/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 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
    (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES


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

(0)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;

instance (Eq a, Eq b) => Eq FiniteMap b a where { 
}
elemFM :: Ord a => a  ->  FiniteMap a b  ->  Bool;
elemFM key fm = case lookupFM fm key of { 
Nothing-> False; 
Just elt-> True; 
 } ;

lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
lookupFM EmptyFM key = Nothing;
lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
 | key_to_find > key = lookupFM fm_r key_to_find
 | otherwise = Just elt;

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

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

(1) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case lookupFM fm key of {
Nothing  -> False;
Just elt  -> True}
"
is transformed to
"elemFM0 Nothing = False;
elemFM0 (Just elt) = True;
"

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

(2)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;

instance (Eq a, Eq b) => Eq FiniteMap a b where { 
}
elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
elemFM key fm = elemFM0 (lookupFM fm key);

elemFM0 Nothing = False;
elemFM0 (Just elt) = True;

lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
lookupFM EmptyFM key = Nothing;
lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
 | key_to_find > key = lookupFM fm_r key_to_find
 | otherwise = Just elt;

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

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

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

(4)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;

instance (Eq a, Eq b) => Eq FiniteMap a b where { 
}
elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
elemFM key fm = elemFM0 (lookupFM fm key);

elemFM0 Nothing = False;
elemFM0 (Just elt) = True;

lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
lookupFM EmptyFM key = Nothing;
lookupFM (Branch key elt vy fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
 | key_to_find > key = lookupFM fm_r key_to_find
 | otherwise = Just elt;

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

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

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"lookupFM EmptyFM key = Nothing;
lookupFM (Branch key elt vy fm_l fm_r) key_to_find|key_to_find < keylookupFM fm_l key_to_find|key_to_find > keylookupFM fm_r key_to_find|otherwiseJust elt;
"
is transformed to
"lookupFM EmptyFM key = lookupFM4 EmptyFM key;
lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
"
"lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
"
"lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
"
"lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
lookupFM2 key elt vy fm_l fm_r key_to_find False = lookupFM1 key elt vy fm_l fm_r key_to_find (key_to_find > key);
"
"lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find = lookupFM2 key elt vy fm_l fm_r key_to_find (key_to_find < key);
"
"lookupFM4 EmptyFM key = Nothing;
lookupFM4 wv ww = lookupFM3 wv ww;
"

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

(6)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;

instance (Eq a, Eq b) => Eq FiniteMap b a where { 
}
elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
elemFM key fm = elemFM0 (lookupFM fm key);

elemFM0 Nothing = False;
elemFM0 (Just elt) = True;

lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
lookupFM EmptyFM key = lookupFM4 EmptyFM key;
lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;

lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;

lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;

lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
lookupFM2 key elt vy fm_l fm_r key_to_find False = lookupFM1 key elt vy fm_l fm_r key_to_find (key_to_find > key);

lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find = lookupFM2 key elt vy fm_l fm_r key_to_find (key_to_find < key);

lookupFM4 EmptyFM key = Nothing;
lookupFM4 wv ww = lookupFM3 wv ww;

