/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) CR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 18 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) DependencyGraphProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 34 ms]
        (22) QDP
        (23) DependencyGraphProof [EQUIVALENT, 0 ms]
        (24) TRUE
    (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) 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;
merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
merge cmp xs [] = xs;
merge cmp [] ys = ys;
merge cmp (x : xs) (y : ys) = case x `cmp` y of { 
GT-> y : merge cmp (x : xs) ys; 
_-> x : merge cmp xs (y : ys); 
 } ;

merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
merge_pairs cmp [] = [];
merge_pairs cmp (xs : []) = xs : [];
merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;

mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
mergesort cmp = mergesort' cmp . map wrap;

mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
mergesort' cmp [] = [];
mergesort' cmp (xs : []) = xs;
mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);

sort :: Ord a => [a]  ->  [a];
sort l = mergesort compare l;

wrap :: a  ->  [a];
wrap x = x : [];

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

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

(1) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case cmp x y of {
GT  -> y : merge cmp (x : xs) ys;
_  -> x : merge cmp xs (y : ys)}
"
is transformed to
"merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
merge0 y cmp x xs ys _ = x : merge cmp xs (y : 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;
merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
merge cmp xs [] = xs;
merge cmp [] ys = ys;
merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);

merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
merge0 y cmp x xs ys _ = x : merge cmp xs (y : ys);

merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
merge_pairs cmp [] = [];
merge_pairs cmp (xs : []) = xs : [];
merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;

mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
mergesort cmp = mergesort' cmp . map wrap;

mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
mergesort' cmp [] = [];
mergesort' cmp (xs : []) = xs;
mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);

sort :: Ord a => [a]  ->  [a];
sort l = mergesort compare l;

wrap :: a  ->  [a];
wrap x = x : [];

}
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;
merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
merge cmp xs [] = xs;
merge cmp [] ys = ys;
merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);

merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
merge0 y cmp x xs ys vy = x : merge cmp xs (y : ys);

merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
merge_pairs cmp [] = [];
merge_pairs cmp (xs : []) = xs : [];
merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;

mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
mergesort cmp = mergesort' cmp . map wrap;

mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
mergesort' cmp [] = [];
mergesort' cmp (xs : []) = xs;
mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);

sort :: Ord a => [a]  ->  [a];
sort l = mergesort compare l;

wrap :: a  ->  [a];
wrap x = x : [];

}
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;
merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
merge cmp xs [] = xs;
merge cmp [] ys = ys;
merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);

merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
merge0 y cmp x xs ys vy = x : merge cmp xs (y : ys);

merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
merge_pairs cmp [] = [];
merge_pairs cmp (xs : []) = xs : [];
merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;

mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
mergesort cmp = mergesort' cmp . map wrap;

mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
mergesort' cmp [] = [];
mergesort' cmp (xs : []) = xs;
mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);

sort :: Ord a => [a]  ->  [a];
sort l = mergesort compare l;

wrap :: a  ->  [a];
wrap x = x : [];

