/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [SOUND, 0 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) 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 { 
}
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) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(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 { 
}
lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
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;
}

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

(3) 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;
"
"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);
"
"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;
"
"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;
"

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

(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 b a where { 
}
lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
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;
}

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

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="FiniteMap.lookupFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="FiniteMap.lookupFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="FiniteMap.lookupFM wx3 wx4",fontsize=16,color="burlywood",shape="triangle"];2076[label="wx3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];4 -> 2076[label="",style="solid", color="burlywood", weight=9];
2076 -> 5[label="",style="solid", color="burlywood", weight=3];
2077[label="wx3/FiniteMap.Branch wx30 wx31 wx32 wx33 wx34",fontsize=10,color="white",style="solid",shape="box"];4 -> 2077[label="",style="solid", color="burlywood", weight=9];
2077 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="FiniteMap.lookupFM FiniteMap.EmptyFM wx4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="FiniteMap.lookupFM (FiniteMap.Branch wx30 wx31 wx32 wx33 wx34) wx4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="FiniteMap.lookupFM4 FiniteMap.EmptyFM wx4",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="FiniteMap.lookupFM3 (FiniteMap.Branch wx30 wx31 wx32 wx33 wx34) wx4",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="Nothing",fontsize=16,color="green",shape="box"];10[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (wx4 < wx30)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (compare wx4 wx30 == LT)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (primCmpInt wx4 wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2078[label="wx4/Pos wx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 2078[label="",style="solid", color="burlywood", weight=9];
2078 -> 13[label="",style="solid", color="burlywood", weight=3];
2079[label="wx4/Neg wx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 2079[label="",style="solid", color="burlywood", weight=9];
2079 -> 14[label="",style="solid", color="burlywood", weight=3];
13[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 (Pos wx40) (primCmpInt (Pos wx40) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2080[label="wx40/Succ wx400",fontsize=10,color="white",style="solid",shape="box"];13 -> 2080[label="",style="solid", color="burlywood", weight=9];
2080 -> 15[label="",style="solid", color="burlywood", weight=3];
2081[label="wx40/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 2081[label="",style="solid", color="burlywood", weight=9];
2081 -> 16[label="",style="solid", color="burlywood", weight=3];
14[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 (Neg wx40) (primCmpInt (Neg wx40) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2082[label="wx40/Succ wx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 2082[label="",style="solid", color="burlywood", weight=9];
2082 -> 17[label="",style="solid", color="burlywood", weight=3];
2083[label="wx40/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 2083[label="",style="solid", color="burlywood", weight=9];
2083 -> 18[label="",style="solid", color="burlywood", weight=3];
15[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2084[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 2084[label="",style="solid", color="burlywood", weight=9];
2084 -> 19[label="",style="solid", color="burlywood", weight=3];
2085[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 2085[label="",style="solid", color="burlywood", weight=9];
2085 -> 20[label="",style="solid", color="burlywood", weight=3];
16[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2086[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 2086[label="",style="solid", color="burlywood", weight=9];
