77.55/61.78 YES 80.46/62.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 80.46/62.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 80.46/62.61 80.46/62.61 80.46/62.61 H-Termination with start terms of the given HASKELL could be proven: 80.46/62.61 80.46/62.61 (0) HASKELL 80.46/62.61 (1) BR [EQUIVALENT, 0 ms] 80.46/62.61 (2) HASKELL 80.46/62.61 (3) COR [EQUIVALENT, 23 ms] 80.46/62.61 (4) HASKELL 80.46/62.61 (5) Narrow [SOUND, 0 ms] 80.46/62.61 (6) AND 80.46/62.61 (7) QDP 80.46/62.61 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 80.46/62.61 (9) YES 80.46/62.61 (10) QDP 80.46/62.61 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 80.46/62.61 (12) YES 80.46/62.61 80.46/62.61 80.46/62.61 ---------------------------------------- 80.46/62.61 80.46/62.61 (0) 80.46/62.61 Obligation: 80.46/62.61 mainModule Main 80.46/62.61 module Main where { 80.46/62.61 import qualified Prelude; 80.46/62.61 data Main.Char = Char MyInt ; 80.46/62.61 80.46/62.61 data MyBool = MyTrue | MyFalse ; 80.46/62.61 80.46/62.61 data MyInt = Pos Main.Nat | Neg Main.Nat ; 80.46/62.61 80.46/62.61 data Main.Nat = Succ Main.Nat | Zero ; 80.46/62.61 80.46/62.61 data Ordering = LT | EQ | GT ; 80.46/62.61 80.46/62.61 asAs :: MyBool -> MyBool -> MyBool; 80.46/62.61 asAs MyFalse x = MyFalse; 80.46/62.61 asAs MyTrue x = x; 80.46/62.61 80.46/62.61 compareChar :: Main.Char -> Main.Char -> Ordering; 80.46/62.61 compareChar = primCmpChar; 80.46/62.61 80.46/62.61 esEsOrdering :: Ordering -> Ordering -> MyBool; 80.46/62.61 esEsOrdering LT LT = MyTrue; 80.46/62.61 esEsOrdering LT EQ = MyFalse; 80.46/62.61 esEsOrdering LT GT = MyFalse; 80.46/62.61 esEsOrdering EQ LT = MyFalse; 80.46/62.61 esEsOrdering EQ EQ = MyTrue; 80.46/62.61 esEsOrdering EQ GT = MyFalse; 80.46/62.61 esEsOrdering GT LT = MyFalse; 80.46/62.61 esEsOrdering GT EQ = MyFalse; 80.46/62.61 esEsOrdering GT GT = MyTrue; 80.46/62.61 80.46/62.61 fsEsOrdering :: Ordering -> Ordering -> MyBool; 80.46/62.61 fsEsOrdering x y = not (esEsOrdering x y); 80.46/62.61 80.46/62.61 gtEsChar :: Main.Char -> Main.Char -> MyBool; 80.46/62.61 gtEsChar x y = fsEsOrdering (compareChar x y) LT; 80.46/62.61 80.46/62.61 isAlpha :: Main.Char -> MyBool; 80.46/62.61 isAlpha c = pePe (isUpper c) (isLower c); 80.46/62.61 80.46/62.61 isLower :: Main.Char -> MyBool; 80.46/62.61 isLower c = pePe (asAs (gtEsChar c (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ 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x = x; 80.46/62.61 pePe MyTrue x = MyTrue; 80.46/62.61 80.46/62.61 primCmpChar :: Main.Char -> Main.Char -> Ordering; 80.46/62.61 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 80.46/62.61 80.46/62.61 primCmpInt :: MyInt -> MyInt -> Ordering; 80.46/62.61 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 80.46/62.61 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 80.46/62.61 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 80.46/62.61 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 80.46/62.61 80.46/62.61 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 80.46/62.61 primCmpNat Main.Zero Main.Zero = EQ; 80.46/62.61 primCmpNat Main.Zero (Main.Succ y) = LT; 80.46/62.61 primCmpNat (Main.Succ x) Main.Zero = GT; 80.46/62.61 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 80.46/62.61 80.46/62.61 } 80.46/62.61 80.46/62.61 ---------------------------------------- 80.46/62.61 80.46/62.61 (1) BR (EQUIVALENT) 80.46/62.61 Replaced joker patterns by fresh variables and removed binding patterns. 