10.59/4.66 YES 12.78/5.26 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 12.78/5.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.78/5.26 12.78/5.26 12.78/5.26 H-Termination with start terms of the given HASKELL could be proven: 12.78/5.26 12.78/5.26 (0) HASKELL 12.78/5.26 (1) LR [EQUIVALENT, 0 ms] 12.78/5.26 (2) HASKELL 12.78/5.26 (3) BR [EQUIVALENT, 0 ms] 12.78/5.26 (4) HASKELL 12.78/5.26 (5) COR [EQUIVALENT, 0 ms] 12.78/5.26 (6) HASKELL 12.78/5.26 (7) Narrow [SOUND, 0 ms] 12.78/5.26 (8) AND 12.78/5.26 (9) QDP 12.78/5.26 (10) TransformationProof [EQUIVALENT, 0 ms] 12.78/5.26 (11) QDP 12.78/5.26 (12) TransformationProof [EQUIVALENT, 0 ms] 12.78/5.26 (13) QDP 12.78/5.26 (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.78/5.26 (15) YES 12.78/5.26 (16) QDP 12.78/5.26 (17) TransformationProof [EQUIVALENT, 0 ms] 12.78/5.26 (18) QDP 12.78/5.26 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.78/5.26 (20) YES 12.78/5.26 (21) QDP 12.78/5.26 (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.78/5.26 (23) YES 12.78/5.26 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (0) 12.78/5.26 Obligation: 12.78/5.26 mainModule Main 12.78/5.26 module FiniteMap where { 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 12.78/5.26 12.78/5.26 instance (Eq a, Eq b) => Eq FiniteMap b a where { 12.78/5.26 } 12.78/5.26 fmToList_GE :: Ord a => FiniteMap a b -> a -> [(a,b)]; 12.78/5.26 fmToList_GE fm fr = foldFM_GE (\key elt rest ->(key,elt) : rest) [] fr fm; 12.78/5.26 12.78/5.26 foldFM_GE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a; 12.78/5.26 foldFM_GE k z fr EmptyFM = z; 12.78/5.26 foldFM_GE k z fr (Branch key elt _ fm_l fm_r) | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l 12.78/5.26 | otherwise = foldFM_GE k z fr fm_r; 12.78/5.26 12.78/5.26 } 12.78/5.26 module Maybe where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 module Main where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (1) LR (EQUIVALENT) 12.78/5.26 Lambda Reductions: 12.78/5.26 The following Lambda expression 12.78/5.26 "\keyeltrest->(key,elt) : rest" 12.78/5.26 is transformed to 12.78/5.26 "fmToList_GE0 key elt rest = (key,elt) : rest; 12.78/5.26 " 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (2) 12.78/5.26 Obligation: 12.78/5.26 mainModule Main 12.78/5.26 module FiniteMap where { 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 12.78/5.26 12.78/5.26 instance (Eq a, Eq b) => Eq FiniteMap b a where { 12.78/5.26 } 12.78/5.26 fmToList_GE :: Ord a => FiniteMap a b -> a -> [(a,b)]; 12.78/5.26 fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm; 12.78/5.26 12.78/5.26 fmToList_GE0 key elt rest = (key,elt) : rest; 12.78/5.26 12.78/5.26 foldFM_GE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c; 12.78/5.26 foldFM_GE k z fr EmptyFM = z; 12.78/5.26 foldFM_GE k z fr (Branch key elt _ fm_l fm_r) | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l 12.78/5.26 | otherwise = foldFM_GE k z fr fm_r; 12.78/5.26 12.78/5.26 } 12.78/5.26 module Maybe where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 module Main where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (3) BR (EQUIVALENT) 12.78/5.26 Replaced joker patterns by fresh variables and removed binding patterns. 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (4) 12.78/5.26 Obligation: 12.78/5.26 mainModule Main 12.78/5.26 module FiniteMap where { 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 12.78/5.26 12.78/5.26 instance (Eq a, Eq b) => Eq FiniteMap b a where { 12.78/5.26 } 12.78/5.26 fmToList_GE :: Ord a => FiniteMap a b -> a -> [(a,b)]; 12.78/5.26 fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm; 12.78/5.26 12.78/5.26 fmToList_GE0 key elt rest = (key,elt) : rest; 12.78/5.26 12.78/5.26 foldFM_GE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c; 12.78/5.26 foldFM_GE k z fr EmptyFM = z; 12.78/5.26 foldFM_GE k z fr (Branch key elt vy fm_l fm_r) | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l 12.78/5.26 | otherwise = foldFM_GE k z fr fm_r; 12.78/5.26 12.78/5.26 } 12.78/5.26 module Maybe where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 module Main where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (5) COR (EQUIVALENT) 12.78/5.26 Cond Reductions: 12.78/5.26 The following Function with conditions 12.78/5.26 "compare x y|x == yEQ|x <= yLT|otherwiseGT; 12.78/5.26 " 12.78/5.26 is transformed to 12.78/5.26 "compare x y = compare3 x y; 12.78/5.26 " 12.78/5.26 "compare1 x y True = LT; 12.78/5.26 compare1 x y False = compare0 x y otherwise; 12.78/5.26 " 12.78/5.26 "compare0 x y True = GT; 12.78/5.26 " 12.78/5.26 "compare2 x y True = EQ; 12.78/5.26 compare2 x y False = compare1 x y (x <= y); 12.78/5.26 " 12.78/5.26 "compare3 x y = compare2 x y (x == y); 12.78/5.26 " 12.78/5.26 The following Function with conditions 12.78/5.26 "undefined |Falseundefined; 12.78/5.26 " 12.78/5.26 is transformed to 12.78/5.26 "undefined = undefined1; 12.78/5.26 " 12.78/5.26 "undefined0 True = undefined; 12.78/5.26 " 12.78/5.26 "undefined1 = undefined0 False; 12.78/5.26 " 12.78/5.26 The following Function with conditions 12.78/5.26 "foldFM_GE k z fr EmptyFM = z; 12.78/5.26 foldFM_GE k z fr (Branch key elt vy fm_l fm_r)|key >= frfoldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l|otherwisefoldFM_GE k z fr fm_r; 12.78/5.26 " 12.78/5.26 is transformed to 12.78/5.26 "foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM; 12.78/5.26 foldFM_GE k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r); 12.78/5.26 " 12.78/5.26 "foldFM_GE1 k z fr key elt vy fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l; 12.78/5.26 foldFM_GE1 k z fr key elt vy fm_l fm_r False = foldFM_GE0 k z fr key elt vy fm_l fm_r otherwise; 12.78/5.26 " 12.78/5.26 "foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r; 12.78/5.26 " 12.78/5.26 "foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE1 k z fr key elt vy fm_l fm_r (key >= fr); 12.78/5.26 " 12.78/5.26 "foldFM_GE3 k z fr EmptyFM = z; 12.78/5.26 foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy; 12.78/5.26 " 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (6) 12.78/5.26 Obligation: 