[label="List.groupByZs1 (==) LT (GT : yw311) (span2Span1 ((==) LT) yw311 ((==) LT) GT yw311 False)",fontsize=16,color="black",shape="box"];74 -> 92[label="",style="solid", color="black", weight=3];
75[label="List.groupByZs1 (==) EQ (LT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) LT yw311 False)",fontsize=16,color="black",shape="box"];75 -> 93[label="",style="solid", color="black", weight=3];
76[label="List.groupByZs1 (==) EQ (EQ : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) EQ yw311 True)",fontsize=16,color="black",shape="box"];76 -> 94[label="",style="solid", color="black", weight=3];
77[label="List.groupByZs1 (==) EQ (GT : yw311) (span2Span1 ((==) EQ) yw311 ((==) EQ) GT yw311 False)",fontsize=16,color="black",shape="box"];77 -> 95[label="",style="solid", color="black", weight=3];
78[label="List.groupByZs1 (==) GT (LT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) LT yw311 False)",fontsize=16,color="black",shape="box"];78 -> 96[label="",style="solid", color="black", weight=3];
79[label="List.groupByZs1 (==) GT (EQ : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) EQ yw311 False)",fontsize=16,color="black",shape="box"];79 -> 97[label="",style="solid", color="black", weight=3];
80[label="List.groupByZs1 (==) GT (GT : yw311) (span2Span1 ((==) GT) yw311 ((==) GT) GT yw311 True)",fontsize=16,color="black",shape="box"];80 -> 98[label="",style="solid", color="black", weight=3];
81[label="LT : span2Ys ((==) LT) yw311",fontsize=16,color="green",shape="box"];81 -> 99[label="",style="dashed", color="green", weight=3];
82[label="List.groupByYs1 (==) LT (EQ : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) EQ yw311 True)",fontsize=16,color="black",shape="box"];82 -> 100[label="",style="solid", color="black", weight=3];
83[label="List.groupByYs1 (==) LT (GT : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) GT yw311 True)",fontsize=16,color="black",shape="box"];83 -> 101[label="",style="solid", color="black", weight=3];
84[label="List.groupByYs1 (==) EQ (LT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) LT yw311 True)",fontsize=16,color="black",shape="box"];84 -> 102[label="",style="solid", color="black", weight=3];
85[label="EQ : span2Ys ((==) EQ) yw311",fontsize=16,color="green",shape="box"];85 -> 103[label="",style="dashed", color="green", weight=3];
86[label="List.groupByYs1 (==) EQ (GT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) GT yw311 True)",fontsize=16,color="black",shape="box"];86 -> 104[label="",style="solid", color="black", weight=3];
87[label="List.groupByYs1 (==) GT (LT : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) LT yw311 True)",fontsize=16,color="black",shape="box"];87 -> 105[label="",style="solid", color="black", weight=3];
88[label="List.groupByYs1 (==) GT (EQ : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) EQ yw311 True)",fontsize=16,color="black",shape="box"];88 -> 106[label="",style="solid", color="black", weight=3];
89[label="GT : span2Ys ((==) GT) yw311",fontsize=16,color="green",shape="box"];89 -> 107[label="",style="dashed", color="green", weight=3];
90[label="List.groupByZs1 (==) LT (LT : yw311) (LT : span2Ys ((==) LT) yw311,span2Zs ((==) LT) yw311)",fontsize=16,color="black",shape="box"];90 -> 108[label="",style="solid", color="black", weight=3];
91[label="List.groupByZs1 (==) LT (EQ : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) EQ yw311 otherwise)",fontsize=16,color="black",shape="box"];91 -> 109[label="",style="solid", color="black", weight=3];
92[label="List.groupByZs1 (==) LT (GT : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) GT yw311 otherwise)",fontsize=16,color="black",shape="box"];92 -> 110[label="",style="solid", color="black", weight=3];
93[label="List.groupByZs1 (==) EQ (LT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) LT yw311 otherwise)",fontsize=16,color="black",shape="box"];93 -> 111[label="",style="solid", color="black", weight=3];
94[label="List.groupByZs1 (==) EQ (EQ : yw311) (EQ : span2Ys ((==) EQ) yw311,span2Zs ((==) EQ) yw311)",fontsize=16,color="black",shape="box"];94 -> 112[label="",style="solid", color="black", weight=3];
95[label="List.groupByZs1 (==) EQ (GT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) GT yw311 otherwise)",fontsize=16,color="black",shape="box"];95 -> 113[label="",style="solid", color="black", weight=3];
96[label="List.groupByZs1 (==) GT (LT : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) LT yw311 otherwise)",fontsize=16,color="black",shape="box"];96 -> 114[label="",style="solid", color="black", weight=3];
97[label="List.groupByZs1 (==) GT (EQ : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) EQ yw311 otherwise)",fontsize=16,color="black",shape="box"];97 -> 115[label="",style="solid", color="black", weight=3];
98[label="List.groupByZs1 (==) GT (GT : yw311) (GT : span2Ys ((==) GT) yw311,span2Zs ((==) GT) yw311)",fontsize=16,color="black",shape="box"];98 -> 116[label="",style="solid", color="black", weight=3];
99[label="span2Ys ((==) LT) yw311",fontsize=16,color="black",shape="triangle"];99 -> 117[label="",style="solid", color="black", weight=3];
100[label="List.groupByYs1 (==) LT (EQ : yw311) ([],EQ : yw311)",fontsize=16,color="black",shape="box"];100 -> 118[label="",style="solid", color="black", weight=3];
101[label="List.groupByYs1 (==) LT (GT : yw311) ([],GT : yw311)",fontsize=16,color="black",shape="box"];101 -> 119[label="",style="solid", color="black", weight=3];
102[label="List.groupByYs1 (==) EQ (LT : yw311) ([],LT : yw311)",fontsize=16,color="black",shape="box"];102 -> 120[label="",style="solid", color="black", weight=3];
103[label="span2Ys ((==) EQ) yw311",fontsize=16,color="black",shape="triangle"];103 -> 121[label="",style="solid", color="black", weight=3];
104[label="List.groupByYs1 (==) EQ (GT : yw311) ([],GT : yw311)",fontsize=16,color="black",shape="box"];104 -> 122[label="",style="solid", color="black", weight=3];
105[label="List.groupByYs1 (==) GT (LT : yw311) ([],LT : yw311)",fontsize=16,color="black",shape="box"];105 -> 123[label="",style="solid", color="black", weight=3];
106[label="List.groupByYs1 (==) GT (EQ : yw311) ([],EQ : yw311)",fontsize=16,color="black",shape="box"];106 -> 124[label="",style="solid", color="black", weight=3];
107[label="span2Ys ((==) GT) yw311",fontsize=16,color="black",shape="triangle"];107 -> 125[label="",style="solid", color="black", weight=3];
108[label="span2Zs ((==) LT) yw311",fontsize=16,color="black",shape="triangle"];108 -> 126[label="",style="solid", color="black", weight=3];
109[label="List.groupByZs1 (==) LT (EQ : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) EQ yw311 True)",fontsize=16,color="black",shape="box"];109 -> 127[label="",style="solid", color="black", weight=3];
110[label="List.groupByZs1 (==) LT (GT : yw311) (span2Span0 ((==) LT) yw311 ((==) LT) GT yw311 True)",fontsize=16,color="black",shape="box"];110 -> 128[label="",style="solid", color="black", weight=3];
111[label="List.groupByZs1 (==) EQ (LT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) LT yw311 True)",fontsize=16,color="black",shape="box"];111 -> 129[label="",style="solid", color="black", weight=3];
112[label="span2Zs ((==) EQ) yw311",fontsize=16,color="black",shape="triangle"];112 -> 130[label="",style="solid", color="black", weight=3];
113[label="List.groupByZs1 (==) EQ (GT : yw311) (span2Span0 ((==) EQ) yw311 ((==) EQ) GT yw311 True)",fontsize=16,color="black",shape="box"];113 -> 131[label="",style="solid", color="black", weight=3];
