11.96/5.12	YES
13.43/5.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
13.43/5.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.43/5.61	
13.43/5.61	
13.43/5.61	H-Termination with start terms of the given HASKELL could be proven:
13.43/5.61	
13.43/5.61	(0) HASKELL
13.43/5.61	(1) BR [EQUIVALENT, 0 ms]
13.43/5.61	(2) HASKELL
13.43/5.61	(3) COR [EQUIVALENT, 0 ms]
13.43/5.61	(4) HASKELL
13.43/5.61	(5) Narrow [SOUND, 0 ms]
13.43/5.61	(6) QDP
13.43/5.61	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
13.43/5.61	(8) AND
13.43/5.61	    (9) QDP
13.43/5.61	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.43/5.61	        (11) YES
13.43/5.61	    (12) QDP
13.43/5.61	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.43/5.61	        (14) YES
13.43/5.61	    (15) QDP
13.43/5.61	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.43/5.61	        (17) YES
13.43/5.61	    (18) QDP
13.43/5.61	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.43/5.61	        (20) YES
13.43/5.61	
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(0)
13.43/5.61	Obligation:
13.43/5.61	mainModule Main 
13.43/5.61	module FiniteMap where {
13.43/5.61	import qualified Main;
13.43/5.61	import qualified Maybe;
13.43/5.61	import qualified Prelude;
13.43/5.61	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.43/5.61	
13.43/5.61	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.43/5.61	}
13.43/5.61	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
13.43/5.61	lookupFM EmptyFM key = Nothing;
13.43/5.61	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
13.43/5.61	 | key_to_find > key = lookupFM fm_r key_to_find
13.43/5.61	 | otherwise = Just elt;
13.43/5.61	
13.43/5.61	}
13.43/5.61	module Maybe where {
13.43/5.61	import qualified FiniteMap;
13.43/5.61	import qualified Main;
13.43/5.61	import qualified Prelude;
13.43/5.61	}
13.43/5.61	module Main where {
13.43/5.61	import qualified FiniteMap;
13.43/5.61	import qualified Maybe;
13.43/5.61	import qualified Prelude;
13.43/5.61	}
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(1) BR (EQUIVALENT)
13.43/5.61	Replaced joker patterns by fresh variables and removed binding patterns.
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(2)
13.43/5.61	Obligation:
13.43/5.61	mainModule Main 
13.43/5.61	module FiniteMap where {
13.43/5.61	import qualified Main;
13.43/5.61	import qualified Maybe;
13.43/5.61	import qualified Prelude;
13.43/5.61	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.43/5.61	
13.43/5.61	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.43/5.61	}
13.43/5.61	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
13.43/5.61	lookupFM EmptyFM key = Nothing;
13.43/5.61	lookupFM (Branch key elt vy fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
13.43/5.61	 | key_to_find > key = lookupFM fm_r key_to_find
13.43/5.61	 | otherwise = Just elt;
13.43/5.61	
13.43/5.61	}
13.43/5.61	module Maybe where {
13.43/5.61	import qualified FiniteMap;
13.43/5.61	import qualified Main;
13.43/5.61	import qualified Prelude;
13.43/5.61	}
13.43/5.61	module Main where {
13.43/5.61	import qualified FiniteMap;
13.43/5.61	import qualified Maybe;
13.43/5.61	import qualified Prelude;
13.43/5.61	}
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(3) COR (EQUIVALENT)
13.43/5.61	Cond Reductions:
13.43/5.61	The following Function with conditions
13.43/5.61	"undefined |Falseundefined;
13.43/5.61	"
13.43/5.61	is transformed to
13.43/5.61	"undefined  = undefined1;
13.43/5.61	"
13.43/5.61	"undefined0 True = undefined;
13.43/5.61	"
13.43/5.61	"undefined1  = undefined0 False;
13.43/5.61	"
13.43/5.61	The following Function with conditions
13.43/5.61	"lookupFM EmptyFM key = Nothing;
13.43/5.61	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;
13.43/5.61	"
13.43/5.61	is transformed to
13.43/5.61	"lookupFM EmptyFM key = lookupFM4 EmptyFM key;
13.43/5.61	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
13.43/5.61	"
13.43/5.61	"lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
13.43/5.61	"
13.43/5.61	"lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
13.43/5.61	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);
13.43/5.61	"
13.43/5.61	"lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
13.43/5.61	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
13.43/5.61	"
13.43/5.61	"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);
13.43/5.61	"
13.43/5.61	"lookupFM4 EmptyFM key = Nothing;
13.43/5.61	lookupFM4 wv ww = lookupFM3 wv ww;
13.43/5.61	"
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(4)
13.43/5.61	Obligation:
13.43/5.61	mainModule Main 
13.43/5.61	module FiniteMap where {
13.43/5.61	import qualified Main;
13.43/5.61	import qualified Maybe;
13.43/5.61	import qualified Prelude;
13.43/5.61	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
13.43/5.61	
13.43/5.61	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.43/5.61	}
13.43/5.61	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
13.43/5.61	lookupFM EmptyFM key = lookupFM4 EmptyFM key;
13.43/5.61	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
13.43/5.61	
13.43/5.61	lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