12.78/5.26 mainModule Main 12.78/5.26 module FiniteMap where { 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 12.78/5.26 12.78/5.26 instance (Eq a, Eq b) => Eq FiniteMap a b where { 12.78/5.26 } 12.78/5.26 fmToList_GE :: Ord b => FiniteMap b a -> b -> [(b,a)]; 12.78/5.26 fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm; 12.78/5.26 12.78/5.26 fmToList_GE0 key elt rest = (key,elt) : rest; 12.78/5.26 12.78/5.26 foldFM_GE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c; 12.78/5.26 foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM; 12.78/5.26 foldFM_GE k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r); 12.78/5.26 12.78/5.26 foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r; 12.78/5.26 12.78/5.26 foldFM_GE1 k z fr key elt vy fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l; 12.78/5.26 foldFM_GE1 k z fr key elt vy fm_l fm_r False = foldFM_GE0 k z fr key elt vy fm_l fm_r otherwise; 12.78/5.26 12.78/5.26 foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE1 k z fr key elt vy fm_l fm_r (key >= fr); 12.78/5.26 12.78/5.26 foldFM_GE3 k z fr EmptyFM = z; 12.78/5.26 foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy; 12.78/5.26 12.78/5.26 } 12.78/5.26 module Maybe where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Main; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 module Main where { 12.78/5.26 import qualified FiniteMap; 12.78/5.26 import qualified Maybe; 12.78/5.26 import qualified Prelude; 12.78/5.26 } 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (7) Narrow (SOUND) 12.78/5.26 Haskell To QDPs 12.78/5.26 12.78/5.26 digraph dp_graph { 12.78/5.26 node [outthreshold=100, inthreshold=100];1[label="FiniteMap.fmToList_GE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 12.78/5.26 3[label="FiniteMap.fmToList_GE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 12.78/5.26 4[label="FiniteMap.fmToList_GE wz3 wz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 12.78/5.26 5[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] wz4 wz3",fontsize=16,color="burlywood",shape="triangle"];170[label="wz3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 170[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 170 -> 6[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 171[label="wz3/FiniteMap.Branch wz30 wz31 wz32 wz33 wz34",fontsize=10,color="white",style="solid",shape="box"];5 -> 171[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 171 -> 7[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 6[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 12.78/5.26 7[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 12.78/5.26 8[label="FiniteMap.foldFM_GE3 FiniteMap.fmToList_GE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 12.78/5.26 9[label="FiniteMap.foldFM_GE2 FiniteMap.fmToList_GE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 12.78/5.26 10[label="[]",fontsize=16,color="green",shape="box"];11[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (wz30 >= wz4)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 12.78/5.26 12[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (compare wz30 wz4 /= LT)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 12.78/5.26 13[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (not (compare wz30 wz4 == LT))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 12.78/5.26 14[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (not (compare3 wz30 wz4 == LT))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 12.78/5.26 15[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (not (compare2 wz30 wz4 (wz30 == wz4) == LT))",fontsize=16,color="burlywood",shape="box"];172[label="wz30/False",fontsize=10,color="white",style="solid",shape="box"];15 -> 172[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 172 -> 16[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 173[label="wz30/True",fontsize=10,color="white",style="solid",shape="box"];15 -> 173[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 173 -> 17[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 16[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] wz4 False wz31 wz32 wz33 wz34 (not (compare2 False wz4 (False == wz4) == LT))",fontsize=16,color="burlywood",shape="box"];174[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];16 -> 174[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 174 -> 18[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 175[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];16 -> 175[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 175 -> 19[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 17[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] wz4 True wz31 wz32 wz33 wz34 (not (compare2 True wz4 (True == wz4) == LT))",fontsize=16,color="burlywood",shape="box"];176[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];17 -> 176[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 176 -> 20[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 177[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];17 -> 177[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 177 -> 21[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 18[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False False wz31 wz32 wz33 wz34 (not (compare2 False False (False == False) == LT))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 12.78/5.26 19[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare2 False True (False == True) == LT))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 12.78/5.26 20[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare2 True False (True == False) == LT))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 12.78/5.26 21[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True True wz31 wz32 wz33 wz34 (not (compare2 True True (True == True) == LT))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 12.78/5.26 22[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False False wz31 wz32 wz33 wz34 (not (compare2 False False True == LT))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3]; 12.78/5.26 23[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare2 