114[label="List.groupByZs1 (==) GT (LT : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) LT yw311 True)",fontsize=16,color="black",shape="box"];114 -> 132[label="",style="solid", color="black", weight=3];
115[label="List.groupByZs1 (==) GT (EQ : yw311) (span2Span0 ((==) GT) yw311 ((==) GT) EQ yw311 True)",fontsize=16,color="black",shape="box"];115 -> 133[label="",style="solid", color="black", weight=3];
116[label="span2Zs ((==) GT) yw311",fontsize=16,color="black",shape="triangle"];116 -> 134[label="",style="solid", color="black", weight=3];
117[label="span2Ys0 ((==) LT) yw311 (span2Vu43 ((==) LT) yw311)",fontsize=16,color="black",shape="box"];117 -> 135[label="",style="solid", color="black", weight=3];
118[label="[]",fontsize=16,color="green",shape="box"];119[label="[]",fontsize=16,color="green",shape="box"];120[label="[]",fontsize=16,color="green",shape="box"];121[label="span2Ys0 ((==) EQ) yw311 (span2Vu43 ((==) EQ) yw311)",fontsize=16,color="black",shape="box"];121 -> 136[label="",style="solid", color="black", weight=3];
122[label="[]",fontsize=16,color="green",shape="box"];123[label="[]",fontsize=16,color="green",shape="box"];124[label="[]",fontsize=16,color="green",shape="box"];125[label="span2Ys0 ((==) GT) yw311 (span2Vu43 ((==) GT) yw311)",fontsize=16,color="black",shape="box"];125 -> 137[label="",style="solid", color="black", weight=3];
126[label="span2Zs0 ((==) LT) yw311 (span2Vu43 ((==) LT) yw311)",fontsize=16,color="black",shape="box"];126 -> 138[label="",style="solid", color="black", weight=3];
127[label="List.groupByZs1 (==) LT (EQ : yw311) ([],EQ : yw311)",fontsize=16,color="black",shape="box"];127 -> 139[label="",style="solid", color="black", weight=3];
128[label="List.groupByZs1 (==) LT (GT : yw311) ([],GT : yw311)",fontsize=16,color="black",shape="box"];128 -> 140[label="",style="solid", color="black", weight=3];
129[label="List.groupByZs1 (==) EQ (LT : yw311) ([],LT : yw311)",fontsize=16,color="black",shape="box"];129 -> 141[label="",style="solid", color="black", weight=3];
130[label="span2Zs0 ((==) EQ) yw311 (span2Vu43 ((==) EQ) yw311)",fontsize=16,color="black",shape="box"];130 -> 142[label="",style="solid", color="black", weight=3];
131[label="List.groupByZs1 (==) EQ (GT : yw311) ([],GT : yw311)",fontsize=16,color="black",shape="box"];131 -> 143[label="",style="solid", color="black", weight=3];
132[label="List.groupByZs1 (==) GT (LT : yw311) ([],LT : yw311)",fontsize=16,color="black",shape="box"];132 -> 144[label="",style="solid", color="black", weight=3];
133[label="List.groupByZs1 (==) GT (EQ : yw311) ([],EQ : yw311)",fontsize=16,color="black",shape="box"];133 -> 145[label="",style="solid", color="black", weight=3];
134[label="span2Zs0 ((==) GT) yw311 (span2Vu43 ((==) GT) yw311)",fontsize=16,color="black",shape="box"];134 -> 146[label="",style="solid", color="black", weight=3];
135[label="span2Ys0 ((==) LT) yw311 (span ((==) LT) yw311)",fontsize=16,color="burlywood",shape="box"];345[label="yw311/yw3110 : yw3111",fontsize=10,color="white",style="solid",shape="box"];135 -> 345[label="",style="solid", color="burlywood", weight=9];
345 -> 147[label="",style="solid", color="burlywood", weight=3];
346[label="yw311/[]",fontsize=10,color="white",style="solid",shape="box"];135 -> 346[label="",style="solid", color="burlywood", weight=9];
346 -> 148[label="",style="solid", color="burlywood", weight=3];
136[label="span2Ys0 ((==) EQ) yw311 (span ((==) EQ) yw311)",fontsize=16,color="burlywood",shape="box"];347[label="yw311/yw3110 : yw3111",fontsize=10,color="white",style="solid",shape="box"];136 -> 347[label="",style="solid", color="burlywood", weight=9];
347 -> 149[label="",style="solid", color="burlywood", weight=3];
348[label="yw311/[]",fontsize=10,color="white",style="solid",shape="box"];136 -> 348[label="",style="solid", color="burlywood", weight=9];
348 -> 150[label="",style="solid", color="burlywood", weight=3];
137[label="span2Ys0 ((==) GT) yw311 (span ((==) GT) yw311)",fontsize=16,color="burlywood",shape="box"];349[label="yw311/yw3110 : yw3111",fontsize=10,color="white",style="solid",shape="box"];137 -> 349[label="",style="solid", color="burlywood", weight=9];
349 -> 151[label="",style="solid", color="burlywood", weight=3];
350[label="yw311/[]",fontsize=10,color="white",style="solid",shape="box"];137 -> 350[label="",style="solid", color="burlywood", weight=9];
350 -> 152[label="",style="solid", color="burlywood", weight=3];
138[label="span2Zs0 ((==) LT) yw311 (span ((==) LT) yw311)",fontsize=16,color="burlywood",shape="box"];351[label="yw311/yw3110 : yw3111",fontsize=10,color="white",style="solid",shape="box"];138 -> 351[label="",style="solid", color="burlywood", weight=9];
351 -> 153[label="",style="solid", color="burlywood", weight=3];
352[label="yw311/[]",fontsize=10,color="white",style="solid",shape="box"];138 -> 352[label="",style="solid", color="burlywood", weight=9];
352 -> 154[label="",style="solid", color="burlywood", weight=3];
139[label="EQ : yw311",fontsize=16,color="green",shape="box"];140[label="GT : yw311",fontsize=16,color="green",shape="box"];141[label="LT : yw311",fontsize=16,color="green",shape="box"];142[label="span2Zs0 ((==) EQ) yw311 (span ((==) EQ) yw311)",fontsize=16,color="burlywood",shape="box"];353[label="yw311/yw3110 : yw3111",fontsize=10,color="white",style="solid",shape="box"];142 -> 353[label="",style="solid", color="burlywood", weight=9];
353 -> 155[label="",style="solid", color="burlywood", weight=3];
354[label="yw311/[]",fontsize=10,color="white",style="solid",shape="box"];142 -> 354[label="",style="solid", color="burlywood", weight=9];
354 -> 156[label="",style="solid", color="burlywood", weight=3];
143[label="GT : yw311",fontsize=16,color="green",shape="box"];144[label="LT : yw311",fontsize=16,color="green",shape="box"];145[label="EQ : yw311",fontsize=16,color="green",shape="box"];146[label="span2Zs0 ((==) GT) yw311 (span ((==) GT) yw311)",fontsize=16,color="burlywood",shape="box"];355[label="yw311/yw3110 : yw3111",fontsize=10,color="white",style="solid",shape="box"];146 -> 355[label="",style="solid", color="burlywood", weight=9];
355 -> 157[label="",style="solid", color="burlywood", weight=3];
356[label="yw311/[]",fontsize=10,color="white",style="solid",shape="box"];146 -> 356[label="",style="solid", color="burlywood", weight=9];
356 -> 158[label="",style="solid", color="burlywood", weight=3];
147[label="span2Ys0 ((==) LT) (yw3110 : yw3111) (span ((==) LT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];147 -> 159[label="",style="solid", color="black", weight=3];
148[label="span2Ys0 ((==) LT) [] (span ((==) LT) [])",fontsize=16,color="black",shape="box"];148 -> 160[label="",style="solid", color="black", weight=3];
149[label="span2Ys0 ((==) EQ) (yw3110 : yw3111) (span ((==) EQ) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];149 -> 161[label="",style="solid", color="black", weight=3];
150[label="span2Ys0 ((==) EQ) [] (span ((==) EQ) [])",fontsize=16,color="black",shape="box"];150 -> 162[label="",style="solid", color="black", weight=3];
151[label="span2Ys0 ((==) GT) (yw3110 : yw3111) (span ((==) GT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];151 -> 163[label="",style="solid", color="black", weight=3];
152[label="span2Ys0 ((==) GT) [] (span ((==) GT) [])",fontsize=16,color="black",shape="box"];152 -> 164[label="",style="solid", color="black", weight=3];
153[label="span2Zs0 ((==) LT) (yw3110 : yw3111) (span ((==) LT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];153 -> 165[label="",style="solid", color="black", weight=3];
