8.66/3.87 YES 10.66/4.43 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 10.66/4.43 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.66/4.43 10.66/4.43 10.66/4.43 H-Termination with start terms of the given HASKELL could be proven: 10.66/4.43 10.66/4.43 (0) HASKELL 10.66/4.43 (1) BR [EQUIVALENT, 0 ms] 10.66/4.43 (2) HASKELL 10.66/4.43 (3) COR [EQUIVALENT, 0 ms] 10.66/4.43 (4) HASKELL 10.66/4.43 (5) Narrow [SOUND, 0 ms] 10.66/4.43 (6) AND 10.66/4.43 (7) QDP 10.66/4.43 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.66/4.43 (9) YES 10.66/4.43 (10) QDP 10.66/4.43 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.66/4.43 (12) YES 10.66/4.43 (13) QDP 10.66/4.43 (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.66/4.43 (15) YES 10.66/4.43 10.66/4.43 10.66/4.43 ---------------------------------------- 10.66/4.43 10.66/4.43 (0) 10.66/4.43 Obligation: 10.66/4.43 mainModule Main 10.66/4.43 module Main where { 10.66/4.43 import qualified Prelude; 10.66/4.43 data Main.Char = Char MyInt ; 10.66/4.43 10.66/4.43 data List a = Cons a (List a) | Nil ; 10.66/4.43 10.66/4.43 data MyBool = MyTrue | MyFalse ; 10.66/4.43 10.66/4.43 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.66/4.43 10.66/4.43 data Main.Nat = Succ Main.Nat | Zero ; 10.66/4.43 10.66/4.43 data Ordering = LT | EQ | GT ; 10.66/4.43 10.66/4.43 compareChar :: Main.Char -> Main.Char -> Ordering; 10.66/4.43 compareChar = primCmpChar; 10.66/4.43 10.66/4.43 esEsOrdering :: Ordering -> Ordering -> MyBool; 10.66/4.43 esEsOrdering LT LT = MyTrue; 10.66/4.43 esEsOrdering LT EQ = MyFalse; 10.66/4.43 esEsOrdering LT GT = MyFalse; 10.66/4.43 esEsOrdering EQ LT = MyFalse; 10.66/4.43 esEsOrdering EQ EQ = MyTrue; 10.66/4.43 esEsOrdering EQ GT = MyFalse; 10.66/4.43 esEsOrdering GT LT = MyFalse; 10.66/4.43 esEsOrdering GT EQ = MyFalse; 10.66/4.43 esEsOrdering GT GT = MyTrue; 10.66/4.43 10.66/4.43 foldl :: (b -> a -> b) -> b -> List a -> b; 10.66/4.43 foldl f z Nil = z; 10.66/4.43 foldl f z (Cons x xs) = foldl f (f z x) xs; 10.66/4.43 10.66/4.43 foldl1 :: (a -> a -> a) -> List a -> a; 10.66/4.43 foldl1 f (Cons x xs) = foldl f x xs; 10.66/4.43 10.66/4.43 fsEsOrdering :: Ordering -> Ordering -> MyBool; 10.66/4.43 fsEsOrdering x y = not (esEsOrdering x y); 10.66/4.43 10.66/4.43 ltEsChar :: Main.Char -> Main.Char -> MyBool; 10.66/4.43 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 10.66/4.43 10.66/4.43 max0 x y MyTrue = x; 10.66/4.43 10.66/4.43 max1 x y MyTrue = y; 10.66/4.43 max1 x y MyFalse = max0 x y otherwise; 10.66/4.43 10.66/4.43 max2 x y = max1 x y (ltEsChar x y); 10.66/4.43 10.66/4.43 maxChar :: Main.Char -> Main.Char -> Main.Char; 10.66/4.43 maxChar x y = max2 x y; 10.66/4.43 10.66/4.43 maximumChar :: List Main.Char -> Main.Char; 10.66/4.43 maximumChar = foldl1 maxChar; 10.66/4.43 10.66/4.43 not :: MyBool -> MyBool; 10.66/4.43 not MyTrue = MyFalse; 10.66/4.43 not MyFalse = MyTrue; 10.66/4.43 10.66/4.43 otherwise :: MyBool; 10.66/4.43 otherwise = MyTrue; 10.66/4.43 10.66/4.43 primCmpChar :: Main.Char -> Main.Char -> Ordering; 10.66/4.43 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 10.66/4.43 10.66/4.43 primCmpInt :: MyInt -> MyInt -> Ordering; 10.66/4.43 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 10.66/4.43 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 10.66/4.43 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 10.66/4.43 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 10.66/4.43 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 10.66/4.43 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 10.66/4.43 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 10.66/4.43 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 10.66/4.43 10.66/4.43 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 10.66/4.43 primCmpNat Main.Zero Main.Zero = EQ; 10.66/4.43 primCmpNat Main.Zero (Main.Succ y) = LT; 10.66/4.43 primCmpNat (Main.Succ x) Main.Zero = GT; 10.66/4.43 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 10.66/4.43 10.66/4.43 } 10.66/4.43 10.66/4.43 ---------------------------------------- 10.66/4.43 10.66/4.43 (1) BR (EQUIVALENT) 10.66/4.43 Replaced joker patterns by fresh variables and removed binding patterns. 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (2) 10.66/4.44 Obligation: 10.66/4.44 mainModule Main 10.66/4.44 module Main where { 10.66/4.44 import qualified Prelude; 10.66/4.44 data Main.Char = Char MyInt ; 10.66/4.44 10.66/4.44 data List a = Cons a (List a) | Nil ; 10.66/4.44 10.66/4.44 data MyBool = MyTrue | MyFalse ; 10.66/4.44 10.66/4.44 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.66/4.44 10.66/4.44 data Main.Nat = Succ Main.Nat | Zero ; 10.66/4.44 10.66/4.44 data Ordering = LT | EQ | GT ; 10.66/4.44 10.66/4.44 compareChar :: Main.Char -> Main.Char -> Ordering; 10.66/4.44 compareChar = primCmpChar; 10.66/4.44 10.66/4.44 esEsOrdering :: Ordering -> Ordering -> MyBool; 10.66/4.44 esEsOrdering LT LT = MyTrue; 10.66/4.44 esEsOrdering LT EQ = MyFalse; 10.66/4.44 esEsOrdering LT GT = MyFalse; 10.66/4.44 esEsOrdering EQ LT = MyFalse; 10.66/4.44 esEsOrdering EQ EQ = MyTrue; 10.66/4.44 esEsOrdering EQ GT = MyFalse; 10.66/4.44 esEsOrdering GT LT = MyFalse; 10.66/4.44 esEsOrdering GT EQ = MyFalse; 10.66/4.44 esEsOrdering GT GT = MyTrue; 10.66/4.44 10.66/4.44 foldl :: (b -> a -> b) -> b -> List a -> b; 10.66/4.44 foldl f z Nil = z; 10.66/4.44 foldl f z (Cons x xs) = foldl f (f z x) xs; 10.66/4.44 10.66/4.44 foldl1 :: (a -> a -> a) -> List a -> a; 10.66/4.44 foldl1 f (Cons x xs) = foldl f x xs; 10.66/4.44 10.66/4.44 fsEsOrdering :: Ordering -> Ordering -> MyBool; 10.66/4.44 fsEsOrdering x y = not (esEsOrdering x y); 10.66/4.44 10.66/4.44 ltEsChar :: Main.Char -> Main.Char -> MyBool; 10.66/4.44 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 10.66/4.44 10.66/4.44 max0 x y MyTrue = x; 10.66/4.44 10.66/4.44 max1 x y MyTrue = y; 10.66/4.44 max1 x y MyFalse = max0 x y otherwise; 10.66/4.44 10.66/4.44 max2 x y = max1 x y (ltEsChar x y); 10.66/4.44 10.66/4.44 maxChar :: Main.Char -> Main.Char -> Main.Char; 10.66/4.44 maxChar x y = max2 x y; 10.66/4.44 10.66/4.44 maximumChar :: List Main.Char -> Main.Char; 10.66/4.44 maximumChar = foldl1 maxChar; 10.66/4.44 10.66/4.44 not :: MyBool -> MyBool; 10.66/4.44 not MyTrue = MyFalse; 10.66/4.44 not MyFalse = MyTrue; 10.66/4.44 10.66/4.44 otherwise :: MyBool; 10.66/4.44 otherwise = MyTrue; 10.66/4.44 10.66/4.44 primCmpChar :: Main.Char -> Main.Char -> Ordering; 10.66/4.44 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 10.66/4.44 10.66/4.44 primCmpInt :: MyInt -> MyInt -> Ordering; 10.66/4.44 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 10.66/4.44 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 10.66/4.44 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 10.66/4.44 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 10.66/4.44 10.66/4.44 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 10.66/4.44 primCmpNat Main.Zero Main.Zero = EQ; 10.66/4.44 primCmpNat Main.Zero (Main.Succ y) = LT; 10.66/4.44 primCmpNat (Main.Succ x) Main.Zero = GT; 10.66/4.44 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 10.66/4.44 10.66/4.44 } 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (3) COR (EQUIVALENT) 10.66/4.44 Cond Reductions: 10.66/4.44 The following Function with conditions 10.66/4.44 "undefined |Falseundefined; 10.66/4.44 " 10.66/4.44 is transformed to 10.66/4.44 "undefined = undefined1; 10.66/4.44 " 10.66/4.44 "undefined0 True = undefined; 10.66/4.44 " 10.66/4.44 "undefined1 = undefined0 False; 10.66/4.44 " 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (4) 10.66/4.44 Obligation: 10.66/4.44 mainModule Main 10.66/4.44 module Main where { 10.66/4.44 import qualified Prelude; 10.66/4.44 data Main.Char = Char MyInt ; 10.66/4.44 10.66/4.44 data List a = Cons a (List a) | Nil ; 10.66/4.44 10.66/4.44 data MyBool = MyTrue | MyFalse ; 10.66/4.44 10.66/4.44 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.66/4.44 10.66/4.44 data Main.Nat = Succ Main.Nat | Zero ; 10.66/4.44 10.66/4.44 data Ordering = LT | EQ | GT ; 10.66/4.44 10.66/4.44 compareChar :: Main.Char -> Main.Char -> Ordering; 10.66/4.44 compareChar = primCmpChar; 10.66/4.44 10.66/4.44 esEsOrdering :: Ordering -> Ordering -> MyBool; 10.66/4.44 esEsOrdering LT LT = MyTrue; 10.66/4.44 esEsOrdering LT EQ = MyFalse; 10.66/4.44 esEsOrdering LT GT = MyFalse; 10.66/4.44 esEsOrdering EQ LT = MyFalse; 10.66/4.44 esEsOrdering EQ EQ = MyTrue; 10.66/4.44 esEsOrdering EQ GT = MyFalse; 10.66/4.44 esEsOrdering GT LT = MyFalse; 10.66/4.44 esEsOrdering GT EQ = MyFalse; 10.66/4.44 esEsOrdering GT GT = MyTrue; 10.66/4.44 10.66/4.44 foldl :: (a -> b -> a) -> a -> List b -> a; 10.66/4.44 foldl f z Nil = z; 10.66/4.44 foldl f z (Cons x xs) = foldl f (f z x) xs; 10.66/4.44 10.66/4.44 foldl1 :: (a -> a -> a) -> List a -> a; 10.66/4.44 foldl1 f (Cons x xs) = foldl f x xs; 10.66/4.44 10.66/4.44 fsEsOrdering :: Ordering -> Ordering -> MyBool; 10.66/4.44 fsEsOrdering x y = not (esEsOrdering x y); 10.66/4.44 10.66/4.44 ltEsChar :: Main.Char -> Main.Char -> MyBool; 10.66/4.44 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 10.66/4.44 10.66/4.44 max0 x y MyTrue = x; 10.66/4.44 10.66/4.44 max1 x y MyTrue = y; 10.66/4.44 max1 x y MyFalse = max0 x y otherwise; 10.66/4.44 10.66/4.44 max2 x y = max1 x y (ltEsChar x y); 10.66/4.44 10.66/4.44 maxChar :: Main.Char -> Main.Char -> Main.Char; 10.66/4.44 maxChar x y = max2 x y; 10.66/4.44 10.66/4.44 maximumChar :: List Main.Char -> Main.Char; 10.66/4.44 maximumChar = foldl1 maxChar; 10.66/4.44 10.66/4.44 not :: MyBool -> MyBool; 10.66/4.44 not MyTrue = MyFalse; 10.66/4.44 not MyFalse = MyTrue; 10.66/4.44 10.66/4.44 otherwise :: MyBool; 10.66/4.44 otherwise = MyTrue; 10.66/4.44 10.66/4.44 primCmpChar :: Main.Char -> Main.Char -> Ordering; 10.66/4.44 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 10.66/4.44 10.66/4.44 primCmpInt :: MyInt -> MyInt -> Ordering; 10.66/4.44 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 10.66/4.44 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 10.66/4.44 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 10.66/4.44 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 10.66/4.44 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 10.66/4.44 10.66/4.44 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 10.66/4.44 primCmpNat Main.Zero Main.Zero = EQ; 10.66/4.44 primCmpNat Main.Zero (Main.Succ y) = LT; 10.66/4.44 primCmpNat (Main.Succ x) Main.Zero = GT; 10.66/4.44 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 10.66/4.44 10.66/4.44 } 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (5) Narrow (SOUND) 10.66/4.44 Haskell To QDPs 10.66/4.44 10.66/4.44 digraph dp_graph { 10.66/4.44 node [outthreshold=100, inthreshold=100];1[label="maximumChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.66/4.44 3[label="maximumChar vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 10.66/4.44 4[label="foldl1 maxChar vx3",fontsize=16,color="burlywood",shape="box"];604[label="vx3/Cons vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 604[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 604 -> 5[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 605[label="vx3/Nil",fontsize=10,color="white",style="solid",shape="box"];4 -> 605[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 605 -> 6[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 5[label="foldl1 maxChar (Cons vx30 vx31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 10.66/4.44 6[label="foldl1 maxChar Nil",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 10.66/4.44 7[label="foldl maxChar vx30 vx31",fontsize=16,color="burlywood",shape="triangle"];606[label="vx31/Cons vx310 vx311",fontsize=10,color="white",style="solid",shape="box"];7 -> 606[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 606 -> 9[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 607[label="vx31/Nil",fontsize=10,color="white",style="solid",shape="box"];7 -> 607[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 607 -> 10[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 8[label="error []",fontsize=16,color="red",shape="box"];9[label="foldl maxChar vx30 (Cons vx310 vx311)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10.66/4.44 10[label="foldl maxChar vx30 Nil",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 10.66/4.44 11 -> 7[label="",style="dashed", color="red", weight=0]; 10.66/4.44 11[label="foldl maxChar (maxChar vx30 vx310) vx311",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 11 -> 14[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 12[label="vx30",fontsize=16,color="green",shape="box"];13[label="vx311",fontsize=16,color="green",shape="box"];14[label="maxChar vx30 vx310",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 10.66/4.44 15[label="max2 vx30 vx310",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 10.66/4.44 16[label="max1 vx30 vx310 (ltEsChar vx30 vx310)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 10.66/4.44 17[label="max1 vx30 vx310 (fsEsOrdering (compareChar vx30 vx310) GT)",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 