False True False == LT))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 12.78/5.26 24[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare2 True False False == LT))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 12.78/5.26 25[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True True wz31 wz32 wz33 wz34 (not (compare2 True True True == LT))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 12.78/5.26 26[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False False wz31 wz32 wz33 wz34 (not (EQ == LT))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 12.78/5.26 27[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare1 False True (False <= True) == LT))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3]; 12.78/5.26 28[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare1 True False (True <= False) == LT))",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3]; 12.78/5.26 29[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True True wz31 wz32 wz33 wz34 (not (EQ == LT))",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 12.78/5.26 30[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False False wz31 wz32 wz33 wz34 (not False)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3]; 12.78/5.26 31[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare1 False True True == LT))",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3]; 12.78/5.26 32[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare1 True False False == LT))",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3]; 12.78/5.26 33[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True True wz31 wz32 wz33 wz34 (not False)",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3]; 12.78/5.26 34[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False False wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3]; 12.78/5.26 35[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 (not (LT == LT))",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 12.78/5.26 36[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare0 True False otherwise == LT))",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 12.78/5.26 37[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True True wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3]; 12.78/5.26 38 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 38[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 False wz31 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] False wz34)) False wz33",fontsize=16,color="magenta"];38 -> 84[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 39[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 (not True)",fontsize=16,color="black",shape="box"];39 -> 44[label="",style="solid", color="black", weight=3]; 12.78/5.26 40[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare0 True False True == LT))",fontsize=16,color="black",shape="box"];40 -> 45[label="",style="solid", color="black", weight=3]; 12.78/5.26 41 -> 46[label="",style="dashed", color="red", weight=0]; 12.78/5.26 41[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] True wz34)) True wz33",fontsize=16,color="magenta"];41 -> 47[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 84 -> 92[label="",style="dashed", color="red", weight=0]; 12.78/5.26 84[label="FiniteMap.fmToList_GE0 False wz31 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] False wz34)",fontsize=16,color="magenta"];84 -> 93[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 83[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False wz33",fontsize=16,color="burlywood",shape="triangle"];178[label="wz33/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];83 -> 178[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 178 -> 94[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 179[label="wz33/FiniteMap.Branch wz330 wz331 wz332 wz333 wz334",fontsize=10,color="white",style="solid",shape="box"];83 -> 179[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 179 -> 95[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 44[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 False",fontsize=16,color="black",shape="box"];44 -> 52[label="",style="solid", color="black", weight=3]; 12.78/5.26 45[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not (GT == LT))",fontsize=16,color="black",shape="box"];45 -> 53[label="",style="solid", color="black", weight=3]; 12.78/5.26 47 -> 5[label="",style="dashed", color="red", weight=0]; 12.78/5.26 47[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] True wz34",fontsize=16,color="magenta"];47 -> 54[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 47 -> 55[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 46[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 wz6) True wz33",fontsize=16,color="burlywood",shape="triangle"];180[label="wz33/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];46 -> 180[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 180 -> 56[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 181[label="wz33/FiniteMap.Branch wz330 wz331 wz332 wz333 wz334",fontsize=10,color="white",style="solid",shape="box"];46 -> 181[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 181 -> 57[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 93 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 93[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] False wz34",fontsize=16,color="magenta"];93 -> 96[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 93 -> 97[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 92[label="FiniteMap.fmToList_GE0 False wz31 wz11",fontsize=16,color="black",shape="triangle"];92 -> 98[label="",style="solid", color="black", weight=3]; 12.78/5.26 94[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];94 -> 101[label="",style="solid", color="black", weight=3]; 12.78/5.26 95[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];95 -> 102[label="",style="solid", color="black", weight=3]; 12.78/5.26 52[label="FiniteMap.foldFM_GE0 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 otherwise",fontsize=16,color="black",shape="box"];52 -> 60[label="",style="solid", color="black", weight=3]; 