154[label="span2Zs0 ((==) LT) [] (span ((==) LT) [])",fontsize=16,color="black",shape="box"];154 -> 166[label="",style="solid", color="black", weight=3];
155[label="span2Zs0 ((==) EQ) (yw3110 : yw3111) (span ((==) EQ) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];155 -> 167[label="",style="solid", color="black", weight=3];
156[label="span2Zs0 ((==) EQ) [] (span ((==) EQ) [])",fontsize=16,color="black",shape="box"];156 -> 168[label="",style="solid", color="black", weight=3];
157[label="span2Zs0 ((==) GT) (yw3110 : yw3111) (span ((==) GT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];157 -> 169[label="",style="solid", color="black", weight=3];
158[label="span2Zs0 ((==) GT) [] (span ((==) GT) [])",fontsize=16,color="black",shape="box"];158 -> 170[label="",style="solid", color="black", weight=3];
159[label="span2Ys0 ((==) LT) (yw3110 : yw3111) (span2 ((==) LT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];159 -> 171[label="",style="solid", color="black", weight=3];
160[label="span2Ys0 ((==) LT) [] (span3 ((==) LT) [])",fontsize=16,color="black",shape="box"];160 -> 172[label="",style="solid", color="black", weight=3];
161[label="span2Ys0 ((==) EQ) (yw3110 : yw3111) (span2 ((==) EQ) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];161 -> 173[label="",style="solid", color="black", weight=3];
162[label="span2Ys0 ((==) EQ) [] (span3 ((==) EQ) [])",fontsize=16,color="black",shape="box"];162 -> 174[label="",style="solid", color="black", weight=3];
163[label="span2Ys0 ((==) GT) (yw3110 : yw3111) (span2 ((==) GT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];163 -> 175[label="",style="solid", color="black", weight=3];
164[label="span2Ys0 ((==) GT) [] (span3 ((==) GT) [])",fontsize=16,color="black",shape="box"];164 -> 176[label="",style="solid", color="black", weight=3];
165[label="span2Zs0 ((==) LT) (yw3110 : yw3111) (span2 ((==) LT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];165 -> 177[label="",style="solid", color="black", weight=3];
166[label="span2Zs0 ((==) LT) [] (span3 ((==) LT) [])",fontsize=16,color="black",shape="box"];166 -> 178[label="",style="solid", color="black", weight=3];
167[label="span2Zs0 ((==) EQ) (yw3110 : yw3111) (span2 ((==) EQ) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];167 -> 179[label="",style="solid", color="black", weight=3];
168[label="span2Zs0 ((==) EQ) [] (span3 ((==) EQ) [])",fontsize=16,color="black",shape="box"];168 -> 180[label="",style="solid", color="black", weight=3];
169[label="span2Zs0 ((==) GT) (yw3110 : yw3111) (span2 ((==) GT) (yw3110 : yw3111))",fontsize=16,color="black",shape="box"];169 -> 181[label="",style="solid", color="black", weight=3];
170[label="span2Zs0 ((==) GT) [] (span3 ((==) GT) [])",fontsize=16,color="black",shape="box"];170 -> 182[label="",style="solid", color="black", weight=3];
171[label="span2Ys0 ((==) LT) (yw3110 : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) yw3110 yw3111 ((==) LT yw3110))",fontsize=16,color="burlywood",shape="box"];357[label="yw3110/LT",fontsize=10,color="white",style="solid",shape="box"];171 -> 357[label="",style="solid", color="burlywood", weight=9];
357 -> 183[label="",style="solid", color="burlywood", weight=3];
358[label="yw3110/EQ",fontsize=10,color="white",style="solid",shape="box"];171 -> 358[label="",style="solid", color="burlywood", weight=9];
358 -> 184[label="",style="solid", color="burlywood", weight=3];
359[label="yw3110/GT",fontsize=10,color="white",style="solid",shape="box"];171 -> 359[label="",style="solid", color="burlywood", weight=9];
359 -> 185[label="",style="solid", color="burlywood", weight=3];
172[label="span2Ys0 ((==) LT) [] ([],[])",fontsize=16,color="black",shape="box"];172 -> 186[label="",style="solid", color="black", weight=3];
173[label="span2Ys0 ((==) EQ) (yw3110 : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) yw3110 yw3111 ((==) EQ yw3110))",fontsize=16,color="burlywood",shape="box"];360[label="yw3110/LT",fontsize=10,color="white",style="solid",shape="box"];173 -> 360[label="",style="solid", color="burlywood", weight=9];
360 -> 187[label="",style="solid", color="burlywood", weight=3];
361[label="yw3110/EQ",fontsize=10,color="white",style="solid",shape="box"];173 -> 361[label="",style="solid", color="burlywood", weight=9];
361 -> 188[label="",style="solid", color="burlywood", weight=3];
362[label="yw3110/GT",fontsize=10,color="white",style="solid",shape="box"];173 -> 362[label="",style="solid", color="burlywood", weight=9];
362 -> 189[label="",style="solid", color="burlywood", weight=3];
174[label="span2Ys0 ((==) EQ) [] ([],[])",fontsize=16,color="black",shape="box"];174 -> 190[label="",style="solid", color="black", weight=3];
175[label="span2Ys0 ((==) GT) (yw3110 : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) yw3110 yw3111 ((==) GT yw3110))",fontsize=16,color="burlywood",shape="box"];363[label="yw3110/LT",fontsize=10,color="white",style="solid",shape="box"];175 -> 363[label="",style="solid", color="burlywood", weight=9];
363 -> 191[label="",style="solid", color="burlywood", weight=3];
364[label="yw3110/EQ",fontsize=10,color="white",style="solid",shape="box"];175 -> 364[label="",style="solid", color="burlywood", weight=9];
364 -> 192[label="",style="solid", color="burlywood", weight=3];
365[label="yw3110/GT",fontsize=10,color="white",style="solid",shape="box"];175 -> 365[label="",style="solid", color="burlywood", weight=9];
365 -> 193[label="",style="solid", color="burlywood", weight=3];
176[label="span2Ys0 ((==) GT) [] ([],[])",fontsize=16,color="black",shape="box"];176 -> 194[label="",style="solid", color="black", weight=3];
177[label="span2Zs0 ((==) LT) (yw3110 : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) yw3110 yw3111 ((==) LT yw3110))",fontsize=16,color="burlywood",shape="box"];366[label="yw3110/LT",fontsize=10,color="white",style="solid",shape="box"];177 -> 366[label="",style="solid", color="burlywood", weight=9];
366 -> 195[label="",style="solid", color="burlywood", weight=3];
367[label="yw3110/EQ",fontsize=10,color="white",style="solid",shape="box"];177 -> 367[label="",style="solid", color="burlywood", weight=9];
367 -> 196[label="",style="solid", color="burlywood", weight=3];
368[label="yw3110/GT",fontsize=10,color="white",style="solid",shape="box"];177 -> 368[label="",style="solid", color="burlywood", weight=9];
368 -> 197[label="",style="solid", color="burlywood", weight=3];
178[label="span2Zs0 ((==) LT) [] ([],[])",fontsize=16,color="black",shape="box"];178 -> 198[label="",style="solid", color="black", weight=3];
179[label="span2Zs0 ((==) EQ) (yw3110 : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) yw3110 yw3111 ((==) EQ yw3110))",fontsize=16,color="burlywood",shape="box"];369[label="yw3110/LT",fontsize=10,color="white",style="solid",shape="box"];179 -> 369[label="",style="solid", color="burlywood", weight=9];
369 -> 199[label="",style="solid", color="burlywood", weight=3];
370[label="yw3110/EQ",fontsize=10,color="white",style="solid",shape="box"];179 -> 370[label="",style="solid", color="burlywood", weight=9];
370 -> 200[label="",style="solid", color="burlywood", weight=3];
371[label="yw3110/GT",fontsize=10,color="white",style="solid",shape="box"];179 -> 371[label="",style="solid", color="burlywood", weight=9];
371 -> 201[label="",style="solid", color="burlywood", weight=3];
180[label="span2Zs0 ((==) EQ) [] ([],[])",fontsize=16,color="black",shape="box"];180 -> 202[label="",style="solid", color="black", weight=3];
