/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) CR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) AND (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] (16) YES (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap b a where { } lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; lookupWithDefaultFM :: Ord a => FiniteMap a b -> b -> a -> b; lookupWithDefaultFM fm deflt key = case lookupFM fm key of { Nothing-> deflt; Just elt-> elt; } ; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) CR (EQUIVALENT) Case Reductions: The following Case expression "case lookupFM fm key of { Nothing -> deflt; Just elt -> elt} " is transformed to "lookupWithDefaultFM0 deflt Nothing = deflt; lookupWithDefaultFM0 deflt (Just elt) = elt; " ---------------------------------------- (2) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { } lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; lookupWithDefaultFM :: Ord b => FiniteMap b a -> a -> b -> a; lookupWithDefaultFM fm deflt key = lookupWithDefaultFM0 deflt (lookupFM fm key); lookupWithDefaultFM0 deflt Nothing = deflt; lookupWithDefaultFM0 deflt (Just elt) = elt; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { } lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt vy fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; lookupWithDefaultFM :: Ord b => FiniteMap b a -> a -> b -> a; lookupWithDefaultFM fm deflt key = lookupWithDefaultFM0 deflt (lookupFM fm key); lookupWithDefaultFM0 deflt Nothing = deflt; lookupWithDefaultFM0 deflt (Just elt) = elt; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " The following Function with conditions "lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt vy fm_l fm_r) key_to_find|key_to_find < keylookupFM fm_l key_to_find|key_to_find > keylookupFM fm_r key_to_find|otherwiseJust elt; " is transformed to "lookupFM EmptyFM key = lookupFM4 EmptyFM key; lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find; " "lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise; " "lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; lookupFM2 key elt vy fm_l fm_r key_to_find False = lookupFM1 key elt vy fm_l fm_r key_to_find (key_to_find > key); " "lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt; " "lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find = lookupFM2 key elt vy fm_l fm_r key_to_find (key_to_find < key); " "lookupFM4 EmptyFM key = Nothing; lookupFM4 wv ww = lookupFM3 wv ww; " ---------------------------------------- (6) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { } lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; lookupFM EmptyFM key = lookupFM4 EmptyFM key; lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find; lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt; lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise; lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; lookupFM2 key elt vy fm_l fm_r key_to_find False = lookupFM1 key elt vy fm_l fm_r key_to_find (key_to_find > key); lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find = lookupFM2 key elt vy fm_l fm_r key_to_find (key_to_find < key); lookupFM4 EmptyFM key = Nothing; lookupFM4 wv ww = lookupFM3 wv ww; lookupWithDefaultFM :: Ord b => FiniteMap b a -> a -> b -> a; lookupWithDefaultFM fm deflt key = lookupWithDefaultFM0 deflt (lookupFM fm key); lookupWithDefaultFM0 deflt Nothing = deflt; lookupWithDefaultFM0 deflt (Just elt) = elt; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="FiniteMap.lookupWithDefaultFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="FiniteMap.lookupWithDefaultFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="FiniteMap.lookupWithDefaultFM wx3 wx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="FiniteMap.lookupWithDefaultFM wx3 wx4 wx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx3 wx5)",fontsize=16,color="burlywood",shape="triangle"];1676[label="wx3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6 -> 1676[label="",style="solid", color="burlywood", weight=9]; 1676 -> 7[label="",style="solid", color="burlywood", weight=3]; 1677[label="wx3/FiniteMap.Branch wx30 wx31 wx32 wx33 wx34",fontsize=10,color="white",style="solid",shape="box"];6 -> 1677[label="",style="solid", color="burlywood", weight=9]; 1677 -> 8[label="",style="solid", color="burlywood", weight=3]; 7[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM FiniteMap.EmptyFM wx5)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM (FiniteMap.Branch wx30 wx31 wx32 wx33 wx34) wx5)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM4 FiniteMap.EmptyFM 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color="burlywood", weight=9]; 1695 -> 35[label="",style="solid", color="burlywood", weight=3]; 26[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx500)) (primCmpInt (Neg (Succ wx500)) (Pos wx300) == LT))",fontsize=16,color="black",shape="box"];26 -> 36[label="",style="solid", color="black", weight=3]; 27[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx500)) (primCmpInt (Neg (Succ wx500)) (Neg wx300) == LT))",fontsize=16,color="black",shape="box"];27 -> 37[label="",style="solid", color="black", weight=3]; 28[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos wx300) == LT))",fontsize=16,color="burlywood",shape="box"];1696[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];28 -> 1696[label="",style="solid", color="burlywood", weight=9]; 1696 -> 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33[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3]; 