12.78/5.26 53[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 (not False)",fontsize=16,color="black",shape="box"];53 -> 61[label="",style="solid", color="black", weight=3]; 12.78/5.26 54[label="wz34",fontsize=16,color="green",shape="box"];55[label="True",fontsize=16,color="green",shape="box"];56[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 wz6) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];56 -> 62[label="",style="solid", color="black", weight=3]; 12.78/5.26 57[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 wz6) True (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];57 -> 63[label="",style="solid", color="black", weight=3]; 12.78/5.26 96[label="[]",fontsize=16,color="green",shape="box"];97[label="wz34",fontsize=16,color="green",shape="box"];98[label="(False,wz31) : wz11",fontsize=16,color="green",shape="box"];101[label="FiniteMap.foldFM_GE3 FiniteMap.fmToList_GE0 wz10 False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];101 -> 106[label="",style="solid", color="black", weight=3]; 12.78/5.26 102[label="FiniteMap.foldFM_GE2 FiniteMap.fmToList_GE0 wz10 False (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];102 -> 107[label="",style="solid", color="black", weight=3]; 12.78/5.26 60[label="FiniteMap.foldFM_GE0 FiniteMap.fmToList_GE0 [] True False wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];60 -> 66[label="",style="solid", color="black", weight=3]; 12.78/5.26 61[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 [] False True wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];61 -> 67[label="",style="solid", color="black", weight=3]; 12.78/5.26 62[label="FiniteMap.foldFM_GE3 FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 wz6) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];62 -> 68[label="",style="solid", color="black", weight=3]; 12.78/5.26 63[label="FiniteMap.foldFM_GE2 FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 wz6) True (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];63 -> 69[label="",style="solid", color="black", weight=3]; 12.78/5.26 106[label="wz10",fontsize=16,color="green",shape="box"];107[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False wz330 wz331 wz332 wz333 wz334 (wz330 >= False)",fontsize=16,color="black",shape="box"];107 -> 109[label="",style="solid", color="black", weight=3]; 12.78/5.26 66 -> 5[label="",style="dashed", color="red", weight=0]; 12.78/5.26 66[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] True wz34",fontsize=16,color="magenta"];66 -> 73[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 66 -> 74[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 67 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 67[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] False wz34)) False wz33",fontsize=16,color="magenta"];67 -> 88[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 68[label="FiniteMap.fmToList_GE0 True wz31 wz6",fontsize=16,color="black",shape="triangle"];68 -> 77[label="",style="solid", color="black", weight=3]; 12.78/5.26 69 -> 78[label="",style="dashed", color="red", weight=0]; 12.78/5.26 69[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz31 wz6) True wz330 wz331 wz332 wz333 wz334 (wz330 >= True)",fontsize=16,color="magenta"];69 -> 79[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 109[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False wz330 wz331 wz332 wz333 wz334 (compare wz330 False /= LT)",fontsize=16,color="black",shape="box"];109 -> 111[label="",style="solid", color="black", weight=3]; 12.78/5.26 73[label="wz34",fontsize=16,color="green",shape="box"];74[label="True",fontsize=16,color="green",shape="box"];88 -> 68[label="",style="dashed", color="red", weight=0]; 12.78/5.26 88[label="FiniteMap.fmToList_GE0 True wz31 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] False wz34)",fontsize=16,color="magenta"];88 -> 99[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 77[label="(True,wz31) : wz6",fontsize=16,color="green",shape="box"];79 -> 68[label="",style="dashed", color="red", weight=0]; 12.78/5.26 79[label="FiniteMap.fmToList_GE0 True wz31 wz6",fontsize=16,color="magenta"];78[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (wz330 >= True)",fontsize=16,color="black",shape="triangle"];78 -> 100[label="",style="solid", color="black", weight=3]; 12.78/5.26 111[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False wz330 wz331 wz332 wz333 wz334 (not (compare wz330 False == LT))",fontsize=16,color="black",shape="box"];111 -> 114[label="",style="solid", color="black", weight=3]; 12.78/5.26 99 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 99[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 [] False wz34",fontsize=16,color="magenta"];99 -> 103[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 99 -> 104[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 100[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (compare wz330 True /= LT)",fontsize=16,color="black",shape="box"];100 -> 105[label="",style="solid", color="black", weight=3]; 12.78/5.26 114[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False wz330 wz331 wz332 wz333 wz334 (not (compare3 wz330 False == LT))",fontsize=16,color="black",shape="box"];114 -> 117[label="",style="solid", color="black", weight=3]; 12.78/5.26 103[label="[]",fontsize=16,color="green",shape="box"];104[label="wz34",fontsize=16,color="green",shape="box"];105[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (not (compare wz330 True == LT))",fontsize=16,color="black",shape="box"];105 -> 108[label="",style="solid", color="black", weight=3]; 12.78/5.26 117[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False wz330 wz331 wz332 wz333 wz334 (not (compare2 wz330 False (wz330 == False) == LT))",fontsize=16,color="burlywood",shape="box"];182[label="wz330/False",fontsize=10,color="white",style="solid",shape="box"];117 -> 182[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 182 -> 120[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 183[label="wz330/True",fontsize=10,color="white",style="solid",shape="box"];117 -> 183[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 