8.25/3.79 YES 10.38/4.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 10.38/4.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.38/4.31 10.38/4.31 10.38/4.31 H-Termination with start terms of the given HASKELL could be proven: 10.38/4.31 10.38/4.31 (0) HASKELL 10.38/4.31 (1) BR [EQUIVALENT, 0 ms] 10.38/4.31 (2) HASKELL 10.38/4.31 (3) COR [EQUIVALENT, 0 ms] 10.38/4.31 (4) HASKELL 10.38/4.31 (5) Narrow [SOUND, 0 ms] 10.38/4.31 (6) AND 10.38/4.31 (7) QDP 10.38/4.31 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.38/4.31 (9) YES 10.38/4.31 (10) QDP 10.38/4.31 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.38/4.31 (12) YES 10.38/4.31 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (0) 10.38/4.31 Obligation: 10.38/4.31 mainModule Main 10.38/4.31 module Main where { 10.38/4.31 import qualified Prelude; 10.38/4.31 data Main.Char = Char MyInt ; 10.38/4.31 10.38/4.31 data MyBool = MyTrue | MyFalse ; 10.38/4.31 10.38/4.31 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.38/4.31 10.38/4.31 data Main.Nat = Succ Main.Nat | Zero ; 10.38/4.31 10.38/4.31 data Ordering = LT | EQ | GT ; 10.38/4.31 10.38/4.31 compareChar :: Main.Char -> Main.Char -> Ordering; 10.38/4.31 compareChar = primCmpChar; 10.38/4.31 10.38/4.31 esEsOrdering :: Ordering -> Ordering -> MyBool; 10.38/4.31 esEsOrdering LT LT = MyTrue; 10.38/4.31 esEsOrdering LT EQ = MyFalse; 10.38/4.31 esEsOrdering LT GT = MyFalse; 10.38/4.31 esEsOrdering EQ LT = MyFalse; 10.38/4.31 esEsOrdering EQ EQ = MyTrue; 10.38/4.31 esEsOrdering EQ GT = MyFalse; 10.38/4.31 esEsOrdering GT LT = MyFalse; 10.38/4.31 esEsOrdering GT EQ = MyFalse; 10.38/4.31 esEsOrdering GT GT = MyTrue; 10.38/4.31 10.38/4.31 fsEsOrdering :: Ordering -> Ordering -> MyBool; 10.38/4.31 fsEsOrdering x y = not (esEsOrdering x y); 10.38/4.31 10.38/4.31 ltEsChar :: Main.Char -> Main.Char -> MyBool; 10.38/4.31 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 10.38/4.31 10.38/4.31 min0 x y MyTrue = y; 10.38/4.31 10.38/4.31 min1 x y MyTrue = x; 10.38/4.31 min1 x y MyFalse = min0 x y otherwise; 10.38/4.31 10.38/4.31 min2 x y = min1 x y (ltEsChar x y); 10.38/4.31 10.38/4.31 minChar :: Main.Char -> Main.Char -> Main.Char; 10.38/4.31 minChar x y = min2 x y; 10.38/4.31 10.38/4.31 not :: MyBool -> MyBool; 10.38/4.31 not MyTrue = MyFalse; 10.38/4.31 not MyFalse = MyTrue; 10.38/4.31 10.38/4.31 otherwise :: MyBool; 10.38/4.31 otherwise = MyTrue; 10.38/4.31 10.38/4.31 primCmpChar :: Main.Char -> Main.Char -> Ordering; 10.38/4.31 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 10.38/4.31 10.38/4.31 primCmpInt :: MyInt -> MyInt -> Ordering; 10.38/4.31 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 10.38/4.31 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 10.38/4.31 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 10.38/4.31 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 10.38/4.31 10.38/4.31 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 10.38/4.31 primCmpNat Main.Zero Main.Zero = EQ; 10.38/4.31 primCmpNat Main.Zero (Main.Succ y) = LT; 10.38/4.31 primCmpNat (Main.Succ x) Main.Zero = GT; 10.38/4.31 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 10.38/4.31 10.38/4.31 } 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (1) BR (EQUIVALENT) 10.38/4.31 Replaced joker patterns by fresh variables and removed binding patterns. 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (2) 10.38/4.31 Obligation: 10.38/4.31 mainModule Main 10.38/4.31 module Main where { 10.38/4.31 import qualified Prelude; 10.38/4.31 data Main.Char = Char MyInt ; 10.38/4.31 10.38/4.31 data MyBool = MyTrue | MyFalse ; 10.38/4.31 10.38/4.31 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.38/4.31 10.38/4.31 data Main.Nat = Succ Main.Nat | Zero ; 10.38/4.31 10.38/4.31 data Ordering = LT | EQ | GT ; 10.38/4.31 10.38/4.31 compareChar :: Main.Char -> Main.Char -> Ordering; 10.38/4.31 compareChar = primCmpChar; 10.38/4.31 10.38/4.31 esEsOrdering :: Ordering -> Ordering -> MyBool; 10.38/4.31 esEsOrdering LT LT = MyTrue; 10.38/4.31 esEsOrdering LT EQ = MyFalse; 10.38/4.31 esEsOrdering LT GT = MyFalse; 10.38/4.31 esEsOrdering EQ LT = MyFalse; 10.38/4.31 esEsOrdering EQ EQ = MyTrue; 10.38/4.31 esEsOrdering EQ GT = MyFalse; 10.38/4.31 esEsOrdering GT LT = MyFalse; 10.38/4.31 esEsOrdering GT EQ = MyFalse; 10.38/4.31 esEsOrdering GT GT = MyTrue; 10.38/4.31 10.38/4.31 fsEsOrdering :: Ordering -> Ordering -> MyBool; 10.38/4.31 fsEsOrdering x y = not (esEsOrdering x y); 10.38/4.31 10.38/4.31 ltEsChar :: Main.Char -> Main.Char -> MyBool; 10.38/4.31 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 10.38/4.31 10.38/4.31 min0 x y MyTrue = y; 10.38/4.31 10.38/4.31 min1 x y MyTrue = x; 10.38/4.31 min1 x y MyFalse = min0 x y otherwise; 10.38/4.31 10.38/4.31 min2 x y = min1 x y (ltEsChar x y); 10.38/4.31 10.38/4.31 minChar :: Main.Char -> Main.Char -> Main.Char; 10.38/4.31 minChar x y = min2 x y; 10.38/4.31 10.38/4.31 not :: MyBool -> MyBool; 10.38/4.31 not MyTrue = MyFalse; 10.38/4.31 not MyFalse = MyTrue; 10.38/4.31 10.38/4.31 otherwise :: MyBool; 10.38/4.31 otherwise = MyTrue; 10.38/4.31 10.38/4.31 primCmpChar :: Main.Char -> Main.Char -> Ordering; 10.38/4.31 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 10.38/4.31 10.38/4.31 primCmpInt :: MyInt -> MyInt -> Ordering; 10.38/4.31 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 