34[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ wx3000)) == LT))",fontsize=16,color="black",shape="box"];34 -> 47[label="",style="solid", color="black", weight=3]; 35[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT))",fontsize=16,color="black",shape="box"];35 -> 48[label="",style="solid", color="black", weight=3]; 36[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx500)) (LT == LT))",fontsize=16,color="black",shape="box"];36 -> 49[label="",style="solid", color="black", weight=3]; 37[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx500)) (primCmpNat wx300 (Succ wx500) == LT))",fontsize=16,color="burlywood",shape="box"];1702[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];37 -> 1702[label="",style="solid", color="burlywood", weight=9]; 1702 -> 50[label="",style="solid", color="burlywood", weight=3]; 1703[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 1703[label="",style="solid", color="burlywood", weight=9]; 1703 -> 51[label="",style="solid", color="burlywood", weight=3]; 38[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ wx3000)) == LT))",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3]; 39[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) 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84[label="",style="solid", color="black", weight=3]; 68[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (GT == LT))",fontsize=16,color="black",shape="box"];68 -> 85[label="",style="solid", color="black", weight=3]; 69[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) False)",fontsize=16,color="black",shape="box"];69 -> 86[label="",style="solid", color="black", weight=3]; 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909[label="",style="solid", color="burlywood", weight=3]; 814[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM2 (Pos (Succ wx81)) wx82 wx83 wx84 wx85 (Pos (Succ wx86)) (primCmpNat Zero wx88 == LT))",fontsize=16,color="burlywood",shape="box"];1710[label="wx88/Succ wx880",fontsize=10,color="white",style="solid",shape="box"];814 -> 1710[label="",style="solid", color="burlywood", weight=9]; 1710 -> 910[label="",style="solid", color="burlywood", weight=3]; 1711[label="wx88/Zero",fontsize=10,color="white",style="solid",shape="box"];814 -> 1711[label="",style="solid", color="burlywood", weight=9]; 1711 -> 911[label="",style="solid", color="burlywood", weight=3]; 91[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx500)) (Pos (Succ wx500) > Pos Zero))",fontsize=16,color="black",shape="box"];91 -> 111[label="",style="solid", color="black", weight=3]; 92[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg 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112[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx500)) (GT == GT))",fontsize=16,color="black",shape="box"];112 -> 133[label="",style="solid", color="black", weight=3]; 113[label="wx33",fontsize=16,color="green",shape="box"];114[label="Pos Zero",fontsize=16,color="green",shape="box"];115[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];115 -> 134[label="",style="solid", color="black", weight=3]; 116[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ wx3000)) == GT))",fontsize=16,color="black",shape="box"];116 -> 135[label="",style="solid", color="black", weight=3]; 117[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) 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wx32 wx33 wx34 (Pos Zero) (GT == GT))",fontsize=16,color="black",shape="box"];135 -> 155[label="",style="solid", color="black", weight=3]; 136[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];136 -> 156[label="",style="solid", color="black", weight=3]; 920 -> 815[label="",style="dashed", color="red", weight=0]; 920[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM2 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (primCmpNat wx970 wx980 == LT))",fontsize=16,color="magenta"];920 -> 929[label="",style="dashed", color="magenta", weight=3]; 920 -> 930[label="",style="dashed", color="magenta", weight=3]; 921[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM2 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (GT == LT))",fontsize=16,color="black",shape="box"];921 -> 931[label="",style="solid", color="black", weight=3]; 922[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM2 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (LT == LT))",fontsize=16,color="black",shape="box"];922 -> 932[label="",style="solid", color="black", weight=3]; 923[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM2 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (EQ == LT))",fontsize=16,color="black",shape="box"];923 -> 933[label="",style="solid", color="black", weight=3]; 142[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];142 -> 164[label="",style="solid", color="black", weight=3]; 143[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ wx3000)) == GT))",fontsize=16,color="black",shape="box"];143 -> 165[label="",style="solid", color="black", weight=3]; 144[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];144 -> 166[label="",style="solid", color="black", weight=3]; 924[label="wx880",fontsize=16,color="green",shape="box"];925[label="wx870",fontsize=16,color="green",shape="box"];926[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM2 (Pos (Succ wx81)) wx82 wx83 wx84 wx85 (Pos (Succ wx86)) False)",fontsize=16,color="black",shape="triangle"];926 -> 934[label="",style="solid", color="black", weight=3]; 