2086 -> 21[label="",style="solid", color="burlywood", weight=3];
2087[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 2087[label="",style="solid", color="burlywood", weight=9];
2087 -> 22[label="",style="solid", color="burlywood", weight=3];
17[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpInt (Neg (Succ wx400)) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2088[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];17 -> 2088[label="",style="solid", color="burlywood", weight=9];
2088 -> 23[label="",style="solid", color="burlywood", weight=3];
2089[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];17 -> 2089[label="",style="solid", color="burlywood", weight=9];
2089 -> 24[label="",style="solid", color="burlywood", weight=3];
18[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2090[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];18 -> 2090[label="",style="solid", color="burlywood", weight=9];
2090 -> 25[label="",style="solid", color="burlywood", weight=3];
2091[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];18 -> 2091[label="",style="solid", color="burlywood", weight=9];
2091 -> 26[label="",style="solid", color="burlywood", weight=3];
19[label="FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) (Pos wx300) == LT)",fontsize=16,color="black",shape="box"];19 -> 27[label="",style="solid", color="black", weight=3];
20[label="FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) (Neg wx300) == LT)",fontsize=16,color="black",shape="box"];20 -> 28[label="",style="solid", color="black", weight=3];
21[label="FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2092[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];21 -> 2092[label="",style="solid", color="burlywood", weight=9];
2092 -> 29[label="",style="solid", color="burlywood", weight=3];
2093[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 2093[label="",style="solid", color="burlywood", weight=9];
2093 -> 30[label="",style="solid", color="burlywood", weight=3];
22[label="FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2094[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];22 -> 2094[label="",style="solid", color="burlywood", weight=9];
2094 -> 31[label="",style="solid", color="burlywood", weight=3];
2095[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 2095[label="",style="solid", color="burlywood", weight=9];
2095 -> 32[label="",style="solid", color="burlywood", weight=3];
23[label="FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpInt (Neg (Succ wx400)) (Pos wx300) == LT)",fontsize=16,color="black",shape="box"];23 -> 33[label="",style="solid", color="black", weight=3];
24[label="FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpInt (Neg (Succ wx400)) (Neg wx300) == LT)",fontsize=16,color="black",shape="box"];24 -> 34[label="",style="solid", color="black", weight=3];
25[label="FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2096[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];25 -> 2096[label="",style="solid", color="burlywood", weight=9];
2096 -> 35[label="",style="solid", color="burlywood", weight=3];
2097[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 2097[label="",style="solid", color="burlywood", weight=9];
2097 -> 36[label="",style="solid", color="burlywood", weight=3];
26[label="FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2098[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];26 -> 2098[label="",style="solid", color="burlywood", weight=9];
2098 -> 37[label="",style="solid", color="burlywood", weight=3];
2099[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 2099[label="",style="solid", color="burlywood", weight=9];
2099 -> 38[label="",style="solid", color="burlywood", weight=3];
27[label="FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) wx300 == LT)",fontsize=16,color="burlywood",shape="box"];2100[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];27 -> 2100[label="",style="solid", color="burlywood", weight=9];
2100 -> 39[label="",style="solid", color="burlywood", weight=3];
2101[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 2101[label="",style="solid", color="burlywood", weight=9];
2101 -> 40[label="",style="solid", color="burlywood", weight=3];
28[label="FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (GT == LT)",fontsize=16,color="black",shape="box"];28 -> 41[label="",style="solid", color="black", weight=3];
29[label="FiniteMap.lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];29 -> 42[label="",style="solid", color="black", weight=3];