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

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="FiniteMap.elemFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="FiniteMap.elemFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="FiniteMap.elemFM wx3 wx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx4 wx3)",fontsize=16,color="burlywood",shape="triangle"];1566[label="wx4/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 1566[label="",style="solid", color="burlywood", weight=9];
1566 -> 6[label="",style="solid", color="burlywood", weight=3];
1567[label="wx4/FiniteMap.Branch wx40 wx41 wx42 wx43 wx44",fontsize=10,color="white",style="solid",shape="box"];5 -> 1567[label="",style="solid", color="burlywood", weight=9];
1567 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="FiniteMap.elemFM0 (FiniteMap.lookupFM FiniteMap.EmptyFM wx3)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="FiniteMap.elemFM0 (FiniteMap.lookupFM (FiniteMap.Branch wx40 wx41 wx42 wx43 wx44) wx3)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="FiniteMap.elemFM0 (FiniteMap.lookupFM4 FiniteMap.EmptyFM wx3)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="FiniteMap.elemFM0 (FiniteMap.lookupFM3 (FiniteMap.Branch wx40 wx41 wx42 wx43 wx44) wx3)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="FiniteMap.elemFM0 Nothing",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 wx3 (wx3 < wx40))",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="False",fontsize=16,color="green",shape="box"];13[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 wx3 (compare wx3 wx40 == LT))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 wx3 (primCmpInt wx3 wx40 == LT))",fontsize=16,color="burlywood",shape="box"];1568[label="wx3/Pos wx30",fontsize=10,color="white",style="solid",shape="box"];14 -> 1568[label="",style="solid", color="burlywood", weight=9];
1568 -> 15[label="",style="solid", color="burlywood", weight=3];
1569[label="wx3/Neg wx30",fontsize=10,color="white",style="solid",shape="box"];14 -> 1569[label="",style="solid", color="burlywood", weight=9];
1569 -> 16[label="",style="solid", color="burlywood", weight=3];
15[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 (Pos wx30) (primCmpInt (Pos wx30) wx40 == LT))",fontsize=16,color="burlywood",shape="box"];1570[label="wx30/Succ wx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 1570[label="",style="solid", color="burlywood", weight=9];
1570 -> 17[label="",style="solid", color="burlywood", weight=3];
1571[label="wx30/Zero",fontsize=10,color="white",style="solid",shape="box"];15 -> 1571[label="",style="solid", color="burlywood", weight=9];
1571 -> 18[label="",style="solid", color="burlywood", weight=3];
16[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 (Neg wx30) (primCmpInt (Neg wx30) wx40 == LT))",fontsize=16,color="burlywood",shape="box"];1572[label="wx30/Succ wx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 1572[label="",style="solid", color="burlywood", weight=9];
1572 -> 19[label="",style="solid", color="burlywood", weight=3];
1573[label="wx30/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 1573[label="",style="solid", color="burlywood", weight=9];
1573 -> 20[label="",style="solid", color="burlywood", weight=3];
17[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (primCmpInt (Pos (Succ wx300)) wx40 == LT))",fontsize=16,color="burlywood",shape="box"];1574[label="wx40/Pos wx400",fontsize=10,color="white",style="solid",shape="box"];17 -> 1574[label="",style="solid", color="burlywood", weight=9];
1574 -> 21[label="",style="solid", color="burlywood", weight=3];
1575[label="wx40/Neg wx400",fontsize=10,color="white",style="solid",shape="box"];17 -> 1575[label="",style="solid", color="burlywood", weight=9];
1575 -> 22[label="",style="solid", color="burlywood", weight=3];
18[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 (Pos Zero) (primCmpInt (Pos Zero) wx40 == LT))",fontsize=16,color="burlywood",shape="box"];1576[label="wx40/Pos wx400",fontsize=10,color="white",style="solid",shape="box"];18 -> 1576[label="",style="solid", color="burlywood", weight=9];
1576 -> 23[label="",style="solid", color="burlywood", weight=3];
1577[label="wx40/Neg wx400",fontsize=10,color="white",style="solid",shape="box"];18 -> 1577[label="",style="solid", color="burlywood", weight=9];
1577 -> 24[label="",style="solid", color="burlywood", weight=3];
19[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 (Neg (Succ wx300)) (primCmpInt (Neg (Succ wx300)) wx40 == LT))",fontsize=16,color="burlywood",shape="box"];1578[label="wx40/Pos wx400",fontsize=10,color="white",style="solid",shape="box"];19 -> 1578[label="",style="solid", color="burlywood", weight=9];
1578 -> 25[label="",style="solid", color="burlywood", weight=3];
1579[label="wx40/Neg wx400",fontsize=10,color="white",style="solid",shape="box"];19 -> 1579[label="",style="solid", color="burlywood", weight=9];
1579 -> 26[label="",style="solid", color="burlywood", weight=3];
20[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) wx40 == LT))",fontsize=16,color="burlywood",shape="box"];1580[label="wx40/Pos wx400",fontsize=10,color="white",style="solid",shape="box"];20 -> 1580[label="",style="solid", color="burlywood", weight=9];
1580 -> 27[label="",style="solid", color="burlywood", weight=3];
1581[label="wx40/Neg wx400",fontsize=10,color="white",style="solid",shape="box"];20 -> 1581[label="",style="solid", color="burlywood", weight=9];
1581 -> 28[label="",style="solid", color="burlywood", weight=3];
21[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos wx400) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (primCmpInt (Pos (Succ wx300)) (Pos wx400) == LT))",fontsize=16,color="black",shape="box"];21 -> 29[label="",style="solid", color="black", weight=3];
22[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg wx400) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (primCmpInt (Pos (Succ wx300)) (Neg wx400) == LT))",fontsize=16,color="black",shape="box"];22 -> 30[label="",style="solid", color="black", weight=3];
23[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos wx400) wx41 wx42 wx43 wx44 (Pos Zero) (primCmpInt (Pos Zero) (Pos wx400) == LT))",fontsize=16,color="burlywood",shape="box"];1582[label="wx400/Succ wx4000",fontsize=10,color="white",style="solid",shape="box"];23 -> 1582[label="",style="solid", color="burlywood", weight=9];
1582 -> 31[label="",style="solid", color="burlywood", weight=3];
1583[label="wx400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 1583[label="",style="solid", color="burlywood", weight=9];
1583 -> 32[label="",style="solid", color="burlywood", weight=3];
24[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg wx400) wx41 wx42 wx43 wx44 (Pos Zero) (primCmpInt (Pos Zero) (Neg wx400) == LT))",fontsize=16,color="burlywood",shape="box"];1584[label="wx400/Succ wx4000",fontsize=10,color="white",style="solid",shape="box"];24 -> 1584[label="",style="solid", color="burlywood", weight=9];
1584 -> 33[label="",style="solid", color="burlywood", weight=3];
1585[label="wx400/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 1585[label="",style="solid", color="burlywood", weight=9];
1585 -> 34[label="",style="solid", color="burlywood", weight=3];