927[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM2 (Pos (Succ wx81)) wx82 wx83 wx84 wx85 (Pos (Succ wx86)) True)",fontsize=16,color="black",shape="box"];927 -> 935[label="",style="solid", color="black", weight=3]; 928 -> 926[label="",style="dashed", color="red", weight=0]; 928[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM2 (Pos (Succ wx81)) wx82 wx83 wx84 wx85 (Pos (Succ wx86)) False)",fontsize=16,color="magenta"];152[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx500)) (primCmpNat (Succ wx500) Zero == GT))",fontsize=16,color="black",shape="box"];152 -> 175[label="",style="solid", color="black", weight=3]; 153 -> 6[label="",style="dashed", color="red", weight=0]; 153[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx34 (Pos (Succ wx500)))",fontsize=16,color="magenta"];153 -> 176[label="",style="dashed", color="magenta", weight=3]; 153 -> 177[label="",style="dashed", color="magenta", weight=3]; 154[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) False)",fontsize=16,color="black",shape="box"];154 -> 178[label="",style="solid", color="black", weight=3]; 155[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) True)",fontsize=16,color="black",shape="box"];155 -> 179[label="",style="solid", color="black", weight=3]; 156[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) False)",fontsize=16,color="black",shape="box"];156 -> 180[label="",style="solid", color="black", weight=3]; 929[label="wx970",fontsize=16,color="green",shape="box"];930[label="wx980",fontsize=16,color="green",shape="box"];931[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM2 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) False)",fontsize=16,color="black",shape="triangle"];931 -> 936[label="",style="solid", color="black", weight=3]; 932[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM2 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) True)",fontsize=16,color="black",shape="box"];932 -> 937[label="",style="solid", color="black", weight=3]; 933 -> 931[label="",style="dashed", color="red", weight=0]; 933[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM2 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) False)",fontsize=16,color="magenta"];164[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) False)",fontsize=16,color="black",shape="box"];164 -> 189[label="",style="solid", color="black", weight=3]; 165[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpNat (Succ wx3000) Zero == GT))",fontsize=16,color="black",shape="box"];165 -> 190[label="",style="solid", color="black", weight=3]; 166[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) False)",fontsize=16,color="black",shape="box"];166 -> 191[label="",style="solid", color="black", weight=3]; 934[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM1 (Pos (Succ wx81)) wx82 wx83 wx84 wx85 (Pos (Succ wx86)) (Pos (Succ wx86) > Pos (Succ wx81)))",fontsize=16,color="black",shape="box"];934 -> 938[label="",style="solid", color="black", weight=3]; 935 -> 6[label="",style="dashed", color="red", weight=0]; 935[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM wx84 (Pos (Succ wx86)))",fontsize=16,color="magenta"];935 -> 939[label="",style="dashed", color="magenta", weight=3]; 935 -> 940[label="",style="dashed", color="magenta", weight=3]; 935 -> 941[label="",style="dashed", color="magenta", weight=3]; 175[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx500)) (GT == GT))",fontsize=16,color="black",shape="box"];175 -> 199[label="",style="solid", color="black", weight=3]; 176[label="wx34",fontsize=16,color="green",shape="box"];177[label="Pos (Succ wx500)",fontsize=16,color="green",shape="box"];178[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];178 -> 200[label="",style="solid", color="black", weight=3]; 179 -> 6[label="",style="dashed", color="red", weight=0]; 179[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx34 (Pos Zero))",fontsize=16,color="magenta"];179 -> 201[label="",style="dashed", color="magenta", weight=3]; 179 -> 202[label="",style="dashed", color="magenta", weight=3]; 180[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];180 -> 203[label="",style="solid", color="black", weight=3]; 936[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM1 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (Neg (Succ wx96) > Neg (Succ wx91)))",fontsize=16,color="black",shape="box"];936 -> 942[label="",style="solid", color="black", weight=3]; 937 -> 6[label="",style="dashed", color="red", weight=0]; 937[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM wx94 (Neg (Succ wx96)))",fontsize=16,color="magenta"];937 -> 943[label="",style="dashed", color="magenta", weight=3]; 937 -> 944[label="",style="dashed", color="magenta", weight=3]; 937 -> 945[label="",style="dashed", color="magenta", weight=3]; 189[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];189 -> 211[label="",style="solid", color="black", weight=3]; 190[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (GT == GT))",fontsize=16,color="black",shape="box"];190 -> 212[label="",style="solid", color="black", weight=3]; 191[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];191 -> 213[label="",style="solid", color="black", weight=3]; 938[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM1 (Pos (Succ wx81)) wx82 wx83 wx84 wx85 (Pos (Succ wx86)) (compare (Pos (Succ wx86)) (Pos (Succ wx81)) == GT))",fontsize=16,color="black",shape="box"];938 -> 946[label="",style="solid", color="black", weight=3]; 