/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) HASKELL
(1) IFR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 22 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) 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;
delete :: Eq a => a  ->  [a]  ->  [a];
delete = deleteBy (==);

deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
deleteBy _ _ [] = [];
deleteBy eq x (y : ys) =  if x `eq` y then ys else y : deleteBy eq x ys;

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

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

(1) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if eq x y then ys else y : deleteBy eq x ys"
is transformed to
"deleteBy0 ys y eq x True = ys;
deleteBy0 ys y eq x False = y : deleteBy eq x 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;
delete :: Eq a => a  ->  [a]  ->  [a];
delete = deleteBy (==);

deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
deleteBy _ _ [] = [];
deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);

deleteBy0 ys y eq x True = ys;
deleteBy0 ys y eq x False = y : deleteBy eq x ys;

}
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.
----------------------------------------

(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;
delete :: Eq a => a  ->  [a]  ->  [a];
delete = deleteBy (==);

deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
deleteBy vy vz [] = [];
deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);

deleteBy0 ys y eq x True = ys;
deleteBy0 ys y eq x False = y : deleteBy eq x ys;

}
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;
"

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

(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;
delete :: Eq a => a  ->  [a]  ->  [a];
delete = deleteBy (==);

deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
deleteBy vy vz [] = [];
deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);

deleteBy0 ys y eq x True = ys;
deleteBy0 ys y eq x False = y : deleteBy eq x ys;