25[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos wx400) wx41 wx42 wx43 wx44 (Neg (Succ wx300)) (primCmpInt (Neg (Succ wx300)) (Pos wx400) == LT))",fontsize=16,color="black",shape="box"];25 -> 35[label="",style="solid", color="black", weight=3];
26[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg wx400) wx41 wx42 wx43 wx44 (Neg (Succ wx300)) (primCmpInt (Neg (Succ wx300)) (Neg wx400) == LT))",fontsize=16,color="black",shape="box"];26 -> 36[label="",style="solid", color="black", weight=3];
27[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos wx400) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) (Pos wx400) == LT))",fontsize=16,color="burlywood",shape="box"];1586[label="wx400/Succ wx4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 1586[label="",style="solid", color="burlywood", weight=9];
1586 -> 37[label="",style="solid", color="burlywood", weight=3];
1587[label="wx400/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 1587[label="",style="solid", color="burlywood", weight=9];
1587 -> 38[label="",style="solid", color="burlywood", weight=3];
28[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg wx400) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) (Neg wx400) == LT))",fontsize=16,color="burlywood",shape="box"];1588[label="wx400/Succ wx4000",fontsize=10,color="white",style="solid",shape="box"];28 -> 1588[label="",style="solid", color="burlywood", weight=9];
1588 -> 39[label="",style="solid", color="burlywood", weight=3];
1589[label="wx400/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 1589[label="",style="solid", color="burlywood", weight=9];
1589 -> 40[label="",style="solid", color="burlywood", weight=3];
29[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos wx400) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (primCmpNat (Succ wx300) wx400 == LT))",fontsize=16,color="burlywood",shape="box"];1590[label="wx400/Succ wx4000",fontsize=10,color="white",style="solid",shape="box"];29 -> 1590[label="",style="solid", color="burlywood", weight=9];
1590 -> 41[label="",style="solid", color="burlywood", weight=3];
1591[label="wx400/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 1591[label="",style="solid", color="burlywood", weight=9];
1591 -> 42[label="",style="solid", color="burlywood", weight=3];
30[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg wx400) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (GT == LT))",fontsize=16,color="black",shape="box"];30 -> 43[label="",style="solid", color="black", weight=3];
31[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos (Succ wx4000)) wx41 wx42 wx43 wx44 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ wx4000)) == LT))",fontsize=16,color="black",shape="box"];31 -> 44[label="",style="solid", color="black", weight=3];
32[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos Zero) wx41 wx42 wx43 wx44 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3];
33[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx4000)) wx41 wx42 wx43 wx44 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ wx4000)) == LT))",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3];
34[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg Zero) wx41 wx42 wx43 wx44 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT))",fontsize=16,color="black",shape="box"];34 -> 47[label="",style="solid", color="black", weight=3];
35[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos wx400) wx41 wx42 wx43 wx44 (Neg (Succ wx300)) (LT == LT))",fontsize=16,color="black",shape="box"];35 -> 48[label="",style="solid", color="black", weight=3];
36[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg wx400) wx41 wx42 wx43 wx44 (Neg (Succ wx300)) (primCmpNat wx400 (Succ wx300) == LT))",fontsize=16,color="burlywood",shape="box"];1592[label="wx400/Succ wx4000",fontsize=10,color="white",style="solid",shape="box"];36 -> 1592[label="",style="solid", color="burlywood", weight=9];
1592 -> 49[label="",style="solid", color="burlywood", weight=3];
1593[label="wx400/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 1593[label="",style="solid", color="burlywood", weight=9];
1593 -> 50[label="",style="solid", color="burlywood", weight=3];
37[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos (Succ wx4000)) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ wx4000)) == LT))",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
38[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos Zero) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
39[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx4000)) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ wx4000)) == LT))",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3];
40[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg Zero) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT))",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3];
41[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos (Succ wx4000)) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (primCmpNat (Succ wx300) (Succ wx4000) == LT))",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3];
42[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos Zero) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (primCmpNat (Succ wx300) Zero == LT))",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3];
43[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg wx400) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) False)",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3];
44[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos (Succ wx4000)) wx41 wx42 wx43 wx44 (Pos Zero) (primCmpNat Zero (Succ wx4000) == LT))",fontsize=16,color="black",shape="box"];44 -> 58[label="",style="solid", color="black", weight=3];
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135[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg Zero) wx41 wx42 wx43 wx44 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];135 -> 155[label="",style="solid", color="black", weight=3];
887 -> 792[label="",style="dashed", color="red", weight=0];
887[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (primCmpNat wx790 wx800 == LT))",fontsize=16,color="magenta"];887 -> 896[label="",style="dashed", color="magenta", weight=3];
887 -> 897[label="",style="dashed", color="magenta", weight=3];
888[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (GT == LT))",fontsize=16,color="black",shape="box"];888 -> 898[label="",style="solid", color="black", weight=3];
889[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (LT == LT))",fontsize=16,color="black",shape="box"];889 -> 899[label="",style="solid", color="black", weight=3];
890[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (EQ == LT))",fontsize=16,color="black",shape="box"];890 -> 900[label="",style="solid", color="black", weight=3];
141[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos Zero) wx41 wx42 wx43 wx44 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];141 -> 163[label="",style="solid", color="black", weight=3];
142[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx4000)) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ wx4000)) == GT))",fontsize=16,color="black",shape="box"];142 -> 164[label="",style="solid", color="black", weight=3];
143[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg Zero) wx41 wx42 wx43 wx44 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];143 -> 165[label="",style="solid", color="black", weight=3];