939[label="wx80",fontsize=16,color="green",shape="box"];940[label="wx84",fontsize=16,color="green",shape="box"];941[label="Pos (Succ wx86)",fontsize=16,color="green",shape="box"];199[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx500)) True)",fontsize=16,color="black",shape="box"];199 -> 223[label="",style="solid", color="black", weight=3]; 200[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) True)",fontsize=16,color="black",shape="box"];200 -> 224[label="",style="solid", color="black", weight=3]; 201[label="wx34",fontsize=16,color="green",shape="box"];202[label="Pos Zero",fontsize=16,color="green",shape="box"];203[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) True)",fontsize=16,color="black",shape="box"];203 -> 225[label="",style="solid", color="black", weight=3]; 942[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM1 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (compare (Neg (Succ wx96)) (Neg (Succ wx91)) == GT))",fontsize=16,color="black",shape="box"];942 -> 947[label="",style="solid", color="black", weight=3]; 943[label="wx90",fontsize=16,color="green",shape="box"];944[label="wx94",fontsize=16,color="green",shape="box"];945[label="Neg (Succ wx96)",fontsize=16,color="green",shape="box"];211[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) True)",fontsize=16,color="black",shape="box"];211 -> 235[label="",style="solid", color="black", weight=3]; 212[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) True)",fontsize=16,color="black",shape="box"];212 -> 236[label="",style="solid", color="black", weight=3]; 213[label="FiniteMap.lookupWithDefaultFM0 wx4 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225[label="FiniteMap.lookupWithDefaultFM0 wx4 (Just wx31)",fontsize=16,color="magenta"];947[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM1 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (primCmpInt (Neg (Succ wx96)) (Neg (Succ wx91)) == GT))",fontsize=16,color="black",shape="box"];947 -> 949[label="",style="solid", color="black", weight=3]; 235 -> 224[label="",style="dashed", color="red", weight=0]; 235[label="FiniteMap.lookupWithDefaultFM0 wx4 (Just wx31)",fontsize=16,color="magenta"];236 -> 6[label="",style="dashed", color="red", weight=0]; 236[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx34 (Neg Zero))",fontsize=16,color="magenta"];236 -> 261[label="",style="dashed", color="magenta", weight=3]; 236 -> 262[label="",style="dashed", color="magenta", weight=3]; 237 -> 224[label="",style="dashed", color="red", weight=0]; 237[label="FiniteMap.lookupWithDefaultFM0 wx4 (Just wx31)",fontsize=16,color="magenta"];948 -> 1428[label="",style="dashed", color="red", weight=0]; 948[label="FiniteMap.lookupWithDefaultFM0 wx80 (FiniteMap.lookupFM1 (Pos (Succ wx81)) wx82 wx83 wx84 wx85 (Pos (Succ wx86)) (primCmpNat (Succ wx86) (Succ wx81) == GT))",fontsize=16,color="magenta"];948 -> 1429[label="",style="dashed", color="magenta", weight=3]; 948 -> 1430[label="",style="dashed", color="magenta", weight=3]; 948 -> 1431[label="",style="dashed", color="magenta", weight=3]; 948 -> 1432[label="",style="dashed", color="magenta", weight=3]; 948 -> 1433[label="",style="dashed", color="magenta", weight=3]; 948 -> 1434[label="",style="dashed", color="magenta", weight=3]; 948 -> 1435[label="",style="dashed", color="magenta", weight=3]; 948 -> 1436[label="",style="dashed", color="magenta", weight=3]; 948 -> 1437[label="",style="dashed", color="magenta", weight=3]; 248[label="wx34",fontsize=16,color="green",shape="box"];249[label="Pos (Succ wx500)",fontsize=16,color="green",shape="box"];250[label="wx31",fontsize=16,color="green",shape="box"];949 -> 1530[label="",style="dashed", color="red", weight=0]; 949[label="FiniteMap.lookupWithDefaultFM0 wx90 (FiniteMap.lookupFM1 (Neg (Succ wx91)) wx92 wx93 wx94 wx95 (Neg (Succ wx96)) (primCmpNat (Succ wx91) (Succ wx96) == GT))",fontsize=16,color="magenta"];949 -> 1531[label="",style="dashed", color="magenta", weight=3]; 949 -> 1532[label="",style="dashed", color="magenta", weight=3]; 949 -> 1533[label="",style="dashed", color="magenta", weight=3]; 949 -> 1534[label="",style="dashed", color="magenta", weight=3]; 949 -> 1535[label="",style="dashed", color="magenta", weight=3]; 949 -> 1536[label="",style="dashed", color="magenta", weight=3]; 949 -> 1537[label="",style="dashed", color="magenta", weight=3]; 949 -> 1538[label="",style="dashed", color="magenta", weight=3]; 949 -> 1539[label="",style="dashed", color="magenta", weight=3]; 261[label="wx34",fontsize=16,color="green",shape="box"];262[label="Neg Zero",fontsize=16,color="green",shape="box"];1429[label="Succ wx86",fontsize=16,color="green",shape="box"];1430[label="wx81",fontsize=16,color="green",shape="box"];1431[label="wx82",fontsize=16,color="green",shape="box"];1432[label="wx83",fontsize=16,color="green",shape="box"];1433[label="wx80",fontsize=16,color="green",shape="box"];1434[label="wx85",fontsize=16,color="green",shape="box"];1435[label="wx84",fontsize=16,color="green",shape="box"];1436[label="wx86",fontsize=16,color="green",shape="box"];1437[label="Succ wx81",fontsize=16,color="green",shape="box"];1428[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat wx181 wx182 == GT))",fontsize=16,color="burlywood",shape="triangle"];1716[label="wx181/Succ wx1810",fontsize=10,color="white",style="solid",shape="box"];1428 -> 1716[label="",style="solid", color="burlywood", weight=9]; 1716 -> 1528[label="",style="solid", color="burlywood", weight=3]; 