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

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
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1471[label="vz118/[]",fontsize=10,color="white",style="solid",shape="box"];1042 -> 1471[label="",style="solid", color="burlywood", weight=9];
1471 -> 1203[label="",style="solid", color="burlywood", weight=3];
1198 -> 17[label="",style="dashed", color="red", weight=0];
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1199 -> 17[label="",style="dashed", color="red", weight=0];
1199[label="List.wrap vz30",fontsize=16,color="magenta"];1197[label="List.merge compare vz120 vz119",fontsize=16,color="burlywood",shape="triangle"];1472[label="vz119/vz1190 : vz1191",fontsize=10,color="white",style="solid",shape="box"];1197 -> 1472[label="",style="solid", color="burlywood", weight=9];
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1473[label="vz119/[]",fontsize=10,color="white",style="solid",shape="box"];1197 -> 1473[label="",style="solid", color="burlywood", weight=9];
1473 -> 1206[label="",style="solid", color="burlywood", weight=3];
1200[label="map List.wrap (vz3110 : vz3111)",fontsize=16,color="black",shape="box"];1200 -> 1207[label="",style="solid", color="black", weight=3];
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1478 -> 1315[label="",style="solid", color="burlywood", weight=3];
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1479 -> 1316[label="",style="solid", color="burlywood", weight=3];
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1227 -> 1042[label="",style="dashed", color="red", weight=0];
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1228 -> 1234[label="",style="dashed", color="magenta", weight=3];
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1481 -> 1349[label="",style="solid", color="burlywood", weight=3];
1482[label="vz1200/Neg vz12000",fontsize=10,color="white",style="solid",shape="box"];1314 -> 1482[label="",style="solid", color="burlywood", weight=9];
1482 -> 1350[label="",style="solid", color="burlywood", weight=3];
1315[label="List.merge0 vz127 compare vz128 vz129 vz130 LT",fontsize=16,color="black",shape="box"];1315 -> 1351[label="",style="solid", color="black", weight=3];
1316[label="List.merge0 vz127 compare vz128 vz129 vz130 EQ",fontsize=16,color="black",shape="box"];1316 -> 1352[label="",style="solid", color="black", weight=3];
1317[label="List.merge0 vz127 compare vz128 vz129 vz130 GT",fontsize=16,color="black",shape="box"];1317 -> 1353[label="",style="solid", color="black", weight=3];
1231[label="List.merge compare vz117 (List.merge compare vz1180 vz11810)",fontsize=16,color="burlywood",shape="box"];1483[label="vz11810/vz118100 : vz118101",fontsize=10,color="white",style="solid",shape="box"];1231 -> 1483[label="",style="solid", color="burlywood", weight=9];
1483 -> 1239[label="",style="solid", color="burlywood", weight=3];
1484[label="vz11810/[]",fontsize=10,color="white",style="solid",shape="box"];1231 -> 1484[label="",style="solid", color="burlywood", weight=9];
1484 -> 1240[label="",style="solid", color="burlywood", weight=3];
1232[label="List.merge_pairs compare vz11811",fontsize=16,color="burlywood",shape="triangle"];1485[label="vz11811/vz118110 : vz118111",fontsize=10,color="white",style="solid",shape="box"];1232 -> 1485[label="",style="solid", color="burlywood", weight=9];
1485 -> 1241[label="",style="solid", color="burlywood", weight=3];
1486[label="vz11811/[]",fontsize=10,color="white",style="solid",shape="box"];1232 -> 1486[label="",style="solid", color="burlywood", weight=9];
1486 -> 1242[label="",style="solid", color="burlywood", weight=3];
1233[label="List.merge compare vz117 vz1180",fontsize=16,color="burlywood",shape="triangle"];1487[label="vz1180/vz11800 : vz11801",fontsize=10,color="white",style="solid",shape="box"];1233 -> 1487[label="",style="solid", color="burlywood", weight=9];
1487 -> 1243[label="",style="solid", color="burlywood", weight=3];
1488[label="vz1180/[]",fontsize=10,color="white",style="solid",shape="box"];1233 -> 1488[label="",style="solid", color="burlywood", weight=9];
1488 -> 1244[label="",style="solid", color="burlywood", weight=3];
1234[label="[]",fontsize=16,color="green",shape="box"];1349[label="primCmpInt (Pos vz12000) vz1190",fontsize=16,color="burlywood",shape="box"];1489[label="vz12000/Succ vz120000",fontsize=10,color="white",style="solid",shape="box"];1349 -> 1489[label="",style="solid", color="burlywood", weight=9];
1489 -> 1397[label="",style="solid", color="burlywood", weight=3];
1490[label="vz12000/Zero",fontsize=10,color="white",style="solid",shape="box"];1349 -> 1490[label="",style="solid", color="burlywood", weight=9];
1490 -> 1398[label="",style="solid", color="burlywood", weight=3];
1350[label="primCmpInt (Neg vz12000) vz1190",fontsize=16,color="burlywood",shape="box"];1491[label="vz12000/Succ vz120000",fontsize=10,color="white",style="solid",shape="box"];1350 -> 1491[label="",style="solid", color="burlywood", weight=9];
1491 -> 1399[label="",style="solid", color="burlywood", weight=3];
1492[label="vz12000/Zero",fontsize=10,color="white",style="solid",shape="box"];1350 -> 1492[label="",style="solid", color="burlywood", weight=9];
1492 -> 1400[label="",style="solid", color="burlywood", weight=3];
1351[label="vz128 : List.merge compare vz129 (vz127 : vz130)",fontsize=16,color="green",shape="box"];1351 -> 1401[label="",style="dashed", color="green", weight=3];
1352[label="vz128 : List.merge compare vz129 (vz127 : vz130)",fontsize=16,color="green",shape="box"];1352 -> 1402[label="",style="dashed", color="green", weight=3];
1353[label="vz127 : List.merge compare (vz128 : vz129) vz130",fontsize=16,color="green",shape="box"];1353 -> 1403[label="",style="dashed", color="green", weight=3];
1239[label="List.merge compare vz117 (List.merge compare vz1180 (vz118100 : vz118101))",fontsize=16,color="burlywood",shape="box"];1493[label="vz1180/vz11800 : vz11801",fontsize=10,color="white",style="solid",shape="box"];1239 -> 1493[label="",style="solid", color="burlywood", weight=9];
1493 -> 1253[label="",style="solid", color="burlywood", weight=3];
1494[label="vz1180/[]",fontsize=10,color="white",style="solid",shape="box"];1239 -> 1494[label="",style="solid", color="burlywood", weight=9];
1494 -> 1254[label="",style="solid", color="burlywood", weight=3];
1240[label="List.merge compare vz117 (List.merge compare vz1180 [])",fontsize=16,color="black",shape="box"];1240 -> 1255[label="",style="solid", color="black", weight=3];
1241[label="List.merge_pairs compare (vz118110 : vz118111)",fontsize=16,color="burlywood",shape="box"];1495[label="vz118111/vz1181110 : vz1181111",fontsize=10,color="white",style="solid",shape="box"];1241 -> 1495[label="",style="solid", color="burlywood", weight=9];
1495 -> 1256[label="",style="solid", color="burlywood", weight=3];
1496[label="vz118111/[]",fontsize=10,color="white",style="solid",shape="box"];1241 -> 1496[label="",style="solid", color="burlywood", weight=9];
1496 -> 1257[label="",style="solid", color="burlywood", weight=3];
1242[label="List.merge_pairs compare []",fontsize=16,color="black",shape="box"];1242 -> 1258[label="",style="solid", color="black", weight=3];
1243[label="List.merge compare vz117 (vz11800 : vz11801)",fontsize=16,color="burlywood",shape="box"];1497[label="vz117/vz1170 : vz1171",fontsize=10,color="white",style="solid",shape="box"];1243 -> 1497[label="",style="solid", color="burlywood", weight=9];
1497 -> 1259[label="",style="solid", color="burlywood", weight=3];
1498[label="vz117/[]",fontsize=10,color="white",style="solid",shape="box"];1243 -> 1498[label="",style="solid", color="burlywood", weight=9];
1498 -> 1260[label="",style="solid", color="burlywood", weight=3];
1244[label="List.merge compare vz117 []",fontsize=16,color="black",shape="box"];1244 -> 1261[label="",style="solid", color="black", weight=3];
1397[label="primCmpInt (Pos (Succ vz120000)) vz1190",fontsize=16,color="burlywood",shape="box"];1499[label="vz1190/Pos vz11900",fontsize=10,color="white",style="solid",shape="box"];1397 -> 1499[label="",style="solid", color="burlywood", weight=9];
1499 -> 1404[label="",style="solid", color="burlywood", weight=3];
1500[label="vz1190/Neg vz11900",fontsize=10,color="white",style="solid",shape="box"];1397 -> 1500[label="",style="solid", color="burlywood", weight=9];
1500 -> 1405[label="",style="solid", color="burlywood", weight=3];
1398[label="primCmpInt (Pos Zero) vz1190",fontsize=16,color="burlywood",shape="box"];1501[label="vz1190/Pos vz11900",fontsize=10,color="white",style="solid",shape="box"];1398 -> 1501[label="",style="solid", color="burlywood", weight=9];
1501 -> 1406[label="",style="solid", color="burlywood", weight=3];
1502[label="vz1190/Neg vz11900",fontsize=10,color="white",style="solid",shape="box"];1398 -> 1502[label="",style="solid", color="burlywood", weight=9];
1502 -> 1407[label="",style="solid", color="burlywood", weight=3];
1399[label="primCmpInt (Neg (Succ vz120000)) vz1190",fontsize=16,color="burlywood",shape="box"];1503[label="vz1190/Pos vz11900",fontsize=10,color="white",style="solid",shape="box"];1399 -> 1503[label="",style="solid", color="burlywood", weight=9];
1503 -> 1408[label="",style="solid", color="burlywood", weight=3];
1504[label="vz1190/Neg vz11900",fontsize=10,color="white",style="solid",shape="box"];1399 -> 1504[label="",style="solid", color="burlywood", weight=9];
1504 -> 1409[label="",style="solid", color="burlywood", weight=3];
1400[label="primCmpInt (Neg Zero) vz1190",fontsize=16,color="burlywood",shape="box"];1505[label="vz1190/Pos vz11900",fontsize=10,color="white",style="solid",shape="box"];1400 -> 1505[label="",style="solid", color="burlywood", weight=9];
1505 -> 1410[label="",style="solid", color="burlywood", weight=3];
1506[label="vz1190/Neg vz11900",fontsize=10,color="white",style="solid",shape="box"];1400 -> 1506[label="",style="solid", color="burlywood", weight=9];
1506 -> 1411[label="",style="solid", color="burlywood", weight=3];
1401 -> 1233[label="",style="dashed", color="red", weight=0];
1401[label="List.merge compare vz129 (vz127 : vz130)",fontsize=16,color="magenta"];1401 -> 1412[label="",style="dashed", color="magenta", weight=3];
1401 -> 1413[label="",style="dashed", color="magenta", weight=3];
1402 -> 1233[label="",style="dashed", color="red", weight=0];
1402[label="List.merge compare vz129 (vz127 : vz130)",fontsize=16,color="magenta"];1402 -> 1414[label="",style="dashed", color="magenta", weight=3];
1402 -> 1415[label="",style="dashed", color="magenta", weight=3];
1403 -> 1233[label="",style="dashed", color="red", weight=0];
1403[label="List.merge compare (vz128 : vz129) vz130",fontsize=16,color="magenta"];1403 -> 1416[label="",style="dashed", color="magenta", weight=3];
1403 -> 1417[label="",style="dashed", color="magenta", weight=3];
1253[label="List.merge compare vz117 (List.merge compare (vz11800 : vz11801) (vz118100 : vz118101))",fontsize=16,color="black",shape="box"];1253 -> 1274[label="",style="solid", color="black", weight=3];
1254[label="List.merge compare vz117 (List.merge compare [] (vz118100 : vz118101))",fontsize=16,color="black",shape="box"];1254 -> 1275[label="",style="solid", color="black", weight=3];
1255 -> 1233[label="",style="dashed", color="red", weight=0];
1255[label="List.merge compare vz117 vz1180",fontsize=16,color="magenta"];1256[label="List.merge_pairs compare (vz118110 : vz1181110 : vz1181111)",fontsize=16,color="black",shape="box"];1256 -> 1276[label="",style="solid", color="black", weight=3];
1257[label="List.merge_pairs compare (vz118110 : [])",fontsize=16,color="black",shape="box"];1257 -> 1277[label="",style="solid", color="black", weight=3];
1258[label="[]",fontsize=16,color="green",shape="box"];1259[label="List.merge compare (vz1170 : vz1171) (vz11800 : vz11801)",fontsize=16,color="black",shape="box"];1259 -> 1278[label="",style="solid", color="black", weight=3];
1260[label="List.merge compare [] (vz11800 : vz11801)",fontsize=16,color="black",shape="box"];1260 -> 1279[label="",style="solid", color="black", weight=3];
1261[label="vz117",fontsize=16,color="green",shape="box"];1404[label="primCmpInt (Pos (Succ vz120000)) (Pos vz11900)",fontsize=16,color="black",shape="box"];1404 -> 1418[label="",style="solid", color="black", weight=3];
1405[label="primCmpInt (Pos (Succ vz120000)) (Neg vz11900)",fontsize=16,color="black",shape="box"];1405 -> 1419[label="",style="solid", color="black", weight=3];
1406[label="primCmpInt (Pos Zero) (Pos vz11900)",fontsize=16,color="burlywood",shape="box"];1507[label="vz11900/Succ vz119000",fontsize=10,color="white",style="solid",shape="box"];1406 -> 1507[label="",style="solid", color="burlywood", weight=9];
1507 -> 1420[label="",style="solid", color="burlywood", weight=3];
1508[label="vz11900/Zero",fontsize=10,color="white",style="solid",shape="box"];1406 -> 1508[label="",style="solid", color="burlywood", weight=9];
1508 -> 1421[label="",style="solid", color="burlywood", weight=3];
1407[label="primCmpInt (Pos Zero) (Neg vz11900)",fontsize=16,color="burlywood",shape="box"];1509[label="vz11900/Succ vz119000",fontsize=10,color="white",style="solid",shape="box"];1407 -> 1509[label="",style="solid", color="burlywood", weight=9];