891[label="wx700",fontsize=16,color="green",shape="box"];892[label="wx710",fontsize=16,color="green",shape="box"];893[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos (Succ wx64)) wx65 wx66 wx67 wx68 (Pos (Succ wx69)) False)",fontsize=16,color="black",shape="triangle"];893 -> 901[label="",style="solid", color="black", weight=3];
894[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos (Succ wx64)) wx65 wx66 wx67 wx68 (Pos (Succ wx69)) True)",fontsize=16,color="black",shape="box"];894 -> 902[label="",style="solid", color="black", weight=3];
895 -> 893[label="",style="dashed", color="red", weight=0];
895[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Pos (Succ wx64)) wx65 wx66 wx67 wx68 (Pos (Succ wx69)) False)",fontsize=16,color="magenta"];151[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos Zero) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (primCmpNat (Succ wx300) Zero == GT))",fontsize=16,color="black",shape="box"];151 -> 174[label="",style="solid", color="black", weight=3];
152 -> 5[label="",style="dashed", color="red", weight=0];
152[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx44 (Pos (Succ wx300)))",fontsize=16,color="magenta"];152 -> 175[label="",style="dashed", color="magenta", weight=3];
152 -> 176[label="",style="dashed", color="magenta", weight=3];
153[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos Zero) wx41 wx42 wx43 wx44 (Pos Zero) False)",fontsize=16,color="black",shape="box"];153 -> 177[label="",style="solid", color="black", weight=3];
154[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx4000)) wx41 wx42 wx43 wx44 (Pos Zero) True)",fontsize=16,color="black",shape="box"];154 -> 178[label="",style="solid", color="black", weight=3];
155[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg Zero) wx41 wx42 wx43 wx44 (Pos Zero) False)",fontsize=16,color="black",shape="box"];155 -> 179[label="",style="solid", color="black", weight=3];
896[label="wx800",fontsize=16,color="green",shape="box"];897[label="wx790",fontsize=16,color="green",shape="box"];898[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) False)",fontsize=16,color="black",shape="triangle"];898 -> 903[label="",style="solid", color="black", weight=3];
899[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) True)",fontsize=16,color="black",shape="box"];899 -> 904[label="",style="solid", color="black", weight=3];
900 -> 898[label="",style="dashed", color="red", weight=0];
900[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) False)",fontsize=16,color="magenta"];163[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos Zero) wx41 wx42 wx43 wx44 (Neg Zero) False)",fontsize=16,color="black",shape="box"];163 -> 188[label="",style="solid", color="black", weight=3];
164[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx4000)) wx41 wx42 wx43 wx44 (Neg Zero) (primCmpNat (Succ wx4000) Zero == GT))",fontsize=16,color="black",shape="box"];164 -> 189[label="",style="solid", color="black", weight=3];
165[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg Zero) wx41 wx42 wx43 wx44 (Neg Zero) False)",fontsize=16,color="black",shape="box"];165 -> 190[label="",style="solid", color="black", weight=3];
901[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx64)) wx65 wx66 wx67 wx68 (Pos (Succ wx69)) (Pos (Succ wx69) > Pos (Succ wx64)))",fontsize=16,color="black",shape="box"];901 -> 905[label="",style="solid", color="black", weight=3];
902 -> 5[label="",style="dashed", color="red", weight=0];
902[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx67 (Pos (Succ wx69)))",fontsize=16,color="magenta"];902 -> 906[label="",style="dashed", color="magenta", weight=3];
902 -> 907[label="",style="dashed", color="magenta", weight=3];
174[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos Zero) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) (GT == GT))",fontsize=16,color="black",shape="box"];174 -> 198[label="",style="solid", color="black", weight=3];
175[label="wx44",fontsize=16,color="green",shape="box"];176[label="Pos (Succ wx300)",fontsize=16,color="green",shape="box"];177[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Pos Zero) wx41 wx42 wx43 wx44 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];177 -> 199[label="",style="solid", color="black", weight=3];
178 -> 5[label="",style="dashed", color="red", weight=0];
178[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx44 (Pos Zero))",fontsize=16,color="magenta"];178 -> 200[label="",style="dashed", color="magenta", weight=3];
178 -> 201[label="",style="dashed", color="magenta", weight=3];
179[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Neg Zero) wx41 wx42 wx43 wx44 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];179 -> 202[label="",style="solid", color="black", weight=3];
903[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (Neg (Succ wx78) > Neg (Succ wx73)))",fontsize=16,color="black",shape="box"];903 -> 908[label="",style="solid", color="black", weight=3];
904 -> 5[label="",style="dashed", color="red", weight=0];
904[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx76 (Neg (Succ wx78)))",fontsize=16,color="magenta"];904 -> 909[label="",style="dashed", color="magenta", weight=3];
904 -> 910[label="",style="dashed", color="magenta", weight=3];
188[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Pos Zero) wx41 wx42 wx43 wx44 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];188 -> 210[label="",style="solid", color="black", weight=3];
189[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx4000)) wx41 wx42 wx43 wx44 (Neg Zero) (GT == GT))",fontsize=16,color="black",shape="box"];189 -> 211[label="",style="solid", color="black", weight=3];
190[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Neg Zero) wx41 wx42 wx43 wx44 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];190 -> 212[label="",style="solid", color="black", weight=3];
905[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx64)) wx65 wx66 wx67 wx68 (Pos (Succ wx69)) (compare (Pos (Succ wx69)) (Pos (Succ wx64)) == GT))",fontsize=16,color="black",shape="box"];905 -> 911[label="",style="solid", color="black", weight=3];
906[label="wx67",fontsize=16,color="green",shape="box"];907[label="Pos (Succ wx69)",fontsize=16,color="green",shape="box"];198[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos Zero) wx41 wx42 wx43 wx44 (Pos (Succ wx300)) True)",fontsize=16,color="black",shape="box"];198 -> 222[label="",style="solid", color="black", weight=3];
199[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Pos Zero) wx41 wx42 wx43 wx44 (Pos Zero) True)",fontsize=16,color="black",shape="box"];199 -> 223[label="",style="solid", color="black", weight=3];
200[label="wx44",fontsize=16,color="green",shape="box"];201[label="Pos Zero",fontsize=16,color="green",shape="box"];202[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Neg Zero) wx41 wx42 wx43 wx44 (Pos Zero) True)",fontsize=16,color="black",shape="box"];202 -> 224[label="",style="solid", color="black", weight=3];
908[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (compare (Neg (Succ wx78)) (Neg (Succ wx73)) == GT))",fontsize=16,color="black",shape="box"];908 -> 912[label="",style="solid", color="black", weight=3];
909[label="wx76",fontsize=16,color="green",shape="box"];910[label="Neg (Succ wx78)",fontsize=16,color="green",shape="box"];210[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Pos Zero) wx41 wx42 wx43 wx44 (Neg Zero) True)",fontsize=16,color="black",shape="box"];210 -> 234[label="",style="solid", color="black", weight=3];