1717[label="wx181/Zero",fontsize=10,color="white",style="solid",shape="box"];1428 -> 1717[label="",style="solid", color="burlywood", weight=9]; 1717 -> 1529[label="",style="solid", color="burlywood", weight=3]; 1531[label="wx91",fontsize=16,color="green",shape="box"];1532[label="Succ wx91",fontsize=16,color="green",shape="box"];1533[label="wx92",fontsize=16,color="green",shape="box"];1534[label="wx95",fontsize=16,color="green",shape="box"];1535[label="wx93",fontsize=16,color="green",shape="box"];1536[label="wx94",fontsize=16,color="green",shape="box"];1537[label="Succ wx96",fontsize=16,color="green",shape="box"];1538[label="wx96",fontsize=16,color="green",shape="box"];1539[label="wx90",fontsize=16,color="green",shape="box"];1530[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat wx191 wx192 == GT))",fontsize=16,color="burlywood",shape="triangle"];1718[label="wx191/Succ wx1910",fontsize=10,color="white",style="solid",shape="box"];1530 -> 1718[label="",style="solid", color="burlywood", weight=9]; 1718 -> 1630[label="",style="solid", color="burlywood", weight=3]; 1719[label="wx191/Zero",fontsize=10,color="white",style="solid",shape="box"];1530 -> 1719[label="",style="solid", color="burlywood", weight=9]; 1719 -> 1631[label="",style="solid", color="burlywood", weight=3]; 1528[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat (Succ wx1810) wx182 == GT))",fontsize=16,color="burlywood",shape="box"];1720[label="wx182/Succ wx1820",fontsize=10,color="white",style="solid",shape="box"];1528 -> 1720[label="",style="solid", color="burlywood", weight=9]; 1720 -> 1632[label="",style="solid", color="burlywood", weight=3]; 1721[label="wx182/Zero",fontsize=10,color="white",style="solid",shape="box"];1528 -> 1721[label="",style="solid", color="burlywood", weight=9]; 1721 -> 1633[label="",style="solid", color="burlywood", weight=3]; 1529[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat Zero wx182 == GT))",fontsize=16,color="burlywood",shape="box"];1722[label="wx182/Succ wx1820",fontsize=10,color="white",style="solid",shape="box"];1529 -> 1722[label="",style="solid", color="burlywood", weight=9]; 1722 -> 1634[label="",style="solid", color="burlywood", weight=3]; 1723[label="wx182/Zero",fontsize=10,color="white",style="solid",shape="box"];1529 -> 1723[label="",style="solid", color="burlywood", weight=9]; 1723 -> 1635[label="",style="solid", color="burlywood", weight=3]; 1630[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat (Succ wx1910) wx192 == GT))",fontsize=16,color="burlywood",shape="box"];1724[label="wx192/Succ wx1920",fontsize=10,color="white",style="solid",shape="box"];1630 -> 1724[label="",style="solid", color="burlywood", weight=9]; 1724 -> 1636[label="",style="solid", color="burlywood", weight=3]; 1725[label="wx192/Zero",fontsize=10,color="white",style="solid",shape="box"];1630 -> 1725[label="",style="solid", color="burlywood", weight=9]; 1725 -> 1637[label="",style="solid", color="burlywood", weight=3]; 1631[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat Zero wx192 == GT))",fontsize=16,color="burlywood",shape="box"];1726[label="wx192/Succ wx1920",fontsize=10,color="white",style="solid",shape="box"];1631 -> 1726[label="",style="solid", color="burlywood", weight=9]; 1726 -> 1638[label="",style="solid", color="burlywood", weight=3]; 1727[label="wx192/Zero",fontsize=10,color="white",style="solid",shape="box"];1631 -> 1727[label="",style="solid", color="burlywood", weight=9]; 1727 -> 1639[label="",style="solid", color="burlywood", weight=3]; 1632[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat (Succ wx1810) (Succ wx1820) == GT))",fontsize=16,color="black",shape="box"];1632 -> 1640[label="",style="solid", color="black", weight=3]; 1633[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat (Succ wx1810) Zero == GT))",fontsize=16,color="black",shape="box"];1633 -> 1641[label="",style="solid", color="black", weight=3]; 1634[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat Zero (Succ wx1820) == GT))",fontsize=16,color="black",shape="box"];1634 -> 1642[label="",style="solid", color="black", weight=3]; 1635[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];1635 -> 1643[label="",style="solid", color="black", weight=3]; 1636[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat (Succ wx1910) (Succ wx1920) == GT))",fontsize=16,color="black",shape="box"];1636 -> 1644[label="",style="solid", color="black", weight=3]; 1637[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat (Succ wx1910) Zero == GT))",fontsize=16,color="black",shape="box"];1637 -> 1645[label="",style="solid", color="black", weight=3]; 1638[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat Zero (Succ wx1920) == GT))",fontsize=16,color="black",shape="box"];1638 -> 1646[label="",style="solid", color="black", weight=3]; 1639[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];1639 -> 1647[label="",style="solid", color="black", weight=3]; 1640 -> 1428[label="",style="dashed", color="red", weight=0]; 1640[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (primCmpNat wx1810 wx1820 == GT))",fontsize=16,color="magenta"];1640 -> 1648[label="",style="dashed", color="magenta", weight=3]; 1640 -> 1649[label="",style="dashed", color="magenta", weight=3]; 1641[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (GT == GT))",fontsize=16,color="black",shape="box"];1641 -> 1650[label="",style="solid", color="black", weight=3]; 