10.38/4.31 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 10.38/4.31 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 10.38/4.31 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 10.38/4.31 10.38/4.31 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 10.38/4.31 primCmpNat Main.Zero Main.Zero = EQ; 10.38/4.31 primCmpNat Main.Zero (Main.Succ y) = LT; 10.38/4.31 primCmpNat (Main.Succ x) Main.Zero = GT; 10.38/4.31 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 10.38/4.31 10.38/4.31 } 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (3) COR (EQUIVALENT) 10.38/4.31 Cond Reductions: 10.38/4.31 The following Function with conditions 10.38/4.31 "undefined |Falseundefined; 10.38/4.31 " 10.38/4.31 is transformed to 10.38/4.31 "undefined = undefined1; 10.38/4.31 " 10.38/4.31 "undefined0 True = undefined; 10.38/4.31 " 10.38/4.31 "undefined1 = undefined0 False; 10.38/4.31 " 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (4) 10.38/4.31 Obligation: 10.38/4.31 mainModule Main 10.38/4.31 module Main where { 10.38/4.31 import qualified Prelude; 10.38/4.31 data Main.Char = Char MyInt ; 10.38/4.31 10.38/4.31 data MyBool = MyTrue | MyFalse ; 10.38/4.31 10.38/4.31 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.38/4.31 10.38/4.31 data Main.Nat = Succ Main.Nat | Zero ; 10.38/4.31 10.38/4.31 data Ordering = LT | EQ | GT ; 10.38/4.31 10.38/4.31 compareChar :: Main.Char -> Main.Char -> Ordering; 10.38/4.31 compareChar = primCmpChar; 10.38/4.31 10.38/4.31 esEsOrdering :: Ordering -> Ordering -> MyBool; 10.38/4.31 esEsOrdering LT LT = MyTrue; 10.38/4.31 esEsOrdering LT EQ = MyFalse; 10.38/4.31 esEsOrdering LT GT = MyFalse; 10.38/4.31 esEsOrdering EQ LT = MyFalse; 10.38/4.31 esEsOrdering EQ EQ = MyTrue; 10.38/4.31 esEsOrdering EQ GT = MyFalse; 10.38/4.31 esEsOrdering GT LT = MyFalse; 10.38/4.31 esEsOrdering GT EQ = MyFalse; 10.38/4.31 esEsOrdering GT GT = MyTrue; 10.38/4.31 10.38/4.31 fsEsOrdering :: Ordering -> Ordering -> MyBool; 10.38/4.31 fsEsOrdering x y = not (esEsOrdering x y); 10.38/4.31 10.38/4.31 ltEsChar :: Main.Char -> Main.Char -> MyBool; 10.38/4.31 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 10.38/4.31 10.38/4.31 min0 x y MyTrue = y; 10.38/4.31 10.38/4.31 min1 x y MyTrue = x; 10.38/4.31 min1 x y MyFalse = min0 x y otherwise; 10.38/4.31 10.38/4.31 min2 x y = min1 x y (ltEsChar x y); 10.38/4.31 10.38/4.31 minChar :: Main.Char -> Main.Char -> Main.Char; 10.38/4.31 minChar x y = min2 x y; 10.38/4.31 10.38/4.31 not :: MyBool -> MyBool; 10.38/4.31 not MyTrue = MyFalse; 10.38/4.31 not MyFalse = MyTrue; 10.38/4.31 10.38/4.31 otherwise :: MyBool; 10.38/4.31 otherwise = MyTrue; 10.38/4.31 10.38/4.31 primCmpChar :: Main.Char -> Main.Char -> Ordering; 10.38/4.31 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 10.38/4.31 10.38/4.31 primCmpInt :: MyInt -> MyInt -> Ordering; 10.38/4.31 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 10.38/4.31 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 10.38/4.31 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 10.38/4.31 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 10.38/4.31 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 10.38/4.31 10.38/4.31 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 10.38/4.31 primCmpNat Main.Zero Main.Zero = EQ; 10.38/4.31 primCmpNat Main.Zero (Main.Succ y) = LT; 10.38/4.31 primCmpNat (Main.Succ x) Main.Zero = GT; 10.38/4.31 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 10.38/4.31 10.38/4.31 } 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (5) Narrow (SOUND) 10.38/4.31 Haskell To QDPs 10.38/4.31 10.38/4.31 digraph dp_graph { 10.38/4.31 node [outthreshold=100, inthreshold=100];1[label="minChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.38/4.31 3[label="minChar vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 10.38/4.31 4[label="minChar vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 10.38/4.31 5[label="min2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 10.38/4.31 6[label="min1 vx3 vx4 (ltEsChar vx3 vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 10.38/4.31 7[label="min1 vx3 vx4 (fsEsOrdering (compareChar vx3 vx4) GT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 10.38/4.31 8[label="min1 vx3 vx4 (not (esEsOrdering (compareChar vx3 vx4) GT))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 10.38/4.31 9[label="min1 vx3 vx4 (not (esEsOrdering (primCmpChar vx3 vx4) GT))",fontsize=16,color="burlywood",shape="box"];594[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];9 -> 594[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 594 -> 10[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 10[label="min1 (Char vx30) vx4 (not (esEsOrdering (primCmpChar (Char vx30) vx4) GT))",fontsize=16,color="burlywood",shape="box"];595[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];10 -> 595[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 595 -> 11[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 11[label="min1 (Char vx30) (Char vx40) (not (esEsOrdering (primCmpChar (Char vx30) (Char vx40)) GT))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 10.38/4.31 12[label="min1 (Char vx30) (Char vx40) (not (esEsOrdering (primCmpInt vx30 vx40) GT))",fontsize=16,color="burlywood",shape="box"];596[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];12 -> 596[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 596 -> 13[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 597[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];12 -> 597[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 597 -> 14[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 13[label="min1 (Char (Pos vx300)) (Char vx40) (not (esEsOrdering (primCmpInt (Pos vx300) vx40) GT))",fontsize=16,color="burlywood",shape="box"];598[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];13 -> 598[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 598 -> 15[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 599[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 599[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 599 -> 16[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 14[label="min1 (Char (Neg vx300)) (Char vx40) (not (esEsOrdering (primCmpInt (Neg vx300) vx40) GT))",fontsize=16,color="burlywood",shape="box"];600[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];14 -> 600[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 600 -> 17[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 601[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 601[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 601 -> 18[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 15[label="min1 (Char (Pos (Succ vx3000))) (Char vx40) (not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) vx40) GT))",fontsize=16,color="burlywood",shape="box"];602[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];15 -> 602[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 602 -> 19[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 603[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];15 -> 603[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 603 -> 20[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 16[label="min1 (Char (Pos Zero)) (Char vx40) (not (esEsOrdering (primCmpInt (Pos Zero) vx40) GT))",fontsize=16,color="burlywood",shape="box"];604[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];16 -> 604[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 604 -> 21[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 605[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];16 -> 605[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 605 -> 22[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 17[label="min1 (Char (Neg (Succ vx3000))) (Char vx40) (not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) vx40) GT))",fontsize=16,color="burlywood",shape="box"];606[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];17 -> 606[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 606 -> 23[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 607[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];17 -> 607[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 607 -> 24[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 18[label="min1 (Char (Neg Zero)) (Char vx40) (not (esEsOrdering (primCmpInt (Neg Zero) vx40) GT))",fontsize=16,color="burlywood",shape="box"];608[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];18 -> 608[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 608 -> 25[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 609[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];18 -> 609[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 609 -> 26[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 19[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos vx400)) (not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) (Pos vx400)) GT))",fontsize=16,color="black",shape="box"];19 -> 27[label="",style="solid", color="black", weight=3]; 10.38/4.31 20[label="min1 (Char (Pos (Succ vx3000))) (Char (Neg vx400)) (not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) (Neg vx400)) GT))",fontsize=16,color="black",shape="box"];20 -> 28[label="",style="solid", color="black", weight=3]; 10.38/4.31 21[label="min1 (Char (Pos Zero)) (Char (Pos vx400)) (not (esEsOrdering (primCmpInt (Pos Zero) (Pos vx400)) GT))",fontsize=16,color="burlywood",shape="box"];610[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];21 -> 610[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 610 -> 29[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 611[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 611[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 611 -> 30[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 22[label="min1 (Char (Pos Zero)) (Char (Neg vx400)) (not (esEsOrdering (primCmpInt (Pos Zero) (Neg vx400)) GT))",fontsize=16,color="burlywood",shape="box"];612[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];22 -> 612[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 612 -> 31[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 613[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 613[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 613 -> 32[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 23[label="min1 (Char (Neg (Succ vx3000))) (Char (Pos vx400)) (not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) (Pos vx400)) GT))",fontsize=16,color="black",shape="box"];23 -> 33[label="",style="solid", color="black", weight=3]; 10.38/4.31 24[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg vx400)) (not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) (Neg vx400)) GT))",fontsize=16,color="black",shape="box"];24 -> 34[label="",style="solid", color="black", weight=3]; 10.38/4.31 25[label="min1 (Char (Neg Zero)) (Char (Pos vx400)) (not (esEsOrdering (primCmpInt (Neg Zero) (Pos vx400)) GT))",fontsize=16,color="burlywood",shape="box"];614[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 614[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 614 -> 35[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 615[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 615[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 615 -> 36[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 26[label="min1 (Char (Neg Zero)) (Char (Neg vx400)) (not (esEsOrdering (primCmpInt (Neg Zero) (Neg vx400)) GT))",fontsize=16,color="burlywood",shape="box"];616[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 616[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 616 -> 37[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 617[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 617[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 617 -> 38[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 27[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos vx400)) (not (esEsOrdering (primCmpNat (Succ vx3000) vx400) GT))",fontsize=16,color="burlywood",shape="box"];618[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 618[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 618 -> 39[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 619[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 619[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 619 -> 40[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 28[label="min1 (Char (Pos (Succ vx3000))) (Char (Neg vx400)) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];28 -> 41[label="",style="solid", color="black", weight=3]; 10.38/4.31 29[label="min1 (Char (Pos Zero)) (Char (Pos (Succ vx4000))) (not (esEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vx4000))) GT))",fontsize=16,color="black",shape="box"];29 -> 42[label="",style="solid", color="black", weight=3]; 10.38/4.31 30[label="min1 (Char (Pos Zero)) (Char (Pos Zero)) (not (esEsOrdering (primCmpInt (Pos Zero) (Pos Zero)) GT))",fontsize=16,color="black",shape="box"];30 -> 43[label="",style="solid", color="black", weight=3]; 10.38/4.31 31[label="min1 (Char (Pos Zero)) (Char (Neg (Succ vx4000))) (not (esEsOrdering (primCmpInt (Pos Zero) (Neg (Succ vx4000))) GT))",fontsize=16,color="black",shape="box"];31 -> 44[label="",style="solid", color="black", weight=3]; 10.38/4.31 32[label="min1 (Char (Pos Zero)) (Char (Neg Zero)) (not (esEsOrdering (primCmpInt (Pos Zero) (Neg Zero)) GT))",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3]; 10.38/4.31 33[label="min1 (Char (Neg (Succ vx3000))) (Char (Pos vx400)) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3]; 10.38/4.31 34[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg vx400)) (not (esEsOrdering (primCmpNat vx400 (Succ vx3000)) GT))",fontsize=16,color="burlywood",shape="box"];620[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];34 -> 620[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 620 -> 47[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 621[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 621[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 621 -> 48[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 35[label="min1 (Char (Neg Zero)) (Char (Pos (Succ vx4000))) (not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vx4000))) GT))",fontsize=16,color="black",shape="box"];35 -> 49[label="",style="solid", color="black", weight=3]; 10.38/4.31 36[label="min1 (Char (Neg Zero)) (Char (Pos Zero)) (not (esEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) GT))",fontsize=16,color="black",shape="box"];36 -> 50[label="",style="solid", color="black", weight=3]; 10.38/4.31 37[label="min1 (Char (Neg Zero)) (Char (Neg (Succ vx4000))) (not (esEsOrdering (primCmpInt (Neg Zero) (Neg (Succ vx4000))) GT))",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3]; 10.38/4.31 38[label="min1 (Char (Neg Zero)) (Char (Neg Zero)) (not (esEsOrdering (primCmpInt (Neg Zero) (Neg Zero)) GT))",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3]; 10.38/4.31 39[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos (Succ vx4000))) (not (esEsOrdering (primCmpNat (Succ vx3000) (Succ vx4000)) GT))",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3]; 10.38/4.31 40[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos Zero)) (not (esEsOrdering (primCmpNat (Succ vx3000) Zero) GT))",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3]; 10.38/4.31 41[label="min1 (Char (Pos (Succ vx3000))) (Char (Neg vx400)) (not MyTrue)",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3]; 10.38/4.31 42[label="min1 (Char (Pos Zero)) (Char (Pos (Succ vx4000))) (not (esEsOrdering (primCmpNat Zero (Succ vx4000)) GT))",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3]; 10.38/4.31 43[label="min1 (Char (Pos Zero)) (Char (Pos Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3]; 10.38/4.31 44[label="min1 (Char (Pos Zero)) (Char (Neg (Succ vx4000))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];44 -> 58[label="",style="solid", color="black", weight=3]; 