211[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx4000)) wx41 wx42 wx43 wx44 (Neg Zero) True)",fontsize=16,color="black",shape="box"];211 -> 235[label="",style="solid", color="black", weight=3];
212[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Neg Zero) wx41 wx42 wx43 wx44 (Neg Zero) True)",fontsize=16,color="black",shape="box"];212 -> 236[label="",style="solid", color="black", weight=3];
911[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx64)) wx65 wx66 wx67 wx68 (Pos (Succ wx69)) (primCmpInt (Pos (Succ wx69)) (Pos (Succ wx64)) == GT))",fontsize=16,color="black",shape="box"];911 -> 913[label="",style="solid", color="black", weight=3];
222 -> 5[label="",style="dashed", color="red", weight=0];
222[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx44 (Pos (Succ wx300)))",fontsize=16,color="magenta"];222 -> 247[label="",style="dashed", color="magenta", weight=3];
222 -> 248[label="",style="dashed", color="magenta", weight=3];
223[label="FiniteMap.elemFM0 (Just wx41)",fontsize=16,color="black",shape="triangle"];223 -> 249[label="",style="solid", color="black", weight=3];
224 -> 223[label="",style="dashed", color="red", weight=0];
224[label="FiniteMap.elemFM0 (Just wx41)",fontsize=16,color="magenta"];912[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (primCmpInt (Neg (Succ wx78)) (Neg (Succ wx73)) == GT))",fontsize=16,color="black",shape="box"];912 -> 914[label="",style="solid", color="black", weight=3];
234 -> 223[label="",style="dashed", color="red", weight=0];
234[label="FiniteMap.elemFM0 (Just wx41)",fontsize=16,color="magenta"];235 -> 5[label="",style="dashed", color="red", weight=0];
235[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx44 (Neg Zero))",fontsize=16,color="magenta"];235 -> 260[label="",style="dashed", color="magenta", weight=3];
235 -> 261[label="",style="dashed", color="magenta", weight=3];
236 -> 223[label="",style="dashed", color="red", weight=0];
236[label="FiniteMap.elemFM0 (Just wx41)",fontsize=16,color="magenta"];913 -> 1344[label="",style="dashed", color="red", weight=0];
913[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx64)) wx65 wx66 wx67 wx68 (Pos (Succ wx69)) (primCmpNat (Succ wx69) (Succ wx64) == GT))",fontsize=16,color="magenta"];913 -> 1345[label="",style="dashed", color="magenta", weight=3];
913 -> 1346[label="",style="dashed", color="magenta", weight=3];
913 -> 1347[label="",style="dashed", color="magenta", weight=3];
913 -> 1348[label="",style="dashed", color="magenta", weight=3];
913 -> 1349[label="",style="dashed", color="magenta", weight=3];
913 -> 1350[label="",style="dashed", color="magenta", weight=3];
913 -> 1351[label="",style="dashed", color="magenta", weight=3];
913 -> 1352[label="",style="dashed", color="magenta", weight=3];
247[label="wx44",fontsize=16,color="green",shape="box"];248[label="Pos (Succ wx300)",fontsize=16,color="green",shape="box"];249[label="True",fontsize=16,color="green",shape="box"];914 -> 1435[label="",style="dashed", color="red", weight=0];
914[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx73)) wx74 wx75 wx76 wx77 (Neg (Succ wx78)) (primCmpNat (Succ wx73) (Succ wx78) == GT))",fontsize=16,color="magenta"];914 -> 1436[label="",style="dashed", color="magenta", weight=3];
914 -> 1437[label="",style="dashed", color="magenta", weight=3];
914 -> 1438[label="",style="dashed", color="magenta", weight=3];
914 -> 1439[label="",style="dashed", color="magenta", weight=3];
914 -> 1440[label="",style="dashed", color="magenta", weight=3];
914 -> 1441[label="",style="dashed", color="magenta", weight=3];
914 -> 1442[label="",style="dashed", color="magenta", weight=3];
914 -> 1443[label="",style="dashed", color="magenta", weight=3];
260[label="wx44",fontsize=16,color="green",shape="box"];261[label="Neg Zero",fontsize=16,color="green",shape="box"];1345[label="wx67",fontsize=16,color="green",shape="box"];1346[label="wx68",fontsize=16,color="green",shape="box"];1347[label="wx69",fontsize=16,color="green",shape="box"];1348[label="wx64",fontsize=16,color="green",shape="box"];1349[label="Succ wx64",fontsize=16,color="green",shape="box"];1350[label="wx66",fontsize=16,color="green",shape="box"];1351[label="wx65",fontsize=16,color="green",shape="box"];1352[label="Succ wx69",fontsize=16,color="green",shape="box"];1344[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat wx152 wx153 == GT))",fontsize=16,color="burlywood",shape="triangle"];1606[label="wx152/Succ wx1520",fontsize=10,color="white",style="solid",shape="box"];1344 -> 1606[label="",style="solid", color="burlywood", weight=9];
1606 -> 1433[label="",style="solid", color="burlywood", weight=3];
1607[label="wx152/Zero",fontsize=10,color="white",style="solid",shape="box"];1344 -> 1607[label="",style="solid", color="burlywood", weight=9];
1607 -> 1434[label="",style="solid", color="burlywood", weight=3];
1436[label="wx73",fontsize=16,color="green",shape="box"];1437[label="wx75",fontsize=16,color="green",shape="box"];1438[label="wx76",fontsize=16,color="green",shape="box"];1439[label="Succ wx78",fontsize=16,color="green",shape="box"];1440[label="wx78",fontsize=16,color="green",shape="box"];1441[label="wx77",fontsize=16,color="green",shape="box"];1442[label="wx74",fontsize=16,color="green",shape="box"];1443[label="Succ wx73",fontsize=16,color="green",shape="box"];1435[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat wx161 wx162 == GT))",fontsize=16,color="burlywood",shape="triangle"];1608[label="wx161/Succ wx1610",fontsize=10,color="white",style="solid",shape="box"];1435 -> 1608[label="",style="solid", color="burlywood", weight=9];
1608 -> 1524[label="",style="solid", color="burlywood", weight=3];
1609[label="wx161/Zero",fontsize=10,color="white",style="solid",shape="box"];1435 -> 1609[label="",style="solid", color="burlywood", weight=9];
1609 -> 1525[label="",style="solid", color="burlywood", weight=3];
1433[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat (Succ wx1520) wx153 == GT))",fontsize=16,color="burlywood",shape="box"];1610[label="wx153/Succ wx1530",fontsize=10,color="white",style="solid",shape="box"];1433 -> 1610[label="",style="solid", color="burlywood", weight=9];
1610 -> 1526[label="",style="solid", color="burlywood", weight=3];
1611[label="wx153/Zero",fontsize=10,color="white",style="solid",shape="box"];1433 -> 1611[label="",style="solid", color="burlywood", weight=9];
1611 -> 1527[label="",style="solid", color="burlywood", weight=3];
1434[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat Zero wx153 == GT))",fontsize=16,color="burlywood",shape="box"];1612[label="wx153/Succ wx1530",fontsize=10,color="white",style="solid",shape="box"];1434 -> 1612[label="",style="solid", color="burlywood", weight=9];
1612 -> 1528[label="",style="solid", color="burlywood", weight=3];
1613[label="wx153/Zero",fontsize=10,color="white",style="solid",shape="box"];1434 -> 1613[label="",style="solid", color="burlywood", weight=9];
1613 -> 1529[label="",style="solid", color="burlywood", weight=3];
1524[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat (Succ wx1610) wx162 == GT))",fontsize=16,color="burlywood",shape="box"];1614[label="wx162/Succ wx1620",fontsize=10,color="white",style="solid",shape="box"];1524 -> 1614[label="",style="solid", color="burlywood", weight=9];