1642[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (LT == GT))",fontsize=16,color="black",shape="box"];1642 -> 1651[label="",style="solid", color="black", weight=3]; 1643[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) (EQ == GT))",fontsize=16,color="black",shape="box"];1643 -> 1652[label="",style="solid", color="black", weight=3]; 1644 -> 1530[label="",style="dashed", color="red", weight=0]; 1644[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (primCmpNat wx1910 wx1920 == GT))",fontsize=16,color="magenta"];1644 -> 1653[label="",style="dashed", color="magenta", weight=3]; 1644 -> 1654[label="",style="dashed", color="magenta", weight=3]; 1645[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (GT == GT))",fontsize=16,color="black",shape="box"];1645 -> 1655[label="",style="solid", color="black", weight=3]; 1646[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (LT == GT))",fontsize=16,color="black",shape="box"];1646 -> 1656[label="",style="solid", color="black", weight=3]; 1647[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) (EQ == GT))",fontsize=16,color="black",shape="box"];1647 -> 1657[label="",style="solid", color="black", weight=3]; 1648[label="wx1810",fontsize=16,color="green",shape="box"];1649[label="wx1820",fontsize=16,color="green",shape="box"];1650[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) True)",fontsize=16,color="black",shape="box"];1650 -> 1658[label="",style="solid", color="black", weight=3]; 1651[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) False)",fontsize=16,color="black",shape="triangle"];1651 -> 1659[label="",style="solid", color="black", weight=3]; 1652 -> 1651[label="",style="dashed", color="red", weight=0]; 1652[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM1 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) False)",fontsize=16,color="magenta"];1653[label="wx1910",fontsize=16,color="green",shape="box"];1654[label="wx1920",fontsize=16,color="green",shape="box"];1655[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) True)",fontsize=16,color="black",shape="box"];1655 -> 1660[label="",style="solid", color="black", weight=3]; 1656[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) False)",fontsize=16,color="black",shape="triangle"];1656 -> 1661[label="",style="solid", color="black", weight=3]; 1657 -> 1656[label="",style="dashed", color="red", weight=0]; 1657[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM1 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) False)",fontsize=16,color="magenta"];1658 -> 6[label="",style="dashed", color="red", weight=0]; 1658[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM wx179 (Pos (Succ wx180)))",fontsize=16,color="magenta"];1658 -> 1662[label="",style="dashed", color="magenta", weight=3]; 1658 -> 1663[label="",style="dashed", color="magenta", weight=3]; 1658 -> 1664[label="",style="dashed", color="magenta", weight=3]; 1659[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM0 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) otherwise)",fontsize=16,color="black",shape="box"];1659 -> 1665[label="",style="solid", color="black", weight=3]; 1660 -> 6[label="",style="dashed", color="red", weight=0]; 1660[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM wx189 (Neg (Succ wx190)))",fontsize=16,color="magenta"];1660 -> 1666[label="",style="dashed", color="magenta", weight=3]; 1660 -> 1667[label="",style="dashed", color="magenta", weight=3]; 1660 -> 1668[label="",style="dashed", color="magenta", weight=3]; 1661[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM0 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) otherwise)",fontsize=16,color="black",shape="box"];1661 -> 1669[label="",style="solid", color="black", weight=3]; 1662[label="wx174",fontsize=16,color="green",shape="box"];1663[label="wx179",fontsize=16,color="green",shape="box"];1664[label="Pos (Succ wx180)",fontsize=16,color="green",shape="box"];1665[label="FiniteMap.lookupWithDefaultFM0 wx174 (FiniteMap.lookupFM0 (Pos (Succ wx175)) wx176 wx177 wx178 wx179 (Pos (Succ wx180)) True)",fontsize=16,color="black",shape="box"];1665 -> 1670[label="",style="solid", color="black", weight=3]; 1666[label="wx184",fontsize=16,color="green",shape="box"];1667[label="wx189",fontsize=16,color="green",shape="box"];1668[label="Neg (Succ wx190)",fontsize=16,color="green",shape="box"];1669[label="FiniteMap.lookupWithDefaultFM0 wx184 (FiniteMap.lookupFM0 (Neg (Succ wx185)) wx186 wx187 wx188 wx189 (Neg (Succ wx190)) True)",fontsize=16,color="black",shape="box"];1669 -> 1671[label="",style="solid", color="black", weight=3]; 1670 -> 224[label="",style="dashed", color="red", weight=0]; 1670[label="FiniteMap.lookupWithDefaultFM0 wx174 (Just wx176)",fontsize=16,color="magenta"];1670 -> 1672[label="",style="dashed", color="magenta", weight=3]; 1670 -> 1673[label="",style="dashed", color="magenta", weight=3]; 1671 -> 224[label="",style="dashed", color="red", weight=0]; 1671[label="FiniteMap.lookupWithDefaultFM0 wx184 (Just wx186)",fontsize=16,color="magenta"];1671 -> 1674[label="",style="dashed", color="magenta", weight=3]; 1671 -> 1675[label="",style="dashed", color="magenta", weight=3]; 