80.46/62.61 ---------------------------------------- 80.46/62.61 80.46/62.61 (2) 80.46/62.61 Obligation: 80.46/62.61 mainModule Main 80.46/62.61 module Main where { 80.46/62.61 import qualified Prelude; 80.46/62.61 data Main.Char = Char MyInt ; 80.46/62.61 80.46/62.61 data MyBool = MyTrue | MyFalse ; 80.46/62.61 80.46/62.61 data MyInt = Pos Main.Nat | Neg Main.Nat ; 80.46/62.61 80.46/62.61 data Main.Nat = Succ Main.Nat | Zero ; 80.46/62.61 80.46/62.61 data Ordering = LT | EQ | GT ; 80.46/62.61 80.46/62.61 asAs :: MyBool -> MyBool -> MyBool; 80.46/62.61 asAs MyFalse x = MyFalse; 80.46/62.61 asAs MyTrue x = x; 80.46/62.61 80.46/62.61 compareChar :: Main.Char -> Main.Char -> Ordering; 80.46/62.61 compareChar = primCmpChar; 80.46/62.61 80.46/62.61 esEsOrdering :: Ordering -> Ordering -> MyBool; 80.46/62.61 esEsOrdering LT LT = MyTrue; 80.46/62.61 esEsOrdering LT EQ = MyFalse; 80.46/62.61 esEsOrdering LT GT = MyFalse; 80.46/62.61 esEsOrdering EQ LT = MyFalse; 80.46/62.61 esEsOrdering EQ EQ = MyTrue; 80.46/62.61 esEsOrdering EQ GT = MyFalse; 80.46/62.61 esEsOrdering GT LT = MyFalse; 80.46/62.61 esEsOrdering GT EQ = MyFalse; 80.46/62.61 esEsOrdering GT GT = MyTrue; 80.46/62.61 80.46/62.61 fsEsOrdering :: Ordering -> Ordering -> MyBool; 80.46/62.61 fsEsOrdering x y = not (esEsOrdering x y); 80.46/62.61 80.46/62.61 gtEsChar :: Main.Char -> Main.Char -> MyBool; 80.46/62.61 gtEsChar x y = fsEsOrdering (compareChar x y) LT; 80.46/62.61 80.46/62.61 isAlpha :: Main.Char -> MyBool; 80.46/62.61 isAlpha c = pePe (isUpper c) (isLower c); 80.46/62.61 80.46/62.61 isLower :: Main.Char -> MyBool; 80.46/62.61 isLower c = pePe (asAs (gtEsChar c (Main.Char (Main.Pos (Main.Succ (Main.Succ 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-> MyBool; 80.46/62.61 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 80.46/62.61 80.46/62.61 not :: MyBool -> MyBool; 80.46/62.61 not MyTrue = MyFalse; 80.46/62.61 not MyFalse = MyTrue; 80.46/62.61 80.46/62.61 pePe :: MyBool -> MyBool -> MyBool; 80.46/62.61 pePe MyFalse x = x; 80.46/62.61 pePe MyTrue x = MyTrue; 80.46/62.61 80.46/62.61 primCmpChar :: Main.Char -> Main.Char -> Ordering; 80.46/62.61 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 80.46/62.61 80.46/62.61 primCmpInt :: MyInt -> MyInt -> Ordering; 80.46/62.61 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 80.46/62.61 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 80.46/62.61 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 80.46/62.61 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 80.46/62.61 80.46/62.61 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 80.46/62.61 primCmpNat Main.Zero Main.Zero = EQ; 80.46/62.61 primCmpNat Main.Zero (Main.Succ y) = LT; 80.46/62.61 primCmpNat (Main.Succ x) Main.Zero = GT; 80.46/62.61 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 80.46/62.61 