10.66/4.44 18[label="max1 vx30 vx310 (not (esEsOrdering (compareChar vx30 vx310) GT))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 10.66/4.44 19[label="max1 vx30 vx310 (not (esEsOrdering (primCmpChar vx30 vx310) GT))",fontsize=16,color="burlywood",shape="box"];608[label="vx30/Char vx300",fontsize=10,color="white",style="solid",shape="box"];19 -> 608[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 608 -> 20[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 20[label="max1 (Char vx300) vx310 (not (esEsOrdering (primCmpChar (Char vx300) vx310) GT))",fontsize=16,color="burlywood",shape="box"];609[label="vx310/Char vx3100",fontsize=10,color="white",style="solid",shape="box"];20 -> 609[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 609 -> 21[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 21[label="max1 (Char vx300) (Char vx3100) (not (esEsOrdering (primCmpChar (Char vx300) (Char vx3100)) GT))",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3]; 10.66/4.44 22[label="max1 (Char vx300) (Char vx3100) (not (esEsOrdering (primCmpInt vx300 vx3100) GT))",fontsize=16,color="burlywood",shape="box"];610[label="vx300/Pos vx3000",fontsize=10,color="white",style="solid",shape="box"];22 -> 610[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 610 -> 23[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 611[label="vx300/Neg vx3000",fontsize=10,color="white",style="solid",shape="box"];22 -> 611[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 611 -> 24[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 23[label="max1 (Char (Pos vx3000)) (Char vx3100) (not (esEsOrdering (primCmpInt (Pos vx3000) vx3100) GT))",fontsize=16,color="burlywood",shape="box"];612[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];23 -> 612[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 612 -> 25[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 613[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 613[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 613 -> 26[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 24[label="max1 (Char (Neg vx3000)) (Char vx3100) (not (esEsOrdering (primCmpInt (Neg vx3000) vx3100) GT))",fontsize=16,color="burlywood",shape="box"];614[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];24 -> 614[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 614 -> 27[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 615[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 615[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 615 -> 28[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 25[label="max1 (Char (Pos (Succ vx30000))) (Char vx3100) (not (esEsOrdering (primCmpInt (Pos (Succ vx30000)) vx3100) GT))",fontsize=16,color="burlywood",shape="box"];616[label="vx3100/Pos vx31000",fontsize=10,color="white",style="solid",shape="box"];25 -> 616[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 616 -> 29[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 617[label="vx3100/Neg vx31000",fontsize=10,color="white",style="solid",shape="box"];25 -> 617[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 617 -> 30[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 26[label="max1 (Char (Pos Zero)) (Char vx3100) (not (esEsOrdering (primCmpInt (Pos Zero) vx3100) GT))",fontsize=16,color="burlywood",shape="box"];618[label="vx3100/Pos vx31000",fontsize=10,color="white",style="solid",shape="box"];26 -> 618[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 618 -> 31[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 619[label="vx3100/Neg vx31000",fontsize=10,color="white",style="solid",shape="box"];26 -> 619[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 619 -> 32[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 27[label="max1 (Char (Neg (Succ vx30000))) (Char vx3100) (not (esEsOrdering (primCmpInt (Neg (Succ vx30000)) vx3100) GT))",fontsize=16,color="burlywood",shape="box"];620[label="vx3100/Pos vx31000",fontsize=10,color="white",style="solid",shape="box"];27 -> 620[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 620 -> 33[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 621[label="vx3100/Neg vx31000",fontsize=10,color="white",style="solid",shape="box"];27 -> 621[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 621 -> 34[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 28[label="max1 (Char (Neg Zero)) (Char vx3100) (not (esEsOrdering (primCmpInt (Neg Zero) vx3100) GT))",fontsize=16,color="burlywood",shape="box"];622[label="vx3100/Pos vx31000",fontsize=10,color="white",style="solid",shape="box"];28 -> 622[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 622 -> 35[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 623[label="vx3100/Neg vx31000",fontsize=10,color="white",style="solid",shape="box"];28 -> 623[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 623 -> 36[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 29[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos vx31000)) (not (esEsOrdering (primCmpInt (Pos (Succ vx30000)) (Pos vx31000)) GT))",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3]; 10.66/4.44 30[label="max1 (Char (Pos (Succ vx30000))) (Char (Neg vx31000)) (not (esEsOrdering (primCmpInt (Pos (Succ vx30000)) (Neg vx31000)) GT))",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3]; 10.66/4.44 31[label="max1 (Char (Pos Zero)) (Char (Pos vx31000)) (not (esEsOrdering (primCmpInt (Pos Zero) (Pos vx31000)) GT))",fontsize=16,color="burlywood",shape="box"];624[label="vx31000/Succ vx310000",fontsize=10,color="white",style="solid",shape="box"];31 -> 624[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 624 -> 39[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 625[label="vx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];31 -> 625[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 625 -> 40[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 32[label="max1 (Char (Pos Zero)) (Char (Neg vx31000)) (not (esEsOrdering (primCmpInt (Pos Zero) (Neg vx31000)) GT))",fontsize=16,color="burlywood",shape="box"];626[label="vx31000/Succ vx310000",fontsize=10,color="white",style="solid",shape="box"];32 -> 626[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 626 -> 41[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 627[label="vx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 627[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 627 -> 42[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 33[label="max1 (Char (Neg (Succ vx30000))) (Char (Pos vx31000)) (not (esEsOrdering (primCmpInt (Neg (Succ vx30000)) (Pos vx31000)) GT))",fontsize=16,color="black",shape="box"];33 -> 43[label="",style="solid", color="black", weight=3]; 10.66/4.44 34[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg vx31000)) (not (esEsOrdering (primCmpInt (Neg (Succ vx30000)) (Neg vx31000)) GT))",fontsize=16,color="black",shape="box"];34 -> 44[label="",style="solid", color="black", weight=3]; 10.66/4.44 35[label="max1 (Char (Neg Zero)) (Char (Pos vx31000)) (not (esEsOrdering (primCmpInt (Neg Zero) (Pos vx31000)) GT))",fontsize=16,color="burlywood",shape="box"];628[label="vx31000/Succ vx310000",fontsize=10,color="white",style="solid",shape="box"];35 -> 628[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 628 -> 45[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 629[label="vx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 629[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 629 -> 46[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 36[label="max1 (Char (Neg Zero)) (Char (Neg vx31000)) (not (esEsOrdering (primCmpInt (Neg Zero) (Neg vx31000)) GT))",fontsize=16,color="burlywood",shape="box"];630[label="vx31000/Succ vx310000",fontsize=10,color="white",style="solid",shape="box"];36 -> 630[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 630 -> 47[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 631[label="vx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 631[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 631 -> 48[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 37[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos vx31000)) (not (esEsOrdering (primCmpNat (Succ vx30000) vx31000) GT))",fontsize=16,color="burlywood",shape="box"];632[label="vx31000/Succ vx310000",fontsize=10,color="white",style="solid",shape="box"];37 -> 632[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 632 -> 49[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 633[label="vx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 633[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 633 -> 50[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 38[label="max1 (Char (Pos (Succ vx30000))) (Char (Neg vx31000)) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];38 -> 51[label="",style="solid", color="black", weight=3]; 10.66/4.44 39[label="max1 (Char (Pos Zero)) (Char (Pos (Succ vx310000))) (not (esEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vx310000))) GT))",fontsize=16,color="black",shape="box"];39 -> 52[label="",style="solid", color="black", weight=3]; 10.66/4.44 40[label="max1 (Char (Pos Zero)) (Char (Pos Zero)) (not (esEsOrdering (primCmpInt (Pos Zero) (Pos Zero)) GT))",fontsize=16,color="black",shape="box"];40 -> 53[label="",style="solid", color="black", weight=3]; 10.66/4.44 41[label="max1 (Char (Pos Zero)) (Char (Neg (Succ vx310000))) (not (esEsOrdering (primCmpInt (Pos Zero) (Neg (Succ vx310000))) GT))",fontsize=16,color="black",shape="box"];41 -> 54[label="",style="solid", color="black", weight=3]; 10.66/4.44 42[label="max1 (Char (Pos Zero)) (Char (Neg Zero)) (not (esEsOrdering (primCmpInt (Pos Zero) (Neg Zero)) GT))",fontsize=16,color="black",shape="box"];42 -> 55[label="",style="solid", color="black", weight=3]; 10.66/4.44 43[label="max1 (Char (Neg (Succ vx30000))) (Char (Pos vx31000)) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];43 -> 56[label="",style="solid", color="black", weight=3]; 10.66/4.44 44[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg vx31000)) (not (esEsOrdering (primCmpNat vx31000 (Succ vx30000)) GT))",fontsize=16,color="burlywood",shape="box"];634[label="vx31000/Succ vx310000",fontsize=10,color="white",style="solid",shape="box"];44 -> 634[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 634 -> 57[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 635[label="vx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];44 -> 635[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 635 -> 58[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 45[label="max1 (Char (Neg Zero)) (Char (Pos (Succ vx310000))) (not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vx310000))) GT))",fontsize=16,color="black",shape="box"];45 -> 59[label="",style="solid", color="black", weight=3]; 10.66/4.44 46[label="max1 (Char (Neg Zero)) (Char (Pos Zero)) (not (esEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) GT))",fontsize=16,color="black",shape="box"];46 -> 60[label="",style="solid", color="black", weight=3]; 10.66/4.44 47[label="max1 (Char (Neg Zero)) (Char (Neg (Succ vx310000))) (not (esEsOrdering (primCmpInt (Neg Zero) (Neg (Succ vx310000))) GT))",fontsize=16,color="black",shape="box"];47 -> 61[label="",style="solid", color="black", weight=3]; 10.66/4.44 48[label="max1 (Char (Neg Zero)) (Char (Neg Zero)) (not (esEsOrdering (primCmpInt (Neg Zero) (Neg Zero)) GT))",fontsize=16,color="black",shape="box"];48 -> 62[label="",style="solid", color="black", weight=3]; 10.66/4.44 49[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos (Succ vx310000))) (not (esEsOrdering (primCmpNat (Succ vx30000) (Succ vx310000)) GT))",fontsize=16,color="black",shape="box"];49 -> 63[label="",style="solid", color="black", weight=3]; 10.66/4.44 50[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos Zero)) (not (esEsOrdering (primCmpNat (Succ vx30000) Zero) GT))",fontsize=16,color="black",shape="box"];50 -> 64[label="",style="solid", color="black", weight=3]; 10.66/4.44 51[label="max1 (Char (Pos (Succ vx30000))) (Char (Neg vx31000)) (not MyTrue)",fontsize=16,color="black",shape="box"];51 -> 65[label="",style="solid", color="black", weight=3]; 10.66/4.44 52[label="max1 (Char (Pos Zero)) (Char (Pos (Succ vx310000))) (not (esEsOrdering (primCmpNat Zero (Succ vx310000)) GT))",fontsize=16,color="black",shape="box"];52 -> 66[label="",style="solid", color="black", weight=3]; 10.66/4.44 53[label="max1 (Char (Pos Zero)) (Char (Pos Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];53 -> 67[label="",style="solid", color="black", weight=3]; 10.66/4.44 54[label="max1 (Char (Pos Zero)) (Char (Neg (Succ vx310000))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];54 -> 68[label="",style="solid", color="black", weight=3]; 10.66/4.44 55[label="max1 (Char (Pos Zero)) (Char (Neg Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];55 -> 69[label="",style="solid", color="black", weight=3]; 10.66/4.44 56[label="max1 (Char (Neg (Succ vx30000))) (Char (Pos vx31000)) (not MyFalse)",fontsize=16,color="black",shape="box"];56 -> 70[label="",style="solid", color="black", weight=3]; 