181[label="span2Zs0 ((==) GT) (yw3110 : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) yw3110 yw3111 ((==) GT yw3110))",fontsize=16,color="burlywood",shape="box"];372[label="yw3110/LT",fontsize=10,color="white",style="solid",shape="box"];181 -> 372[label="",style="solid", color="burlywood", weight=9];
372 -> 203[label="",style="solid", color="burlywood", weight=3];
373[label="yw3110/EQ",fontsize=10,color="white",style="solid",shape="box"];181 -> 373[label="",style="solid", color="burlywood", weight=9];
373 -> 204[label="",style="solid", color="burlywood", weight=3];
374[label="yw3110/GT",fontsize=10,color="white",style="solid",shape="box"];181 -> 374[label="",style="solid", color="burlywood", weight=9];
374 -> 205[label="",style="solid", color="burlywood", weight=3];
182[label="span2Zs0 ((==) GT) [] ([],[])",fontsize=16,color="black",shape="box"];182 -> 206[label="",style="solid", color="black", weight=3];
183[label="span2Ys0 ((==) LT) (LT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) LT yw3111 ((==) LT LT))",fontsize=16,color="black",shape="box"];183 -> 207[label="",style="solid", color="black", weight=3];
184[label="span2Ys0 ((==) LT) (EQ : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) EQ yw3111 ((==) LT EQ))",fontsize=16,color="black",shape="box"];184 -> 208[label="",style="solid", color="black", weight=3];
185[label="span2Ys0 ((==) LT) (GT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) GT yw3111 ((==) LT GT))",fontsize=16,color="black",shape="box"];185 -> 209[label="",style="solid", color="black", weight=3];
186[label="[]",fontsize=16,color="green",shape="box"];187[label="span2Ys0 ((==) EQ) (LT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) LT yw3111 ((==) EQ LT))",fontsize=16,color="black",shape="box"];187 -> 210[label="",style="solid", color="black", weight=3];
188[label="span2Ys0 ((==) EQ) (EQ : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) EQ yw3111 ((==) EQ EQ))",fontsize=16,color="black",shape="box"];188 -> 211[label="",style="solid", color="black", weight=3];
189[label="span2Ys0 ((==) EQ) (GT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) GT yw3111 ((==) EQ GT))",fontsize=16,color="black",shape="box"];189 -> 212[label="",style="solid", color="black", weight=3];
190[label="[]",fontsize=16,color="green",shape="box"];191[label="span2Ys0 ((==) GT) (LT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) LT yw3111 ((==) GT LT))",fontsize=16,color="black",shape="box"];191 -> 213[label="",style="solid", color="black", weight=3];
192[label="span2Ys0 ((==) GT) (EQ : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) EQ yw3111 ((==) GT EQ))",fontsize=16,color="black",shape="box"];192 -> 214[label="",style="solid", color="black", weight=3];
193[label="span2Ys0 ((==) GT) (GT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) GT yw3111 ((==) GT GT))",fontsize=16,color="black",shape="box"];193 -> 215[label="",style="solid", color="black", weight=3];
194[label="[]",fontsize=16,color="green",shape="box"];195[label="span2Zs0 ((==) LT) (LT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) LT yw3111 ((==) LT LT))",fontsize=16,color="black",shape="box"];195 -> 216[label="",style="solid", color="black", weight=3];
196[label="span2Zs0 ((==) LT) (EQ : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) EQ yw3111 ((==) LT EQ))",fontsize=16,color="black",shape="box"];196 -> 217[label="",style="solid", color="black", weight=3];
197[label="span2Zs0 ((==) LT) (GT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) GT yw3111 ((==) LT GT))",fontsize=16,color="black",shape="box"];197 -> 218[label="",style="solid", color="black", weight=3];
198[label="[]",fontsize=16,color="green",shape="box"];199[label="span2Zs0 ((==) EQ) (LT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) LT yw3111 ((==) EQ LT))",fontsize=16,color="black",shape="box"];199 -> 219[label="",style="solid", color="black", weight=3];
200[label="span2Zs0 ((==) EQ) (EQ : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) EQ yw3111 ((==) EQ EQ))",fontsize=16,color="black",shape="box"];200 -> 220[label="",style="solid", color="black", weight=3];
201[label="span2Zs0 ((==) EQ) (GT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) GT yw3111 ((==) EQ GT))",fontsize=16,color="black",shape="box"];201 -> 221[label="",style="solid", color="black", weight=3];
202[label="[]",fontsize=16,color="green",shape="box"];203[label="span2Zs0 ((==) GT) (LT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) LT yw3111 ((==) GT LT))",fontsize=16,color="black",shape="box"];203 -> 222[label="",style="solid", color="black", weight=3];
204[label="span2Zs0 ((==) GT) (EQ : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) EQ yw3111 ((==) GT EQ))",fontsize=16,color="black",shape="box"];204 -> 223[label="",style="solid", color="black", weight=3];
205[label="span2Zs0 ((==) GT) (GT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) GT yw3111 ((==) GT GT))",fontsize=16,color="black",shape="box"];205 -> 224[label="",style="solid", color="black", weight=3];
206[label="[]",fontsize=16,color="green",shape="box"];207[label="span2Ys0 ((==) LT) (LT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) LT yw3111 True)",fontsize=16,color="black",shape="box"];207 -> 225[label="",style="solid", color="black", weight=3];
208[label="span2Ys0 ((==) LT) (EQ : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) EQ yw3111 False)",fontsize=16,color="black",shape="box"];208 -> 226[label="",style="solid", color="black", weight=3];
209[label="span2Ys0 ((==) LT) (GT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) GT yw3111 False)",fontsize=16,color="black",shape="box"];209 -> 227[label="",style="solid", color="black", weight=3];
210[label="span2Ys0 ((==) EQ) (LT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) LT yw3111 False)",fontsize=16,color="black",shape="box"];210 -> 228[label="",style="solid", color="black", weight=3];
211[label="span2Ys0 ((==) EQ) (EQ : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) EQ yw3111 True)",fontsize=16,color="black",shape="box"];211 -> 229[label="",style="solid", color="black", weight=3];
212[label="span2Ys0 ((==) EQ) (GT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) GT yw3111 False)",fontsize=16,color="black",shape="box"];212 -> 230[label="",style="solid", color="black", weight=3];
213[label="span2Ys0 ((==) GT) (LT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) LT yw3111 False)",fontsize=16,color="black",shape="box"];213 -> 231[label="",style="solid", color="black", weight=3];
214[label="span2Ys0 ((==) GT) (EQ : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) EQ yw3111 False)",fontsize=16,color="black",shape="box"];214 -> 232[label="",style="solid", color="black", weight=3];
215[label="span2Ys0 ((==) GT) (GT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) GT yw3111 True)",fontsize=16,color="black",shape="box"];215 -> 233[label="",style="solid", color="black", weight=3];
216[label="span2Zs0 ((==) LT) (LT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) LT yw3111 True)",fontsize=16,color="black",shape="box"];216 -> 234[label="",style="solid", color="black", weight=3];
217[label="span2Zs0 ((==) LT) (EQ : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) EQ yw3111 False)",fontsize=16,color="black",shape="box"];217 -> 235[label="",style="solid", color="black", weight=3];
218[label="span2Zs0 ((==) LT) (GT : yw3111) (span2Span1 ((==) LT) yw3111 ((==) LT) GT yw3111 False)",fontsize=16,color="black",shape="box"];218 -> 236[label="",style="solid", color="black", weight=3];