1672[label="wx176",fontsize=16,color="green",shape="box"];1673[label="wx174",fontsize=16,color="green",shape="box"];1674[label="wx186",fontsize=16,color="green",shape="box"];1675[label="wx184",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx870), Zero, h) -> new_lookupWithDefaultFM00(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx86), Succ(wx81), h) new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, Succ(wx1810), Succ(wx1820), ba) -> new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, wx1810, wx1820, ba) new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM0(wx4, wx3000, wx31, wx32, wx33, wx34, wx500, wx500, wx3000, bb) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx970), Zero, bc) -> new_lookupWithDefaultFM04(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx91), Succ(wx96), bc) new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM03(wx4, wx3000, wx31, wx32, wx33, wx34, wx500, wx3000, wx500, bb) new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Zero), bb) new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, Succ(wx1910), Succ(wx1920), bd) -> new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, wx1910, wx1920, bd) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx970), Succ(wx980), bc) -> new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, wx970, wx980, bc) new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Neg(Zero), bb) new_lookupWithDefaultFM01(wx4, Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Succ(wx500)), bb) new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Pos(Zero), bb) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Zero, Zero, bc) -> new_lookupWithDefaultFM05(wx90, wx91, wx92, wx93, wx94, wx95, wx96, bc) new_lookupWithDefaultFM05(wx90, wx91, wx92, wx93, wx94, wx95, wx96, bc) -> new_lookupWithDefaultFM04(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx91), Succ(wx96), bc) new_lookupWithDefaultFM02(wx80, wx81, wx82, wx83, wx84, wx85, wx86, h) -> new_lookupWithDefaultFM00(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx86), Succ(wx81), h) new_lookupWithDefaultFM01(wx4, Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Succ(wx500)), bb) new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx870), Succ(wx880), h) -> new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, wx870, wx880, h) new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, Succ(wx1910), Zero, bd) -> new_lookupWithDefaultFM01(wx184, wx189, Neg(Succ(wx190)), bd) new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, Succ(wx1810), Zero, ba) -> new_lookupWithDefaultFM01(wx174, wx179, Pos(Succ(wx180)), ba) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Zero, Succ(wx980), bc) -> new_lookupWithDefaultFM01(wx90, wx94, Neg(Succ(wx96)), bc) new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Zero, Zero, h) -> new_lookupWithDefaultFM02(wx80, wx81, wx82, wx83, wx84, wx85, wx86, h) new_lookupWithDefaultFM01(wx4, Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Succ(wx500)), bb) new_lookupWithDefaultFM01(wx4, Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Succ(wx500)), bb) new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Zero, Succ(wx880), h) -> new_lookupWithDefaultFM01(wx80, wx84, Pos(Succ(wx86)), h) new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Zero), bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (9) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs. ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Zero), bb) new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Pos(Zero), bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Zero), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 *new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Pos(Zero), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Neg(Zero), bb) new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Zero), bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (15) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Neg(Zero), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 *new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Zero), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 ---------------------------------------- (16) YES ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, Succ(wx1910), Succ(wx1920), bd) -> new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, wx1910, wx1920, bd) new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, Succ(wx1910), Zero, bd) -> new_lookupWithDefaultFM01(wx184, wx189, Neg(Succ(wx190)), bd) new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM03(wx4, wx3000, wx31, wx32, wx33, wx34, wx500, wx3000, wx500, bb) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx970), Zero, bc) -> new_lookupWithDefaultFM04(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx91), Succ(wx96), bc) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx970), Succ(wx980), bc) -> new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, wx970, wx980, bc) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Zero, Zero, bc) -> new_lookupWithDefaultFM05(wx90, wx91, wx92, wx93, wx94, wx95, wx96, bc) new_lookupWithDefaultFM05(wx90, wx91, wx92, wx93, wx94, wx95, wx96, bc) -> new_lookupWithDefaultFM04(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx91), Succ(wx96), bc) new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Zero, Succ(wx980), bc) -> new_lookupWithDefaultFM01(wx90, wx94, Neg(Succ(wx96)), bc) new_lookupWithDefaultFM01(wx4, Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Succ(wx500)), bb) new_lookupWithDefaultFM01(wx4, Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Succ(wx500)), bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, Succ(wx1910), Succ(wx1920), bd) -> new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, wx1910, wx1920, bd) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 *new_lookupWithDefaultFM04(wx184, wx185, wx186, wx187, wx188, wx189, wx190, Succ(wx1910), Zero, bd) -> new_lookupWithDefaultFM01(wx184, wx189, Neg(Succ(wx190)), bd) The graph contains the following edges 1 >= 1, 6 >= 2, 10 >= 4 *new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx970), Zero, bc) -> new_lookupWithDefaultFM04(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx91), Succ(wx96), bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 10 *new_lookupWithDefaultFM05(wx90, wx91, wx92, wx93, wx94, wx95, wx96, bc) -> new_lookupWithDefaultFM04(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx91), Succ(wx96), bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 10 *new_lookupWithDefaultFM01(wx4, Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM03(wx4, wx3000, wx31, wx32, wx33, wx34, wx500, wx3000, wx500, bb) The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 > 7, 2 > 8, 3 > 9, 4 >= 10 *new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Zero, Succ(wx980), bc) -> new_lookupWithDefaultFM01(wx90, wx94, Neg(Succ(wx96)), bc) The graph contains the following edges 1 >= 1, 5 >= 2, 10 >= 4 *new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Succ(wx970), Succ(wx980), bc) -> new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, wx970, wx980, bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 *new_lookupWithDefaultFM03(wx90, wx91, wx92, wx93, wx94, wx95, wx96, Zero, Zero, bc) -> new_lookupWithDefaultFM05(wx90, wx91, wx92, wx93, wx94, wx95, wx96, bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 8 *new_lookupWithDefaultFM01(wx4, Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Succ(wx500)), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 *new_lookupWithDefaultFM01(wx4, Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx33, Neg(Succ(wx500)), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, Succ(wx1810), Succ(wx1820), ba) -> new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, wx1810, wx1820, ba) new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, Succ(wx1810), Zero, ba) -> new_lookupWithDefaultFM01(wx174, wx179, Pos(Succ(wx180)), ba) new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM0(wx4, wx3000, wx31, wx32, wx33, wx34, wx500, wx500, wx3000, bb) new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx870), Zero, h) -> new_lookupWithDefaultFM00(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx86), Succ(wx81), h) new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx870), Succ(wx880), h) -> new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, wx870, wx880, h) new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Zero, Zero, h) -> new_lookupWithDefaultFM02(wx80, wx81, wx82, wx83, wx84, wx85, wx86, h) new_lookupWithDefaultFM02(wx80, wx81, wx82, wx83, wx84, wx85, wx86, h) -> new_lookupWithDefaultFM00(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx86), Succ(wx81), h) new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Zero, Succ(wx880), h) -> new_lookupWithDefaultFM01(wx80, wx84, Pos(Succ(wx86)), h) new_lookupWithDefaultFM01(wx4, Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Succ(wx500)), bb) new_lookupWithDefaultFM01(wx4, Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Succ(wx500)), bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, Succ(wx1810), Succ(wx1820), ba) -> new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, wx1810, wx1820, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 *new_lookupWithDefaultFM00(wx174, wx175, wx176, wx177, wx178, wx179, wx180, Succ(wx1810), Zero, ba) -> new_lookupWithDefaultFM01(wx174, wx179, Pos(Succ(wx180)), ba) The graph contains the following edges 1 >= 1, 6 >= 2, 10 >= 4 *new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx870), Zero, h) -> new_lookupWithDefaultFM00(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx86), Succ(wx81), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 10 *new_lookupWithDefaultFM02(wx80, wx81, wx82, wx83, wx84, wx85, wx86, h) -> new_lookupWithDefaultFM00(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx86), Succ(wx81), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 10 *new_lookupWithDefaultFM01(wx4, Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM0(wx4, wx3000, wx31, wx32, wx33, wx34, wx500, wx500, wx3000, bb) The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 > 7, 3 > 8, 2 > 9, 4 >= 10 *new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Zero, Succ(wx880), h) -> new_lookupWithDefaultFM01(wx80, wx84, Pos(Succ(wx86)), h) The graph contains the following edges 1 >= 1, 5 >= 2, 10 >= 4 *new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Succ(wx870), Succ(wx880), h) -> new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, wx870, wx880, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 *new_lookupWithDefaultFM0(wx80, wx81, wx82, wx83, wx84, wx85, wx86, Zero, Zero, h) -> new_lookupWithDefaultFM02(wx80, wx81, wx82, wx83, wx84, wx85, wx86, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 8 *new_lookupWithDefaultFM01(wx4, Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Succ(wx500)), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 *new_lookupWithDefaultFM01(wx4, Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx500)), bb) -> new_lookupWithDefaultFM01(wx4, wx34, Pos(Succ(wx500)), bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 ---------------------------------------- (22) YES