1509 -> 1422[label="",style="solid", color="burlywood", weight=3];
1510[label="vz11900/Zero",fontsize=10,color="white",style="solid",shape="box"];1407 -> 1510[label="",style="solid", color="burlywood", weight=9];
1510 -> 1423[label="",style="solid", color="burlywood", weight=3];
1408[label="primCmpInt (Neg (Succ vz120000)) (Pos vz11900)",fontsize=16,color="black",shape="box"];1408 -> 1424[label="",style="solid", color="black", weight=3];
1409[label="primCmpInt (Neg (Succ vz120000)) (Neg vz11900)",fontsize=16,color="black",shape="box"];1409 -> 1425[label="",style="solid", color="black", weight=3];
1410[label="primCmpInt (Neg Zero) (Pos vz11900)",fontsize=16,color="burlywood",shape="box"];1511[label="vz11900/Succ vz119000",fontsize=10,color="white",style="solid",shape="box"];1410 -> 1511[label="",style="solid", color="burlywood", weight=9];
1511 -> 1426[label="",style="solid", color="burlywood", weight=3];
1512[label="vz11900/Zero",fontsize=10,color="white",style="solid",shape="box"];1410 -> 1512[label="",style="solid", color="burlywood", weight=9];
1512 -> 1427[label="",style="solid", color="burlywood", weight=3];
1411[label="primCmpInt (Neg Zero) (Neg vz11900)",fontsize=16,color="burlywood",shape="box"];1513[label="vz11900/Succ vz119000",fontsize=10,color="white",style="solid",shape="box"];1411 -> 1513[label="",style="solid", color="burlywood", weight=9];
1513 -> 1428[label="",style="solid", color="burlywood", weight=3];
1514[label="vz11900/Zero",fontsize=10,color="white",style="solid",shape="box"];1411 -> 1514[label="",style="solid", color="burlywood", weight=9];
1514 -> 1429[label="",style="solid", color="burlywood", weight=3];
1412[label="vz129",fontsize=16,color="green",shape="box"];1413[label="vz127 : vz130",fontsize=16,color="green",shape="box"];1414[label="vz129",fontsize=16,color="green",shape="box"];1415[label="vz127 : vz130",fontsize=16,color="green",shape="box"];1416[label="vz128 : vz129",fontsize=16,color="green",shape="box"];1417[label="vz130",fontsize=16,color="green",shape="box"];1274 -> 1233[label="",style="dashed", color="red", weight=0];
1274[label="List.merge compare vz117 (List.merge0 vz118100 compare vz11800 vz11801 vz118101 (compare vz11800 vz118100))",fontsize=16,color="magenta"];1274 -> 1294[label="",style="dashed", color="magenta", weight=3];
1275 -> 1233[label="",style="dashed", color="red", weight=0];
1275[label="List.merge compare vz117 (vz118100 : vz118101)",fontsize=16,color="magenta"];1275 -> 1295[label="",style="dashed", color="magenta", weight=3];
1276[label="List.merge compare vz118110 vz1181110 : List.merge_pairs compare vz1181111",fontsize=16,color="green",shape="box"];1276 -> 1296[label="",style="dashed", color="green", weight=3];
1276 -> 1297[label="",style="dashed", color="green", weight=3];
1277[label="vz118110 : []",fontsize=16,color="green",shape="box"];1278 -> 1298[label="",style="dashed", color="red", weight=0];
1278[label="List.merge0 vz11800 compare vz1170 vz1171 vz11801 (compare vz1170 vz11800)",fontsize=16,color="magenta"];1278 -> 1304[label="",style="dashed", color="magenta", weight=3];
1278 -> 1305[label="",style="dashed", color="magenta", weight=3];
1278 -> 1306[label="",style="dashed", color="magenta", weight=3];
1278 -> 1307[label="",style="dashed", color="magenta", weight=3];
1278 -> 1308[label="",style="dashed", color="magenta", weight=3];
1279[label="vz11800 : vz11801",fontsize=16,color="green",shape="box"];1418[label="primCmpNat (Succ vz120000) vz11900",fontsize=16,color="burlywood",shape="triangle"];1515[label="vz11900/Succ vz119000",fontsize=10,color="white",style="solid",shape="box"];1418 -> 1515[label="",style="solid", color="burlywood", weight=9];
1515 -> 1430[label="",style="solid", color="burlywood", weight=3];
1516[label="vz11900/Zero",fontsize=10,color="white",style="solid",shape="box"];1418 -> 1516[label="",style="solid", color="burlywood", weight=9];
1516 -> 1431[label="",style="solid", color="burlywood", weight=3];
1419[label="GT",fontsize=16,color="green",shape="box"];1420[label="primCmpInt (Pos Zero) (Pos (Succ vz119000))",fontsize=16,color="black",shape="box"];1420 -> 1432[label="",style="solid", color="black", weight=3];
1421[label="primCmpInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];1421 -> 1433[label="",style="solid", color="black", weight=3];
1422[label="primCmpInt (Pos Zero) (Neg (Succ vz119000))",fontsize=16,color="black",shape="box"];1422 -> 1434[label="",style="solid", color="black", weight=3];
1423[label="primCmpInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1423 -> 1435[label="",style="solid", color="black", weight=3];
1424[label="LT",fontsize=16,color="green",shape="box"];1425[label="primCmpNat vz11900 (Succ vz120000)",fontsize=16,color="burlywood",shape="triangle"];1517[label="vz11900/Succ vz119000",fontsize=10,color="white",style="solid",shape="box"];1425 -> 1517[label="",style="solid", color="burlywood", weight=9];
1517 -> 1436[label="",style="solid", color="burlywood", weight=3];
1518[label="vz11900/Zero",fontsize=10,color="white",style="solid",shape="box"];1425 -> 1518[label="",style="solid", color="burlywood", weight=9];
1518 -> 1437[label="",style="solid", color="burlywood", weight=3];
1426[label="primCmpInt (Neg Zero) (Pos (Succ vz119000))",fontsize=16,color="black",shape="box"];1426 -> 1438[label="",style="solid", color="black", weight=3];
1427[label="primCmpInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];1427 -> 1439[label="",style="solid", color="black", weight=3];
1428[label="primCmpInt (Neg Zero) (Neg (Succ vz119000))",fontsize=16,color="black",shape="box"];1428 -> 1440[label="",style="solid", color="black", weight=3];
1429[label="primCmpInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1429 -> 1441[label="",style="solid", color="black", weight=3];
1294 -> 1298[label="",style="dashed", color="red", weight=0];
1294[label="List.merge0 vz118100 compare vz11800 vz11801 vz118101 (compare vz11800 vz118100)",fontsize=16,color="magenta"];1294 -> 1309[label="",style="dashed", color="magenta", weight=3];
1294 -> 1310[label="",style="dashed", color="magenta", weight=3];
1294 -> 1311[label="",style="dashed", color="magenta", weight=3];
1294 -> 1312[label="",style="dashed", color="magenta", weight=3];
1294 -> 1313[label="",style="dashed", color="magenta", weight=3];
1295[label="vz118100 : vz118101",fontsize=16,color="green",shape="box"];1296 -> 1233[label="",style="dashed", color="red", weight=0];
1296[label="List.merge compare vz118110 vz1181110",fontsize=16,color="magenta"];1296 -> 1318[label="",style="dashed", color="magenta", weight=3];
1296 -> 1319[label="",style="dashed", color="magenta", weight=3];
1297 -> 1232[label="",style="dashed", color="red", weight=0];
1297[label="List.merge_pairs compare vz1181111",fontsize=16,color="magenta"];1297 -> 1320[label="",style="dashed", color="magenta", weight=3];
1304[label="vz11801",fontsize=16,color="green",shape="box"];1305[label="vz1170",fontsize=16,color="green",shape="box"];1306[label="compare vz1170 vz11800",fontsize=16,color="blue",shape="box"];1519[label="compare :: Double -> Double -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1519[label="",style="solid", color="blue", weight=9];
1519 -> 1321[label="",style="solid", color="blue", weight=3];
1520[label="compare :: Bool -> Bool -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1520[label="",style="solid", color="blue", weight=9];
1520 -> 1322[label="",style="solid", color="blue", weight=3];
1521[label="compare :: ((@2) a b) -> ((@2) a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1521[label="",style="solid", color="blue", weight=9];
1521 -> 1323[label="",style="solid", color="blue", weight=3];
1522[label="compare :: (Ratio a) -> (Ratio a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1522[label="",style="solid", color="blue", weight=9];
1522 -> 1324[label="",style="solid", color="blue", weight=3];
1523[label="compare :: () -> () -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1523[label="",style="solid", color="blue", weight=9];
1523 -> 1325[label="",style="solid", color="blue", weight=3];
1524[label="compare :: (Maybe a) -> (Maybe a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1524[label="",style="solid", color="blue", weight=9];
1524 -> 1326[label="",style="solid", color="blue", weight=3];
1525[label="compare :: Integer -> Integer -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1525[label="",style="solid", color="blue", weight=9];
1525 -> 1327[label="",style="solid", color="blue", weight=3];
1526[label="compare :: (Either a b) -> (Either a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1526[label="",style="solid", color="blue", weight=9];
1526 -> 1328[label="",style="solid", color="blue", weight=3];
1527[label="compare :: ([] a) -> ([] a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1527[label="",style="solid", color="blue", weight=9];
1527 -> 1329[label="",style="solid", color="blue", weight=3];
1528[label="compare :: Int -> Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1528[label="",style="solid", color="blue", weight=9];
1528 -> 1330[label="",style="solid", color="blue", weight=3];
1529[label="compare :: Float -> Float -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1529[label="",style="solid", color="blue", weight=9];
1529 -> 1331[label="",style="solid", color="blue", weight=3];
1530[label="compare :: Ordering -> Ordering -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1530[label="",style="solid", color="blue", weight=9];
1530 -> 1332[label="",style="solid", color="blue", weight=3];
1531[label="compare :: ((@3) a b c) -> ((@3) a b c) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1531[label="",style="solid", color="blue", weight=9];
1531 -> 1333[label="",style="solid", color="blue", weight=3];
1532[label="compare :: Char -> Char -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1306 -> 1532[label="",style="solid", color="blue", weight=9];
1532 -> 1334[label="",style="solid", color="blue", weight=3];
1307[label="vz11800",fontsize=16,color="green",shape="box"];1308[label="vz1171",fontsize=16,color="green",shape="box"];1430[label="primCmpNat (Succ vz120000) (Succ vz119000)",fontsize=16,color="black",shape="box"];1430 -> 1442[label="",style="solid", color="black", weight=3];
1431[label="primCmpNat (Succ vz120000) Zero",fontsize=16,color="black",shape="box"];1431 -> 1443[label="",style="solid", color="black", weight=3];
1432 -> 1425[label="",style="dashed", color="red", weight=0];
1432[label="primCmpNat Zero (Succ vz119000)",fontsize=16,color="magenta"];1432 -> 1444[label="",style="dashed", color="magenta", weight=3];
1432 -> 1445[label="",style="dashed", color="magenta", weight=3];
1433[label="EQ",fontsize=16,color="green",shape="box"];1434[label="GT",fontsize=16,color="green",shape="box"];1435[label="EQ",fontsize=16,color="green",shape="box"];1436[label="primCmpNat (Succ vz119000) (Succ vz120000)",fontsize=16,color="black",shape="box"];1436 -> 1446[label="",style="solid", color="black", weight=3];
1437[label="primCmpNat Zero (Succ vz120000)",fontsize=16,color="black",shape="box"];1437 -> 1447[label="",style="solid", color="black", weight=3];
1438[label="LT",fontsize=16,color="green",shape="box"];1439[label="EQ",fontsize=16,color="green",shape="box"];1440 -> 1418[label="",style="dashed", color="red", weight=0];
1440[label="primCmpNat (Succ vz119000) Zero",fontsize=16,color="magenta"];1440 -> 1448[label="",style="dashed", color="magenta", weight=3];
1440 -> 1449[label="",style="dashed", color="magenta", weight=3];
1441[label="EQ",fontsize=16,color="green",shape="box"];1309[label="vz118101",fontsize=16,color="green",shape="box"];1310[label="vz11800",fontsize=16,color="green",shape="box"];1311[label="compare vz11800 vz118100",fontsize=16,color="blue",shape="box"];1533[label="compare :: Double -> Double -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1533[label="",style="solid", color="blue", weight=9];
1533 -> 1335[label="",style="solid", color="blue", weight=3];
1534[label="compare :: Bool -> Bool -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1534[label="",style="solid", color="blue", weight=9];
1534 -> 1336[label="",style="solid", color="blue", weight=3];
1535[label="compare :: ((@2) a b) -> ((@2) a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1535[label="",style="solid", color="blue", weight=9];
1535 -> 1337[label="",style="solid", color="blue", weight=3];
1536[label="compare :: (Ratio a) -> (Ratio a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1536[label="",style="solid", color="blue", weight=9];
1536 -> 1338[label="",style="solid", color="blue", weight=3];
1537[label="compare :: () -> () -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1537[label="",style="solid", color="blue", weight=9];
1537 -> 1339[label="",style="solid", color="blue", weight=3];
1538[label="compare :: (Maybe a) -> (Maybe a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1538[label="",style="solid", color="blue", weight=9];
1538 -> 1340[label="",style="solid", color="blue", weight=3];
1539[label="compare :: Integer -> Integer -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1539[label="",style="solid", color="blue", weight=9];
1539 -> 1341[label="",style="solid", color="blue", weight=3];