13.43/5.61	
13.43/5.61	lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
13.43/5.61	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
13.43/5.61	
13.43/5.61	lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
13.43/5.61	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);
13.43/5.61	
13.43/5.61	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);
13.43/5.61	
13.43/5.61	lookupFM4 EmptyFM key = Nothing;
13.43/5.61	lookupFM4 wv ww = lookupFM3 wv ww;
13.43/5.61	
13.43/5.61	}
13.43/5.61	module Maybe where {
13.43/5.61	import qualified FiniteMap;
13.43/5.61	import qualified Main;
13.43/5.61	import qualified Prelude;
13.43/5.61	}
13.43/5.61	module Main where {
13.43/5.61	import qualified FiniteMap;
13.43/5.61	import qualified Maybe;
13.43/5.61	import qualified Prelude;
13.43/5.61	}
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(5) Narrow (SOUND)
13.43/5.61	Haskell To QDPs
13.43/5.61	
13.43/5.61	digraph dp_graph {
13.43/5.61	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.lookupFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.43/5.61	3[label="FiniteMap.lookupFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
13.43/5.61	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];
13.43/5.61	2076 -> 5[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2077 -> 6[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	5[label="FiniteMap.lookupFM FiniteMap.EmptyFM wx4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
13.43/5.61	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];
13.43/5.61	7[label="FiniteMap.lookupFM4 FiniteMap.EmptyFM wx4",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2078 -> 13[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2079[label="wx4/Neg wx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 2079[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2079 -> 14[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2080 -> 15[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2081[label="wx40/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 2081[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2081 -> 16[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2082 -> 17[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2083[label="wx40/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 2083[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2083 -> 18[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2084 -> 19[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2085[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 2085[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2085 -> 20[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2086 -> 21[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2087[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 2087[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2087 -> 22[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2088 -> 23[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2089[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];17 -> 2089[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2089 -> 24[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2090 -> 25[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2091[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];18 -> 2091[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2091 -> 26[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2092 -> 29[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2093[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 2093[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2093 -> 30[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2094 -> 31[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2095[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 2095[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2095 -> 32[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2096 -> 35[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2097[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 2097[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2097 -> 36[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2098 -> 37[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2099[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 2099[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2099 -> 38[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2100 -> 39[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2101[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 2101[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2101 -> 40[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
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13.43/5.61	1147[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat (Succ wx1230) (Succ wx1240) == LT)",fontsize=16,color="black",shape="box"];1147 -> 1155[label="",style="solid", color="black", weight=3];
13.43/5.61	1148[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat (Succ wx1230) Zero == LT)",fontsize=16,color="black",shape="box"];1148 -> 1156[label="",style="solid", color="black", weight=3];