219[label="span2Zs0 ((==) EQ) (LT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) LT yw3111 False)",fontsize=16,color="black",shape="box"];219 -> 237[label="",style="solid", color="black", weight=3];
220[label="span2Zs0 ((==) EQ) (EQ : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) EQ yw3111 True)",fontsize=16,color="black",shape="box"];220 -> 238[label="",style="solid", color="black", weight=3];
221[label="span2Zs0 ((==) EQ) (GT : yw3111) (span2Span1 ((==) EQ) yw3111 ((==) EQ) GT yw3111 False)",fontsize=16,color="black",shape="box"];221 -> 239[label="",style="solid", color="black", weight=3];
222[label="span2Zs0 ((==) GT) (LT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) LT yw3111 False)",fontsize=16,color="black",shape="box"];222 -> 240[label="",style="solid", color="black", weight=3];
223[label="span2Zs0 ((==) GT) (EQ : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) EQ yw3111 False)",fontsize=16,color="black",shape="box"];223 -> 241[label="",style="solid", color="black", weight=3];
224[label="span2Zs0 ((==) GT) (GT : yw3111) (span2Span1 ((==) GT) yw3111 ((==) GT) GT yw3111 True)",fontsize=16,color="black",shape="box"];224 -> 242[label="",style="solid", color="black", weight=3];
225 -> 243[label="",style="dashed", color="red", weight=0];
225[label="span2Ys0 ((==) LT) (LT : yw3111) (LT : span2Ys ((==) LT) yw3111,span2Zs ((==) LT) yw3111)",fontsize=16,color="magenta"];225 -> 244[label="",style="dashed", color="magenta", weight=3];
225 -> 245[label="",style="dashed", color="magenta", weight=3];
226[label="span2Ys0 ((==) LT) (EQ : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) EQ yw3111 otherwise)",fontsize=16,color="black",shape="box"];226 -> 246[label="",style="solid", color="black", weight=3];
227[label="span2Ys0 ((==) LT) (GT : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) GT yw3111 otherwise)",fontsize=16,color="black",shape="box"];227 -> 247[label="",style="solid", color="black", weight=3];
228[label="span2Ys0 ((==) EQ) (LT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) LT yw3111 otherwise)",fontsize=16,color="black",shape="box"];228 -> 248[label="",style="solid", color="black", weight=3];
229 -> 249[label="",style="dashed", color="red", weight=0];
229[label="span2Ys0 ((==) EQ) (EQ : yw3111) (EQ : span2Ys ((==) EQ) yw3111,span2Zs ((==) EQ) yw3111)",fontsize=16,color="magenta"];229 -> 250[label="",style="dashed", color="magenta", weight=3];
229 -> 251[label="",style="dashed", color="magenta", weight=3];
230[label="span2Ys0 ((==) EQ) (GT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) GT yw3111 otherwise)",fontsize=16,color="black",shape="box"];230 -> 252[label="",style="solid", color="black", weight=3];
231[label="span2Ys0 ((==) GT) (LT : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) LT yw3111 otherwise)",fontsize=16,color="black",shape="box"];231 -> 253[label="",style="solid", color="black", weight=3];
232[label="span2Ys0 ((==) GT) (EQ : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) EQ yw3111 otherwise)",fontsize=16,color="black",shape="box"];232 -> 254[label="",style="solid", color="black", weight=3];
233 -> 255[label="",style="dashed", color="red", weight=0];
233[label="span2Ys0 ((==) GT) (GT : yw3111) (GT : span2Ys ((==) GT) yw3111,span2Zs ((==) GT) yw3111)",fontsize=16,color="magenta"];233 -> 256[label="",style="dashed", color="magenta", weight=3];
233 -> 257[label="",style="dashed", color="magenta", weight=3];
234 -> 258[label="",style="dashed", color="red", weight=0];
234[label="span2Zs0 ((==) LT) (LT : yw3111) (LT : span2Ys ((==) LT) yw3111,span2Zs ((==) LT) yw3111)",fontsize=16,color="magenta"];234 -> 259[label="",style="dashed", color="magenta", weight=3];
234 -> 260[label="",style="dashed", color="magenta", weight=3];
235[label="span2Zs0 ((==) LT) (EQ : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) EQ yw3111 otherwise)",fontsize=16,color="black",shape="box"];235 -> 261[label="",style="solid", color="black", weight=3];
236[label="span2Zs0 ((==) LT) (GT : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) GT yw3111 otherwise)",fontsize=16,color="black",shape="box"];236 -> 262[label="",style="solid", color="black", weight=3];
237[label="span2Zs0 ((==) EQ) (LT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) LT yw3111 otherwise)",fontsize=16,color="black",shape="box"];237 -> 263[label="",style="solid", color="black", weight=3];
238 -> 264[label="",style="dashed", color="red", weight=0];
238[label="span2Zs0 ((==) EQ) (EQ : yw3111) (EQ : span2Ys ((==) EQ) yw3111,span2Zs ((==) EQ) yw3111)",fontsize=16,color="magenta"];238 -> 265[label="",style="dashed", color="magenta", weight=3];
238 -> 266[label="",style="dashed", color="magenta", weight=3];
239[label="span2Zs0 ((==) EQ) (GT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) GT yw3111 otherwise)",fontsize=16,color="black",shape="box"];239 -> 267[label="",style="solid", color="black", weight=3];
240[label="span2Zs0 ((==) GT) (LT : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) LT yw3111 otherwise)",fontsize=16,color="black",shape="box"];240 -> 268[label="",style="solid", color="black", weight=3];
241[label="span2Zs0 ((==) GT) (EQ : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) EQ yw3111 otherwise)",fontsize=16,color="black",shape="box"];241 -> 269[label="",style="solid", color="black", weight=3];
242 -> 270[label="",style="dashed", color="red", weight=0];
242[label="span2Zs0 ((==) GT) (GT : yw3111) (GT : span2Ys ((==) GT) yw3111,span2Zs ((==) GT) yw3111)",fontsize=16,color="magenta"];242 -> 271[label="",style="dashed", color="magenta", weight=3];
242 -> 272[label="",style="dashed", color="magenta", weight=3];
244 -> 108[label="",style="dashed", color="red", weight=0];
244[label="span2Zs ((==) LT) yw3111",fontsize=16,color="magenta"];244 -> 273[label="",style="dashed", color="magenta", weight=3];
245 -> 99[label="",style="dashed", color="red", weight=0];
245[label="span2Ys ((==) LT) yw3111",fontsize=16,color="magenta"];245 -> 274[label="",style="dashed", color="magenta", weight=3];
243[label="span2Ys0 ((==) LT) (LT : yw3111) (LT : yw5,yw4)",fontsize=16,color="black",shape="triangle"];243 -> 275[label="",style="solid", color="black", weight=3];
246[label="span2Ys0 ((==) LT) (EQ : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) EQ yw3111 True)",fontsize=16,color="black",shape="box"];246 -> 276[label="",style="solid", color="black", weight=3];
247[label="span2Ys0 ((==) LT) (GT : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) GT yw3111 True)",fontsize=16,color="black",shape="box"];247 -> 277[label="",style="solid", color="black", weight=3];
248[label="span2Ys0 ((==) EQ) (LT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) LT yw3111 True)",fontsize=16,color="black",shape="box"];248 -> 278[label="",style="solid", color="black", weight=3];
250 -> 112[label="",style="dashed", color="red", weight=0];
250[label="span2Zs ((==) EQ) yw3111",fontsize=16,color="magenta"];250 -> 279[label="",style="dashed", color="magenta", weight=3];
251 -> 103[label="",style="dashed", color="red", weight=0];
251[label="span2Ys ((==) EQ) yw3111",fontsize=16,color="magenta"];251 -> 280[label="",style="dashed", color="magenta", weight=3];
249[label="span2Ys0 ((==) EQ) (EQ : yw3111) (EQ : yw7,yw6)",fontsize=16,color="black",shape="triangle"];249 -> 281[label="",style="solid", color="black", weight=3];
252[label="span2Ys0 ((==) EQ) (GT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) GT yw3111 True)",fontsize=16,color="black",shape="box"];252 -> 282[label="",style="solid", color="black", weight=3];