1540[label="compare :: (Either a b) -> (Either a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1540[label="",style="solid", color="blue", weight=9];
1540 -> 1342[label="",style="solid", color="blue", weight=3];
1541[label="compare :: ([] a) -> ([] a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1541[label="",style="solid", color="blue", weight=9];
1541 -> 1343[label="",style="solid", color="blue", weight=3];
1542[label="compare :: Int -> Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1542[label="",style="solid", color="blue", weight=9];
1542 -> 1344[label="",style="solid", color="blue", weight=3];
1543[label="compare :: Float -> Float -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1543[label="",style="solid", color="blue", weight=9];
1543 -> 1345[label="",style="solid", color="blue", weight=3];
1544[label="compare :: Ordering -> Ordering -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1544[label="",style="solid", color="blue", weight=9];
1544 -> 1346[label="",style="solid", color="blue", weight=3];
1545[label="compare :: ((@3) a b c) -> ((@3) a b c) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1545[label="",style="solid", color="blue", weight=9];
1545 -> 1347[label="",style="solid", color="blue", weight=3];
1546[label="compare :: Char -> Char -> Ordering",fontsize=10,color="white",style="solid",shape="box"];1311 -> 1546[label="",style="solid", color="blue", weight=9];
1546 -> 1348[label="",style="solid", color="blue", weight=3];
1312[label="vz118100",fontsize=16,color="green",shape="box"];1313[label="vz11801",fontsize=16,color="green",shape="box"];1318[label="vz118110",fontsize=16,color="green",shape="box"];1319[label="vz1181110",fontsize=16,color="green",shape="box"];1320[label="vz1181111",fontsize=16,color="green",shape="box"];1321[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1321 -> 1354[label="",style="solid", color="black", weight=3];
1322[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1322 -> 1355[label="",style="solid", color="black", weight=3];
1323[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1323 -> 1356[label="",style="solid", color="black", weight=3];
1324[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1324 -> 1357[label="",style="solid", color="black", weight=3];
1325[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1325 -> 1358[label="",style="solid", color="black", weight=3];
1326[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1326 -> 1359[label="",style="solid", color="black", weight=3];
1327[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1327 -> 1360[label="",style="solid", color="black", weight=3];
1328[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1328 -> 1361[label="",style="solid", color="black", weight=3];
1329[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1329 -> 1362[label="",style="solid", color="black", weight=3];
1330 -> 1301[label="",style="dashed", color="red", weight=0];
1330[label="compare vz1170 vz11800",fontsize=16,color="magenta"];1330 -> 1363[label="",style="dashed", color="magenta", weight=3];
1330 -> 1364[label="",style="dashed", color="magenta", weight=3];
1331[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1331 -> 1365[label="",style="solid", color="black", weight=3];
1332[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1332 -> 1366[label="",style="solid", color="black", weight=3];
1333[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1333 -> 1367[label="",style="solid", color="black", weight=3];
1334[label="compare vz1170 vz11800",fontsize=16,color="black",shape="triangle"];1334 -> 1368[label="",style="solid", color="black", weight=3];
1442[label="primCmpNat vz120000 vz119000",fontsize=16,color="burlywood",shape="triangle"];1547[label="vz120000/Succ vz1200000",fontsize=10,color="white",style="solid",shape="box"];1442 -> 1547[label="",style="solid", color="burlywood", weight=9];
1547 -> 1450[label="",style="solid", color="burlywood", weight=3];
1548[label="vz120000/Zero",fontsize=10,color="white",style="solid",shape="box"];1442 -> 1548[label="",style="solid", color="burlywood", weight=9];
1548 -> 1451[label="",style="solid", color="burlywood", weight=3];
1443[label="GT",fontsize=16,color="green",shape="box"];1444[label="vz119000",fontsize=16,color="green",shape="box"];1445[label="Zero",fontsize=16,color="green",shape="box"];1446 -> 1442[label="",style="dashed", color="red", weight=0];
1446[label="primCmpNat vz119000 vz120000",fontsize=16,color="magenta"];1446 -> 1452[label="",style="dashed", color="magenta", weight=3];
1446 -> 1453[label="",style="dashed", color="magenta", weight=3];
1447[label="LT",fontsize=16,color="green",shape="box"];1448[label="Zero",fontsize=16,color="green",shape="box"];1449[label="vz119000",fontsize=16,color="green",shape="box"];1335 -> 1321[label="",style="dashed", color="red", weight=0];
1335[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1335 -> 1369[label="",style="dashed", color="magenta", weight=3];
1335 -> 1370[label="",style="dashed", color="magenta", weight=3];
1336 -> 1322[label="",style="dashed", color="red", weight=0];
1336[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1336 -> 1371[label="",style="dashed", color="magenta", weight=3];
1336 -> 1372[label="",style="dashed", color="magenta", weight=3];
1337 -> 1323[label="",style="dashed", color="red", weight=0];
1337[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1337 -> 1373[label="",style="dashed", color="magenta", weight=3];
1337 -> 1374[label="",style="dashed", color="magenta", weight=3];
1338 -> 1324[label="",style="dashed", color="red", weight=0];
1338[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1338 -> 1375[label="",style="dashed", color="magenta", weight=3];
1338 -> 1376[label="",style="dashed", color="magenta", weight=3];
1339 -> 1325[label="",style="dashed", color="red", weight=0];
1339[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1339 -> 1377[label="",style="dashed", color="magenta", weight=3];
1339 -> 1378[label="",style="dashed", color="magenta", weight=3];
1340 -> 1326[label="",style="dashed", color="red", weight=0];
1340[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1340 -> 1379[label="",style="dashed", color="magenta", weight=3];
1340 -> 1380[label="",style="dashed", color="magenta", weight=3];
1341 -> 1327[label="",style="dashed", color="red", weight=0];
1341[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1341 -> 1381[label="",style="dashed", color="magenta", weight=3];
1341 -> 1382[label="",style="dashed", color="magenta", weight=3];
1342 -> 1328[label="",style="dashed", color="red", weight=0];
1342[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1342 -> 1383[label="",style="dashed", color="magenta", weight=3];
1342 -> 1384[label="",style="dashed", color="magenta", weight=3];
1343 -> 1329[label="",style="dashed", color="red", weight=0];
1343[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1343 -> 1385[label="",style="dashed", color="magenta", weight=3];
1343 -> 1386[label="",style="dashed", color="magenta", weight=3];
1344 -> 1301[label="",style="dashed", color="red", weight=0];
1344[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1344 -> 1387[label="",style="dashed", color="magenta", weight=3];
1344 -> 1388[label="",style="dashed", color="magenta", weight=3];
1345 -> 1331[label="",style="dashed", color="red", weight=0];
1345[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1345 -> 1389[label="",style="dashed", color="magenta", weight=3];
1345 -> 1390[label="",style="dashed", color="magenta", weight=3];
1346 -> 1332[label="",style="dashed", color="red", weight=0];
1346[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1346 -> 1391[label="",style="dashed", color="magenta", weight=3];
1346 -> 1392[label="",style="dashed", color="magenta", weight=3];
1347 -> 1333[label="",style="dashed", color="red", weight=0];
1347[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1347 -> 1393[label="",style="dashed", color="magenta", weight=3];
1347 -> 1394[label="",style="dashed", color="magenta", weight=3];
1348 -> 1334[label="",style="dashed", color="red", weight=0];
1348[label="compare vz11800 vz118100",fontsize=16,color="magenta"];1348 -> 1395[label="",style="dashed", color="magenta", weight=3];
1348 -> 1396[label="",style="dashed", color="magenta", weight=3];
1354[label="error []",fontsize=16,color="red",shape="box"];1355[label="error []",fontsize=16,color="red",shape="box"];1356[label="error []",fontsize=16,color="red",shape="box"];1357[label="error []",fontsize=16,color="red",shape="box"];1358[label="error []",fontsize=16,color="red",shape="box"];1359[label="error []",fontsize=16,color="red",shape="box"];1360[label="error []",fontsize=16,color="red",shape="box"];1361[label="error []",fontsize=16,color="red",shape="box"];1362[label="error []",fontsize=16,color="red",shape="box"];1363[label="vz1170",fontsize=16,color="green",shape="box"];1364[label="vz11800",fontsize=16,color="green",shape="box"];1365[label="error []",fontsize=16,color="red",shape="box"];1366[label="error []",fontsize=16,color="red",shape="box"];1367[label="error []",fontsize=16,color="red",shape="box"];1368[label="error []",fontsize=16,color="red",shape="box"];1450[label="primCmpNat (Succ vz1200000) vz119000",fontsize=16,color="burlywood",shape="box"];1549[label="vz119000/Succ vz1190000",fontsize=10,color="white",style="solid",shape="box"];1450 -> 1549[label="",style="solid", color="burlywood", weight=9];
1549 -> 1454[label="",style="solid", color="burlywood", weight=3];
1550[label="vz119000/Zero",fontsize=10,color="white",style="solid",shape="box"];1450 -> 1550[label="",style="solid", color="burlywood", weight=9];
1550 -> 1455[label="",style="solid", color="burlywood", weight=3];
1451[label="primCmpNat Zero vz119000",fontsize=16,color="burlywood",shape="box"];1551[label="vz119000/Succ vz1190000",fontsize=10,color="white",style="solid",shape="box"];1451 -> 1551[label="",style="solid", color="burlywood", weight=9];
1551 -> 1456[label="",style="solid", color="burlywood", weight=3];
1552[label="vz119000/Zero",fontsize=10,color="white",style="solid",shape="box"];1451 -> 1552[label="",style="solid", color="burlywood", weight=9];
1552 -> 1457[label="",style="solid", color="burlywood", weight=3];
1452[label="vz119000",fontsize=16,color="green",shape="box"];1453[label="vz120000",fontsize=16,color="green",shape="box"];1369[label="vz118100",fontsize=16,color="green",shape="box"];1370[label="vz11800",fontsize=16,color="green",shape="box"];1371[label="vz118100",fontsize=16,color="green",shape="box"];1372[label="vz11800",fontsize=16,color="green",shape="box"];1373[label="vz118100",fontsize=16,color="green",shape="box"];1374[label="vz11800",fontsize=16,color="green",shape="box"];1375[label="vz118100",fontsize=16,color="green",shape="box"];1376[label="vz11800",fontsize=16,color="green",shape="box"];1377[label="vz118100",fontsize=16,color="green",shape="box"];1378[label="vz11800",fontsize=16,color="green",shape="box"];1379[label="vz118100",fontsize=16,color="green",shape="box"];1380[label="vz11800",fontsize=16,color="green",shape="box"];1381[label="vz118100",fontsize=16,color="green",shape="box"];1382[label="vz11800",fontsize=16,color="green",shape="box"];1383[label="vz118100",fontsize=16,color="green",shape="box"];1384[label="vz11800",fontsize=16,color="green",shape="box"];1385[label="vz118100",fontsize=16,color="green",shape="box"];1386[label="vz11800",fontsize=16,color="green",shape="box"];1387[label="vz11800",fontsize=16,color="green",shape="box"];1388[label="vz118100",fontsize=16,color="green",shape="box"];1389[label="vz118100",fontsize=16,color="green",shape="box"];1390[label="vz11800",fontsize=16,color="green",shape="box"];1391[label="vz118100",fontsize=16,color="green",shape="box"];1392[label="vz11800",fontsize=16,color="green",shape="box"];1393[label="vz118100",fontsize=16,color="green",shape="box"];1394[label="vz11800",fontsize=16,color="green",shape="box"];1395[label="vz118100",fontsize=16,color="green",shape="box"];1396[label="vz11800",fontsize=16,color="green",shape="box"];1454[label="primCmpNat (Succ vz1200000) (Succ vz1190000)",fontsize=16,color="black",shape="box"];1454 -> 1458[label="",style="solid", color="black", weight=3];
1455[label="primCmpNat (Succ vz1200000) Zero",fontsize=16,color="black",shape="box"];1455 -> 1459[label="",style="solid", color="black", weight=3];
1456[label="primCmpNat Zero (Succ vz1190000)",fontsize=16,color="black",shape="box"];1456 -> 1460[label="",style="solid", color="black", weight=3];
1457[label="primCmpNat Zero Zero",fontsize=16,color="black",shape="box"];1457 -> 1461[label="",style="solid", color="black", weight=3];
1458 -> 1442[label="",style="dashed", color="red", weight=0];
1458[label="primCmpNat vz1200000 vz1190000",fontsize=16,color="magenta"];1458 -> 1462[label="",style="dashed", color="magenta", weight=3];
1458 -> 1463[label="",style="dashed", color="magenta", weight=3];
1459[label="GT",fontsize=16,color="green",shape="box"];1460[label="LT",fontsize=16,color="green",shape="box"];1461[label="EQ",fontsize=16,color="green",shape="box"];1462[label="vz1200000",fontsize=16,color="green",shape="box"];1463[label="vz1190000",fontsize=16,color="green",shape="box"];}