10.38/4.31 45[label="min1 (Char (Pos Zero)) (Char (Neg Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];45 -> 59[label="",style="solid", color="black", weight=3]; 10.38/4.31 46[label="min1 (Char (Neg (Succ vx3000))) (Char (Pos vx400)) (not MyFalse)",fontsize=16,color="black",shape="box"];46 -> 60[label="",style="solid", color="black", weight=3]; 10.38/4.31 47[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg (Succ vx4000))) (not (esEsOrdering (primCmpNat (Succ vx4000) (Succ vx3000)) GT))",fontsize=16,color="black",shape="box"];47 -> 61[label="",style="solid", color="black", weight=3]; 10.38/4.31 48[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg Zero)) (not (esEsOrdering (primCmpNat Zero (Succ vx3000)) GT))",fontsize=16,color="black",shape="box"];48 -> 62[label="",style="solid", color="black", weight=3]; 10.38/4.31 49[label="min1 (Char (Neg Zero)) (Char (Pos (Succ vx4000))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];49 -> 63[label="",style="solid", color="black", weight=3]; 10.38/4.31 50[label="min1 (Char (Neg Zero)) (Char (Pos Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];50 -> 64[label="",style="solid", color="black", weight=3]; 10.38/4.31 51[label="min1 (Char (Neg Zero)) (Char (Neg (Succ vx4000))) (not (esEsOrdering (primCmpNat (Succ vx4000) Zero) GT))",fontsize=16,color="black",shape="box"];51 -> 65[label="",style="solid", color="black", weight=3]; 10.38/4.31 52[label="min1 (Char (Neg Zero)) (Char (Neg Zero)) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];52 -> 66[label="",style="solid", color="black", weight=3]; 10.38/4.31 53 -> 456[label="",style="dashed", color="red", weight=0]; 10.38/4.31 53[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos (Succ vx4000))) (not (esEsOrdering (primCmpNat vx3000 vx4000) GT))",fontsize=16,color="magenta"];53 -> 457[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 53 -> 458[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 53 -> 459[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 53 -> 460[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 54[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos Zero)) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];54 -> 69[label="",style="solid", color="black", weight=3]; 10.38/4.31 55[label="min1 (Char (Pos (Succ vx3000))) (Char (Neg vx400)) MyFalse",fontsize=16,color="black",shape="box"];55 -> 70[label="",style="solid", color="black", weight=3]; 10.38/4.31 56[label="min1 (Char (Pos Zero)) (Char (Pos (Succ vx4000))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];56 -> 71[label="",style="solid", color="black", weight=3]; 10.38/4.31 57[label="min1 (Char (Pos Zero)) (Char (Pos Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];57 -> 72[label="",style="solid", color="black", weight=3]; 10.38/4.31 58[label="min1 (Char (Pos Zero)) (Char (Neg (Succ vx4000))) (not MyTrue)",fontsize=16,color="black",shape="box"];58 -> 73[label="",style="solid", color="black", weight=3]; 10.38/4.31 59[label="min1 (Char (Pos Zero)) (Char (Neg Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];59 -> 74[label="",style="solid", color="black", weight=3]; 10.38/4.31 60[label="min1 (Char (Neg (Succ vx3000))) (Char (Pos vx400)) MyTrue",fontsize=16,color="black",shape="box"];60 -> 75[label="",style="solid", color="black", weight=3]; 10.38/4.31 61 -> 526[label="",style="dashed", color="red", weight=0]; 10.38/4.31 61[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg (Succ vx4000))) (not (esEsOrdering (primCmpNat vx4000 vx3000) GT))",fontsize=16,color="magenta"];61 -> 527[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 61 -> 528[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 61 -> 529[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 61 -> 530[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 62[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg Zero)) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];62 -> 78[label="",style="solid", color="black", weight=3]; 10.38/4.31 63[label="min1 (Char (Neg Zero)) (Char (Pos (Succ vx4000))) (not MyFalse)",fontsize=16,color="black",shape="box"];63 -> 79[label="",style="solid", color="black", weight=3]; 10.38/4.31 64[label="min1 (Char (Neg Zero)) (Char (Pos Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];64 -> 80[label="",style="solid", color="black", weight=3]; 10.38/4.31 65[label="min1 (Char (Neg Zero)) (Char (Neg (Succ vx4000))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];65 -> 81[label="",style="solid", color="black", weight=3]; 10.38/4.31 66[label="min1 (Char (Neg Zero)) (Char (Neg Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];66 -> 82[label="",style="solid", color="black", weight=3]; 10.38/4.31 457[label="vx3000",fontsize=16,color="green",shape="box"];458[label="vx4000",fontsize=16,color="green",shape="box"];459[label="vx3000",fontsize=16,color="green",shape="box"];460[label="vx4000",fontsize=16,color="green",shape="box"];456[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat vx43 vx44) GT))",fontsize=16,color="burlywood",shape="triangle"];622[label="vx43/Succ vx430",fontsize=10,color="white",style="solid",shape="box"];456 -> 622[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 622 -> 493[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 623[label="vx43/Zero",fontsize=10,color="white",style="solid",shape="box"];456 -> 623[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 623 -> 494[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 69[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos Zero)) (not MyTrue)",fontsize=16,color="black",shape="box"];69 -> 87[label="",style="solid", color="black", weight=3]; 10.38/4.31 70[label="min0 (Char (Pos (Succ vx3000))) (Char (Neg vx400)) otherwise",fontsize=16,color="black",shape="box"];70 -> 88[label="",style="solid", color="black", weight=3]; 10.38/4.31 71[label="min1 (Char (Pos Zero)) (Char (Pos (Succ vx4000))) (not MyFalse)",fontsize=16,color="black",shape="box"];71 -> 89[label="",style="solid", color="black", weight=3]; 10.38/4.31 72[label="min1 (Char (Pos Zero)) (Char (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];72 -> 90[label="",style="solid", color="black", weight=3]; 10.38/4.31 73[label="min1 (Char (Pos Zero)) (Char (Neg (Succ vx4000))) MyFalse",fontsize=16,color="black",shape="box"];73 -> 91[label="",style="solid", color="black", weight=3]; 10.38/4.31 74[label="min1 (Char (Pos Zero)) (Char (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];74 -> 92[label="",style="solid", color="black", weight=3]; 10.38/4.31 75[label="Char (Neg (Succ vx3000))",fontsize=16,color="green",shape="box"];527[label="vx4000",fontsize=16,color="green",shape="box"];528[label="vx3000",fontsize=16,color="green",shape="box"];529[label="vx3000",fontsize=16,color="green",shape="box"];530[label="vx4000",fontsize=16,color="green",shape="box"];526[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat vx52 vx53) GT))",fontsize=16,color="burlywood",shape="triangle"];624[label="vx52/Succ vx520",fontsize=10,color="white",style="solid",shape="box"];526 -> 624[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 624 -> 567[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 625[label="vx52/Zero",fontsize=10,color="white",style="solid",shape="box"];526 -> 625[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 625 -> 568[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 78[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg Zero)) (not MyFalse)",fontsize=16,color="black",shape="box"];78 -> 97[label="",style="solid", color="black", weight=3]; 10.38/4.31 79[label="min1 (Char (Neg Zero)) (Char (Pos (Succ vx4000))) MyTrue",fontsize=16,color="black",shape="box"];79 -> 98[label="",style="solid", color="black", weight=3]; 10.38/4.31 80[label="min1 (Char (Neg Zero)) (Char (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];80 -> 99[label="",style="solid", color="black", weight=3]; 10.38/4.31 81[label="min1 (Char (Neg Zero)) (Char (Neg (Succ vx4000))) (not MyTrue)",fontsize=16,color="black",shape="box"];81 -> 100[label="",style="solid", color="black", weight=3]; 10.38/4.31 82[label="min1 (Char (Neg Zero)) (Char (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];82 -> 101[label="",style="solid", color="black", weight=3]; 10.38/4.31 493[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat (Succ vx430) vx44) GT))",fontsize=16,color="burlywood",shape="box"];626[label="vx44/Succ vx440",fontsize=10,color="white",style="solid",shape="box"];493 -> 626[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 626 -> 499[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 627[label="vx44/Zero",fontsize=10,color="white",style="solid",shape="box"];493 -> 627[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 627 -> 500[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 494[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat Zero vx44) GT))",fontsize=16,color="burlywood",shape="box"];628[label="vx44/Succ vx440",fontsize=10,color="white",style="solid",shape="box"];494 -> 628[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 628 -> 501[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 629[label="vx44/Zero",fontsize=10,color="white",style="solid",shape="box"];494 -> 629[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 629 -> 502[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 87[label="min1 (Char (Pos (Succ vx3000))) (Char (Pos Zero)) MyFalse",fontsize=16,color="black",shape="box"];87 -> 106[label="",style="solid", color="black", weight=3]; 10.38/4.31 88[label="min0 (Char (Pos (Succ vx3000))) (Char (Neg vx400)) MyTrue",fontsize=16,color="black",shape="box"];88 -> 107[label="",style="solid", color="black", weight=3]; 10.38/4.31 89[label="min1 (Char (Pos Zero)) (Char (Pos (Succ vx4000))) MyTrue",fontsize=16,color="black",shape="box"];89 -> 108[label="",style="solid", color="black", weight=3]; 10.38/4.31 90[label="Char (Pos Zero)",fontsize=16,color="green",shape="box"];91[label="min0 (Char (Pos Zero)) (Char (Neg (Succ vx4000))) otherwise",fontsize=16,color="black",shape="box"];91 -> 109[label="",style="solid", color="black", weight=3]; 10.38/4.31 92[label="Char (Pos Zero)",fontsize=16,color="green",shape="box"];567[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat (Succ vx520) vx53) GT))",fontsize=16,color="burlywood",shape="box"];630[label="vx53/Succ vx530",fontsize=10,color="white",style="solid",shape="box"];567 -> 630[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 630 -> 571[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 631[label="vx53/Zero",fontsize=10,color="white",style="solid",shape="box"];567 -> 631[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 