253[label="span2Ys0 ((==) GT) (LT : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) LT yw3111 True)",fontsize=16,color="black",shape="box"];253 -> 283[label="",style="solid", color="black", weight=3];
254[label="span2Ys0 ((==) GT) (EQ : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) EQ yw3111 True)",fontsize=16,color="black",shape="box"];254 -> 284[label="",style="solid", color="black", weight=3];
256 -> 116[label="",style="dashed", color="red", weight=0];
256[label="span2Zs ((==) GT) yw3111",fontsize=16,color="magenta"];256 -> 285[label="",style="dashed", color="magenta", weight=3];
257 -> 107[label="",style="dashed", color="red", weight=0];
257[label="span2Ys ((==) GT) yw3111",fontsize=16,color="magenta"];257 -> 286[label="",style="dashed", color="magenta", weight=3];
255[label="span2Ys0 ((==) GT) (GT : yw3111) (GT : yw9,yw8)",fontsize=16,color="black",shape="triangle"];255 -> 287[label="",style="solid", color="black", weight=3];
259 -> 108[label="",style="dashed", color="red", weight=0];
259[label="span2Zs ((==) LT) yw3111",fontsize=16,color="magenta"];259 -> 288[label="",style="dashed", color="magenta", weight=3];
260 -> 99[label="",style="dashed", color="red", weight=0];
260[label="span2Ys ((==) LT) yw3111",fontsize=16,color="magenta"];260 -> 289[label="",style="dashed", color="magenta", weight=3];
258[label="span2Zs0 ((==) LT) (LT : yw3111) (LT : yw11,yw10)",fontsize=16,color="black",shape="triangle"];258 -> 290[label="",style="solid", color="black", weight=3];
261[label="span2Zs0 ((==) LT) (EQ : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) EQ yw3111 True)",fontsize=16,color="black",shape="box"];261 -> 291[label="",style="solid", color="black", weight=3];
262[label="span2Zs0 ((==) LT) (GT : yw3111) (span2Span0 ((==) LT) yw3111 ((==) LT) GT yw3111 True)",fontsize=16,color="black",shape="box"];262 -> 292[label="",style="solid", color="black", weight=3];
263[label="span2Zs0 ((==) EQ) (LT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) LT yw3111 True)",fontsize=16,color="black",shape="box"];263 -> 293[label="",style="solid", color="black", weight=3];
265 -> 103[label="",style="dashed", color="red", weight=0];
265[label="span2Ys ((==) EQ) yw3111",fontsize=16,color="magenta"];265 -> 294[label="",style="dashed", color="magenta", weight=3];
266 -> 112[label="",style="dashed", color="red", weight=0];
266[label="span2Zs ((==) EQ) yw3111",fontsize=16,color="magenta"];266 -> 295[label="",style="dashed", color="magenta", weight=3];
264[label="span2Zs0 ((==) EQ) (EQ : yw3111) (EQ : yw13,yw12)",fontsize=16,color="black",shape="triangle"];264 -> 296[label="",style="solid", color="black", weight=3];
267[label="span2Zs0 ((==) EQ) (GT : yw3111) (span2Span0 ((==) EQ) yw3111 ((==) EQ) GT yw3111 True)",fontsize=16,color="black",shape="box"];267 -> 297[label="",style="solid", color="black", weight=3];
268[label="span2Zs0 ((==) GT) (LT : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) LT yw3111 True)",fontsize=16,color="black",shape="box"];268 -> 298[label="",style="solid", color="black", weight=3];
269[label="span2Zs0 ((==) GT) (EQ : yw3111) (span2Span0 ((==) GT) yw3111 ((==) GT) EQ yw3111 True)",fontsize=16,color="black",shape="box"];269 -> 299[label="",style="solid", color="black", weight=3];
271 -> 116[label="",style="dashed", color="red", weight=0];
271[label="span2Zs ((==) GT) yw3111",fontsize=16,color="magenta"];271 -> 300[label="",style="dashed", color="magenta", weight=3];
272 -> 107[label="",style="dashed", color="red", weight=0];
272[label="span2Ys ((==) GT) yw3111",fontsize=16,color="magenta"];272 -> 301[label="",style="dashed", color="magenta", weight=3];
270[label="span2Zs0 ((==) GT) (GT : yw3111) (GT : yw15,yw14)",fontsize=16,color="black",shape="triangle"];270 -> 302[label="",style="solid", color="black", weight=3];
273[label="yw3111",fontsize=16,color="green",shape="box"];274[label="yw3111",fontsize=16,color="green",shape="box"];275[label="LT : yw5",fontsize=16,color="green",shape="box"];276[label="span2Ys0 ((==) LT) (EQ : yw3111) ([],EQ : yw3111)",fontsize=16,color="black",shape="box"];276 -> 303[label="",style="solid", color="black", weight=3];
277[label="span2Ys0 ((==) LT) (GT : yw3111) ([],GT : yw3111)",fontsize=16,color="black",shape="box"];277 -> 304[label="",style="solid", color="black", weight=3];
278[label="span2Ys0 ((==) EQ) (LT : yw3111) ([],LT : yw3111)",fontsize=16,color="black",shape="box"];278 -> 305[label="",style="solid", color="black", weight=3];
279[label="yw3111",fontsize=16,color="green",shape="box"];280[label="yw3111",fontsize=16,color="green",shape="box"];281[label="EQ : yw7",fontsize=16,color="green",shape="box"];282[label="span2Ys0 ((==) EQ) (GT : yw3111) ([],GT : yw3111)",fontsize=16,color="black",shape="box"];282 -> 306[label="",style="solid", color="black", weight=3];
283[label="span2Ys0 ((==) GT) (LT : yw3111) ([],LT : yw3111)",fontsize=16,color="black",shape="box"];283 -> 307[label="",style="solid", color="black", weight=3];
284[label="span2Ys0 ((==) GT) (EQ : yw3111) ([],EQ : yw3111)",fontsize=16,color="black",shape="box"];284 -> 308[label="",style="solid", color="black", weight=3];
285[label="yw3111",fontsize=16,color="green",shape="box"];286[label="yw3111",fontsize=16,color="green",shape="box"];287[label="GT : yw9",fontsize=16,color="green",shape="box"];288[label="yw3111",fontsize=16,color="green",shape="box"];289[label="yw3111",fontsize=16,color="green",shape="box"];290[label="yw10",fontsize=16,color="green",shape="box"];291[label="span2Zs0 ((==) LT) (EQ : yw3111) ([],EQ : yw3111)",fontsize=16,color="black",shape="box"];291 -> 309[label="",style="solid", color="black", weight=3];
292[label="span2Zs0 ((==) LT) (GT : yw3111) ([],GT : yw3111)",fontsize=16,color="black",shape="box"];292 -> 310[label="",style="solid", color="black", weight=3];
293[label="span2Zs0 ((==) EQ) (LT : yw3111) ([],LT : yw3111)",fontsize=16,color="black",shape="box"];293 -> 311[label="",style="solid", color="black", weight=3];
294[label="yw3111",fontsize=16,color="green",shape="box"];295[label="yw3111",fontsize=16,color="green",shape="box"];296[label="yw12",fontsize=16,color="green",shape="box"];297[label="span2Zs0 ((==) EQ) (GT : yw3111) ([],GT : yw3111)",fontsize=16,color="black",shape="box"];297 -> 312[label="",style="solid", color="black", weight=3];
298[label="span2Zs0 ((==) GT) (LT : yw3111) ([],LT : yw3111)",fontsize=16,color="black",shape="box"];298 -> 313[label="",style="solid", color="black", weight=3];
299[label="span2Zs0 ((==) GT) (EQ : yw3111) ([],EQ : yw3111)",fontsize=16,color="black",shape="box"];299 -> 314[label="",style="solid", color="black", weight=3];
300[label="yw3111",fontsize=16,color="green",shape="box"];301[label="yw3111",fontsize=16,color="green",shape="box"];302[label="yw14",fontsize=16,color="green",shape="box"];303[label="[]",fontsize=16,color="green",shape="box"];304[label="[]",fontsize=16,color="green",shape="box"];305[label="[]",fontsize=16,color="green",shape="box"];306[label="[]",fontsize=16,color="green",shape="box"];307[label="[]",fontsize=16,color="green",shape="box"];308[label="[]",fontsize=16,color="green",shape="box"];309[label="EQ : yw3111",fontsize=16,color="green",shape="box"];310[label="GT : yw3111",fontsize=16,color="green",shape="box"];311[label="LT : yw3111",fontsize=16,color="green",shape="box"];312[label="GT : yw3111",fontsize=16,color="green",shape="box"];313[label="LT : yw3111",fontsize=16,color="green",shape="box"];314[label="EQ : yw3111",fontsize=16,color="green",shape="box"];}