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

(8)
Complex Obligation (AND)

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

(9)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primCmpNat(Succ(vz1200000), Succ(vz1190000)) -> new_primCmpNat(vz1200000, vz1190000)

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

(10) 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_primCmpNat(Succ(vz1200000), Succ(vz1190000)) -> new_primCmpNat(vz1200000, vz1190000)
The graph contains the following edges 1 > 1, 2 > 2


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

(11)
YES

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

(12)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_mergesort'(vz117, :(vz1180, []), ba) -> new_mergesort'(new_merge2(vz117, vz1180, ba), [], ba)
   new_mergesort'(vz117, :(vz1180, :(vz11810, vz11811)), ba) -> new_mergesort'(new_merge1(vz117, vz1180, vz11810, ba), new_merge_pairs0(vz11811, ba), ba)

The TRS R consists of the following rules:

   new_compare14(vz11800, vz118100, app(app(app(ty_@3, bc), bd), be)) -> new_compare4(vz11800, vz118100, bc, bd, be)
   new_compare14(vz11800, vz118100, app(app(ty_Either, cc), cd)) -> new_compare11(vz11800, vz118100, cc, cd)
   new_compare(vz1170, vz11800, ty_Float) -> new_compare2(vz1170, vz11800)
   new_compare13(Pos(Succ(vz120000)), Neg(vz11900)) -> GT
   new_compare13(Neg(Zero), Pos(Succ(vz119000))) -> LT
   new_compare13(Neg(Zero), Neg(Zero)) -> EQ
   new_compare(vz1170, vz11800, app(ty_[], cb)) -> new_compare12(vz1170, vz11800, cb)
   new_primCmpNat0(vz120000, Succ(vz119000)) -> new_primCmpNat1(vz120000, vz119000)
   new_compare(vz1170, vz11800, ty_Int) -> new_compare13(vz1170, vz11800)
   new_compare14(vz11800, vz118100, app(ty_Ratio, bh)) -> new_compare7(vz11800, vz118100, bh)
   new_primCmpNat1(Zero, Zero) -> EQ
   new_compare13(Pos(Succ(vz120000)), Pos(vz11900)) -> new_primCmpNat0(vz120000, vz11900)
   new_merge_pairs0(:(vz118110, []), ba) -> :(vz118110, [])
   new_compare13(Neg(Zero), Neg(Succ(vz119000))) -> new_primCmpNat0(vz119000, Zero)
   new_merge1(vz117, :(vz11800, vz11801), :(vz118100, vz118101), ba) -> new_merge2(vz117, new_merge00(vz118100, vz11800, vz11801, vz118101, new_compare14(vz11800, vz118100, ba), ba), ba)
   new_compare(vz1170, vz11800, ty_Bool) -> new_compare0(vz1170, vz11800)
   new_compare8(vz1170, vz11800) -> error([])
   new_primCmpNat1(Succ(vz1200000), Zero) -> GT
   new_compare13(Pos(Zero), Pos(Succ(vz119000))) -> new_primCmpNat2(Zero, vz119000)
   new_compare14(vz11800, vz118100, app(app(ty_@2, bf), bg)) -> new_compare6(vz11800, vz118100, bf, bg)
   new_compare13(Neg(Succ(vz120000)), Neg(vz11900)) -> new_primCmpNat2(vz11900, vz120000)
   new_compare13(Neg(Succ(vz120000)), Pos(vz11900)) -> LT
   new_merge2([], :(vz11800, vz11801), ba) -> :(vz11800, vz11801)
   new_compare14(vz11800, vz118100, ty_Float) -> new_compare2(vz11800, vz118100)
   new_compare0(vz1170, vz11800) -> error([])
   new_compare14(vz11800, vz118100, app(ty_[], cb)) -> new_compare12(vz11800, vz118100, cb)
   new_compare14(vz11800, vz118100, ty_Int) -> new_compare13(vz11800, vz118100)
   new_compare14(vz11800, vz118100, ty_Double) -> new_compare8(vz11800, vz118100)
   new_compare(vz1170, vz11800, app(app(ty_Either, cc), cd)) -> new_compare11(vz1170, vz11800, cc, cd)
   new_compare14(vz11800, vz118100, ty_Char) -> new_compare5(vz11800, vz118100)
   new_primCmpNat2(Succ(vz119000), vz120000) -> new_primCmpNat1(vz119000, vz120000)
   new_merge_pairs0(:(vz118110, :(vz1181110, vz1181111)), ba) -> :(new_merge2(vz118110, vz1181110, ba), new_merge_pairs0(vz1181111, ba))
   new_compare(vz1170, vz11800, app(app(ty_@2, bf), bg)) -> new_compare6(vz1170, vz11800, bf, bg)
   new_primCmpNat0(vz120000, Zero) -> GT
   new_merge00(vz127, vz128, vz129, vz130, LT, ca) -> :(vz128, new_merge2(vz129, :(vz127, vz130), ca))
   new_compare13(Pos(Zero), Pos(Zero)) -> EQ
   new_primCmpNat2(Zero, vz120000) -> LT
   new_compare13(Pos(Zero), Neg(Zero)) -> EQ
   new_compare13(Neg(Zero), Pos(Zero)) -> EQ
   new_merge2(:(vz1170, vz1171), :(vz11800, vz11801), ba) -> new_merge00(vz11800, vz1170, vz1171, vz11801, new_compare(vz1170, vz11800, ba), ba)
   new_primCmpNat1(Succ(vz1200000), Succ(vz1190000)) -> new_primCmpNat1(vz1200000, vz1190000)
   new_compare14(vz11800, vz118100, app(ty_Maybe, bb)) -> new_compare3(vz11800, vz118100, bb)
   new_compare14(vz11800, vz118100, ty_Ordering) -> new_compare1(vz11800, vz118100)
   new_merge2(vz117, [], ba) -> vz117
   new_compare(vz1170, vz11800, app(ty_Ratio, bh)) -> new_compare7(vz1170, vz11800, bh)
   new_compare(vz1170, vz11800, ty_@0) -> new_compare9(vz1170, vz11800)
   new_compare(vz1170, vz11800, app(app(app(ty_@3, bc), bd), be)) -> new_compare4(vz1170, vz11800, bc, bd, be)
   new_merge_pairs0([], ba) -> []
   new_merge1(vz117, [], :(vz118100, vz118101), ba) -> new_merge2(vz117, :(vz118100, vz118101), ba)
   new_compare2(vz1170, vz11800) -> error([])
   new_compare13(Pos(Zero), Neg(Succ(vz119000))) -> GT
   new_compare7(vz1170, vz11800, bh) -> error([])
   new_primCmpNat1(Zero, Succ(vz1190000)) -> LT
   new_compare3(vz1170, vz11800, bb) -> error([])
   new_merge00(vz127, vz128, vz129, vz130, GT, ca) -> :(vz127, new_merge2(:(vz128, vz129), vz130, ca))
   new_compare(vz1170, vz11800, ty_Double) -> new_compare8(vz1170, vz11800)
   new_compare14(vz11800, vz118100, ty_@0) -> new_compare9(vz11800, vz118100)
   new_compare5(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, ty_Char) -> new_compare5(vz1170, vz11800)
   new_compare14(vz11800, vz118100, ty_Integer) -> new_compare10(vz11800, vz118100)
   new_compare4(vz1170, vz11800, bc, bd, be) -> error([])
   new_merge00(vz127, vz128, vz129, vz130, EQ, ca) -> :(vz128, new_merge2(vz129, :(vz127, vz130), ca))
   new_compare10(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, app(ty_Maybe, bb)) -> new_compare3(vz1170, vz11800, bb)
   new_compare(vz1170, vz11800, ty_Integer) -> new_compare10(vz1170, vz11800)
   new_compare12(vz1170, vz11800, cb) -> error([])
   new_compare(vz1170, vz11800, ty_Ordering) -> new_compare1(vz1170, vz11800)
   new_compare11(vz1170, vz11800, cc, cd) -> error([])
   new_compare1(vz1170, vz11800) -> error([])
   new_compare14(vz11800, vz118100, ty_Bool) -> new_compare0(vz11800, vz118100)
   new_compare6(vz1170, vz11800, bf, bg) -> error([])
   new_merge1(vz117, vz1180, [], ba) -> new_merge2(vz117, vz1180, ba)
   new_compare9(vz1170, vz11800) -> error([])

The set Q consists of the following terms:

   new_compare14(x0, x1, app(ty_Maybe, x2))
   new_primCmpNat2(Succ(x0), x1)
   new_compare1(x0, x1)
   new_merge1(x0, [], :(x1, x2), x3)
   new_merge1(x0, x1, [], x2)
   new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_compare13(Neg(Zero), Neg(Zero))
   new_compare(x0, x1, ty_Int)
   new_compare10(x0, x1)
   new_compare13(Neg(Zero), Neg(Succ(x0)))
   new_compare13(Pos(Succ(x0)), Pos(x1))
   new_compare0(x0, x1)
   new_compare(x0, x1, app(ty_[], x2))
   new_compare14(x0, x1, ty_Char)
   new_compare14(x0, x1, ty_@0)
   new_compare11(x0, x1, x2, x3)
   new_merge2(:(x0, x1), :(x2, x3), x4)
   new_compare14(x0, x1, ty_Double)
   new_compare(x0, x1, app(app(ty_Either, x2), x3))
   new_compare14(x0, x1, app(app(ty_Either, x2), x3))
   new_compare(x0, x1, ty_Integer)
   new_compare14(x0, x1, ty_Ordering)
   new_compare(x0, x1, ty_Ordering)
   new_compare13(Pos(Zero), Pos(Zero))
   new_primCmpNat0(x0, Succ(x1))
   new_compare13(Pos(Succ(x0)), Neg(x1))
   new_compare13(Neg(Succ(x0)), Pos(x1))
   new_compare9(x0, x1)
   new_compare14(x0, x1, app(ty_[], x2))
   new_compare13(Neg(Succ(x0)), Neg(x1))
   new_merge_pairs0(:(x0, :(x1, x2)), x3)
   new_compare4(x0, x1, x2, x3, x4)
   new_merge2(x0, [], x1)
   new_compare(x0, x1, ty_Bool)
   new_primCmpNat1(Zero, Zero)
   new_compare2(x0, x1)
   new_compare(x0, x1, app(app(ty_@2, x2), x3))
   new_compare14(x0, x1, ty_Int)
   new_primCmpNat0(x0, Zero)
   new_compare12(x0, x1, x2)
   new_compare13(Neg(Zero), Pos(Succ(x0)))
   new_compare13(Pos(Zero), Neg(Succ(x0)))
   new_merge00(x0, x1, x2, x3, GT, x4)
   new_primCmpNat2(Zero, x0)
   new_primCmpNat1(Succ(x0), Zero)
   new_compare(x0, x1, app(ty_Maybe, x2))
   new_compare(x0, x1, ty_@0)
   new_compare14(x0, x1, app(ty_Ratio, x2))
   new_compare(x0, x1, ty_Char)
   new_compare(x0, x1, ty_Float)
   new_primCmpNat1(Succ(x0), Succ(x1))
   new_compare(x0, x1, ty_Double)
   new_merge00(x0, x1, x2, x3, LT, x4)
   new_compare7(x0, x1, x2)
   new_merge1(x0, :(x1, x2), :(x3, x4), x5)
   new_compare13(Pos(Zero), Pos(Succ(x0)))
   new_merge_pairs0(:(x0, []), x1)
   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_primCmpNat1(Zero, Succ(x0))
   new_compare5(x0, x1)
   new_compare14(x0, x1, ty_Integer)
   new_merge2([], :(x0, x1), x2)
   new_merge00(x0, x1, x2, x3, EQ, x4)
   new_compare6(x0, x1, x2, x3)
   new_compare3(x0, x1, x2)
   new_compare13(Pos(Zero), Neg(Zero))
   new_compare13(Neg(Zero), Pos(Zero))
   new_compare14(x0, x1, ty_Bool)
   new_compare14(x0, x1, app(app(ty_@2, x2), x3))
   new_compare8(x0, x1)
   new_compare(x0, x1, app(ty_Ratio, x2))
   new_merge_pairs0([], x0)
   new_compare14(x0, x1, ty_Float)

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

(13) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
----------------------------------------

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

   new_mergesort'(vz117, :(vz1180, :(vz11810, vz11811)), ba) -> new_mergesort'(new_merge1(vz117, vz1180, vz11810, ba), new_merge_pairs0(vz11811, ba), ba)

The TRS R consists of the following rules:

   new_compare14(vz11800, vz118100, app(app(app(ty_@3, bc), bd), be)) -> new_compare4(vz11800, vz118100, bc, bd, be)
   new_compare14(vz11800, vz118100, app(app(ty_Either, cc), cd)) -> new_compare11(vz11800, vz118100, cc, cd)
   new_compare(vz1170, vz11800, ty_Float) -> new_compare2(vz1170, vz11800)
   new_compare13(Pos(Succ(vz120000)), Neg(vz11900)) -> GT
   new_compare13(Neg(Zero), Pos(Succ(vz119000))) -> LT
   new_compare13(Neg(Zero), Neg(Zero)) -> EQ
   new_compare(vz1170, vz11800, app(ty_[], cb)) -> new_compare12(vz1170, vz11800, cb)
   new_primCmpNat0(vz120000, Succ(vz119000)) -> new_primCmpNat1(vz120000, vz119000)
   new_compare(vz1170, vz11800, ty_Int) -> new_compare13(vz1170, vz11800)
   new_compare14(vz11800, vz118100, app(ty_Ratio, bh)) -> new_compare7(vz11800, vz118100, bh)
   new_primCmpNat1(Zero, Zero) -> EQ
   new_compare13(Pos(Succ(vz120000)), Pos(vz11900)) -> new_primCmpNat0(vz120000, vz11900)
   new_merge_pairs0(:(vz118110, []), ba) -> :(vz118110, [])
   new_compare13(Neg(Zero), Neg(Succ(vz119000))) -> new_primCmpNat0(vz119000, Zero)
   new_merge1(vz117, :(vz11800, vz11801), :(vz118100, vz118101), ba) -> new_merge2(vz117, new_merge00(vz118100, vz11800, vz11801, vz118101, new_compare14(vz11800, vz118100, ba), ba), ba)
   new_compare(vz1170, vz11800, ty_Bool) -> new_compare0(vz1170, vz11800)
   new_compare8(vz1170, vz11800) -> error([])
   new_primCmpNat1(Succ(vz1200000), Zero) -> GT
   new_compare13(Pos(Zero), Pos(Succ(vz119000))) -> new_primCmpNat2(Zero, vz119000)
   new_compare14(vz11800, vz118100, app(app(ty_@2, bf), bg)) -> new_compare6(vz11800, vz118100, bf, bg)
   new_compare13(Neg(Succ(vz120000)), Neg(vz11900)) -> new_primCmpNat2(vz11900, vz120000)
   new_compare13(Neg(Succ(vz120000)), Pos(vz11900)) -> LT
   new_merge2([], :(vz11800, vz11801), ba) -> :(vz11800, vz11801)
   new_compare14(vz11800, vz118100, ty_Float) -> new_compare2(vz11800, vz118100)
   new_compare0(vz1170, vz11800) -> error([])
   new_compare14(vz11800, vz118100, app(ty_[], cb)) -> new_compare12(vz11800, vz118100, cb)
   new_compare14(vz11800, vz118100, ty_Int) -> new_compare13(vz11800, vz118100)
   new_compare14(vz11800, vz118100, ty_Double) -> new_compare8(vz11800, vz118100)
   new_compare(vz1170, vz11800, app(app(ty_Either, cc), cd)) -> new_compare11(vz1170, vz11800, cc, cd)
   new_compare14(vz11800, vz118100, ty_Char) -> new_compare5(vz11800, vz118100)
   new_primCmpNat2(Succ(vz119000), vz120000) -> new_primCmpNat1(vz119000, vz120000)
   new_merge_pairs0(:(vz118110, :(vz1181110, vz1181111)), ba) -> :(new_merge2(vz118110, vz1181110, ba), new_merge_pairs0(vz1181111, ba))
   new_compare(vz1170, vz11800, app(app(ty_@2, bf), bg)) -> new_compare6(vz1170, vz11800, bf, bg)
   new_primCmpNat0(vz120000, Zero) -> GT
   new_merge00(vz127, vz128, vz129, vz130, LT, ca) -> :(vz128, new_merge2(vz129, :(vz127, vz130), ca))
   new_compare13(Pos(Zero), Pos(Zero)) -> EQ
   new_primCmpNat2(Zero, vz120000) -> LT
   new_compare13(Pos(Zero), Neg(Zero)) -> EQ
   new_compare13(Neg(Zero), Pos(Zero)) -> EQ
   new_merge2(:(vz1170, vz1171), :(vz11800, vz11801), ba) -> new_merge00(vz11800, vz1170, vz1171, vz11801, new_compare(vz1170, vz11800, ba), ba)
   new_primCmpNat1(Succ(vz1200000), Succ(vz1190000)) -> new_primCmpNat1(vz1200000, vz1190000)
   new_compare14(vz11800, vz118100, app(ty_Maybe, bb)) -> new_compare3(vz11800, vz118100, bb)
   new_compare14(vz11800, vz118100, ty_Ordering) -> new_compare1(vz11800, vz118100)
   new_merge2(vz117, [], ba) -> vz117
   new_compare(vz1170, vz11800, app(ty_Ratio, bh)) -> new_compare7(vz1170, vz11800, bh)
   new_compare(vz1170, vz11800, ty_@0) -> new_compare9(vz1170, vz11800)
   new_compare(vz1170, vz11800, app(app(app(ty_@3, bc), bd), be)) -> new_compare4(vz1170, vz11800, bc, bd, be)
   new_merge_pairs0([], ba) -> []
   new_merge1(vz117, [], :(vz118100, vz118101), ba) -> new_merge2(vz117, :(vz118100, vz118101), ba)
   new_compare2(vz1170, vz11800) -> error([])
   new_compare13(Pos(Zero), Neg(Succ(vz119000))) -> GT
   new_compare7(vz1170, vz11800, bh) -> error([])
   new_primCmpNat1(Zero, Succ(vz1190000)) -> LT
   new_compare3(vz1170, vz11800, bb) -> error([])
   new_merge00(vz127, vz128, vz129, vz130, GT, ca) -> :(vz127, new_merge2(:(vz128, vz129), vz130, ca))
   new_compare(vz1170, vz11800, ty_Double) -> new_compare8(vz1170, vz11800)
   new_compare14(vz11800, vz118100, ty_@0) -> new_compare9(vz11800, vz118100)
   new_compare5(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, ty_Char) -> new_compare5(vz1170, vz11800)
   new_compare14(vz11800, vz118100, ty_Integer) -> new_compare10(vz11800, vz118100)
   new_compare4(vz1170, vz11800, bc, bd, be) -> error([])
   new_merge00(vz127, vz128, vz129, vz130, EQ, ca) -> :(vz128, new_merge2(vz129, :(vz127, vz130), ca))
   new_compare10(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, app(ty_Maybe, bb)) -> new_compare3(vz1170, vz11800, bb)
   new_compare(vz1170, vz11800, ty_Integer) -> new_compare10(vz1170, vz11800)
   new_compare12(vz1170, vz11800, cb) -> error([])
   new_compare(vz1170, vz11800, ty_Ordering) -> new_compare1(vz1170, vz11800)
   new_compare11(vz1170, vz11800, cc, cd) -> error([])
   new_compare1(vz1170, vz11800) -> error([])
   new_compare14(vz11800, vz118100, ty_Bool) -> new_compare0(vz11800, vz118100)
   new_compare6(vz1170, vz11800, bf, bg) -> error([])
   new_merge1(vz117, vz1180, [], ba) -> new_merge2(vz117, vz1180, ba)
   new_compare9(vz1170, vz11800) -> error([])