1614 -> 1530[label="",style="solid", color="burlywood", weight=3];
1615[label="wx162/Zero",fontsize=10,color="white",style="solid",shape="box"];1524 -> 1615[label="",style="solid", color="burlywood", weight=9];
1615 -> 1531[label="",style="solid", color="burlywood", weight=3];
1525[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat Zero wx162 == GT))",fontsize=16,color="burlywood",shape="box"];1616[label="wx162/Succ wx1620",fontsize=10,color="white",style="solid",shape="box"];1525 -> 1616[label="",style="solid", color="burlywood", weight=9];
1616 -> 1532[label="",style="solid", color="burlywood", weight=3];
1617[label="wx162/Zero",fontsize=10,color="white",style="solid",shape="box"];1525 -> 1617[label="",style="solid", color="burlywood", weight=9];
1617 -> 1533[label="",style="solid", color="burlywood", weight=3];
1526[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat (Succ wx1520) (Succ wx1530) == GT))",fontsize=16,color="black",shape="box"];1526 -> 1534[label="",style="solid", color="black", weight=3];
1527[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat (Succ wx1520) Zero == GT))",fontsize=16,color="black",shape="box"];1527 -> 1535[label="",style="solid", color="black", weight=3];
1528[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat Zero (Succ wx1530) == GT))",fontsize=16,color="black",shape="box"];1528 -> 1536[label="",style="solid", color="black", weight=3];
1529[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];1529 -> 1537[label="",style="solid", color="black", weight=3];
1530[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat (Succ wx1610) (Succ wx1620) == GT))",fontsize=16,color="black",shape="box"];1530 -> 1538[label="",style="solid", color="black", weight=3];
1531[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat (Succ wx1610) Zero == GT))",fontsize=16,color="black",shape="box"];1531 -> 1539[label="",style="solid", color="black", weight=3];
1532[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat Zero (Succ wx1620) == GT))",fontsize=16,color="black",shape="box"];1532 -> 1540[label="",style="solid", color="black", weight=3];
1533[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];1533 -> 1541[label="",style="solid", color="black", weight=3];
1534 -> 1344[label="",style="dashed", color="red", weight=0];
1534[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (primCmpNat wx1520 wx1530 == GT))",fontsize=16,color="magenta"];1534 -> 1542[label="",style="dashed", color="magenta", weight=3];
1534 -> 1543[label="",style="dashed", color="magenta", weight=3];
1535[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (GT == GT))",fontsize=16,color="black",shape="box"];1535 -> 1544[label="",style="solid", color="black", weight=3];
1536[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (LT == GT))",fontsize=16,color="black",shape="box"];1536 -> 1545[label="",style="solid", color="black", weight=3];
1537[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) (EQ == GT))",fontsize=16,color="black",shape="box"];1537 -> 1546[label="",style="solid", color="black", weight=3];
1538 -> 1435[label="",style="dashed", color="red", weight=0];
1538[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (primCmpNat wx1610 wx1620 == GT))",fontsize=16,color="magenta"];1538 -> 1547[label="",style="dashed", color="magenta", weight=3];
1538 -> 1548[label="",style="dashed", color="magenta", weight=3];
1539[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (GT == GT))",fontsize=16,color="black",shape="box"];1539 -> 1549[label="",style="solid", color="black", weight=3];
1540[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (LT == GT))",fontsize=16,color="black",shape="box"];1540 -> 1550[label="",style="solid", color="black", weight=3];
1541[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) (EQ == GT))",fontsize=16,color="black",shape="box"];1541 -> 1551[label="",style="solid", color="black", weight=3];
1542[label="wx1530",fontsize=16,color="green",shape="box"];1543[label="wx1520",fontsize=16,color="green",shape="box"];1544[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) True)",fontsize=16,color="black",shape="box"];1544 -> 1552[label="",style="solid", color="black", weight=3];
1545[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) False)",fontsize=16,color="black",shape="triangle"];1545 -> 1553[label="",style="solid", color="black", weight=3];
1546 -> 1545[label="",style="dashed", color="red", weight=0];
1546[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) False)",fontsize=16,color="magenta"];1547[label="wx1620",fontsize=16,color="green",shape="box"];1548[label="wx1610",fontsize=16,color="green",shape="box"];1549[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) True)",fontsize=16,color="black",shape="box"];1549 -> 1554[label="",style="solid", color="black", weight=3];
1550[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) False)",fontsize=16,color="black",shape="triangle"];1550 -> 1555[label="",style="solid", color="black", weight=3];
1551 -> 1550[label="",style="dashed", color="red", weight=0];
1551[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) False)",fontsize=16,color="magenta"];1552 -> 5[label="",style="dashed", color="red", weight=0];
1552[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx150 (Pos (Succ wx151)))",fontsize=16,color="magenta"];1552 -> 1556[label="",style="dashed", color="magenta", weight=3];
1552 -> 1557[label="",style="dashed", color="magenta", weight=3];
1553[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) otherwise)",fontsize=16,color="black",shape="box"];1553 -> 1558[label="",style="solid", color="black", weight=3];
1554 -> 5[label="",style="dashed", color="red", weight=0];
1554[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx159 (Neg (Succ wx160)))",fontsize=16,color="magenta"];1554 -> 1559[label="",style="dashed", color="magenta", weight=3];
1554 -> 1560[label="",style="dashed", color="magenta", weight=3];
1555[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) otherwise)",fontsize=16,color="black",shape="box"];1555 -> 1561[label="",style="solid", color="black", weight=3];
1556[label="wx150",fontsize=16,color="green",shape="box"];1557[label="Pos (Succ wx151)",fontsize=16,color="green",shape="box"];1558[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Pos (Succ wx146)) wx147 wx148 wx149 wx150 (Pos (Succ wx151)) True)",fontsize=16,color="black",shape="box"];1558 -> 1562[label="",style="solid", color="black", weight=3];
1559[label="wx159",fontsize=16,color="green",shape="box"];1560[label="Neg (Succ wx160)",fontsize=16,color="green",shape="box"];1561[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 (Neg (Succ wx155)) wx156 wx157 wx158 wx159 (Neg (Succ wx160)) True)",fontsize=16,color="black",shape="box"];1561 -> 1563[label="",style="solid", color="black", weight=3];
1562 -> 223[label="",style="dashed", color="red", weight=0];
1562[label="FiniteMap.elemFM0 (Just wx147)",fontsize=16,color="magenta"];1562 -> 1564[label="",style="dashed", color="magenta", weight=3];
1563 -> 223[label="",style="dashed", color="red", weight=0];
1563[label="FiniteMap.elemFM0 (Just wx156)",fontsize=16,color="magenta"];1563 -> 1565[label="",style="dashed", color="magenta", weight=3];
1564[label="wx147",fontsize=16,color="green",shape="box"];1565[label="wx156",fontsize=16,color="green",shape="box"];}