----------------------------------------

(10)
Complex Obligation (AND)

----------------------------------------

(11)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_groupBy(:(yw30, yw31)) -> new_groupBy(new_groupByZs1(yw30, yw31))

The TRS R consists of the following rules:

   new_groupByZs1(EQ, :(GT, yw311)) -> :(GT, yw311)
   new_groupByZs1(GT, :(GT, yw311)) -> new_span2Zs4(yw311)
   new_span2Ys2(:(GT, yw3111)) -> []
   new_span2Zs4(:(EQ, yw3111)) -> :(EQ, yw3111)
   new_span2Zs4(:(GT, yw3111)) -> new_span2Zs01(yw3111, new_span2Ys4(yw3111), new_span2Zs4(yw3111))
   new_span2Zs3(:(GT, yw3111)) -> :(GT, yw3111)
   new_span2Zs4([]) -> []
   new_groupByZs1(LT, :(GT, yw311)) -> :(GT, yw311)
   new_span2Ys2(:(LT, yw3111)) -> new_span2Ys00(yw3111, new_span2Ys2(yw3111), new_span2Zs2(yw3111))
   new_span2Ys4(:(LT, yw3111)) -> []
   new_span2Ys3(:(EQ, yw3111)) -> new_span2Ys01(yw3111, new_span2Ys3(yw3111), new_span2Zs3(yw3111))
   new_span2Zs4(:(LT, yw3111)) -> :(LT, yw3111)
   new_span2Ys2([]) -> []
   new_groupByZs1(GT, :(LT, yw311)) -> :(LT, yw311)
   new_span2Ys01(yw3111, yw7, yw6) -> :(EQ, yw7)
   new_span2Zs01(yw3111, yw15, yw14) -> yw14
   new_span2Zs2(:(EQ, yw3111)) -> :(EQ, yw3111)
   new_span2Ys4(:(EQ, yw3111)) -> []
   new_span2Ys02(yw3111, yw9, yw8) -> :(GT, yw9)
   new_span2Zs3([]) -> []
   new_span2Ys00(yw3111, yw5, yw4) -> :(LT, yw5)
   new_span2Ys4([]) -> []
   new_span2Ys4(:(GT, yw3111)) -> new_span2Ys02(yw3111, new_span2Ys4(yw3111), new_span2Zs4(yw3111))
   new_groupByZs1(EQ, :(EQ, yw311)) -> new_span2Zs3(yw311)
   new_span2Ys3(:(GT, yw3111)) -> []
   new_groupByZs1(LT, :(LT, yw311)) -> new_span2Zs2(yw311)
   new_span2Ys3(:(LT, yw3111)) -> []
   new_span2Zs2(:(GT, yw3111)) -> :(GT, yw3111)
   new_span2Zs2(:(LT, yw3111)) -> new_span2Zs02(yw3111, new_span2Ys2(yw3111), new_span2Zs2(yw3111))
   new_groupByZs1(LT, :(EQ, yw311)) -> :(EQ, yw311)
   new_span2Ys2(:(EQ, yw3111)) -> []
   new_span2Zs3(:(LT, yw3111)) -> :(LT, yw3111)
   new_groupByZs1(GT, :(EQ, yw311)) -> :(EQ, yw311)
   new_span2Ys3([]) -> []
   new_span2Zs2([]) -> []
   new_groupByZs1(EQ, :(LT, yw311)) -> :(LT, yw311)
   new_span2Zs02(yw3111, yw11, yw10) -> yw10
   new_groupByZs1(yw30, []) -> []
   new_span2Zs3(:(EQ, yw3111)) -> new_span2Zs00(yw3111, new_span2Ys3(yw3111), new_span2Zs3(yw3111))
   new_span2Zs00(yw3111, yw13, yw12) -> yw12

The set Q consists of the following terms:

   new_groupByZs1(GT, :(LT, x0))
   new_groupByZs1(EQ, :(GT, x0))
   new_span2Ys2(:(LT, x0))
   new_span2Zs2(:(LT, x0))
   new_groupByZs1(EQ, :(EQ, x0))
   new_groupByZs1(x0, [])
   new_span2Zs01(x0, x1, x2)
   new_groupByZs1(LT, :(GT, x0))
   new_groupByZs1(LT, :(EQ, x0))
   new_span2Ys4(:(GT, x0))
   new_span2Ys4(:(EQ, x0))
   new_span2Zs3(:(LT, x0))
   new_span2Zs2(:(EQ, x0))
   new_groupByZs1(GT, :(GT, x0))
   new_span2Zs4(:(LT, x0))
   new_groupByZs1(GT, :(EQ, x0))
   new_span2Ys00(x0, x1, x2)
   new_groupByZs1(EQ, :(LT, x0))
   new_span2Ys01(x0, x1, x2)
   new_span2Ys4([])
   new_span2Zs2([])
   new_span2Zs3([])
   new_span2Zs3(:(GT, x0))
   new_groupByZs1(LT, :(LT, x0))
   new_span2Ys3(:(GT, x0))
   new_span2Zs02(x0, x1, x2)
   new_span2Zs3(:(EQ, x0))
   new_span2Ys02(x0, x1, x2)
   new_span2Ys4(:(LT, x0))
   new_span2Zs2(:(GT, x0))
   new_span2Ys3(:(EQ, x0))
   new_span2Zs00(x0, x1, x2)
   new_span2Ys3([])
   new_span2Zs4(:(GT, x0))
   new_span2Zs4(:(EQ, x0))
   new_span2Zs4([])
   new_span2Ys3(:(LT, x0))
   new_span2Ys2(:(GT, x0))
   new_span2Ys2(:(EQ, x0))
   new_span2Ys2([])

We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(12) QDPSizeChangeProof (EQUIVALENT)
We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. 