30[label="FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];30 -> 43[label="",style="solid", color="black", weight=3];
31[label="FiniteMap.lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];31 -> 44[label="",style="solid", color="black", weight=3];
32[label="FiniteMap.lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3];
33[label="FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (LT == LT)",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3];
34[label="FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpNat wx300 (Succ wx400) == LT)",fontsize=16,color="burlywood",shape="box"];2102[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];34 -> 2102[label="",style="solid", color="burlywood", weight=9];
2102 -> 47[label="",style="solid", color="burlywood", weight=3];
2103[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 2103[label="",style="solid", color="burlywood", weight=9];
2103 -> 48[label="",style="solid", color="burlywood", weight=3];
35[label="FiniteMap.lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];35 -> 49[label="",style="solid", color="black", weight=3];
36[label="FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];36 -> 50[label="",style="solid", color="black", weight=3];
37[label="FiniteMap.lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
38[label="FiniteMap.lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
39[label="FiniteMap.lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) (Succ wx3000) == LT)",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3];
40[label="FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) Zero == LT)",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3];
41[label="FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) False",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3];
42[label="FiniteMap.lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpNat Zero (Succ wx3000) == LT)",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3];
43[label="FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3];
44[label="FiniteMap.lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (GT == LT)",fontsize=16,color="black",shape="box"];44 -> 58[label="",style="solid", color="black", weight=3];
45[label="FiniteMap.lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];45 -> 59[label="",style="solid", color="black", weight=3];
46[label="FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) True",fontsize=16,color="black",shape="box"];46 -> 60[label="",style="solid", color="black", weight=3];
47[label="FiniteMap.lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpNat (Succ wx3000) (Succ wx400) == LT)",fontsize=16,color="black",shape="box"];47 -> 61[label="",style="solid", color="black", weight=3];
48[label="FiniteMap.lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpNat Zero (Succ wx400) == LT)",fontsize=16,color="black",shape="box"];48 -> 62[label="",style="solid", color="black", weight=3];
49[label="FiniteMap.lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (LT == LT)",fontsize=16,color="black",shape="box"];49 -> 63[label="",style="solid", color="black", weight=3];
50[label="FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];50 -> 64[label="",style="solid", color="black", weight=3];
51[label="FiniteMap.lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpNat (Succ wx3000) Zero == LT)",fontsize=16,color="black",shape="box"];51 -> 65[label="",style="solid", color="black", weight=3];
52[label="FiniteMap.lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];52 -> 66[label="",style="solid", color="black", weight=3];
53 -> 973[label="",style="dashed", color="red", weight=0];
53[label="FiniteMap.lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat wx400 wx3000 == LT)",fontsize=16,color="magenta"];53 -> 974[label="",style="dashed", color="magenta", weight=3];
53 -> 975[label="",style="dashed", color="magenta", weight=3];
53 -> 976[label="",style="dashed", color="magenta", weight=3];
53 -> 977[label="",style="dashed", color="magenta", weight=3];
53 -> 978[label="",style="dashed", color="magenta", weight=3];
53 -> 979[label="",style="dashed", color="magenta", weight=3];
53 -> 980[label="",style="dashed", color="magenta", weight=3];
53 -> 981[label="",style="dashed", color="magenta", weight=3];
54[label="FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (GT == LT)",fontsize=16,color="black",shape="box"];54 -> 69[label="",style="solid", color="black", weight=3];
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1151 -> 973[label="",style="dashed", color="red", weight=0];