183 -> 121[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 108[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (not (compare3 wz330 True == LT))",fontsize=16,color="black",shape="box"];108 -> 110[label="",style="solid", color="black", weight=3]; 12.78/5.26 120[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False False wz331 wz332 wz333 wz334 (not (compare2 False False (False == False) == LT))",fontsize=16,color="black",shape="box"];120 -> 124[label="",style="solid", color="black", weight=3]; 12.78/5.26 121[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare2 True False (True == False) == LT))",fontsize=16,color="black",shape="box"];121 -> 125[label="",style="solid", color="black", weight=3]; 12.78/5.26 110[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (not (compare2 wz330 True (wz330 == True) == LT))",fontsize=16,color="burlywood",shape="box"];184[label="wz330/False",fontsize=10,color="white",style="solid",shape="box"];110 -> 184[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 184 -> 112[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 185[label="wz330/True",fontsize=10,color="white",style="solid",shape="box"];110 -> 185[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 185 -> 113[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 124[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False False wz331 wz332 wz333 wz334 (not (compare2 False False True == LT))",fontsize=16,color="black",shape="box"];124 -> 128[label="",style="solid", color="black", weight=3]; 12.78/5.26 125[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare2 True False False == LT))",fontsize=16,color="black",shape="box"];125 -> 129[label="",style="solid", color="black", weight=3]; 12.78/5.26 112[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare2 False True (False == True) == LT))",fontsize=16,color="black",shape="box"];112 -> 115[label="",style="solid", color="black", weight=3]; 12.78/5.26 113[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True True wz331 wz332 wz333 wz334 (not (compare2 True True (True == True) == LT))",fontsize=16,color="black",shape="box"];113 -> 116[label="",style="solid", color="black", weight=3]; 12.78/5.26 128[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False False wz331 wz332 wz333 wz334 (not (EQ == LT))",fontsize=16,color="black",shape="box"];128 -> 132[label="",style="solid", color="black", weight=3]; 12.78/5.26 129[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare1 True False (True <= False) == LT))",fontsize=16,color="black",shape="box"];129 -> 133[label="",style="solid", color="black", weight=3]; 12.78/5.26 115[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare2 False True False == LT))",fontsize=16,color="black",shape="box"];115 -> 118[label="",style="solid", color="black", weight=3]; 12.78/5.26 116[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True True wz331 wz332 wz333 wz334 (not (compare2 True True True == LT))",fontsize=16,color="black",shape="box"];116 -> 119[label="",style="solid", color="black", weight=3]; 12.78/5.26 132[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False False wz331 wz332 wz333 wz334 (not False)",fontsize=16,color="black",shape="box"];132 -> 138[label="",style="solid", color="black", weight=3]; 12.78/5.26 133[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare1 True False False == LT))",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3]; 12.78/5.26 118[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare1 False True (False <= True) == LT))",fontsize=16,color="black",shape="box"];118 -> 122[label="",style="solid", color="black", weight=3]; 12.78/5.26 119[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True True wz331 wz332 wz333 wz334 (not (EQ == LT))",fontsize=16,color="black",shape="box"];119 -> 123[label="",style="solid", color="black", weight=3]; 12.78/5.26 138[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False False wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];138 -> 143[label="",style="solid", color="black", weight=3]; 12.78/5.26 139[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare0 True False otherwise == LT))",fontsize=16,color="black",shape="box"];139 -> 144[label="",style="solid", color="black", weight=3]; 12.78/5.26 122[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare1 False True True == LT))",fontsize=16,color="black",shape="box"];122 -> 126[label="",style="solid", color="black", weight=3]; 12.78/5.26 123[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True True wz331 wz332 wz333 wz334 (not False)",fontsize=16,color="black",shape="box"];123 -> 127[label="",style="solid", color="black", weight=3]; 12.78/5.26 143 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 143[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 False wz331 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False wz334)) False wz333",fontsize=16,color="magenta"];143 -> 148[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 143 -> 149[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 144[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare0 True False True == LT))",fontsize=16,color="black",shape="box"];144 -> 150[label="",style="solid", color="black", weight=3]; 12.78/5.26 126[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (LT == LT))",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3]; 12.78/5.26 127[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True True wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];127 -> 131[label="",style="solid", color="black", weight=3]; 12.78/5.26 148 -> 92[label="",style="dashed", color="red", weight=0]; 12.78/5.26 148[label="FiniteMap.fmToList_GE0 False wz331 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False wz334)",fontsize=16,color="magenta"];148 -> 154[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 148 -> 155[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 149[label="wz333",fontsize=16,color="green",shape="box"];150[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (GT == LT))",fontsize=16,color="black",shape="box"];150 -> 156[label="",style="solid", color="black", weight=3]; 