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

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="List.delete",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="List.delete wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="List.delete wu3 wu4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="List.deleteBy (==) wu3 wu4",fontsize=16,color="burlywood",shape="box"];186[label="wu4/wu40 : wu41",fontsize=10,color="white",style="solid",shape="box"];5 -> 186[label="",style="solid", color="burlywood", weight=9];
186 -> 6[label="",style="solid", color="burlywood", weight=3];
187[label="wu4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 187[label="",style="solid", color="burlywood", weight=9];
187 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="List.deleteBy (==) wu3 (wu40 : wu41)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="List.deleteBy (==) wu3 []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="List.deleteBy0 wu41 wu40 (==) wu3 ((==) wu3 wu40)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="[]",fontsize=16,color="green",shape="box"];10[label="List.deleteBy0 wu41 wu40 primEqChar wu3 (primEqChar wu3 wu40)",fontsize=16,color="burlywood",shape="triangle"];188[label="wu3/Char wu30",fontsize=10,color="white",style="solid",shape="box"];10 -> 188[label="",style="solid", color="burlywood", weight=9];
188 -> 11[label="",style="solid", color="burlywood", weight=3];
11[label="List.deleteBy0 wu41 wu40 primEqChar (Char wu30) (primEqChar (Char wu30) wu40)",fontsize=16,color="burlywood",shape="box"];189[label="wu40/Char wu400",fontsize=10,color="white",style="solid",shape="box"];11 -> 189[label="",style="solid", color="burlywood", weight=9];
189 -> 12[label="",style="solid", color="burlywood", weight=3];
12[label="List.deleteBy0 wu41 (Char wu400) primEqChar (Char wu30) (primEqChar (Char wu30) (Char wu400))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="List.deleteBy0 wu41 (Char wu400) primEqChar (Char wu30) (primEqNat wu30 wu400)",fontsize=16,color="burlywood",shape="box"];190[label="wu30/Succ wu300",fontsize=10,color="white",style="solid",shape="box"];13 -> 190[label="",style="solid", color="burlywood", weight=9];
190 -> 14[label="",style="solid", color="burlywood", weight=3];
191[label="wu30/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 191[label="",style="solid", color="burlywood", weight=9];
191 -> 15[label="",style="solid", color="burlywood", weight=3];
14[label="List.deleteBy0 wu41 (Char wu400) primEqChar (Char (Succ wu300)) (primEqNat (Succ wu300) wu400)",fontsize=16,color="burlywood",shape="box"];192[label="wu400/Succ wu4000",fontsize=10,color="white",style="solid",shape="box"];14 -> 192[label="",style="solid", color="burlywood", weight=9];
192 -> 16[label="",style="solid", color="burlywood", weight=3];
193[label="wu400/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 193[label="",style="solid", color="burlywood", weight=9];
193 -> 17[label="",style="solid", color="burlywood", weight=3];
15[label="List.deleteBy0 wu41 (Char wu400) primEqChar (Char Zero) (primEqNat Zero wu400)",fontsize=16,color="burlywood",shape="box"];194[label="wu400/Succ wu4000",fontsize=10,color="white",style="solid",shape="box"];15 -> 194[label="",style="solid", color="burlywood", weight=9];
194 -> 18[label="",style="solid", color="burlywood", weight=3];
195[label="wu400/Zero",fontsize=10,color="white",style="solid",shape="box"];15 -> 195[label="",style="solid", color="burlywood", weight=9];
195 -> 19[label="",style="solid", color="burlywood", weight=3];
16[label="List.deleteBy0 wu41 (Char (Succ wu4000)) primEqChar (Char (Succ wu300)) (primEqNat (Succ wu300) (Succ wu4000))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="List.deleteBy0 wu41 (Char Zero) primEqChar (Char (Succ wu300)) (primEqNat (Succ wu300) Zero)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="List.deleteBy0 wu41 (Char (Succ wu4000)) primEqChar (Char Zero) (primEqNat Zero (Succ wu4000))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="List.deleteBy0 wu41 (Char Zero) primEqChar (Char Zero) (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20 -> 133[label="",style="dashed", color="red", weight=0];
20[label="List.deleteBy0 wu41 (Char (Succ wu4000)) primEqChar (Char (Succ wu300)) (primEqNat wu300 wu4000)",fontsize=16,color="magenta"];20 -> 134[label="",style="dashed", color="magenta", weight=3];
20 -> 135[label="",style="dashed", color="magenta", weight=3];
20 -> 136[label="",style="dashed", color="magenta", weight=3];
20 -> 137[label="",style="dashed", color="magenta", weight=3];
20 -> 138[label="",style="dashed", color="magenta", weight=3];
21[label="List.deleteBy0 wu41 (Char Zero) primEqChar (Char (Succ wu300)) False",fontsize=16,color="black",shape="box"];21 -> 26[label="",style="solid", color="black", weight=3];
22[label="List.deleteBy0 wu41 (Char (Succ wu4000)) primEqChar (Char Zero) False",fontsize=16,color="black",shape="box"];22 -> 27[label="",style="solid", color="black", weight=3];
23[label="List.deleteBy0 wu41 (Char Zero) primEqChar (Char Zero) True",fontsize=16,color="black",shape="box"];23 -> 28[label="",style="solid", color="black", weight=3];
134[label="wu4000",fontsize=16,color="green",shape="box"];135[label="wu300",fontsize=16,color="green",shape="box"];136[label="wu4000",fontsize=16,color="green",shape="box"];137[label="wu41",fontsize=16,color="green",shape="box"];138[label="wu300",fontsize=16,color="green",shape="box"];133[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat wu20 wu21)",fontsize=16,color="burlywood",shape="triangle"];196[label="wu20/Succ wu200",fontsize=10,color="white",style="solid",shape="box"];133 -> 196[label="",style="solid", color="burlywood", weight=9];
196 -> 169[label="",style="solid", color="burlywood", weight=3];
197[label="wu20/Zero",fontsize=10,color="white",style="solid",shape="box"];133 -> 197[label="",style="solid", color="burlywood", weight=9];
197 -> 170[label="",style="solid", color="burlywood", weight=3];
26[label="Char Zero : List.deleteBy primEqChar (Char (Succ wu300)) wu41",fontsize=16,color="green",shape="box"];26 -> 33[label="",style="dashed", color="green", weight=3];