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1163 -> 1161[label="",style="dashed", color="red", weight=0];
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150 -> 4[label="",style="dashed", color="red", weight=0];
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150 -> 174[label="",style="dashed", color="magenta", weight=3];
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1168[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) False",fontsize=16,color="magenta"];161[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) False",fontsize=16,color="black",shape="box"];161 -> 186[label="",style="solid", color="black", weight=3];
162[label="FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpNat (Succ wx3000) Zero == GT)",fontsize=16,color="black",shape="box"];162 -> 187[label="",style="solid", color="black", weight=3];
163[label="FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) False",fontsize=16,color="black",shape="box"];163 -> 188[label="",style="solid", color="black", weight=3];
1169[label="FiniteMap.lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (Pos (Succ wx113) > Pos (Succ wx108))",fontsize=16,color="black",shape="box"];1169 -> 1173[label="",style="solid", color="black", weight=3];
1170 -> 4[label="",style="dashed", color="red", weight=0];
1170[label="FiniteMap.lookupFM wx111 (Pos (Succ wx113))",fontsize=16,color="magenta"];1170 -> 1174[label="",style="dashed", color="magenta", weight=3];
1170 -> 1175[label="",style="dashed", color="magenta", weight=3];
172[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (GT == GT)",fontsize=16,color="black",shape="box"];172 -> 196[label="",style="solid", color="black", weight=3];
173[label="wx34",fontsize=16,color="green",shape="box"];174[label="Pos (Succ wx400)",fontsize=16,color="green",shape="box"];175[label="FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];175 -> 197[label="",style="solid", color="black", weight=3];
176 -> 4[label="",style="dashed", color="red", weight=0];
176[label="FiniteMap.lookupFM wx34 (Pos Zero)",fontsize=16,color="magenta"];176 -> 198[label="",style="dashed", color="magenta", weight=3];
176 -> 199[label="",style="dashed", color="magenta", weight=3];
177[label="FiniteMap.lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];177 -> 200[label="",style="solid", color="black", weight=3];
1171[label="FiniteMap.lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (Neg (Succ wx122) > Neg (Succ wx117))",fontsize=16,color="black",shape="box"];1171 -> 1176[label="",style="solid", color="black", weight=3];
1172 -> 4[label="",style="dashed", color="red", weight=0];
1172[label="FiniteMap.lookupFM wx120 (Neg (Succ wx122))",fontsize=16,color="magenta"];1172 -> 1177[label="",style="dashed", color="magenta", weight=3];
1172 -> 1178[label="",style="dashed", color="magenta", weight=3];
186[label="FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];186 -> 208[label="",style="solid", color="black", weight=3];
187[label="FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];187 -> 209[label="",style="solid", color="black", weight=3];
188[label="FiniteMap.lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];188 -> 210[label="",style="solid", color="black", weight=3];
1173[label="FiniteMap.lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (compare (Pos (Succ wx113)) (Pos (Succ wx108)) == GT)",fontsize=16,color="black",shape="box"];1173 -> 1179[label="",style="solid", color="black", weight=3];
1174[label="wx111",fontsize=16,color="green",shape="box"];1175[label="Pos (Succ wx113)",fontsize=16,color="green",shape="box"];196[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) True",fontsize=16,color="black",shape="box"];196 -> 220[label="",style="solid", color="black", weight=3];
197[label="FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) True",fontsize=16,color="black",shape="box"];197 -> 221[label="",style="solid", color="black", weight=3];
198[label="wx34",fontsize=16,color="green",shape="box"];199[label="Pos Zero",fontsize=16,color="green",shape="box"];200[label="FiniteMap.lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) True",fontsize=16,color="black",shape="box"];200 -> 222[label="",style="solid", color="black", weight=3];
1176[label="FiniteMap.lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (compare (Neg (Succ wx122)) (Neg (Succ wx117)) == GT)",fontsize=16,color="black",shape="box"];1176 -> 1180[label="",style="solid", color="black", weight=3];
1177[label="wx120",fontsize=16,color="green",shape="box"];1178[label="Neg (Succ wx122)",fontsize=16,color="green",shape="box"];208[label="FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) True",fontsize=16,color="black",shape="box"];208 -> 232[label="",style="solid", color="black", weight=3];