631 -> 572[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 568[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat Zero vx53) GT))",fontsize=16,color="burlywood",shape="box"];632[label="vx53/Succ vx530",fontsize=10,color="white",style="solid",shape="box"];568 -> 632[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 632 -> 573[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 633[label="vx53/Zero",fontsize=10,color="white",style="solid",shape="box"];568 -> 633[label="",style="solid", color="burlywood", weight=9]; 10.38/4.31 633 -> 574[label="",style="solid", color="burlywood", weight=3]; 10.38/4.31 97[label="min1 (Char (Neg (Succ vx3000))) (Char (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];97 -> 114[label="",style="solid", color="black", weight=3]; 10.38/4.31 98[label="Char (Neg Zero)",fontsize=16,color="green",shape="box"];99[label="Char (Neg Zero)",fontsize=16,color="green",shape="box"];100[label="min1 (Char (Neg Zero)) (Char (Neg (Succ vx4000))) MyFalse",fontsize=16,color="black",shape="box"];100 -> 115[label="",style="solid", color="black", weight=3]; 10.38/4.31 101[label="Char (Neg Zero)",fontsize=16,color="green",shape="box"];499[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat (Succ vx430) (Succ vx440)) GT))",fontsize=16,color="black",shape="box"];499 -> 507[label="",style="solid", color="black", weight=3]; 10.38/4.31 500[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat (Succ vx430) Zero) GT))",fontsize=16,color="black",shape="box"];500 -> 508[label="",style="solid", color="black", weight=3]; 10.38/4.31 501[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat Zero (Succ vx440)) GT))",fontsize=16,color="black",shape="box"];501 -> 509[label="",style="solid", color="black", weight=3]; 10.38/4.31 502[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat Zero Zero) GT))",fontsize=16,color="black",shape="box"];502 -> 510[label="",style="solid", color="black", weight=3]; 10.38/4.31 106[label="min0 (Char (Pos (Succ vx3000))) (Char (Pos Zero)) otherwise",fontsize=16,color="black",shape="box"];106 -> 121[label="",style="solid", color="black", weight=3]; 10.38/4.31 107[label="Char (Neg vx400)",fontsize=16,color="green",shape="box"];108[label="Char (Pos Zero)",fontsize=16,color="green",shape="box"];109[label="min0 (Char (Pos Zero)) (Char (Neg (Succ vx4000))) MyTrue",fontsize=16,color="black",shape="box"];109 -> 122[label="",style="solid", color="black", weight=3]; 10.38/4.31 571[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat (Succ vx520) (Succ vx530)) GT))",fontsize=16,color="black",shape="box"];571 -> 577[label="",style="solid", color="black", weight=3]; 10.38/4.31 572[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat (Succ vx520) Zero) GT))",fontsize=16,color="black",shape="box"];572 -> 578[label="",style="solid", color="black", weight=3]; 10.38/4.31 573[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat Zero (Succ vx530)) GT))",fontsize=16,color="black",shape="box"];573 -> 579[label="",style="solid", color="black", weight=3]; 10.38/4.31 574[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat Zero Zero) GT))",fontsize=16,color="black",shape="box"];574 -> 580[label="",style="solid", color="black", weight=3]; 10.38/4.31 114[label="Char (Neg (Succ vx3000))",fontsize=16,color="green",shape="box"];115[label="min0 (Char (Neg Zero)) (Char (Neg (Succ vx4000))) otherwise",fontsize=16,color="black",shape="box"];115 -> 128[label="",style="solid", color="black", weight=3]; 10.38/4.31 507 -> 456[label="",style="dashed", color="red", weight=0]; 10.38/4.31 507[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering (primCmpNat vx430 vx440) GT))",fontsize=16,color="magenta"];507 -> 515[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 507 -> 516[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 508[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];508 -> 517[label="",style="solid", color="black", weight=3]; 10.38/4.31 509[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];509 -> 518[label="",style="solid", color="black", weight=3]; 10.38/4.31 510[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];510 -> 519[label="",style="solid", color="black", weight=3]; 10.38/4.31 121[label="min0 (Char (Pos (Succ vx3000))) (Char (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];121 -> 136[label="",style="solid", color="black", weight=3]; 10.38/4.31 122[label="Char (Neg (Succ vx4000))",fontsize=16,color="green",shape="box"];577 -> 526[label="",style="dashed", color="red", weight=0]; 10.38/4.31 577[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering (primCmpNat vx520 vx530) GT))",fontsize=16,color="magenta"];577 -> 582[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 577 -> 583[label="",style="dashed", color="magenta", weight=3]; 10.38/4.31 578[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering GT GT))",fontsize=16,color="black",shape="box"];578 -> 584[label="",style="solid", color="black", weight=3]; 10.38/4.31 579[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering LT GT))",fontsize=16,color="black",shape="box"];579 -> 585[label="",style="solid", color="black", weight=3]; 10.38/4.31 580[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];580 -> 586[label="",style="solid", color="black", weight=3]; 10.38/4.31 128[label="min0 (Char (Neg Zero)) (Char (Neg (Succ vx4000))) MyTrue",fontsize=16,color="black",shape="box"];128 -> 144[label="",style="solid", color="black", weight=3]; 10.38/4.31 515[label="vx430",fontsize=16,color="green",shape="box"];516[label="vx440",fontsize=16,color="green",shape="box"];517[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not MyTrue)",fontsize=16,color="black",shape="box"];517 -> 569[label="",style="solid", color="black", weight=3]; 10.38/4.31 518[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not MyFalse)",fontsize=16,color="black",shape="triangle"];518 -> 570[label="",style="solid", color="black", weight=3]; 10.38/4.31 519 -> 518[label="",style="dashed", color="red", weight=0]; 10.38/4.31 519[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) (not MyFalse)",fontsize=16,color="magenta"];136[label="Char (Pos Zero)",fontsize=16,color="green",shape="box"];582[label="vx530",fontsize=16,color="green",shape="box"];583[label="vx520",fontsize=16,color="green",shape="box"];584[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not MyTrue)",fontsize=16,color="black",shape="box"];584 -> 588[label="",style="solid", color="black", weight=3]; 10.38/4.31 585[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not MyFalse)",fontsize=16,color="black",shape="triangle"];585 -> 589[label="",style="solid", color="black", weight=3]; 10.38/4.31 586 -> 585[label="",style="dashed", color="red", weight=0]; 10.38/4.31 586[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) (not MyFalse)",fontsize=16,color="magenta"];144[label="Char (Neg (Succ vx4000))",fontsize=16,color="green",shape="box"];569[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) MyFalse",fontsize=16,color="black",shape="box"];569 -> 575[label="",style="solid", color="black", weight=3]; 10.38/4.31 570[label="min1 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) MyTrue",fontsize=16,color="black",shape="box"];570 -> 576[label="",style="solid", color="black", weight=3]; 10.38/4.31 588[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) MyFalse",fontsize=16,color="black",shape="box"];588 -> 590[label="",style="solid", color="black", weight=3]; 10.38/4.31 589[label="min1 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) MyTrue",fontsize=16,color="black",shape="box"];589 -> 591[label="",style="solid", color="black", weight=3]; 10.38/4.31 575[label="min0 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) otherwise",fontsize=16,color="black",shape="box"];575 -> 581[label="",style="solid", color="black", weight=3]; 10.38/4.31 576[label="Char (Pos (Succ vx41))",fontsize=16,color="green",shape="box"];590[label="min0 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) otherwise",fontsize=16,color="black",shape="box"];590 -> 592[label="",style="solid", color="black", weight=3]; 10.38/4.31 591[label="Char (Neg (Succ vx50))",fontsize=16,color="green",shape="box"];581[label="min0 (Char (Pos (Succ vx41))) (Char (Pos (Succ vx42))) MyTrue",fontsize=16,color="black",shape="box"];581 -> 587[label="",style="solid", color="black", weight=3]; 10.38/4.31 592[label="min0 (Char (Neg (Succ vx50))) (Char (Neg (Succ vx51))) MyTrue",fontsize=16,color="black",shape="box"];592 -> 593[label="",style="solid", color="black", weight=3]; 10.38/4.31 587[label="Char (Pos (Succ vx42))",fontsize=16,color="green",shape="box"];593[label="Char (Neg (Succ vx51))",fontsize=16,color="green",shape="box"];} 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (6) 10.38/4.31 Complex Obligation (AND) 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (7) 10.38/4.31 Obligation: 10.38/4.31 Q DP problem: 10.38/4.31 The TRS P consists of the following rules: 10.38/4.31 10.38/4.31 new_min1(vx50, vx51, Main.Succ(vx520), Main.Succ(vx530)) -> new_min1(vx50, vx51, vx520, vx530) 10.38/4.31 10.38/4.31 R is empty. 10.38/4.31 Q is empty. 10.38/4.31 We have to consider all minimal (P,Q,R)-chains. 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (8) QDPSizeChangeProof (EQUIVALENT) 10.38/4.31 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. 10.38/4.31 10.38/4.31 From the DPs we obtained the following set of size-change graphs: 10.38/4.31 *new_min1(vx50, vx51, Main.Succ(vx520), Main.Succ(vx530)) -> new_min1(vx50, vx51, vx520, vx530) 10.38/4.31 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 10.38/4.31 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (9) 10.38/4.31 YES 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (10) 10.38/4.31 Obligation: 10.38/4.31 Q DP problem: 10.38/4.31 The TRS P consists of the following rules: 10.38/4.31 10.38/4.31 new_min10(vx41, vx42, Main.Succ(vx430), Main.Succ(vx440)) -> new_min10(vx41, vx42, vx430, vx440) 10.38/4.31 10.38/4.31 R is empty. 10.38/4.31 Q is empty. 10.38/4.31 We have to consider all minimal (P,Q,R)-chains. 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (11) QDPSizeChangeProof (EQUIVALENT) 10.38/4.31 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. 10.38/4.31 10.38/4.31 From the DPs we obtained the following set of size-change graphs: 10.38/4.31 *new_min10(vx41, vx42, Main.Succ(vx430), Main.Succ(vx440)) -> new_min10(vx41, vx42, vx430, vx440) 10.38/4.31 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 10.38/4.31 10.38/4.31 10.38/4.31 ---------------------------------------- 10.38/4.31 10.38/4.31 (12) 10.38/4.31 YES 10.38/4.35 EOF