12.78/5.26 130[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 (not True)",fontsize=16,color="black",shape="box"];130 -> 134[label="",style="solid", color="black", weight=3]; 12.78/5.26 131 -> 46[label="",style="dashed", color="red", weight=0]; 12.78/5.26 131[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz331 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz9 True wz334)) True wz333",fontsize=16,color="magenta"];131 -> 135[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 131 -> 136[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 131 -> 137[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 154[label="wz331",fontsize=16,color="green",shape="box"];155 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 155[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False wz334",fontsize=16,color="magenta"];155 -> 162[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 156[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 (not False)",fontsize=16,color="black",shape="box"];156 -> 163[label="",style="solid", color="black", weight=3]; 12.78/5.26 134[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 False",fontsize=16,color="black",shape="box"];134 -> 140[label="",style="solid", color="black", weight=3]; 12.78/5.26 135[label="wz331",fontsize=16,color="green",shape="box"];136[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz9 True wz334",fontsize=16,color="burlywood",shape="triangle"];186[label="wz334/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];136 -> 186[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 186 -> 141[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 187[label="wz334/FiniteMap.Branch wz3340 wz3341 wz3342 wz3343 wz3344",fontsize=10,color="white",style="solid",shape="box"];136 -> 187[label="",style="solid", color="burlywood", weight=9]; 12.78/5.26 187 -> 142[label="",style="solid", color="burlywood", weight=3]; 12.78/5.26 137[label="wz333",fontsize=16,color="green",shape="box"];162[label="wz334",fontsize=16,color="green",shape="box"];163[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz10 False True wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];163 -> 164[label="",style="solid", color="black", weight=3]; 12.78/5.26 140[label="FiniteMap.foldFM_GE0 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 otherwise",fontsize=16,color="black",shape="box"];140 -> 145[label="",style="solid", color="black", weight=3]; 12.78/5.26 141[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];141 -> 146[label="",style="solid", color="black", weight=3]; 12.78/5.26 142[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz9 True (FiniteMap.Branch wz3340 wz3341 wz3342 wz3343 wz3344)",fontsize=16,color="black",shape="box"];142 -> 147[label="",style="solid", color="black", weight=3]; 12.78/5.26 164 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 164[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 (FiniteMap.fmToList_GE0 True wz331 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False wz334)) False wz333",fontsize=16,color="magenta"];164 -> 165[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 164 -> 166[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 145[label="FiniteMap.foldFM_GE0 FiniteMap.fmToList_GE0 wz9 True False wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];145 -> 151[label="",style="solid", color="black", weight=3]; 12.78/5.26 146[label="FiniteMap.foldFM_GE3 FiniteMap.fmToList_GE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];146 -> 152[label="",style="solid", color="black", weight=3]; 12.78/5.26 147[label="FiniteMap.foldFM_GE2 FiniteMap.fmToList_GE0 wz9 True (FiniteMap.Branch wz3340 wz3341 wz3342 wz3343 wz3344)",fontsize=16,color="black",shape="box"];147 -> 153[label="",style="solid", color="black", weight=3]; 12.78/5.26 165 -> 68[label="",style="dashed", color="red", weight=0]; 12.78/5.26 165[label="FiniteMap.fmToList_GE0 True wz331 (FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False wz334)",fontsize=16,color="magenta"];165 -> 167[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 165 -> 168[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 166[label="wz333",fontsize=16,color="green",shape="box"];151 -> 136[label="",style="dashed", color="red", weight=0]; 12.78/5.26 151[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz9 True wz334",fontsize=16,color="magenta"];152[label="wz9",fontsize=16,color="green",shape="box"];153 -> 78[label="",style="dashed", color="red", weight=0]; 12.78/5.26 153[label="FiniteMap.foldFM_GE1 FiniteMap.fmToList_GE0 wz9 True wz3340 wz3341 wz3342 wz3343 wz3344 (wz3340 >= True)",fontsize=16,color="magenta"];153 -> 157[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 153 -> 158[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 153 -> 159[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 153 -> 160[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 153 -> 161[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 167[label="wz331",fontsize=16,color="green",shape="box"];168 -> 83[label="",style="dashed", color="red", weight=0]; 12.78/5.26 168[label="FiniteMap.foldFM_GE FiniteMap.fmToList_GE0 wz10 False wz334",fontsize=16,color="magenta"];168 -> 169[label="",style="dashed", color="magenta", weight=3]; 12.78/5.26 157[label="wz3341",fontsize=16,color="green",shape="box"];158[label="wz3343",fontsize=16,color="green",shape="box"];159[label="wz3344",fontsize=16,color="green",shape="box"];160[label="wz3340",fontsize=16,color="green",shape="box"];161[label="wz3342",fontsize=16,color="green",shape="box"];169[label="wz334",fontsize=16,color="green",shape="box"];} 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (8) 12.78/5.26 Complex Obligation (AND) 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (9) 12.78/5.26 Obligation: 12.78/5.26 Q DP problem: 12.78/5.26 The TRS P consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_fmToList_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_fmToList_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 12.78/5.26 The TRS R consists of the following rules: 12.78/5.26 12.78/5.26 new_fmToList_GE00(wz31, wz11, h) -> :(@2(False, wz31), wz11) 12.78/5.26 new_fmToList_GE0(wz31, wz6, h) -> :(@2(True, wz31), wz6) 12.78/5.26 new_foldFM_GE5(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_fmToList_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 new_foldFM_GE5(wz10, EmptyFM, h) -> wz10 12.78/5.26 new_foldFM_GE5(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_fmToList_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 12.78/5.26 The set Q consists of the following terms: 12.78/5.26 12.78/5.26 new_foldFM_GE5(x0, Branch(False, x1, x2, x3, x4), x5) 12.78/5.26 new_foldFM_GE5(x0, Branch(True, x1, x2, x3, x4), x5) 12.78/5.26 new_fmToList_GE00(x0, x1, x2) 12.78/5.26 new_foldFM_GE5(x0, EmptyFM, x1) 12.78/5.26 new_fmToList_GE0(x0, x1, x2) 12.78/5.26 12.78/5.26 We have to consider all minimal (P,Q,R)-chains. 