209[label="FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) True",fontsize=16,color="black",shape="box"];209 -> 233[label="",style="solid", color="black", weight=3];
210[label="FiniteMap.lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) True",fontsize=16,color="black",shape="box"];210 -> 234[label="",style="solid", color="black", weight=3];
1179[label="FiniteMap.lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpInt (Pos (Succ wx113)) (Pos (Succ wx108)) == GT)",fontsize=16,color="black",shape="box"];1179 -> 1181[label="",style="solid", color="black", weight=3];
220 -> 4[label="",style="dashed", color="red", weight=0];
220[label="FiniteMap.lookupFM wx34 (Pos (Succ wx400))",fontsize=16,color="magenta"];220 -> 245[label="",style="dashed", color="magenta", weight=3];
220 -> 246[label="",style="dashed", color="magenta", weight=3];
221[label="Just wx31",fontsize=16,color="green",shape="box"];222[label="Just wx31",fontsize=16,color="green",shape="box"];1180[label="FiniteMap.lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpInt (Neg (Succ wx122)) (Neg (Succ wx117)) == GT)",fontsize=16,color="black",shape="box"];1180 -> 1182[label="",style="solid", color="black", weight=3];
232[label="Just wx31",fontsize=16,color="green",shape="box"];233 -> 4[label="",style="dashed", color="red", weight=0];
233[label="FiniteMap.lookupFM wx34 (Neg Zero)",fontsize=16,color="magenta"];233 -> 257[label="",style="dashed", color="magenta", weight=3];
233 -> 258[label="",style="dashed", color="magenta", weight=3];
234[label="Just wx31",fontsize=16,color="green",shape="box"];1181 -> 1856[label="",style="dashed", color="red", weight=0];
1181[label="FiniteMap.lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat (Succ wx113) (Succ wx108) == GT)",fontsize=16,color="magenta"];1181 -> 1857[label="",style="dashed", color="magenta", weight=3];
1181 -> 1858[label="",style="dashed", color="magenta", weight=3];
1181 -> 1859[label="",style="dashed", color="magenta", weight=3];
1181 -> 1860[label="",style="dashed", color="magenta", weight=3];
1181 -> 1861[label="",style="dashed", color="magenta", weight=3];
1181 -> 1862[label="",style="dashed", color="magenta", weight=3];
1181 -> 1863[label="",style="dashed", color="magenta", weight=3];
1181 -> 1864[label="",style="dashed", color="magenta", weight=3];
245[label="wx34",fontsize=16,color="green",shape="box"];246[label="Pos (Succ wx400)",fontsize=16,color="green",shape="box"];1182 -> 1947[label="",style="dashed", color="red", weight=0];
1182[label="FiniteMap.lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat (Succ wx117) (Succ wx122) == GT)",fontsize=16,color="magenta"];1182 -> 1948[label="",style="dashed", color="magenta", weight=3];
1182 -> 1949[label="",style="dashed", color="magenta", weight=3];
1182 -> 1950[label="",style="dashed", color="magenta", weight=3];
1182 -> 1951[label="",style="dashed", color="magenta", weight=3];
1182 -> 1952[label="",style="dashed", color="magenta", weight=3];
1182 -> 1953[label="",style="dashed", color="magenta", weight=3];
1182 -> 1954[label="",style="dashed", color="magenta", weight=3];
1182 -> 1955[label="",style="dashed", color="magenta", weight=3];
257[label="wx34",fontsize=16,color="green",shape="box"];258[label="Neg Zero",fontsize=16,color="green",shape="box"];1857[label="wx110",fontsize=16,color="green",shape="box"];1858[label="wx109",fontsize=16,color="green",shape="box"];1859[label="Succ wx108",fontsize=16,color="green",shape="box"];1860[label="wx112",fontsize=16,color="green",shape="box"];1861[label="wx108",fontsize=16,color="green",shape="box"];1862[label="wx111",fontsize=16,color="green",shape="box"];1863[label="wx113",fontsize=16,color="green",shape="box"];1864[label="Succ wx113",fontsize=16,color="green",shape="box"];1856[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat wx234 wx235 == GT)",fontsize=16,color="burlywood",shape="triangle"];2116[label="wx234/Succ wx2340",fontsize=10,color="white",style="solid",shape="box"];1856 -> 2116[label="",style="solid", color="burlywood", weight=9];
2116 -> 1945[label="",style="solid", color="burlywood", weight=3];
2117[label="wx234/Zero",fontsize=10,color="white",style="solid",shape="box"];1856 -> 2117[label="",style="solid", color="burlywood", weight=9];
2117 -> 1946[label="",style="solid", color="burlywood", weight=3];