The set Q consists of the following terms:

   new_compare14(x0, x1, app(ty_Maybe, x2))
   new_primCmpNat2(Succ(x0), x1)
   new_compare1(x0, x1)
   new_merge1(x0, [], :(x1, x2), x3)
   new_merge1(x0, x1, [], x2)
   new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_compare13(Neg(Zero), Neg(Zero))
   new_compare(x0, x1, ty_Int)
   new_compare10(x0, x1)
   new_compare13(Neg(Zero), Neg(Succ(x0)))
   new_compare13(Pos(Succ(x0)), Pos(x1))
   new_compare0(x0, x1)
   new_compare(x0, x1, app(ty_[], x2))
   new_compare14(x0, x1, ty_Char)
   new_compare14(x0, x1, ty_@0)
   new_compare11(x0, x1, x2, x3)
   new_merge2(:(x0, x1), :(x2, x3), x4)
   new_compare14(x0, x1, ty_Double)
   new_compare(x0, x1, app(app(ty_Either, x2), x3))
   new_compare14(x0, x1, app(app(ty_Either, x2), x3))
   new_compare(x0, x1, ty_Integer)
   new_compare14(x0, x1, ty_Ordering)
   new_compare(x0, x1, ty_Ordering)
   new_compare13(Pos(Zero), Pos(Zero))
   new_primCmpNat0(x0, Succ(x1))
   new_compare13(Pos(Succ(x0)), Neg(x1))
   new_compare13(Neg(Succ(x0)), Pos(x1))
   new_compare9(x0, x1)
   new_compare14(x0, x1, app(ty_[], x2))
   new_compare13(Neg(Succ(x0)), Neg(x1))
   new_merge_pairs0(:(x0, :(x1, x2)), x3)
   new_compare4(x0, x1, x2, x3, x4)
   new_merge2(x0, [], x1)
   new_compare(x0, x1, ty_Bool)
   new_primCmpNat1(Zero, Zero)
   new_compare2(x0, x1)
   new_compare(x0, x1, app(app(ty_@2, x2), x3))
   new_compare14(x0, x1, ty_Int)
   new_primCmpNat0(x0, Zero)
   new_compare12(x0, x1, x2)
   new_compare13(Neg(Zero), Pos(Succ(x0)))
   new_compare13(Pos(Zero), Neg(Succ(x0)))
   new_merge00(x0, x1, x2, x3, GT, x4)
   new_primCmpNat2(Zero, x0)
   new_primCmpNat1(Succ(x0), Zero)
   new_compare(x0, x1, app(ty_Maybe, x2))
   new_compare(x0, x1, ty_@0)
   new_compare14(x0, x1, app(ty_Ratio, x2))
   new_compare(x0, x1, ty_Char)
   new_compare(x0, x1, ty_Float)
   new_primCmpNat1(Succ(x0), Succ(x1))
   new_compare(x0, x1, ty_Double)
   new_merge00(x0, x1, x2, x3, LT, x4)
   new_compare7(x0, x1, x2)
   new_merge1(x0, :(x1, x2), :(x3, x4), x5)
   new_compare13(Pos(Zero), Pos(Succ(x0)))
   new_merge_pairs0(:(x0, []), x1)
   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_primCmpNat1(Zero, Succ(x0))
   new_compare5(x0, x1)
   new_compare14(x0, x1, ty_Integer)
   new_merge2([], :(x0, x1), x2)
   new_merge00(x0, x1, x2, x3, EQ, x4)
   new_compare6(x0, x1, x2, x3)
   new_compare3(x0, x1, x2)
   new_compare13(Pos(Zero), Neg(Zero))
   new_compare13(Neg(Zero), Pos(Zero))
   new_compare14(x0, x1, ty_Bool)
   new_compare14(x0, x1, app(app(ty_@2, x2), x3))
   new_compare8(x0, x1)
   new_compare(x0, x1, app(ty_Ratio, x2))
   new_merge_pairs0([], x0)
   new_compare14(x0, x1, ty_Float)

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

(15) 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) = 1
   POL(LT) = 0
   POL(Succ(x_1)) = 1 + x_1
   POL(Zero) = 1
   POL([]) = 0
   POL(new_merge2(x_1, x_2, x_3)) = x_1
   POL(new_merge_pairs0(x_1, x_2)) = x_1
   POL(new_primCmpNat0(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_primCmpNat1(x_1, x_2)) = 1
   POL(new_primCmpNat2(x_1, x_2)) = 1 + x_1 + x_2




From the DPs we obtained the following set of size-change graphs:
*new_mergesort'(vz117, :(vz1180, :(vz11810, vz11811)), ba) -> new_mergesort'(new_merge1(vz117, vz1180, vz11810, ba), new_merge_pairs0(vz11811, ba), ba) (allowed arguments on rhs = {2, 3})
The graph contains the following edges 2 > 2, 3 >= 3



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

   new_merge_pairs0([], ba) -> []
   new_merge_pairs0(:(vz118110, []), ba) -> :(vz118110, [])
   new_merge_pairs0(:(vz118110, :(vz1181110, vz1181111)), ba) -> :(new_merge2(vz118110, vz1181110, ba), new_merge_pairs0(vz1181111, ba))

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

(16)
YES

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

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

   new_merge_pairs(:(vz118110, :(vz1181110, vz1181111)), ba) -> new_merge_pairs(vz1181111, ba)

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_merge_pairs(:(vz118110, :(vz1181110, vz1181111)), ba) -> new_merge_pairs(vz1181111, ba)
The graph contains the following edges 1 > 1, 2 >= 2


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

(19)
YES

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

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

   new_merge0(vz127, vz128, vz129, vz130, EQ, ba) -> new_merge(vz129, :(vz127, vz130), ba)
   new_merge0(vz127, vz128, vz129, vz130, GT, ba) -> new_merge(:(vz128, vz129), vz130, ba)
   new_merge0(vz127, vz128, vz129, vz130, LT, ba) -> new_merge(vz129, :(vz127, vz130), ba)
   new_merge(:(vz1170, vz1171), :(vz11800, vz11801), bb) -> new_merge0(vz11800, vz1170, vz1171, vz11801, new_compare(vz1170, vz11800, bb), bb)

The TRS R consists of the following rules:

   new_primCmpNat2(Zero, vz120000) -> LT
   new_compare13(Pos(Zero), Neg(Zero)) -> EQ
   new_compare13(Neg(Zero), Pos(Zero)) -> EQ
   new_compare(vz1170, vz11800, ty_Float) -> new_compare2(vz1170, vz11800)
   new_compare13(Pos(Succ(vz120000)), Neg(vz11900)) -> GT
   new_primCmpNat1(Succ(vz1200000), Succ(vz1190000)) -> new_primCmpNat1(vz1200000, vz1190000)
   new_compare13(Neg(Zero), Pos(Succ(vz119000))) -> LT
   new_compare13(Neg(Zero), Neg(Zero)) -> EQ
   new_compare(vz1170, vz11800, app(ty_[], cd)) -> new_compare12(vz1170, vz11800, cd)
   new_primCmpNat0(vz120000, Succ(vz119000)) -> new_primCmpNat1(vz120000, vz119000)
   new_compare(vz1170, vz11800, app(ty_Ratio, ca)) -> new_compare7(vz1170, vz11800, ca)
   new_compare(vz1170, vz11800, ty_Int) -> new_compare13(vz1170, vz11800)
   new_compare(vz1170, vz11800, ty_@0) -> new_compare9(vz1170, vz11800)
   new_compare(vz1170, vz11800, app(app(app(ty_@3, bd), be), bf)) -> new_compare4(vz1170, vz11800, bd, be, bf)
   new_primCmpNat1(Zero, Zero) -> EQ
   new_compare2(vz1170, vz11800) -> error([])
   new_compare13(Pos(Succ(vz120000)), Pos(vz11900)) -> new_primCmpNat0(vz120000, vz11900)
   new_compare13(Neg(Zero), Neg(Succ(vz119000))) -> new_primCmpNat0(vz119000, Zero)
   new_compare13(Pos(Zero), Neg(Succ(vz119000))) -> GT
   new_compare7(vz1170, vz11800, ca) -> error([])
   new_primCmpNat1(Zero, Succ(vz1190000)) -> LT
   new_compare3(vz1170, vz11800, bc) -> error([])
   new_compare(vz1170, vz11800, ty_Double) -> new_compare8(vz1170, vz11800)
   new_compare(vz1170, vz11800, ty_Bool) -> new_compare0(vz1170, vz11800)
   new_compare8(vz1170, vz11800) -> error([])
   new_primCmpNat1(Succ(vz1200000), Zero) -> GT
   new_compare13(Pos(Zero), Pos(Succ(vz119000))) -> new_primCmpNat2(Zero, vz119000)
   new_compare13(Neg(Succ(vz120000)), Neg(vz11900)) -> new_primCmpNat2(vz11900, vz120000)
   new_compare5(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, ty_Char) -> new_compare5(vz1170, vz11800)
   new_compare13(Neg(Succ(vz120000)), Pos(vz11900)) -> LT
   new_compare4(vz1170, vz11800, bd, be, bf) -> error([])
   new_compare10(vz1170, vz11800) -> error([])
   new_compare0(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, app(ty_Maybe, bc)) -> new_compare3(vz1170, vz11800, bc)
   new_compare(vz1170, vz11800, ty_Integer) -> new_compare10(vz1170, vz11800)
   new_compare12(vz1170, vz11800, cd) -> error([])
   new_compare(vz1170, vz11800, ty_Ordering) -> new_compare1(vz1170, vz11800)
   new_compare(vz1170, vz11800, app(app(ty_Either, cb), cc)) -> new_compare11(vz1170, vz11800, cb, cc)
   new_compare11(vz1170, vz11800, cb, cc) -> error([])
   new_compare1(vz1170, vz11800) -> error([])
   new_primCmpNat2(Succ(vz119000), vz120000) -> new_primCmpNat1(vz119000, vz120000)
   new_compare(vz1170, vz11800, app(app(ty_@2, bg), bh)) -> new_compare6(vz1170, vz11800, bg, bh)
   new_primCmpNat0(vz120000, Zero) -> GT
   new_compare6(vz1170, vz11800, bg, bh) -> error([])
   new_compare9(vz1170, vz11800) -> error([])
   new_compare13(Pos(Zero), Pos(Zero)) -> EQ