13.43/5.61	1149[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat Zero (Succ wx1240) == LT)",fontsize=16,color="black",shape="box"];1149 -> 1157[label="",style="solid", color="black", weight=3];
13.43/5.61	1150[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];1150 -> 1158[label="",style="solid", color="black", weight=3];
13.43/5.61	119[label="wx33",fontsize=16,color="green",shape="box"];120[label="Neg (Succ wx400)",fontsize=16,color="green",shape="box"];121[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];121 -> 139[label="",style="solid", color="black", weight=3];
13.43/5.61	122[label="FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (compare (Neg Zero) (Neg (Succ wx3000)) == GT)",fontsize=16,color="black",shape="box"];122 -> 140[label="",style="solid", color="black", weight=3];
13.43/5.61	123[label="FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];123 -> 141[label="",style="solid", color="black", weight=3];
13.43/5.61	1151 -> 973[label="",style="dashed", color="red", weight=0];
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13.43/5.61	1151 -> 1160[label="",style="dashed", color="magenta", weight=3];
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13.43/5.61	1153[label="FiniteMap.lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (LT == LT)",fontsize=16,color="black",shape="box"];1153 -> 1162[label="",style="solid", color="black", weight=3];
13.43/5.61	1154[label="FiniteMap.lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (EQ == LT)",fontsize=16,color="black",shape="box"];1154 -> 1163[label="",style="solid", color="black", weight=3];
13.43/5.61	129[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];129 -> 149[label="",style="solid", color="black", weight=3];
13.43/5.61	130[label="FiniteMap.lookupFM1 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) True",fontsize=16,color="black",shape="box"];130 -> 150[label="",style="solid", color="black", weight=3];
13.43/5.61	131[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];131 -> 151[label="",style="solid", color="black", weight=3];
13.43/5.61	132[label="FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="box"];132 -> 152[label="",style="solid", color="black", weight=3];
13.43/5.61	133[label="FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];133 -> 153[label="",style="solid", color="black", weight=3];
13.43/5.61	1155 -> 1060[label="",style="dashed", color="red", weight=0];
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13.43/5.61	1155 -> 1165[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1156[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (GT == LT)",fontsize=16,color="black",shape="box"];1156 -> 1166[label="",style="solid", color="black", weight=3];
13.43/5.61	1157[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (LT == LT)",fontsize=16,color="black",shape="box"];1157 -> 1167[label="",style="solid", color="black", weight=3];
13.43/5.61	1158[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (EQ == LT)",fontsize=16,color="black",shape="box"];1158 -> 1168[label="",style="solid", color="black", weight=3];
13.43/5.61	139[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];139 -> 161[label="",style="solid", color="black", weight=3];
13.43/5.61	140[label="FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ wx3000)) == GT)",fontsize=16,color="black",shape="box"];140 -> 162[label="",style="solid", color="black", weight=3];
13.43/5.61	141[label="FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];141 -> 163[label="",style="solid", color="black", weight=3];
13.43/5.61	1159[label="wx1150",fontsize=16,color="green",shape="box"];1160[label="wx1140",fontsize=16,color="green",shape="box"];1161[label="FiniteMap.lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) False",fontsize=16,color="black",shape="triangle"];1161 -> 1169[label="",style="solid", color="black", weight=3];
13.43/5.61	1162[label="FiniteMap.lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) True",fontsize=16,color="black",shape="box"];1162 -> 1170[label="",style="solid", color="black", weight=3];
13.43/5.61	1163 -> 1161[label="",style="dashed", color="red", weight=0];
13.43/5.61	1163[label="FiniteMap.lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) False",fontsize=16,color="magenta"];149[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) Zero == GT)",fontsize=16,color="black",shape="box"];149 -> 172[label="",style="solid", color="black", weight=3];
13.43/5.61	150 -> 4[label="",style="dashed", color="red", weight=0];
13.43/5.61	150[label="FiniteMap.lookupFM wx34 (Pos (Succ wx400))",fontsize=16,color="magenta"];150 -> 173[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	150 -> 174[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	151[label="FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) False",fontsize=16,color="black",shape="box"];151 -> 175[label="",style="solid", color="black", weight=3];
13.43/5.61	152[label="FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) True",fontsize=16,color="black",shape="box"];152 -> 176[label="",style="solid", color="black", weight=3];
13.43/5.61	153[label="FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) False",fontsize=16,color="black",shape="box"];153 -> 177[label="",style="solid", color="black", weight=3];