27[label="Char (Succ wu4000) : List.deleteBy primEqChar (Char Zero) wu41",fontsize=16,color="green",shape="box"];27 -> 34[label="",style="dashed", color="green", weight=3];
28[label="wu41",fontsize=16,color="green",shape="box"];169[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat (Succ wu200) wu21)",fontsize=16,color="burlywood",shape="box"];198[label="wu21/Succ wu210",fontsize=10,color="white",style="solid",shape="box"];169 -> 198[label="",style="solid", color="burlywood", weight=9];
198 -> 171[label="",style="solid", color="burlywood", weight=3];
199[label="wu21/Zero",fontsize=10,color="white",style="solid",shape="box"];169 -> 199[label="",style="solid", color="burlywood", weight=9];
199 -> 172[label="",style="solid", color="burlywood", weight=3];
170[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat Zero wu21)",fontsize=16,color="burlywood",shape="box"];200[label="wu21/Succ wu210",fontsize=10,color="white",style="solid",shape="box"];170 -> 200[label="",style="solid", color="burlywood", weight=9];
200 -> 173[label="",style="solid", color="burlywood", weight=3];
201[label="wu21/Zero",fontsize=10,color="white",style="solid",shape="box"];170 -> 201[label="",style="solid", color="burlywood", weight=9];
201 -> 174[label="",style="solid", color="burlywood", weight=3];
33[label="List.deleteBy primEqChar (Char (Succ wu300)) wu41",fontsize=16,color="burlywood",shape="triangle"];202[label="wu41/wu410 : wu411",fontsize=10,color="white",style="solid",shape="box"];33 -> 202[label="",style="solid", color="burlywood", weight=9];
202 -> 39[label="",style="solid", color="burlywood", weight=3];
203[label="wu41/[]",fontsize=10,color="white",style="solid",shape="box"];33 -> 203[label="",style="solid", color="burlywood", weight=9];
203 -> 40[label="",style="solid", color="burlywood", weight=3];
34[label="List.deleteBy primEqChar (Char Zero) wu41",fontsize=16,color="burlywood",shape="box"];204[label="wu41/wu410 : wu411",fontsize=10,color="white",style="solid",shape="box"];34 -> 204[label="",style="solid", color="burlywood", weight=9];
204 -> 41[label="",style="solid", color="burlywood", weight=3];
205[label="wu41/[]",fontsize=10,color="white",style="solid",shape="box"];34 -> 205[label="",style="solid", color="burlywood", weight=9];
205 -> 42[label="",style="solid", color="burlywood", weight=3];
171[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat (Succ wu200) (Succ wu210))",fontsize=16,color="black",shape="box"];171 -> 175[label="",style="solid", color="black", weight=3];
172[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat (Succ wu200) Zero)",fontsize=16,color="black",shape="box"];172 -> 176[label="",style="solid", color="black", weight=3];
173[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat Zero (Succ wu210))",fontsize=16,color="black",shape="box"];173 -> 177[label="",style="solid", color="black", weight=3];
174[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];174 -> 178[label="",style="solid", color="black", weight=3];
39[label="List.deleteBy primEqChar (Char (Succ wu300)) (wu410 : wu411)",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
40[label="List.deleteBy primEqChar (Char (Succ wu300)) []",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
41[label="List.deleteBy primEqChar (Char Zero) (wu410 : wu411)",fontsize=16,color="black",shape="box"];41 -> 50[label="",style="solid", color="black", weight=3];
42[label="List.deleteBy primEqChar (Char Zero) []",fontsize=16,color="black",shape="box"];42 -> 51[label="",style="solid", color="black", weight=3];
175 -> 133[label="",style="dashed", color="red", weight=0];
175[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) (primEqNat wu200 wu210)",fontsize=16,color="magenta"];175 -> 179[label="",style="dashed", color="magenta", weight=3];
175 -> 180[label="",style="dashed", color="magenta", weight=3];
176[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) False",fontsize=16,color="black",shape="triangle"];176 -> 181[label="",style="solid", color="black", weight=3];
177 -> 176[label="",style="dashed", color="red", weight=0];
177[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) False",fontsize=16,color="magenta"];178[label="List.deleteBy0 wu17 (Char (Succ wu18)) primEqChar (Char (Succ wu19)) True",fontsize=16,color="black",shape="box"];178 -> 182[label="",style="solid", color="black", weight=3];
48 -> 10[label="",style="dashed", color="red", weight=0];
48[label="List.deleteBy0 wu411 wu410 primEqChar (Char (Succ wu300)) (primEqChar (Char (Succ wu300)) wu410)",fontsize=16,color="magenta"];48 -> 58[label="",style="dashed", color="magenta", weight=3];
48 -> 59[label="",style="dashed", color="magenta", weight=3];
48 -> 60[label="",style="dashed", color="magenta", weight=3];
49[label="[]",fontsize=16,color="green",shape="box"];50 -> 10[label="",style="dashed", color="red", weight=0];
50[label="List.deleteBy0 wu411 wu410 primEqChar (Char Zero) (primEqChar (Char Zero) wu410)",fontsize=16,color="magenta"];50 -> 61[label="",style="dashed", color="magenta", weight=3];
50 -> 62[label="",style="dashed", color="magenta", weight=3];
50 -> 63[label="",style="dashed", color="magenta", weight=3];
51[label="[]",fontsize=16,color="green",shape="box"];179[label="wu200",fontsize=16,color="green",shape="box"];180[label="wu210",fontsize=16,color="green",shape="box"];181[label="Char (Succ wu18) : List.deleteBy primEqChar (Char (Succ wu19)) wu17",fontsize=16,color="green",shape="box"];181 -> 183[label="",style="dashed", color="green", weight=3];
182[label="wu17",fontsize=16,color="green",shape="box"];58[label="wu411",fontsize=16,color="green",shape="box"];59[label="wu410",fontsize=16,color="green",shape="box"];60[label="Char (Succ wu300)",fontsize=16,color="green",shape="box"];61[label="wu411",fontsize=16,color="green",shape="box"];62[label="wu410",fontsize=16,color="green",shape="box"];63[label="Char Zero",fontsize=16,color="green",shape="box"];183 -> 33[label="",style="dashed", color="red", weight=0];
183[label="List.deleteBy primEqChar (Char (Succ wu19)) wu17",fontsize=16,color="magenta"];183 -> 184[label="",style="dashed", color="magenta", weight=3];
183 -> 185[label="",style="dashed", color="magenta", weight=3];
184[label="wu19",fontsize=16,color="green",shape="box"];185[label="wu17",fontsize=16,color="green",shape="box"];}