The set Q consists of the following terms:

   new_primCmpNat2(Zero, x0)
   new_compare3(x0, x1, x2)
   new_primCmpNat1(Succ(x0), Zero)
   new_primCmpNat2(Succ(x0), x1)
   new_compare1(x0, x1)
   new_compare(x0, x1, ty_@0)
   new_compare(x0, x1, app(app(ty_@2, x2), x3))
   new_compare(x0, x1, ty_Char)
   new_compare(x0, x1, ty_Float)
   new_primCmpNat1(Succ(x0), Succ(x1))
   new_compare13(Neg(Zero), Neg(Zero))
   new_compare(x0, x1, ty_Double)
   new_compare6(x0, x1, x2, x3)
   new_compare(x0, x1, ty_Int)
   new_compare10(x0, x1)
   new_compare13(Neg(Zero), Neg(Succ(x0)))
   new_compare13(Pos(Succ(x0)), Pos(x1))
   new_compare7(x0, x1, x2)
   new_compare0(x0, x1)
   new_compare(x0, x1, app(ty_Ratio, x2))
   new_compare13(Pos(Zero), Pos(Succ(x0)))
   new_compare4(x0, x1, x2, x3, x4)
   new_compare11(x0, x1, x2, x3)
   new_primCmpNat1(Zero, Succ(x0))
   new_compare5(x0, x1)
   new_compare(x0, x1, ty_Integer)
   new_compare(x0, x1, app(app(ty_Either, x2), x3))
   new_compare(x0, x1, ty_Ordering)
   new_compare13(Pos(Zero), Pos(Zero))
   new_primCmpNat0(x0, Succ(x1))
   new_compare13(Pos(Succ(x0)), Neg(x1))
   new_compare13(Neg(Succ(x0)), Pos(x1))
   new_compare9(x0, x1)
   new_compare13(Neg(Succ(x0)), Neg(x1))
   new_compare13(Pos(Zero), Neg(Zero))
   new_compare13(Neg(Zero), Pos(Zero))
   new_compare(x0, x1, ty_Bool)
   new_primCmpNat1(Zero, Zero)
   new_compare2(x0, x1)
   new_compare8(x0, x1)
   new_compare(x0, x1, app(ty_Maybe, x2))
   new_primCmpNat0(x0, Zero)
   new_compare(x0, x1, app(ty_[], x2))
   new_compare13(Neg(Zero), Pos(Succ(x0)))
   new_compare13(Pos(Zero), Neg(Succ(x0)))
   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_compare12(x0, x1, x2)

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

(21) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   new_merge(:(vz1170, vz1171), :(vz11800, vz11801), bb) -> new_merge0(vz11800, vz1170, vz1171, vz11801, new_compare(vz1170, vz11800, bb), bb)
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

   POL(:(x_1, x_2)) = 1 + x_1 + x_2
   POL(EQ) = 0
   POL(GT) = 0
   POL(LT) = 0
   POL(Neg(x_1)) = 0
   POL(Pos(x_1)) = 0
   POL(Succ(x_1)) = x_1
   POL(Zero) = 0
   POL([]) = 1
   POL(app(x_1, x_2)) = 1 + x_1 + x_2
   POL(error(x_1)) = 1 + x_1
   POL(new_compare(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(new_compare0(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_compare1(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_compare10(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_compare11(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4
   POL(new_compare12(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(new_compare13(x_1, x_2)) = 0
   POL(new_compare2(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_compare3(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(new_compare4(x_1, x_2, x_3, x_4, x_5)) = 1 + x_1 + x_2 + x_3 + x_4 + x_5
   POL(new_compare5(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_compare6(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4
   POL(new_compare7(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(new_compare8(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_compare9(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_merge(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(new_merge0(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_1 + x_2 + x_3 + x_4 + x_6
   POL(new_primCmpNat0(x_1, x_2)) = 1 + x_1
   POL(new_primCmpNat1(x_1, x_2)) = 1
   POL(new_primCmpNat2(x_1, x_2)) = 1 + x_2
   POL(ty_@0) = 1
   POL(ty_@2) = 1
   POL(ty_@3) = 1
   POL(ty_Bool) = 1
   POL(ty_Char) = 1
   POL(ty_Double) = 1
   POL(ty_Either) = 1
   POL(ty_Float) = 1
   POL(ty_Int) = 1
   POL(ty_Integer) = 1
   POL(ty_Maybe) = 1
   POL(ty_Ordering) = 1
   POL(ty_Ratio) = 1
   POL(ty_[]) = 1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none


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

(22)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_merge0(vz127, vz128, vz129, vz130, EQ, ba) -> new_merge(vz129, :(vz127, vz130), ba)
   new_merge0(vz127, vz128, vz129, vz130, GT, ba) -> new_merge(:(vz128, vz129), vz130, ba)
   new_merge0(vz127, vz128, vz129, vz130, LT, ba) -> new_merge(vz129, :(vz127, vz130), ba)

The TRS R consists of the following rules:

   new_primCmpNat2(Zero, vz120000) -> LT
   new_compare13(Pos(Zero), Neg(Zero)) -> EQ
   new_compare13(Neg(Zero), Pos(Zero)) -> EQ
   new_compare(vz1170, vz11800, ty_Float) -> new_compare2(vz1170, vz11800)
   new_compare13(Pos(Succ(vz120000)), Neg(vz11900)) -> GT
   new_primCmpNat1(Succ(vz1200000), Succ(vz1190000)) -> new_primCmpNat1(vz1200000, vz1190000)
   new_compare13(Neg(Zero), Pos(Succ(vz119000))) -> LT
   new_compare13(Neg(Zero), Neg(Zero)) -> EQ
   new_compare(vz1170, vz11800, app(ty_[], cd)) -> new_compare12(vz1170, vz11800, cd)
   new_primCmpNat0(vz120000, Succ(vz119000)) -> new_primCmpNat1(vz120000, vz119000)
   new_compare(vz1170, vz11800, app(ty_Ratio, ca)) -> new_compare7(vz1170, vz11800, ca)
   new_compare(vz1170, vz11800, ty_Int) -> new_compare13(vz1170, vz11800)
   new_compare(vz1170, vz11800, ty_@0) -> new_compare9(vz1170, vz11800)
   new_compare(vz1170, vz11800, app(app(app(ty_@3, bd), be), bf)) -> new_compare4(vz1170, vz11800, bd, be, bf)
   new_primCmpNat1(Zero, Zero) -> EQ
   new_compare2(vz1170, vz11800) -> error([])
   new_compare13(Pos(Succ(vz120000)), Pos(vz11900)) -> new_primCmpNat0(vz120000, vz11900)
   new_compare13(Neg(Zero), Neg(Succ(vz119000))) -> new_primCmpNat0(vz119000, Zero)
   new_compare13(Pos(Zero), Neg(Succ(vz119000))) -> GT
   new_compare7(vz1170, vz11800, ca) -> error([])
   new_primCmpNat1(Zero, Succ(vz1190000)) -> LT
   new_compare3(vz1170, vz11800, bc) -> error([])
   new_compare(vz1170, vz11800, ty_Double) -> new_compare8(vz1170, vz11800)
   new_compare(vz1170, vz11800, ty_Bool) -> new_compare0(vz1170, vz11800)
   new_compare8(vz1170, vz11800) -> error([])
   new_primCmpNat1(Succ(vz1200000), Zero) -> GT
   new_compare13(Pos(Zero), Pos(Succ(vz119000))) -> new_primCmpNat2(Zero, vz119000)
   new_compare13(Neg(Succ(vz120000)), Neg(vz11900)) -> new_primCmpNat2(vz11900, vz120000)
   new_compare5(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, ty_Char) -> new_compare5(vz1170, vz11800)
   new_compare13(Neg(Succ(vz120000)), Pos(vz11900)) -> LT
   new_compare4(vz1170, vz11800, bd, be, bf) -> error([])
   new_compare10(vz1170, vz11800) -> error([])
   new_compare0(vz1170, vz11800) -> error([])
   new_compare(vz1170, vz11800, app(ty_Maybe, bc)) -> new_compare3(vz1170, vz11800, bc)
   new_compare(vz1170, vz11800, ty_Integer) -> new_compare10(vz1170, vz11800)
   new_compare12(vz1170, vz11800, cd) -> error([])
   new_compare(vz1170, vz11800, ty_Ordering) -> new_compare1(vz1170, vz11800)
   new_compare(vz1170, vz11800, app(app(ty_Either, cb), cc)) -> new_compare11(vz1170, vz11800, cb, cc)
   new_compare11(vz1170, vz11800, cb, cc) -> error([])
   new_compare1(vz1170, vz11800) -> error([])
   new_primCmpNat2(Succ(vz119000), vz120000) -> new_primCmpNat1(vz119000, vz120000)
   new_compare(vz1170, vz11800, app(app(ty_@2, bg), bh)) -> new_compare6(vz1170, vz11800, bg, bh)
   new_primCmpNat0(vz120000, Zero) -> GT
   new_compare6(vz1170, vz11800, bg, bh) -> error([])
   new_compare9(vz1170, vz11800) -> error([])
   new_compare13(Pos(Zero), Pos(Zero)) -> EQ

The set Q consists of the following terms:

   new_primCmpNat2(Zero, x0)
   new_compare3(x0, x1, x2)
   new_primCmpNat1(Succ(x0), Zero)
   new_primCmpNat2(Succ(x0), x1)
   new_compare1(x0, x1)
   new_compare(x0, x1, ty_@0)
   new_compare(x0, x1, app(app(ty_@2, x2), x3))
   new_compare(x0, x1, ty_Char)
   new_compare(x0, x1, ty_Float)
   new_primCmpNat1(Succ(x0), Succ(x1))
   new_compare13(Neg(Zero), Neg(Zero))
   new_compare(x0, x1, ty_Double)
   new_compare6(x0, x1, x2, x3)
   new_compare(x0, x1, ty_Int)
   new_compare10(x0, x1)
   new_compare13(Neg(Zero), Neg(Succ(x0)))
   new_compare13(Pos(Succ(x0)), Pos(x1))
   new_compare7(x0, x1, x2)
   new_compare0(x0, x1)
   new_compare(x0, x1, app(ty_Ratio, x2))
   new_compare13(Pos(Zero), Pos(Succ(x0)))
   new_compare4(x0, x1, x2, x3, x4)
   new_compare11(x0, x1, x2, x3)
   new_primCmpNat1(Zero, Succ(x0))
   new_compare5(x0, x1)
   new_compare(x0, x1, ty_Integer)
   new_compare(x0, x1, app(app(ty_Either, x2), x3))
   new_compare(x0, x1, ty_Ordering)
   new_compare13(Pos(Zero), Pos(Zero))
   new_primCmpNat0(x0, Succ(x1))
   new_compare13(Pos(Succ(x0)), Neg(x1))
   new_compare13(Neg(Succ(x0)), Pos(x1))
   new_compare9(x0, x1)
   new_compare13(Neg(Succ(x0)), Neg(x1))
   new_compare13(Pos(Zero), Neg(Zero))
   new_compare13(Neg(Zero), Pos(Zero))
   new_compare(x0, x1, ty_Bool)
   new_primCmpNat1(Zero, Zero)
   new_compare2(x0, x1)
   new_compare8(x0, x1)
   new_compare(x0, x1, app(ty_Maybe, x2))
   new_primCmpNat0(x0, Zero)
   new_compare(x0, x1, app(ty_[], x2))
   new_compare13(Neg(Zero), Pos(Succ(x0)))
   new_compare13(Pos(Zero), Neg(Succ(x0)))
   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_compare12(x0, x1, x2)

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

(23) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.
----------------------------------------

(24)
TRUE

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

(25)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_map(:(vz3110, vz3111)) -> new_map(vz3111)

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

(26) 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_map(:(vz3110, vz3111)) -> new_map(vz3111)
The graph contains the following edges 1 > 1


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

(27)
YES