1948[label="wx119",fontsize=16,color="green",shape="box"];1949[label="wx120",fontsize=16,color="green",shape="box"];1950[label="Succ wx117",fontsize=16,color="green",shape="box"];1951[label="wx117",fontsize=16,color="green",shape="box"];1952[label="wx118",fontsize=16,color="green",shape="box"];1953[label="wx121",fontsize=16,color="green",shape="box"];1954[label="wx122",fontsize=16,color="green",shape="box"];1955[label="Succ wx122",fontsize=16,color="green",shape="box"];1947[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat wx243 wx244 == GT)",fontsize=16,color="burlywood",shape="triangle"];2118[label="wx243/Succ wx2430",fontsize=10,color="white",style="solid",shape="box"];1947 -> 2118[label="",style="solid", color="burlywood", weight=9];
2118 -> 2036[label="",style="solid", color="burlywood", weight=3];
2119[label="wx243/Zero",fontsize=10,color="white",style="solid",shape="box"];1947 -> 2119[label="",style="solid", color="burlywood", weight=9];
2119 -> 2037[label="",style="solid", color="burlywood", weight=3];
1945[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat (Succ wx2340) wx235 == GT)",fontsize=16,color="burlywood",shape="box"];2120[label="wx235/Succ wx2350",fontsize=10,color="white",style="solid",shape="box"];1945 -> 2120[label="",style="solid", color="burlywood", weight=9];
2120 -> 2038[label="",style="solid", color="burlywood", weight=3];
2121[label="wx235/Zero",fontsize=10,color="white",style="solid",shape="box"];1945 -> 2121[label="",style="solid", color="burlywood", weight=9];
2121 -> 2039[label="",style="solid", color="burlywood", weight=3];
1946[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat Zero wx235 == GT)",fontsize=16,color="burlywood",shape="box"];2122[label="wx235/Succ wx2350",fontsize=10,color="white",style="solid",shape="box"];1946 -> 2122[label="",style="solid", color="burlywood", weight=9];
2122 -> 2040[label="",style="solid", color="burlywood", weight=3];
2123[label="wx235/Zero",fontsize=10,color="white",style="solid",shape="box"];1946 -> 2123[label="",style="solid", color="burlywood", weight=9];
2123 -> 2041[label="",style="solid", color="burlywood", weight=3];
2036[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat (Succ wx2430) wx244 == GT)",fontsize=16,color="burlywood",shape="box"];2124[label="wx244/Succ wx2440",fontsize=10,color="white",style="solid",shape="box"];2036 -> 2124[label="",style="solid", color="burlywood", weight=9];
2124 -> 2042[label="",style="solid", color="burlywood", weight=3];
2125[label="wx244/Zero",fontsize=10,color="white",style="solid",shape="box"];2036 -> 2125[label="",style="solid", color="burlywood", weight=9];
2125 -> 2043[label="",style="solid", color="burlywood", weight=3];
2037[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat Zero wx244 == GT)",fontsize=16,color="burlywood",shape="box"];2126[label="wx244/Succ wx2440",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2126[label="",style="solid", color="burlywood", weight=9];
2126 -> 2044[label="",style="solid", color="burlywood", weight=3];
2127[label="wx244/Zero",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2127[label="",style="solid", color="burlywood", weight=9];
2127 -> 2045[label="",style="solid", color="burlywood", weight=3];
2038[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat (Succ wx2340) (Succ wx2350) == GT)",fontsize=16,color="black",shape="box"];2038 -> 2046[label="",style="solid", color="black", weight=3];
2039[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat (Succ wx2340) Zero == GT)",fontsize=16,color="black",shape="box"];2039 -> 2047[label="",style="solid", color="black", weight=3];
2040[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat Zero (Succ wx2350) == GT)",fontsize=16,color="black",shape="box"];2040 -> 2048[label="",style="solid", color="black", weight=3];
2041[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];2041 -> 2049[label="",style="solid", color="black", weight=3];
2042[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat (Succ wx2430) (Succ wx2440) == GT)",fontsize=16,color="black",shape="box"];2042 -> 2050[label="",style="solid", color="black", weight=3];
2043[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat (Succ wx2430) Zero == GT)",fontsize=16,color="black",shape="box"];2043 -> 2051[label="",style="solid", color="black", weight=3];
2044[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat Zero (Succ wx2440) == GT)",fontsize=16,color="black",shape="box"];2044 -> 2052[label="",style="solid", color="black", weight=3];
2045[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];2045 -> 2053[label="",style="solid", color="black", weight=3];
2046 -> 1856[label="",style="dashed", color="red", weight=0];