13.43/5.61	1164[label="wx1240",fontsize=16,color="green",shape="box"];1165[label="wx1230",fontsize=16,color="green",shape="box"];1166[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) False",fontsize=16,color="black",shape="triangle"];1166 -> 1171[label="",style="solid", color="black", weight=3];
13.43/5.61	1167[label="FiniteMap.lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) True",fontsize=16,color="black",shape="box"];1167 -> 1172[label="",style="solid", color="black", weight=3];
13.43/5.61	1168 -> 1166[label="",style="dashed", color="red", weight=0];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	1170 -> 4[label="",style="dashed", color="red", weight=0];
13.43/5.61	1170[label="FiniteMap.lookupFM wx111 (Pos (Succ wx113))",fontsize=16,color="magenta"];1170 -> 1174[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1170 -> 1175[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	176 -> 4[label="",style="dashed", color="red", weight=0];
13.43/5.61	176[label="FiniteMap.lookupFM wx34 (Pos Zero)",fontsize=16,color="magenta"];176 -> 198[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	176 -> 199[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	1172 -> 4[label="",style="dashed", color="red", weight=0];
13.43/5.61	1172[label="FiniteMap.lookupFM wx120 (Neg (Succ wx122))",fontsize=16,color="magenta"];1172 -> 1177[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1172 -> 1178[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	220 -> 4[label="",style="dashed", color="red", weight=0];
13.43/5.61	220[label="FiniteMap.lookupFM wx34 (Pos (Succ wx400))",fontsize=16,color="magenta"];220 -> 245[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	220 -> 246[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	232[label="Just wx31",fontsize=16,color="green",shape="box"];233 -> 4[label="",style="dashed", color="red", weight=0];
13.43/5.61	233[label="FiniteMap.lookupFM wx34 (Neg Zero)",fontsize=16,color="magenta"];233 -> 257[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	233 -> 258[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	234[label="Just wx31",fontsize=16,color="green",shape="box"];1181 -> 1856[label="",style="dashed", color="red", weight=0];
13.43/5.61	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];
13.43/5.61	1181 -> 1858[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1181 -> 1859[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1181 -> 1860[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1181 -> 1861[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1181 -> 1862[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1181 -> 1863[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1181 -> 1864[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	1182 -> 1949[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1182 -> 1950[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1182 -> 1951[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1182 -> 1952[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1182 -> 1953[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1182 -> 1954[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	1182 -> 1955[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	2116 -> 1945[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2117[label="wx234/Zero",fontsize=10,color="white",style="solid",shape="box"];1856 -> 2117[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2117 -> 1946[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2118 -> 2036[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2119[label="wx243/Zero",fontsize=10,color="white",style="solid",shape="box"];1947 -> 2119[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2119 -> 2037[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2120 -> 2038[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2121[label="wx235/Zero",fontsize=10,color="white",style="solid",shape="box"];1945 -> 2121[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2121 -> 2039[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2122 -> 2040[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2123[label="wx235/Zero",fontsize=10,color="white",style="solid",shape="box"];1946 -> 2123[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2123 -> 2041[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2124 -> 2042[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2125[label="wx244/Zero",fontsize=10,color="white",style="solid",shape="box"];2036 -> 2125[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2125 -> 2043[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	2126 -> 2044[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	2127[label="wx244/Zero",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2127[label="",style="solid", color="burlywood", weight=9];
13.43/5.61	2127 -> 2045[label="",style="solid", color="burlywood", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2046 -> 1856[label="",style="dashed", color="red", weight=0];
13.43/5.61	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];