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (10) TransformationProof (EQUIVALENT) 12.78/5.26 By rewriting [LPAR04] the rule new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_fmToList_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) at position [0] we obtained the following new rules [LPAR04]: 12.78/5.26 12.78/5.26 (new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(True, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h),new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(True, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h)) 12.78/5.26 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (11) 12.78/5.26 Obligation: 12.78/5.26 Q DP problem: 12.78/5.26 The TRS P consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_fmToList_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(True, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h) 12.78/5.26 12.78/5.26 The TRS R consists of the following rules: 12.78/5.26 12.78/5.26 new_fmToList_GE00(wz31, wz11, h) -> :(@2(False, wz31), wz11) 12.78/5.26 new_fmToList_GE0(wz31, wz6, h) -> :(@2(True, wz31), wz6) 12.78/5.26 new_foldFM_GE5(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_fmToList_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 new_foldFM_GE5(wz10, EmptyFM, h) -> wz10 12.78/5.26 new_foldFM_GE5(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_fmToList_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 12.78/5.26 The set Q consists of the following terms: 12.78/5.26 12.78/5.26 new_foldFM_GE5(x0, Branch(False, x1, x2, x3, x4), x5) 12.78/5.26 new_foldFM_GE5(x0, Branch(True, x1, x2, x3, x4), x5) 12.78/5.26 new_fmToList_GE00(x0, x1, x2) 12.78/5.26 new_foldFM_GE5(x0, EmptyFM, x1) 12.78/5.26 new_fmToList_GE0(x0, x1, x2) 12.78/5.26 12.78/5.26 We have to consider all minimal (P,Q,R)-chains. 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (12) TransformationProof (EQUIVALENT) 12.78/5.26 By rewriting [LPAR04] the rule new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_fmToList_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) at position [0] we obtained the following new rules [LPAR04]: 12.78/5.26 12.78/5.26 (new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(False, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h),new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(False, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h)) 12.78/5.26 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (13) 12.78/5.26 Obligation: 12.78/5.26 Q DP problem: 12.78/5.26 The TRS P consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(True, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h) 12.78/5.26 new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(False, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h) 12.78/5.26 12.78/5.26 The TRS R consists of the following rules: 12.78/5.26 12.78/5.26 new_fmToList_GE00(wz31, wz11, h) -> :(@2(False, wz31), wz11) 12.78/5.26 new_fmToList_GE0(wz31, wz6, h) -> :(@2(True, wz31), wz6) 12.78/5.26 new_foldFM_GE5(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_fmToList_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 new_foldFM_GE5(wz10, EmptyFM, h) -> wz10 12.78/5.26 new_foldFM_GE5(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_fmToList_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) 12.78/5.26 12.78/5.26 The set Q consists of the following terms: 12.78/5.26 12.78/5.26 new_foldFM_GE5(x0, Branch(False, x1, x2, x3, x4), x5) 12.78/5.26 new_foldFM_GE5(x0, Branch(True, x1, x2, x3, x4), x5) 12.78/5.26 new_fmToList_GE00(x0, x1, x2) 12.78/5.26 new_foldFM_GE5(x0, EmptyFM, x1) 12.78/5.26 new_fmToList_GE0(x0, x1, x2) 12.78/5.26 12.78/5.26 We have to consider all minimal (P,Q,R)-chains. 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (14) QDPSizeChangeProof (EQUIVALENT) 12.78/5.26 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. 12.78/5.26 12.78/5.26 From the DPs we obtained the following set of size-change graphs: 12.78/5.26 *new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h) 12.78/5.26 The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(True, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h) 12.78/5.26 The graph contains the following edges 2 > 2, 3 >= 3 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(@2(False, wz331), new_foldFM_GE5(wz10, wz334, h)), wz333, h) 12.78/5.26 The graph contains the following edges 2 > 2, 3 >= 3 12.78/5.26 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (15) 12.78/5.26 YES 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (16) 12.78/5.26 Obligation: 12.78/5.26 Q DP problem: 12.78/5.26 The TRS P consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(new_fmToList_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h) 12.78/5.26 new_foldFM_GE1(wz9, True, wz331, wz332, wz333, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 new_foldFM_GE(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 new_foldFM_GE1(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE(wz9, wz334, h) 12.78/5.26 new_foldFM_GE1(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE0(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h) 12.78/5.26 12.78/5.26 The TRS R consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE2(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE10(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 