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

(8)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_deleteBy0(wu17, wu18, wu19, Succ(wu200), Zero) -> new_deleteBy(wu19, wu17)
   new_deleteBy00(wu17, wu18, wu19) -> new_deleteBy(wu19, wu17)
   new_deleteBy01(:(wu410, wu411), Char(Succ(wu4000)), Char(Zero)) -> new_deleteBy01(wu411, wu410, Char(Zero))
   new_deleteBy0(wu17, wu18, wu19, Succ(wu200), Succ(wu210)) -> new_deleteBy0(wu17, wu18, wu19, wu200, wu210)
   new_deleteBy01(:(wu410, wu411), Char(Zero), Char(Succ(wu300))) -> new_deleteBy01(wu411, wu410, Char(Succ(wu300)))
   new_deleteBy(wu300, :(wu410, wu411)) -> new_deleteBy01(wu411, wu410, Char(Succ(wu300)))
   new_deleteBy01(wu41, Char(Succ(wu4000)), Char(Succ(wu300))) -> new_deleteBy0(wu41, wu4000, wu300, wu300, wu4000)
   new_deleteBy0(wu17, wu18, wu19, Zero, Succ(wu210)) -> new_deleteBy00(wu17, wu18, wu19)

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

(9) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs.
----------------------------------------

(10)
Complex Obligation (AND)

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

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

   new_deleteBy01(:(wu410, wu411), Char(Succ(wu4000)), Char(Zero)) -> new_deleteBy01(wu411, wu410, Char(Zero))

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

(12) 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_deleteBy01(:(wu410, wu411), Char(Succ(wu4000)), Char(Zero)) -> new_deleteBy01(wu411, wu410, Char(Zero))
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3


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

(13)
YES

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

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

   new_deleteBy(wu300, :(wu410, wu411)) -> new_deleteBy01(wu411, wu410, Char(Succ(wu300)))
   new_deleteBy01(:(wu410, wu411), Char(Zero), Char(Succ(wu300))) -> new_deleteBy01(wu411, wu410, Char(Succ(wu300)))
   new_deleteBy01(wu41, Char(Succ(wu4000)), Char(Succ(wu300))) -> new_deleteBy0(wu41, wu4000, wu300, wu300, wu4000)
   new_deleteBy0(wu17, wu18, wu19, Succ(wu200), Zero) -> new_deleteBy(wu19, wu17)
   new_deleteBy0(wu17, wu18, wu19, Succ(wu200), Succ(wu210)) -> new_deleteBy0(wu17, wu18, wu19, wu200, wu210)
   new_deleteBy0(wu17, wu18, wu19, Zero, Succ(wu210)) -> new_deleteBy00(wu17, wu18, wu19)
   new_deleteBy00(wu17, wu18, wu19) -> new_deleteBy(wu19, wu17)

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

(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_deleteBy01(:(wu410, wu411), Char(Zero), Char(Succ(wu300))) -> new_deleteBy01(wu411, wu410, Char(Succ(wu300)))
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3


*new_deleteBy01(wu41, Char(Succ(wu4000)), Char(Succ(wu300))) -> new_deleteBy0(wu41, wu4000, wu300, wu300, wu4000)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4, 2 > 5


*new_deleteBy(wu300, :(wu410, wu411)) -> new_deleteBy01(wu411, wu410, Char(Succ(wu300)))
The graph contains the following edges 2 > 1, 2 > 2


*new_deleteBy0(wu17, wu18, wu19, Succ(wu200), Zero) -> new_deleteBy(wu19, wu17)
The graph contains the following edges 3 >= 1, 1 >= 2


*new_deleteBy00(wu17, wu18, wu19) -> new_deleteBy(wu19, wu17)
The graph contains the following edges 3 >= 1, 1 >= 2


*new_deleteBy0(wu17, wu18, wu19, Succ(wu200), Succ(wu210)) -> new_deleteBy0(wu17, wu18, wu19, wu200, wu210)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 > 5


*new_deleteBy0(wu17, wu18, wu19, Zero, Succ(wu210)) -> new_deleteBy00(wu17, wu18, wu19)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3


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

(16)
YES