10.66/4.44 57[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg (Succ vx310000))) (not (esEsOrdering (primCmpNat (Succ vx310000) (Succ vx30000)) GT))",fontsize=16,color="black",shape="box"];57 -> 71[label="",style="solid", color="black", weight=3]; 10.66/4.44 58[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg Zero)) (not (esEsOrdering (primCmpNat Zero (Succ vx30000)) GT))",fontsize=16,color="black",shape="box"];58 -> 72[label="",style="solid", color="black", weight=3]; 10.66/4.44 59[label="max1 (Char (Neg Zero)) (Char (Pos (Succ vx310000))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];59 -> 73[label="",style="solid", color="black", weight=3]; 10.66/4.44 60[label="max1 (Char (Neg Zero)) (Char (Pos Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];60 -> 74[label="",style="solid", color="black", weight=3]; 10.66/4.44 61[label="max1 (Char (Neg Zero)) (Char (Neg (Succ vx310000))) (not (esEsOrdering (primCmpNat (Succ vx310000) Zero) GT))",fontsize=16,color="black",shape="box"];61 -> 75[label="",style="solid", color="black", weight=3]; 10.66/4.44 62[label="max1 (Char (Neg Zero)) (Char (Neg Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];62 -> 76[label="",style="solid", color="black", weight=3]; 10.66/4.44 63 -> 466[label="",style="dashed", color="red", weight=0]; 10.66/4.44 63[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos (Succ vx310000))) (not (esEsOrdering (primCmpNat vx30000 vx310000) GT))",fontsize=16,color="magenta"];63 -> 467[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 63 -> 468[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 63 -> 469[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 63 -> 470[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 64[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos Zero)) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];64 -> 79[label="",style="solid", color="black", weight=3]; 10.66/4.44 65[label="max1 (Char (Pos (Succ vx30000))) (Char (Neg vx31000)) MyFalse",fontsize=16,color="black",shape="box"];65 -> 80[label="",style="solid", color="black", weight=3]; 10.66/4.44 66[label="max1 (Char (Pos Zero)) (Char (Pos (Succ vx310000))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];66 -> 81[label="",style="solid", color="black", weight=3]; 10.66/4.44 67[label="max1 (Char (Pos Zero)) (Char (Pos Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];67 -> 82[label="",style="solid", color="black", weight=3]; 10.66/4.44 68[label="max1 (Char (Pos Zero)) (Char (Neg (Succ vx310000))) (not MyTrue)",fontsize=16,color="black",shape="box"];68 -> 83[label="",style="solid", color="black", weight=3]; 10.66/4.44 69[label="max1 (Char (Pos Zero)) (Char (Neg Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];69 -> 84[label="",style="solid", color="black", weight=3]; 10.66/4.44 70[label="max1 (Char (Neg (Succ vx30000))) (Char (Pos vx31000)) MyTrue",fontsize=16,color="black",shape="box"];70 -> 85[label="",style="solid", color="black", weight=3]; 10.66/4.44 71 -> 536[label="",style="dashed", color="red", weight=0]; 10.66/4.44 71[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg (Succ vx310000))) (not (esEsOrdering (primCmpNat vx310000 vx30000) GT))",fontsize=16,color="magenta"];71 -> 537[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 71 -> 538[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 71 -> 539[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 71 -> 540[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 72[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg Zero)) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];72 -> 88[label="",style="solid", color="black", weight=3]; 10.66/4.44 73[label="max1 (Char (Neg Zero)) (Char (Pos (Succ vx310000))) (not MyFalse)",fontsize=16,color="black",shape="box"];73 -> 89[label="",style="solid", color="black", weight=3]; 10.66/4.44 74[label="max1 (Char (Neg Zero)) (Char (Pos Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];74 -> 90[label="",style="solid", color="black", weight=3]; 10.66/4.44 75[label="max1 (Char (Neg Zero)) (Char (Neg (Succ vx310000))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];75 -> 91[label="",style="solid", color="black", weight=3]; 10.66/4.44 76[label="max1 (Char (Neg Zero)) (Char (Neg Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];76 -> 92[label="",style="solid", color="black", weight=3]; 10.66/4.44 467[label="vx310000",fontsize=16,color="green",shape="box"];468[label="vx30000",fontsize=16,color="green",shape="box"];469[label="vx30000",fontsize=16,color="green",shape="box"];470[label="vx310000",fontsize=16,color="green",shape="box"];466[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat vx42 vx43) GT))",fontsize=16,color="burlywood",shape="triangle"];636[label="vx42/Succ vx420",fontsize=10,color="white",style="solid",shape="box"];466 -> 636[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 636 -> 503[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 637[label="vx42/Zero",fontsize=10,color="white",style="solid",shape="box"];466 -> 637[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 637 -> 504[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 79[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos Zero)) (not MyTrue)",fontsize=16,color="black",shape="box"];79 -> 97[label="",style="solid", color="black", weight=3]; 10.66/4.44 80[label="max0 (Char (Pos (Succ vx30000))) (Char (Neg vx31000)) otherwise",fontsize=16,color="black",shape="box"];80 -> 98[label="",style="solid", color="black", weight=3]; 10.66/4.44 81[label="max1 (Char (Pos Zero)) (Char (Pos (Succ vx310000))) (not MyFalse)",fontsize=16,color="black",shape="box"];81 -> 99[label="",style="solid", color="black", weight=3]; 10.66/4.44 82[label="max1 (Char (Pos Zero)) (Char (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];82 -> 100[label="",style="solid", color="black", weight=3]; 10.66/4.44 83[label="max1 (Char (Pos Zero)) (Char (Neg (Succ vx310000))) MyFalse",fontsize=16,color="black",shape="box"];83 -> 101[label="",style="solid", color="black", weight=3]; 10.66/4.44 84[label="max1 (Char (Pos Zero)) (Char (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];84 -> 102[label="",style="solid", color="black", weight=3]; 10.66/4.44 85[label="Char (Pos vx31000)",fontsize=16,color="green",shape="box"];537[label="vx310000",fontsize=16,color="green",shape="box"];538[label="vx310000",fontsize=16,color="green",shape="box"];539[label="vx30000",fontsize=16,color="green",shape="box"];540[label="vx30000",fontsize=16,color="green",shape="box"];536[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat vx51 vx52) GT))",fontsize=16,color="burlywood",shape="triangle"];638[label="vx51/Succ vx510",fontsize=10,color="white",style="solid",shape="box"];536 -> 638[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 638 -> 577[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 639[label="vx51/Zero",fontsize=10,color="white",style="solid",shape="box"];536 -> 639[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 639 -> 578[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 88[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];88 -> 107[label="",style="solid", color="black", weight=3]; 10.66/4.44 89[label="max1 (Char (Neg Zero)) (Char (Pos (Succ vx310000))) MyTrue",fontsize=16,color="black",shape="box"];89 -> 108[label="",style="solid", color="black", weight=3]; 10.66/4.44 90[label="max1 (Char (Neg Zero)) (Char (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];90 -> 109[label="",style="solid", color="black", weight=3]; 10.66/4.44 91[label="max1 (Char (Neg Zero)) (Char (Neg (Succ vx310000))) (not MyTrue)",fontsize=16,color="black",shape="box"];91 -> 110[label="",style="solid", color="black", weight=3]; 10.66/4.44 92[label="max1 (Char (Neg Zero)) (Char (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];92 -> 111[label="",style="solid", color="black", weight=3]; 10.66/4.44 503[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat (Succ vx420) vx43) GT))",fontsize=16,color="burlywood",shape="box"];640[label="vx43/Succ vx430",fontsize=10,color="white",style="solid",shape="box"];503 -> 640[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 640 -> 509[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 641[label="vx43/Zero",fontsize=10,color="white",style="solid",shape="box"];503 -> 641[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 641 -> 510[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 504[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat Zero vx43) GT))",fontsize=16,color="burlywood",shape="box"];642[label="vx43/Succ vx430",fontsize=10,color="white",style="solid",shape="box"];504 -> 642[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 642 -> 511[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 643[label="vx43/Zero",fontsize=10,color="white",style="solid",shape="box"];504 -> 643[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 643 -> 512[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 97[label="max1 (Char (Pos (Succ vx30000))) (Char (Pos Zero)) MyFalse",fontsize=16,color="black",shape="box"];97 -> 116[label="",style="solid", color="black", weight=3]; 10.66/4.44 98[label="max0 (Char (Pos (Succ vx30000))) (Char (Neg vx31000)) MyTrue",fontsize=16,color="black",shape="box"];98 -> 117[label="",style="solid", color="black", weight=3]; 10.66/4.44 99[label="max1 (Char (Pos Zero)) (Char (Pos (Succ vx310000))) MyTrue",fontsize=16,color="black",shape="box"];99 -> 118[label="",style="solid", color="black", weight=3]; 10.66/4.44 100[label="Char (Pos Zero)",fontsize=16,color="green",shape="box"];101[label="max0 (Char (Pos Zero)) (Char (Neg (Succ vx310000))) otherwise",fontsize=16,color="black",shape="box"];101 -> 119[label="",style="solid", color="black", weight=3]; 10.66/4.44 102[label="Char (Neg Zero)",fontsize=16,color="green",shape="box"];577[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat (Succ vx510) vx52) GT))",fontsize=16,color="burlywood",shape="box"];644[label="vx52/Succ vx520",fontsize=10,color="white",style="solid",shape="box"];577 -> 644[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 644 -> 581[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 645[label="vx52/Zero",fontsize=10,color="white",style="solid",shape="box"];577 -> 645[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 645 -> 582[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 578[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat Zero vx52) GT))",fontsize=16,color="burlywood",shape="box"];646[label="vx52/Succ vx520",fontsize=10,color="white",style="solid",shape="box"];578 -> 646[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 646 -> 583[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 647[label="vx52/Zero",fontsize=10,color="white",style="solid",shape="box"];578 -> 647[label="",style="solid", color="burlywood", weight=9]; 10.66/4.44 647 -> 584[label="",style="solid", color="burlywood", weight=3]; 10.66/4.44 107[label="max1 (Char (Neg (Succ vx30000))) (Char (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];107 -> 124[label="",style="solid", color="black", weight=3]; 10.66/4.44 108[label="Char (Pos (Succ vx310000))",fontsize=16,color="green",shape="box"];109[label="Char (Pos Zero)",fontsize=16,color="green",shape="box"];110[label="max1 (Char (Neg Zero)) (Char (Neg (Succ vx310000))) MyFalse",fontsize=16,color="black",shape="box"];110 -> 125[label="",style="solid", color="black", weight=3]; 10.66/4.44 111[label="Char (Neg Zero)",fontsize=16,color="green",shape="box"];509[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat (Succ vx420) (Succ vx430)) GT))",fontsize=16,color="black",shape="box"];509 -> 517[label="",style="solid", color="black", weight=3]; 10.66/4.44 510[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat (Succ vx420) Zero) GT))",fontsize=16,color="black",shape="box"];510 -> 518[label="",style="solid", color="black", weight=3]; 10.66/4.44 511[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat Zero (Succ vx430)) GT))",fontsize=16,color="black",shape="box"];511 -> 519[label="",style="solid", color="black", weight=3]; 10.66/4.44 512[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat Zero Zero) GT))",fontsize=16,color="black",shape="box"];512 -> 520[label="",style="solid", color="black", weight=3]; 10.66/4.44 116[label="max0 (Char (Pos (Succ vx30000))) (Char (Pos Zero)) otherwise",fontsize=16,color="black",shape="box"];116 -> 131[label="",style="solid", color="black", weight=3]; 10.66/4.44 117[label="Char (Pos (Succ vx30000))",fontsize=16,color="green",shape="box"];118[label="Char (Pos (Succ vx310000))",fontsize=16,color="green",shape="box"];119[label="max0 (Char (Pos Zero)) (Char (Neg (Succ vx310000))) MyTrue",fontsize=16,color="black",shape="box"];119 -> 132[label="",style="solid", color="black", weight=3]; 10.66/4.44 581[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat (Succ vx510) (Succ vx520)) GT))",fontsize=16,color="black",shape="box"];581 -> 587[label="",style="solid", color="black", weight=3]; 10.66/4.44 582[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat (Succ vx510) Zero) GT))",fontsize=16,color="black",shape="box"];582 -> 588[label="",style="solid", color="black", weight=3]; 10.66/4.44 583[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat Zero (Succ vx520)) GT))",fontsize=16,color="black",shape="box"];583 -> 589[label="",style="solid", color="black", weight=3]; 10.66/4.44 584[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat Zero Zero) GT))",fontsize=16,color="black",shape="box"];584 -> 590[label="",style="solid", color="black", weight=3]; 10.66/4.44 124[label="Char (Neg Zero)",fontsize=16,color="green",shape="box"];125[label="max0 (Char (Neg Zero)) (Char (Neg (Succ vx310000))) otherwise",fontsize=16,color="black",shape="box"];125 -> 138[label="",style="solid", color="black", weight=3]; 10.66/4.44 517 -> 466[label="",style="dashed", color="red", weight=0]; 10.66/4.44 517[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering (primCmpNat vx420 vx430) GT))",fontsize=16,color="magenta"];517 -> 525[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 517 -> 526[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 518[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];518 -> 527[label="",style="solid", color="black", weight=3]; 10.66/4.44 519[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];519 -> 528[label="",style="solid", color="black", weight=3]; 10.66/4.44 520[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];520 -> 529[label="",style="solid", color="black", weight=3]; 10.66/4.44 131[label="max0 (Char (Pos (Succ vx30000))) (Char (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];131 -> 146[label="",style="solid", color="black", weight=3]; 10.66/4.44 132[label="Char (Pos Zero)",fontsize=16,color="green",shape="box"];587 -> 536[label="",style="dashed", color="red", weight=0]; 10.66/4.44 587[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering (primCmpNat vx510 vx520) GT))",fontsize=16,color="magenta"];587 -> 592[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 587 -> 593[label="",style="dashed", color="magenta", weight=3]; 10.66/4.44 588[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];588 -> 594[label="",style="solid", color="black", weight=3]; 10.66/4.44 589[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];589 -> 595[label="",style="solid", color="black", weight=3]; 10.66/4.44 590[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];590 -> 596[label="",style="solid", color="black", weight=3]; 10.66/4.44 138[label="max0 (Char (Neg Zero)) (Char (Neg (Succ vx310000))) MyTrue",fontsize=16,color="black",shape="box"];138 -> 154[label="",style="solid", color="black", weight=3]; 10.66/4.44 525[label="vx420",fontsize=16,color="green",shape="box"];526[label="vx430",fontsize=16,color="green",shape="box"];527[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not MyTrue)",fontsize=16,color="black",shape="box"];527 -> 579[label="",style="solid", color="black", weight=3]; 10.66/4.44 528[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not MyFalse)",fontsize=16,color="black",shape="triangle"];528 -> 580[label="",style="solid", color="black", weight=3]; 10.66/4.44 529 -> 528[label="",style="dashed", color="red", weight=0]; 10.66/4.44 529[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) (not MyFalse)",fontsize=16,color="magenta"];146[label="Char (Pos (Succ vx30000))",fontsize=16,color="green",shape="box"];592[label="vx510",fontsize=16,color="green",shape="box"];593[label="vx520",fontsize=16,color="green",shape="box"];594[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not MyTrue)",fontsize=16,color="black",shape="box"];594 -> 598[label="",style="solid", color="black", weight=3]; 10.66/4.44 595[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not MyFalse)",fontsize=16,color="black",shape="triangle"];595 -> 599[label="",style="solid", color="black", weight=3]; 10.66/4.44 596 -> 595[label="",style="dashed", color="red", weight=0]; 10.66/4.44 596[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) (not MyFalse)",fontsize=16,color="magenta"];154[label="Char (Neg Zero)",fontsize=16,color="green",shape="box"];579[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) MyFalse",fontsize=16,color="black",shape="box"];579 -> 585[label="",style="solid", color="black", weight=3]; 10.66/4.44 580[label="max1 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) MyTrue",fontsize=16,color="black",shape="box"];580 -> 586[label="",style="solid", color="black", weight=3]; 10.66/4.44 598[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) MyFalse",fontsize=16,color="black",shape="box"];598 -> 600[label="",style="solid", color="black", weight=3]; 10.66/4.44 599[label="max1 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) MyTrue",fontsize=16,color="black",shape="box"];599 -> 601[label="",style="solid", color="black", weight=3]; 10.66/4.44 585[label="max0 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) otherwise",fontsize=16,color="black",shape="box"];585 -> 591[label="",style="solid", color="black", weight=3]; 10.66/4.44 586[label="Char (Pos (Succ vx41))",fontsize=16,color="green",shape="box"];600[label="max0 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) otherwise",fontsize=16,color="black",shape="box"];600 -> 602[label="",style="solid", color="black", weight=3]; 10.66/4.44 601[label="Char (Neg (Succ vx50))",fontsize=16,color="green",shape="box"];591[label="max0 (Char (Pos (Succ vx40))) (Char (Pos (Succ vx41))) MyTrue",fontsize=16,color="black",shape="box"];591 -> 597[label="",style="solid", color="black", weight=3]; 10.66/4.44 602[label="max0 (Char (Neg (Succ vx49))) (Char (Neg (Succ vx50))) MyTrue",fontsize=16,color="black",shape="box"];602 -> 603[label="",style="solid", color="black", weight=3]; 10.66/4.44 597[label="Char (Pos (Succ vx40))",fontsize=16,color="green",shape="box"];603[label="Char (Neg (Succ vx49))",fontsize=16,color="green",shape="box"];} 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (6) 10.66/4.44 Complex Obligation (AND) 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (7) 10.66/4.44 Obligation: 10.66/4.44 Q DP problem: 10.66/4.44 The TRS P consists of the following rules: 10.66/4.44 10.66/4.44 new_max1(vx49, vx50, Main.Succ(vx510), Main.Succ(vx520)) -> new_max1(vx49, vx50, vx510, vx520) 10.66/4.44 10.66/4.44 R is empty. 10.66/4.44 Q is empty. 10.66/4.44 We have to consider all minimal (P,Q,R)-chains. 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (8) QDPSizeChangeProof (EQUIVALENT) 10.66/4.44 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. 