new_fmToList_GE0(wz31, wz6, h) -> :(@2(True, wz31), wz6) 12.78/5.26 new_foldFM_GE10(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE3(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h) 12.78/5.26 new_foldFM_GE3(wz31, wz6, EmptyFM, h) -> new_fmToList_GE0(wz31, wz6, h) 12.78/5.26 new_foldFM_GE10(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE2(wz9, wz334, h) 12.78/5.26 new_foldFM_GE2(wz9, EmptyFM, h) -> wz9 12.78/5.26 new_foldFM_GE3(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE10(new_fmToList_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h) 12.78/5.26 12.78/5.26 The set Q consists of the following terms: 12.78/5.26 12.78/5.26 new_foldFM_GE10(x0, True, x1, x2, x3, x4, x5) 12.78/5.26 new_foldFM_GE2(x0, Branch(x1, x2, x3, x4, x5), x6) 12.78/5.26 new_foldFM_GE10(x0, False, x1, x2, x3, x4, x5) 12.78/5.26 new_foldFM_GE3(x0, x1, EmptyFM, x2) 12.78/5.26 new_foldFM_GE2(x0, EmptyFM, x1) 12.78/5.26 new_foldFM_GE3(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.78/5.26 new_fmToList_GE0(x0, x1, x2) 12.78/5.26 12.78/5.26 We have to consider all minimal (P,Q,R)-chains. 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (17) TransformationProof (EQUIVALENT) 12.78/5.26 By rewriting [LPAR04] the rule new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(new_fmToList_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h) at position [0] we obtained the following new rules [LPAR04]: 12.78/5.26 12.78/5.26 (new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(@2(True, wz31), wz6), wz330, wz331, wz332, wz333, wz334, h),new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(@2(True, wz31), wz6), wz330, wz331, wz332, wz333, wz334, h)) 12.78/5.26 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (18) 12.78/5.26 Obligation: 12.78/5.26 Q DP problem: 12.78/5.26 The TRS P consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE1(wz9, True, wz331, wz332, wz333, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 new_foldFM_GE(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 new_foldFM_GE1(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE(wz9, wz334, h) 12.78/5.26 new_foldFM_GE1(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE0(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h) 12.78/5.26 new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(@2(True, wz31), wz6), wz330, wz331, wz332, wz333, wz334, h) 12.78/5.26 12.78/5.26 The TRS R consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE2(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE10(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 new_fmToList_GE0(wz31, wz6, h) -> :(@2(True, wz31), wz6) 12.78/5.26 new_foldFM_GE10(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE3(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h) 12.78/5.26 new_foldFM_GE3(wz31, wz6, EmptyFM, h) -> new_fmToList_GE0(wz31, wz6, h) 12.78/5.26 new_foldFM_GE10(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE2(wz9, wz334, h) 12.78/5.26 new_foldFM_GE2(wz9, EmptyFM, h) -> wz9 12.78/5.26 new_foldFM_GE3(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE10(new_fmToList_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h) 12.78/5.26 12.78/5.26 The set Q consists of the following terms: 12.78/5.26 12.78/5.26 new_foldFM_GE10(x0, True, x1, x2, x3, x4, x5) 12.78/5.26 new_foldFM_GE2(x0, Branch(x1, x2, x3, x4, x5), x6) 12.78/5.26 new_foldFM_GE10(x0, False, x1, x2, x3, x4, x5) 12.78/5.26 new_foldFM_GE3(x0, x1, EmptyFM, x2) 12.78/5.26 new_foldFM_GE2(x0, EmptyFM, x1) 12.78/5.26 new_foldFM_GE3(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.78/5.26 new_fmToList_GE0(x0, x1, x2) 12.78/5.26 12.78/5.26 We have to consider all minimal (P,Q,R)-chains. 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (19) QDPSizeChangeProof (EQUIVALENT) 12.78/5.26 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. 12.78/5.26 12.78/5.26 From the DPs we obtained the following set of size-change graphs: 12.78/5.26 *new_foldFM_GE1(wz9, True, wz331, wz332, wz333, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 The graph contains the following edges 1 >= 1, 6 > 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 7 >= 7 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE1(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE(wz9, wz334, h) 12.78/5.26 The graph contains the following edges 1 >= 1, 6 >= 2, 7 >= 3 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE1(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE0(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h) 12.78/5.26 The graph contains the following edges 3 >= 1, 5 >= 3, 7 >= 4 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h) 12.78/5.26 The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(@2(True, wz31), wz6), wz330, wz331, wz332, wz333, wz334, h) 12.78/5.26 The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7 12.78/5.26 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (20) 12.78/5.26 YES 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (21) 12.78/5.26 Obligation: 12.78/5.26 Q DP problem: 12.78/5.26 The TRS P consists of the following rules: 12.78/5.26 12.78/5.26 new_foldFM_GE6(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h) 12.78/5.26 new_foldFM_GE6(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h) 12.78/5.26 12.78/5.26 R is empty. 12.78/5.26 Q is empty. 12.78/5.26 We have to consider all minimal (P,Q,R)-chains. 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (22) QDPSizeChangeProof (EQUIVALENT) 12.78/5.26 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. 12.78/5.26 12.78/5.26 From the DPs we obtained the following set of size-change graphs: 12.78/5.26 *new_foldFM_GE6(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h) 12.78/5.26 The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3 12.78/5.26 12.78/5.26 12.78/5.26 *new_foldFM_GE6(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h) 12.78/5.26 The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 12.78/5.26 12.78/5.26 12.78/5.26 ---------------------------------------- 12.78/5.26 12.78/5.26 (23) 12.78/5.26 YES 12.95/5.30 EOF