13.43/5.61	2046 -> 2055[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2050 -> 1947[label="",style="dashed", color="red", weight=0];
13.43/5.61	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];
13.43/5.61	2050 -> 2060[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2058 -> 2057[label="",style="dashed", color="red", weight=0];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2063 -> 2062[label="",style="dashed", color="red", weight=0];
13.43/5.61	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];
13.43/5.61	2064[label="FiniteMap.lookupFM wx232 (Pos (Succ wx233))",fontsize=16,color="magenta"];2064 -> 2068[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	2064 -> 2069[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	2066 -> 4[label="",style="dashed", color="red", weight=0];
13.43/5.61	2066[label="FiniteMap.lookupFM wx241 (Neg (Succ wx242))",fontsize=16,color="magenta"];2066 -> 2071[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	2066 -> 2072[label="",style="dashed", color="magenta", weight=3];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	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];
13.43/5.61	2074[label="Just wx229",fontsize=16,color="green",shape="box"];2075[label="Just wx238",fontsize=16,color="green",shape="box"];}
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(6)
13.43/5.61	Obligation:
13.43/5.61	Q DP problem:
13.43/5.61	The TRS P consists of the following rules:
13.43/5.61	
13.43/5.61	   new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) -> new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
13.43/5.61	   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) -> new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
13.43/5.61	   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)
13.43/5.61	   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) -> new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
13.43/5.61	   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)
13.43/5.61	   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)
13.43/5.61	   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)
13.43/5.61	   new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
13.43/5.61	   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx34, Pos(Zero), bb)
13.43/5.61	   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) -> new_lookupFM(wx111, Pos(Succ(wx113)), h)
13.43/5.61	   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) -> new_lookupFM(wx120, Neg(Succ(wx122)), bc)
13.43/5.61	   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) -> new_lookupFM(wx241, Neg(Succ(wx242)), bd)
13.43/5.61	   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx34, Neg(Zero), bb)
13.43/5.61	   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx33, Neg(Zero), bb)
13.43/5.61	   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) -> new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
13.43/5.61	   new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
13.43/5.61	   new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) -> new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
13.43/5.61	   new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) -> new_lookupFM(wx232, Pos(Succ(wx233)), ba)
13.43/5.61	   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx33, Pos(Zero), bb)
13.43/5.61	   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) -> new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
13.43/5.61	
13.43/5.61	R is empty.
13.43/5.61	Q is empty.
13.43/5.61	We have to consider all minimal (P,Q,R)-chains.
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(7) DependencyGraphProof (EQUIVALENT)
13.43/5.61	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs.
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(8)
13.43/5.61	Complex Obligation (AND)
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(9)
13.43/5.61	Obligation:
13.43/5.61	Q DP problem:
13.43/5.61	The TRS P consists of the following rules:
13.43/5.61	
13.43/5.61	   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx33, Neg(Zero), bb)
13.43/5.61	   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx34, Neg(Zero), bb)
13.43/5.61	
13.43/5.61	R is empty.
13.43/5.61	Q is empty.
13.43/5.61	We have to consider all minimal (P,Q,R)-chains.
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(10) QDPSizeChangeProof (EQUIVALENT)
13.43/5.61	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. 
13.43/5.61	
13.43/5.61	From the DPs we obtained the following set of size-change graphs:
13.43/5.61	*new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx33, Neg(Zero), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupFM(wx34, Neg(Zero), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(11)
13.43/5.61	YES
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(12)
13.43/5.61	Obligation:
13.43/5.61	Q DP problem:
13.43/5.61	The TRS P consists of the following rules:
13.43/5.61	
13.43/5.61	   new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx33, Pos(Zero), bb)
13.43/5.61	   new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx34, Pos(Zero), bb)
13.43/5.61	
13.43/5.61	R is empty.