10.66/4.44 10.66/4.44 From the DPs we obtained the following set of size-change graphs: 10.66/4.44 *new_max1(vx49, vx50, Main.Succ(vx510), Main.Succ(vx520)) -> new_max1(vx49, vx50, vx510, vx520) 10.66/4.44 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 10.66/4.44 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (9) 10.66/4.44 YES 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (10) 10.66/4.44 Obligation: 10.66/4.44 Q DP problem: 10.66/4.44 The TRS P consists of the following rules: 10.66/4.44 10.66/4.44 new_max10(vx40, vx41, Main.Succ(vx420), Main.Succ(vx430)) -> new_max10(vx40, vx41, vx420, vx430) 10.66/4.44 10.66/4.44 R is empty. 10.66/4.44 Q is empty. 10.66/4.44 We have to consider all minimal (P,Q,R)-chains. 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (11) QDPSizeChangeProof (EQUIVALENT) 10.66/4.44 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. 10.66/4.44 10.66/4.44 From the DPs we obtained the following set of size-change graphs: 10.66/4.44 *new_max10(vx40, vx41, Main.Succ(vx420), Main.Succ(vx430)) -> new_max10(vx40, vx41, vx420, vx430) 10.66/4.44 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 10.66/4.44 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (12) 10.66/4.44 YES 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (13) 10.66/4.44 Obligation: 10.66/4.44 Q DP problem: 10.66/4.44 The TRS P consists of the following rules: 10.66/4.44 10.66/4.44 new_foldl(vx30, Cons(vx310, vx311)) -> new_foldl(new_max11(vx30, vx310), vx311) 10.66/4.44 10.66/4.44 The TRS R consists of the following rules: 10.66/4.44 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Succ(vx30000))), Main.Char(Main.Neg(Main.Succ(vx310000)))) -> new_max13(vx30000, vx310000, vx310000, vx30000) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Pos(Main.Succ(vx310000)))) -> Main.Char(Main.Pos(Main.Succ(vx310000))) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Succ(vx30000))), Main.Char(Main.Pos(vx31000))) -> Main.Char(Main.Pos(vx31000)) 10.66/4.44 new_max13(vx49, vx50, Main.Succ(vx510), Main.Zero) -> Main.Char(Main.Neg(Main.Succ(vx49))) 10.66/4.44 new_max12(vx40, vx41, Main.Succ(vx420), Main.Succ(vx430)) -> new_max12(vx40, vx41, vx420, vx430) 10.66/4.44 new_max13(vx49, vx50, Main.Zero, Main.Succ(vx520)) -> new_max15(vx49, vx50) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Neg(Main.Zero))) -> Main.Char(Main.Neg(Main.Zero)) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Succ(vx30000))), Main.Char(Main.Pos(Main.Succ(vx310000)))) -> new_max12(vx30000, vx310000, vx30000, vx310000) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Pos(Main.Zero))) -> Main.Char(Main.Pos(Main.Zero)) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Succ(vx30000))), Main.Char(Main.Neg(Main.Zero))) -> Main.Char(Main.Neg(Main.Zero)) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Neg(Main.Succ(vx310000)))) -> Main.Char(Main.Neg(Main.Zero)) 10.66/4.44 new_max12(vx40, vx41, Main.Succ(vx420), Main.Zero) -> Main.Char(Main.Pos(Main.Succ(vx40))) 10.66/4.44 new_max12(vx40, vx41, Main.Zero, Main.Succ(vx430)) -> new_max14(vx40, vx41) 10.66/4.44 new_max13(vx49, vx50, Main.Zero, Main.Zero) -> new_max15(vx49, vx50) 10.66/4.44 new_max12(vx40, vx41, Main.Zero, Main.Zero) -> new_max14(vx40, vx41) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Pos(Main.Zero))) -> Main.Char(Main.Pos(Main.Zero)) 10.66/4.44 new_max14(vx40, vx41) -> Main.Char(Main.Pos(Main.Succ(vx41))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Succ(vx30000))), Main.Char(Main.Pos(Main.Zero))) -> Main.Char(Main.Pos(Main.Succ(vx30000))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Pos(Main.Succ(vx310000)))) -> Main.Char(Main.Pos(Main.Succ(vx310000))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Neg(Main.Zero))) -> Main.Char(Main.Neg(Main.Zero)) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Neg(Main.Succ(vx310000)))) -> Main.Char(Main.Pos(Main.Zero)) 10.66/4.44 new_max13(vx49, vx50, Main.Succ(vx510), Main.Succ(vx520)) -> new_max13(vx49, vx50, vx510, vx520) 10.66/4.44 new_max15(vx49, vx50) -> Main.Char(Main.Neg(Main.Succ(vx50))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Succ(vx30000))), Main.Char(Main.Neg(vx31000))) -> Main.Char(Main.Pos(Main.Succ(vx30000))) 10.66/4.44 10.66/4.44 The set Q consists of the following terms: 10.66/4.44 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Succ(x0))), Main.Char(Main.Neg(Main.Zero))) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Neg(Main.Zero))) 10.66/4.44 new_max13(x0, x1, Main.Succ(x2), Main.Succ(x3)) 10.66/4.44 new_max13(x0, x1, Main.Succ(x2), Main.Zero) 10.66/4.44 new_max13(x0, x1, Main.Zero, Main.Zero) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Pos(Main.Succ(x0)))) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Pos(Main.Succ(x0)))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Neg(Main.Succ(x0)))) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Neg(Main.Succ(x0)))) 10.66/4.44 new_max12(x0, x1, Main.Zero, Main.Succ(x2)) 10.66/4.44 new_max12(x0, x1, Main.Succ(x2), Main.Succ(x3)) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Succ(x0))), Main.Char(Main.Pos(x1))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Succ(x0))), Main.Char(Main.Neg(x1))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Pos(Main.Zero))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Succ(x0))), Main.Char(Main.Pos(Main.Zero))) 10.66/4.44 new_max12(x0, x1, Main.Zero, Main.Zero) 10.66/4.44 new_max14(x0, x1) 10.66/4.44 new_max13(x0, x1, Main.Zero, Main.Succ(x2)) 10.66/4.44 new_max12(x0, x1, Main.Succ(x2), Main.Zero) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Succ(x0))), Main.Char(Main.Neg(Main.Succ(x1)))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Succ(x0))), Main.Char(Main.Pos(Main.Succ(x1)))) 10.66/4.44 new_max15(x0, x1) 10.66/4.44 new_max11(Main.Char(Main.Neg(Main.Zero)), Main.Char(Main.Pos(Main.Zero))) 10.66/4.44 new_max11(Main.Char(Main.Pos(Main.Zero)), Main.Char(Main.Neg(Main.Zero))) 10.66/4.44 10.66/4.44 We have to consider all minimal (P,Q,R)-chains. 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (14) QDPSizeChangeProof (EQUIVALENT) 10.66/4.44 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. 10.66/4.44 10.66/4.44 From the DPs we obtained the following set of size-change graphs: 10.66/4.44 *new_foldl(vx30, Cons(vx310, vx311)) -> new_foldl(new_max11(vx30, vx310), vx311) 10.66/4.44 The graph contains the following edges 2 > 2 10.66/4.44 10.66/4.44 10.66/4.44 ---------------------------------------- 10.66/4.44 10.66/4.44 (15) 10.66/4.44 YES 10.89/4.48 EOF