2046[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat wx2340 wx2350 == GT)",fontsize=16,color="magenta"];2046 -> 2054[label="",style="dashed", color="magenta", weight=3];
2046 -> 2055[label="",style="dashed", color="magenta", weight=3];
2047[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (GT == GT)",fontsize=16,color="black",shape="box"];2047 -> 2056[label="",style="solid", color="black", weight=3];
2048[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (LT == GT)",fontsize=16,color="black",shape="box"];2048 -> 2057[label="",style="solid", color="black", weight=3];
2049[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (EQ == GT)",fontsize=16,color="black",shape="box"];2049 -> 2058[label="",style="solid", color="black", weight=3];
2050 -> 1947[label="",style="dashed", color="red", weight=0];
2050[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat wx2430 wx2440 == GT)",fontsize=16,color="magenta"];2050 -> 2059[label="",style="dashed", color="magenta", weight=3];
2050 -> 2060[label="",style="dashed", color="magenta", weight=3];
2051[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (GT == GT)",fontsize=16,color="black",shape="box"];2051 -> 2061[label="",style="solid", color="black", weight=3];
2052[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (LT == GT)",fontsize=16,color="black",shape="box"];2052 -> 2062[label="",style="solid", color="black", weight=3];
2053[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (EQ == GT)",fontsize=16,color="black",shape="box"];2053 -> 2063[label="",style="solid", color="black", weight=3];
2054[label="wx2350",fontsize=16,color="green",shape="box"];2055[label="wx2340",fontsize=16,color="green",shape="box"];2056[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) True",fontsize=16,color="black",shape="box"];2056 -> 2064[label="",style="solid", color="black", weight=3];
2057[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) False",fontsize=16,color="black",shape="triangle"];2057 -> 2065[label="",style="solid", color="black", weight=3];
2058 -> 2057[label="",style="dashed", color="red", weight=0];
2058[label="FiniteMap.lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) False",fontsize=16,color="magenta"];2059[label="wx2430",fontsize=16,color="green",shape="box"];2060[label="wx2440",fontsize=16,color="green",shape="box"];2061[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) True",fontsize=16,color="black",shape="box"];2061 -> 2066[label="",style="solid", color="black", weight=3];
2062[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) False",fontsize=16,color="black",shape="triangle"];2062 -> 2067[label="",style="solid", color="black", weight=3];
2063 -> 2062[label="",style="dashed", color="red", weight=0];
2063[label="FiniteMap.lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) False",fontsize=16,color="magenta"];2064 -> 4[label="",style="dashed", color="red", weight=0];
2064[label="FiniteMap.lookupFM wx232 (Pos (Succ wx233))",fontsize=16,color="magenta"];2064 -> 2068[label="",style="dashed", color="magenta", weight=3];
2064 -> 2069[label="",style="dashed", color="magenta", weight=3];
2065[label="FiniteMap.lookupFM0 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) otherwise",fontsize=16,color="black",shape="box"];2065 -> 2070[label="",style="solid", color="black", weight=3];
2066 -> 4[label="",style="dashed", color="red", weight=0];
2066[label="FiniteMap.lookupFM wx241 (Neg (Succ wx242))",fontsize=16,color="magenta"];2066 -> 2071[label="",style="dashed", color="magenta", weight=3];
2066 -> 2072[label="",style="dashed", color="magenta", weight=3];
2067[label="FiniteMap.lookupFM0 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) otherwise",fontsize=16,color="black",shape="box"];2067 -> 2073[label="",style="solid", color="black", weight=3];
2068[label="wx232",fontsize=16,color="green",shape="box"];2069[label="Pos (Succ wx233)",fontsize=16,color="green",shape="box"];2070[label="FiniteMap.lookupFM0 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) True",fontsize=16,color="black",shape="box"];2070 -> 2074[label="",style="solid", color="black", weight=3];
2071[label="wx241",fontsize=16,color="green",shape="box"];2072[label="Neg (Succ wx242)",fontsize=16,color="green",shape="box"];2073[label="FiniteMap.lookupFM0 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) True",fontsize=16,color="black",shape="box"];2073 -> 2075[label="",style="solid", color="black", weight=3];
2074[label="Just wx229",fontsize=16,color="green",shape="box"];2075[label="Just wx238",fontsize=16,color="green",shape="box"];}