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

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

   new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Zero), bb) -> new_elemFM01(wx43, Pos(Zero), bb)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx700), Zero, h) -> new_elemFM00(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx69), Succ(wx64), h)
   new_elemFM01(Branch(Pos(Zero), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM01(wx44, Pos(Succ(wx300)), bb)
   new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Zero), bb) -> new_elemFM01(wx44, Pos(Zero), bb)
   new_elemFM01(Branch(Neg(Zero), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM01(wx43, Neg(Succ(wx300)), bb)
   new_elemFM01(Branch(Neg(wx400), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM01(wx44, Pos(Succ(wx300)), bb)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Zero, Zero, h) -> new_elemFM02(wx64, wx65, wx66, wx67, wx68, wx69, h)
   new_elemFM02(wx64, wx65, wx66, wx67, wx68, wx69, h) -> new_elemFM00(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx69), Succ(wx64), h)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Zero, Succ(wx800), bc) -> new_elemFM01(wx76, Neg(Succ(wx78)), bc)
   new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, Succ(wx1520), Succ(wx1530), ba) -> new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, wx1520, wx1530, ba)
   new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, Succ(wx1520), Zero, ba) -> new_elemFM01(wx150, Pos(Succ(wx151)), ba)
   new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Zero), bb) -> new_elemFM01(wx44, Neg(Zero), bb)
   new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM0(wx4000, wx41, wx42, wx43, wx44, wx300, wx300, wx4000, bb)
   new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Zero), bb) -> new_elemFM01(wx43, Neg(Zero), bb)
   new_elemFM05(wx73, wx74, wx75, wx76, wx77, wx78, bc) -> new_elemFM04(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx73), Succ(wx78), bc)
   new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, Succ(wx1610), Succ(wx1620), bd) -> new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, wx1610, wx1620, bd)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Zero, Succ(wx710), h) -> new_elemFM01(wx67, Pos(Succ(wx69)), h)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx790), Zero, bc) -> new_elemFM04(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx73), Succ(wx78), bc)
   new_elemFM01(Branch(Pos(wx400), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM01(wx43, Neg(Succ(wx300)), bb)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx790), Succ(wx800), bc) -> new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, wx790, wx800, bc)
   new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM03(wx4000, wx41, wx42, wx43, wx44, wx300, wx4000, wx300, bb)
   new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, Succ(wx1610), Zero, bd) -> new_elemFM01(wx159, Neg(Succ(wx160)), bd)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx700), Succ(wx710), h) -> new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, wx700, wx710, h)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Zero, Zero, bc) -> new_elemFM05(wx73, wx74, wx75, wx76, wx77, wx78, bc)

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 4 SCCs.
----------------------------------------

(10)
Complex Obligation (AND)

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

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

   new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Zero), bb) -> new_elemFM01(wx43, Neg(Zero), bb)
   new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Zero), bb) -> new_elemFM01(wx44, Neg(Zero), bb)

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_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Zero), bb) -> new_elemFM01(wx43, Neg(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Zero), bb) -> new_elemFM01(wx44, Neg(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(13)
YES