13.43/5.61	Q is empty.
13.43/5.61	We have to consider all minimal (P,Q,R)-chains.
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(13) QDPSizeChangeProof (EQUIVALENT)
13.43/5.61	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. 
13.43/5.61	
13.43/5.61	From the DPs we obtained the following set of size-change graphs:
13.43/5.61	*new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx33, Pos(Zero), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupFM(wx34, Pos(Zero), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(14)
13.43/5.61	YES
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(15)
13.43/5.61	Obligation:
13.43/5.61	Q DP problem:
13.43/5.61	The TRS P consists of the following rules:
13.43/5.61	
13.43/5.61	   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)
13.43/5.61	   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) -> new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
13.43/5.61	   new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) -> new_lookupFM(wx232, Pos(Succ(wx233)), ba)
13.43/5.61	   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)
13.43/5.61	   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) -> new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
13.43/5.61	   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) -> new_lookupFM(wx111, Pos(Succ(wx113)), h)
13.43/5.61	   new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) -> new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
13.43/5.61	   new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
13.43/5.61	
13.43/5.61	R is empty.
13.43/5.61	Q is empty.
13.43/5.61	We have to consider all minimal (P,Q,R)-chains.
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(16) QDPSizeChangeProof (EQUIVALENT)
13.43/5.61	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. 
13.43/5.61	
13.43/5.61	From the DPs we obtained the following set of size-change graphs:
13.43/5.61	*new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) -> new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) -> new_lookupFM(wx232, Pos(Succ(wx233)), ba)
13.43/5.61	The graph contains the following edges 5 >= 1, 9 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*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)
13.43/5.61	The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 1 > 8, 3 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) -> new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*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)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) -> new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) -> new_lookupFM(wx111, Pos(Succ(wx113)), h)
13.43/5.61	The graph contains the following edges 4 >= 1, 9 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) -> new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) -> new_lookupFM(wx34, Pos(Succ(wx400)), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(17)
13.43/5.61	YES
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(18)
13.43/5.61	Obligation:
13.43/5.61	Q DP problem:
13.43/5.61	The TRS P consists of the following rules:
13.43/5.61	
13.43/5.61	   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)
13.43/5.61	   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)
13.43/5.61	   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) -> new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
13.43/5.61	   new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) -> new_lookupFM(wx241, Neg(Succ(wx242)), bd)
13.43/5.61	   new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
13.43/5.61	   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) -> new_lookupFM(wx120, Neg(Succ(wx122)), bc)
13.43/5.61	   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) -> new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
13.43/5.61	   new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) -> new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
13.43/5.61	   new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
13.43/5.61	
13.43/5.61	R is empty.
13.43/5.61	Q is empty.
13.43/5.61	We have to consider all minimal (P,Q,R)-chains.
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(19) QDPSizeChangeProof (EQUIVALENT)
13.43/5.61	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. 
13.43/5.61	
13.43/5.61	From the DPs we obtained the following set of size-change graphs:
13.43/5.61	*new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) -> new_lookupFM(wx120, Neg(Succ(wx122)), bc)
13.43/5.61	The graph contains the following edges 4 >= 1, 9 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) -> new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) -> new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*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)
13.43/5.61	The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 1 > 7, 2 > 8, 3 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) -> new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*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)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) -> new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
13.43/5.61	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) -> new_lookupFM(wx241, Neg(Succ(wx242)), bd)
13.43/5.61	The graph contains the following edges 5 >= 1, 9 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	*new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) -> new_lookupFM(wx33, Neg(Succ(wx400)), bb)
13.43/5.61	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.43/5.61	
13.43/5.61	
13.43/5.61	----------------------------------------
13.43/5.61	
13.43/5.61	(20)
13.43/5.61	YES
13.61/9.07	EOF