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

(6)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) -> new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) -> new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Zero, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) -> new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM2(wx3000, wx31, wx32, wx33, wx34, wx400, wx400, wx3000, bb)
   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM21(wx3000, wx31, wx32, wx33, wx34, wx400, wx3000, wx400, bb)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Zero, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
   new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx34, Pos(Zero), bb)
   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) -> new_lookupFM(wx111, Pos(Succ(wx113)), h)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) -> new_lookupFM(wx120, Neg(Succ(wx122)), bc)
   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) -> new_lookupFM(wx241, Neg(Succ(wx242)), bd)
   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx34, Neg(Zero), bb)
   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx33, Neg(Zero), bb)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) -> new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
   new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
   new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
   new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) -> new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
   new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) -> new_lookupFM(wx232, Pos(Succ(wx233)), ba)
   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx33, Pos(Zero), bb)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) -> new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)

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

(7) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs.
----------------------------------------

(8)
Complex Obligation (AND)

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

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

   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx33, Neg(Zero), bb)
   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx34, Neg(Zero), bb)

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_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx33, Neg(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx34, Neg(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(11)
YES

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

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

   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx33, Pos(Zero), bb)
   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx34, Pos(Zero), bb)

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

(13) 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_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx33, Pos(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx34, Pos(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(14)
YES

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

(15)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Zero, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) -> new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) -> new_lookupFM(wx232, Pos(Succ(wx233)), ba)
   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM2(wx3000, wx31, wx32, wx33, wx34, wx400, wx400, wx3000, bb)
   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) -> new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) -> new_lookupFM(wx111, Pos(Succ(wx113)), h)
   new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
   new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) -> new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
   new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)

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

(16) 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_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) -> new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, 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_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) -> new_lookupFM(wx232, Pos(Succ(wx233)), ba)
The graph contains the following edges 5 >= 1, 9 >= 3


*new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM2(wx3000, wx31, wx32, wx33, wx34, wx400, wx400, wx3000, 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_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) -> new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, 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_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Zero, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9


*new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9


*new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) -> new_lookupFM(wx111, Pos(Succ(wx113)), h)
The graph contains the following edges 4 >= 1, 9 >= 3


*new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) -> new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7


*new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(17)
YES

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

(18)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM21(wx3000, wx31, wx32, wx33, wx34, wx400, wx3000, wx400, bb)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Zero, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) -> new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) -> new_lookupFM(wx241, Neg(Succ(wx242)), bd)
   new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
   new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) -> new_lookupFM(wx120, Neg(Succ(wx122)), bc)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) -> new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) -> new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
   new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)

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

(19) 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_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) -> new_lookupFM(wx120, Neg(Succ(wx122)), bc)
The graph contains the following edges 4 >= 1, 9 >= 3


*new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) -> new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, 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_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) -> new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, 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_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM21(wx3000, wx31, wx32, wx33, wx34, wx400, wx3000, wx400, 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_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9


*new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Zero, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9


*new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) -> new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7


*new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) -> new_lookupFM(wx241, Neg(Succ(wx242)), bd)
The graph contains the following edges 5 >= 1, 9 >= 3


*new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


*new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(20)
YES