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

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

   new_elemFM01(Branch(Pos(wx400), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM01(wx43, Neg(Succ(wx300)), bb)
   new_elemFM01(Branch(Neg(Zero), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM01(wx43, Neg(Succ(wx300)), bb)
   new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM03(wx4000, wx41, wx42, wx43, wx44, wx300, wx4000, wx300, bb)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Zero, Succ(wx800), bc) -> new_elemFM01(wx76, Neg(Succ(wx78)), bc)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx790), Zero, bc) -> new_elemFM04(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx73), Succ(wx78), bc)
   new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, Succ(wx1610), Succ(wx1620), bd) -> new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, wx1610, wx1620, bd)
   new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, Succ(wx1610), Zero, bd) -> new_elemFM01(wx159, Neg(Succ(wx160)), bd)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx790), Succ(wx800), bc) -> new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, wx790, wx800, bc)
   new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Zero, Zero, bc) -> new_elemFM05(wx73, wx74, wx75, wx76, wx77, wx78, bc)
   new_elemFM05(wx73, wx74, wx75, wx76, wx77, wx78, bc) -> new_elemFM04(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx73), Succ(wx78), bc)

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_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM03(wx4000, wx41, wx42, wx43, wx44, wx300, wx4000, wx300, bb)
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 1 > 7, 2 > 8, 3 >= 9


*new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Zero, Succ(wx800), bc) -> new_elemFM01(wx76, Neg(Succ(wx78)), bc)
The graph contains the following edges 4 >= 1, 9 >= 3


*new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, Succ(wx1610), Zero, bd) -> new_elemFM01(wx159, Neg(Succ(wx160)), bd)
The graph contains the following edges 5 >= 1, 9 >= 3


*new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx790), Succ(wx800), bc) -> new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, wx790, wx800, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9


*new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, Succ(wx1610), Succ(wx1620), bd) -> new_elemFM04(wx155, wx156, wx157, wx158, wx159, wx160, wx1610, wx1620, bd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9


*new_elemFM05(wx73, wx74, wx75, wx76, wx77, wx78, bc) -> new_elemFM04(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx73), Succ(wx78), bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9


*new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx790), Zero, bc) -> new_elemFM04(wx73, wx74, wx75, wx76, wx77, wx78, Succ(wx73), Succ(wx78), bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9


*new_elemFM03(wx73, wx74, wx75, wx76, wx77, wx78, Zero, Zero, bc) -> new_elemFM05(wx73, wx74, wx75, wx76, wx77, wx78, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7


*new_elemFM01(Branch(Pos(wx400), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM01(wx43, Neg(Succ(wx300)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_elemFM01(Branch(Neg(Zero), wx41, wx42, wx43, wx44), Neg(Succ(wx300)), bb) -> new_elemFM01(wx43, Neg(Succ(wx300)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(16)
YES

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

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

   new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, Succ(wx1520), Succ(wx1530), ba) -> new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, wx1520, wx1530, ba)
   new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, Succ(wx1520), Zero, ba) -> new_elemFM01(wx150, Pos(Succ(wx151)), ba)
   new_elemFM01(Branch(Pos(Zero), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM01(wx44, Pos(Succ(wx300)), bb)
   new_elemFM01(Branch(Neg(wx400), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM01(wx44, Pos(Succ(wx300)), bb)
   new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM0(wx4000, wx41, wx42, wx43, wx44, wx300, wx300, wx4000, bb)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx700), Zero, h) -> new_elemFM00(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx69), Succ(wx64), h)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Zero, Zero, h) -> new_elemFM02(wx64, wx65, wx66, wx67, wx68, wx69, h)
   new_elemFM02(wx64, wx65, wx66, wx67, wx68, wx69, h) -> new_elemFM00(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx69), Succ(wx64), h)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Zero, Succ(wx710), h) -> new_elemFM01(wx67, Pos(Succ(wx69)), h)
   new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx700), Succ(wx710), h) -> new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, wx700, wx710, h)

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_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, Succ(wx1520), Succ(wx1530), ba) -> new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, wx1520, wx1530, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9


*new_elemFM00(wx146, wx147, wx148, wx149, wx150, wx151, Succ(wx1520), Zero, ba) -> new_elemFM01(wx150, Pos(Succ(wx151)), ba)
The graph contains the following edges 5 >= 1, 9 >= 3


*new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM0(wx4000, wx41, wx42, wx43, wx44, wx300, wx300, wx4000, bb)
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 1 > 8, 3 >= 9


*new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Zero, Succ(wx710), h) -> new_elemFM01(wx67, Pos(Succ(wx69)), h)
The graph contains the following edges 4 >= 1, 9 >= 3


*new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx700), Zero, h) -> new_elemFM00(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx69), Succ(wx64), h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9


*new_elemFM02(wx64, wx65, wx66, wx67, wx68, wx69, h) -> new_elemFM00(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx69), Succ(wx64), h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9


*new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Succ(wx700), Succ(wx710), h) -> new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, wx700, wx710, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9


*new_elemFM0(wx64, wx65, wx66, wx67, wx68, wx69, Zero, Zero, h) -> new_elemFM02(wx64, wx65, wx66, wx67, wx68, wx69, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7


*new_elemFM01(Branch(Pos(Zero), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM01(wx44, Pos(Succ(wx300)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_elemFM01(Branch(Neg(wx400), wx41, wx42, wx43, wx44), Pos(Succ(wx300)), bb) -> new_elemFM01(wx44, Pos(Succ(wx300)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(19)
YES

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

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

   new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Zero), bb) -> new_elemFM01(wx44, Pos(Zero), bb)
   new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Zero), bb) -> new_elemFM01(wx43, Pos(Zero), bb)

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

(21) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_elemFM01(Branch(Neg(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Zero), bb) -> new_elemFM01(wx44, Pos(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_elemFM01(Branch(Pos(Succ(wx4000)), wx41, wx42, wx43, wx44), Pos(Zero), bb) -> new_elemFM01(wx43, Pos(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(22)
YES