Order:Polynomial interpretation [POLO]:

   POL(:(x_1, x_2)) = 1 + x_2
   POL(EQ) = 0
   POL(GT) = 0
   POL(LT) = 0
   POL([]) = 1
   POL(new_groupByZs1(x_1, x_2)) = x_2
   POL(new_span2Ys00(x_1, x_2, x_3)) = 1 + x_2
   POL(new_span2Ys01(x_1, x_2, x_3)) = 1 + x_2
   POL(new_span2Ys02(x_1, x_2, x_3)) = 1 + x_2
   POL(new_span2Ys2(x_1)) = 1 + x_1
   POL(new_span2Ys3(x_1)) = 1 + x_1
   POL(new_span2Ys4(x_1)) = 1 + x_1
   POL(new_span2Zs00(x_1, x_2, x_3)) = 1 + x_3
   POL(new_span2Zs01(x_1, x_2, x_3)) = 1 + x_3
   POL(new_span2Zs02(x_1, x_2, x_3)) = 1 + x_3
   POL(new_span2Zs2(x_1)) = x_1
   POL(new_span2Zs3(x_1)) = 1 + x_1
   POL(new_span2Zs4(x_1)) = 1 + x_1




From the DPs we obtained the following set of size-change graphs:
*new_groupBy(:(yw30, yw31)) -> new_groupBy(new_groupByZs1(yw30, yw31)) (allowed arguments on rhs = {1})
The graph contains the following edges 1 > 1



We oriented the following set of usable rules [AAECC05,FROCOS05].

   new_span2Zs4([]) -> []
   new_span2Zs4(:(LT, yw3111)) -> :(LT, yw3111)
   new_span2Zs4(:(GT, yw3111)) -> new_span2Zs01(yw3111, new_span2Ys4(yw3111), new_span2Zs4(yw3111))
   new_span2Zs4(:(EQ, yw3111)) -> :(EQ, yw3111)
   new_span2Zs3([]) -> []
   new_span2Zs3(:(LT, yw3111)) -> :(LT, yw3111)
   new_span2Zs3(:(GT, yw3111)) -> :(GT, yw3111)
   new_span2Zs3(:(EQ, yw3111)) -> new_span2Zs00(yw3111, new_span2Ys3(yw3111), new_span2Zs3(yw3111))
   new_span2Zs2([]) -> []
   new_span2Zs2(:(LT, yw3111)) -> new_span2Zs02(yw3111, new_span2Ys2(yw3111), new_span2Zs2(yw3111))
   new_span2Zs2(:(GT, yw3111)) -> :(GT, yw3111)
   new_span2Zs2(:(EQ, yw3111)) -> :(EQ, yw3111)
   new_span2Zs02(yw3111, yw11, yw10) -> yw10
   new_span2Zs01(yw3111, yw15, yw14) -> yw14
   new_span2Zs00(yw3111, yw13, yw12) -> yw12
   new_span2Ys4([]) -> []
   new_span2Ys4(:(LT, yw3111)) -> []
   new_span2Ys4(:(GT, yw3111)) -> new_span2Ys02(yw3111, new_span2Ys4(yw3111), new_span2Zs4(yw3111))
   new_span2Ys4(:(EQ, yw3111)) -> []
   new_span2Ys3([]) -> []
   new_span2Ys3(:(LT, yw3111)) -> []
   new_span2Ys3(:(GT, yw3111)) -> []
   new_span2Ys3(:(EQ, yw3111)) -> new_span2Ys01(yw3111, new_span2Ys3(yw3111), new_span2Zs3(yw3111))
   new_span2Ys2([]) -> []
   new_span2Ys2(:(LT, yw3111)) -> new_span2Ys00(yw3111, new_span2Ys2(yw3111), new_span2Zs2(yw3111))
   new_span2Ys2(:(GT, yw3111)) -> []
   new_span2Ys2(:(EQ, yw3111)) -> []
   new_span2Ys02(yw3111, yw9, yw8) -> :(GT, yw9)
   new_span2Ys01(yw3111, yw7, yw6) -> :(EQ, yw7)
   new_span2Ys00(yw3111, yw5, yw4) -> :(LT, yw5)
   new_groupByZs1(yw30, []) -> []
   new_groupByZs1(LT, :(LT, yw311)) -> new_span2Zs2(yw311)
   new_groupByZs1(LT, :(GT, yw311)) -> :(GT, yw311)
   new_groupByZs1(LT, :(EQ, yw311)) -> :(EQ, yw311)
   new_groupByZs1(GT, :(LT, yw311)) -> :(LT, yw311)
   new_groupByZs1(GT, :(GT, yw311)) -> new_span2Zs4(yw311)
   new_groupByZs1(GT, :(EQ, yw311)) -> :(EQ, yw311)
   new_groupByZs1(EQ, :(LT, yw311)) -> :(LT, yw311)
   new_groupByZs1(EQ, :(GT, yw311)) -> :(GT, yw311)
   new_groupByZs1(EQ, :(EQ, yw311)) -> new_span2Zs3(yw311)

----------------------------------------

(13)
YES

----------------------------------------

(14)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_span2Zs(:(GT, yw3111)) -> new_span2Zs(yw3111)
   new_span2Ys(:(GT, yw3111)) -> new_span2Zs(yw3111)
   new_span2Ys(:(GT, yw3111)) -> new_span2Ys(yw3111)
   new_span2Zs(:(GT, yw3111)) -> new_span2Ys(yw3111)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(15) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*new_span2Zs(:(GT, yw3111)) -> new_span2Zs(yw3111)
The graph contains the following edges 1 > 1


*new_span2Zs(:(GT, yw3111)) -> new_span2Ys(yw3111)
The graph contains the following edges 1 > 1


*new_span2Ys(:(GT, yw3111)) -> new_span2Zs(yw3111)
The graph contains the following edges 1 > 1


*new_span2Ys(:(GT, yw3111)) -> new_span2Ys(yw3111)
The graph contains the following edges 1 > 1


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(16)
YES

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(17)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_span2Zs0(:(EQ, yw3111)) -> new_span2Ys0(yw3111)
   new_span2Ys0(:(EQ, yw3111)) -> new_span2Zs0(yw3111)
   new_span2Zs0(:(EQ, yw3111)) -> new_span2Zs0(yw3111)
   new_span2Ys0(:(EQ, yw3111)) -> new_span2Ys0(yw3111)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(18) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*new_span2Ys0(:(EQ, yw3111)) -> new_span2Zs0(yw3111)
The graph contains the following edges 1 > 1


*new_span2Ys0(:(EQ, yw3111)) -> new_span2Ys0(yw3111)
The graph contains the following edges 1 > 1


*new_span2Zs0(:(EQ, yw3111)) -> new_span2Zs0(yw3111)
The graph contains the following edges 1 > 1


*new_span2Zs0(:(EQ, yw3111)) -> new_span2Ys0(yw3111)
The graph contains the following edges 1 > 1


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(19)
YES

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(20)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_span2Zs1(:(LT, yw3111)) -> new_span2Zs1(yw3111)
   new_span2Ys1(:(LT, yw3111)) -> new_span2Ys1(yw3111)
   new_span2Zs1(:(LT, yw3111)) -> new_span2Ys1(yw3111)
   new_span2Ys1(:(LT, yw3111)) -> new_span2Zs1(yw3111)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(21) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*new_span2Zs1(:(LT, yw3111)) -> new_span2Zs1(yw3111)
The graph contains the following edges 1 > 1


*new_span2Zs1(:(LT, yw3111)) -> new_span2Ys1(yw3111)
The graph contains the following edges 1 > 1


*new_span2Ys1(:(LT, yw3111)) -> new_span2Zs1(yw3111)
The graph contains the following edges 1 > 1


*new_span2Ys1(:(LT, yw3111)) -> new_span2Ys1(yw3111)
The graph contains the following edges 1 > 1


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(22)
YES