80.46/62.61 } 80.46/62.61 80.46/62.61 ---------------------------------------- 80.46/62.61 80.46/62.61 (3) COR (EQUIVALENT) 80.46/62.61 Cond Reductions: 80.46/62.61 The following Function with conditions 80.46/62.61 "undefined |Falseundefined; 80.46/62.61 " 80.46/62.61 is transformed to 80.46/62.61 "undefined = undefined1; 80.46/62.61 " 80.46/62.61 "undefined0 True = undefined; 80.46/62.61 " 80.46/62.61 "undefined1 = undefined0 False; 80.46/62.61 " 80.46/62.61 80.46/62.61 ---------------------------------------- 80.46/62.61 80.46/62.61 (4) 80.46/62.61 Obligation: 80.46/62.61 mainModule Main 80.46/62.61 module Main where { 80.46/62.61 import qualified Prelude; 80.46/62.61 data Main.Char = Char MyInt ; 80.46/62.61 80.46/62.61 data MyBool = MyTrue | MyFalse ; 80.46/62.61 80.46/62.61 data MyInt = Pos Main.Nat | Neg Main.Nat ; 80.46/62.61 80.46/62.61 data Main.Nat = Succ Main.Nat | Zero ; 80.46/62.61 80.46/62.61 data Ordering = LT | EQ | GT ; 80.46/62.61 80.46/62.61 asAs :: MyBool -> MyBool -> MyBool; 80.46/62.61 asAs MyFalse x = MyFalse; 80.46/62.61 asAs MyTrue x = x; 80.46/62.61 80.46/62.61 compareChar :: Main.Char -> Main.Char -> Ordering; 80.46/62.61 compareChar = primCmpChar; 80.46/62.61 80.46/62.61 esEsOrdering :: Ordering -> Ordering -> MyBool; 80.46/62.61 esEsOrdering LT LT = MyTrue; 80.46/62.61 esEsOrdering LT EQ = MyFalse; 80.46/62.61 esEsOrdering LT GT = MyFalse; 80.46/62.61 esEsOrdering EQ LT = MyFalse; 80.46/62.61 esEsOrdering EQ EQ = MyTrue; 80.46/62.61 esEsOrdering EQ GT = MyFalse; 80.46/62.61 esEsOrdering GT LT = MyFalse; 80.46/62.61 esEsOrdering GT EQ = MyFalse; 80.46/62.61 esEsOrdering GT GT = MyTrue; 80.46/62.61 80.46/62.61 fsEsOrdering :: Ordering -> Ordering -> MyBool; 80.46/62.61 fsEsOrdering x y = not (esEsOrdering x y); 80.46/62.61 80.46/62.61 gtEsChar :: Main.Char -> Main.Char -> MyBool; 80.46/62.61 gtEsChar x y = fsEsOrdering (compareChar x y) LT; 80.46/62.61 80.46/62.61 isAlpha :: Main.Char -> MyBool; 80.46/62.61 isAlpha c = pePe (isUpper c) (isLower c); 80.46/62.61 80.46/62.61 isLower :: Main.Char -> MyBool; 80.46/62.61 isLower c = pePe (asAs (gtEsChar c (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ 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x = x; 80.46/62.61 pePe MyTrue x = MyTrue; 80.46/62.61 80.46/62.61 primCmpChar :: Main.Char -> Main.Char -> Ordering; 80.46/62.61 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 80.46/62.61 80.46/62.61 primCmpInt :: MyInt -> MyInt -> Ordering; 80.46/62.61 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 80.46/62.61 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 80.46/62.61 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 80.46/62.61 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 80.46/62.61 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 80.46/62.61 80.46/62.61 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 80.46/62.61 primCmpNat Main.Zero Main.Zero = EQ; 80.46/62.61 primCmpNat Main.Zero (Main.Succ y) = LT; 80.46/62.61 primCmpNat (Main.Succ x) Main.Zero = GT; 80.46/62.61 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 80.46/62.61 80.46/62.61 } 80.46/62.61 80.46/62.61 ---------------------------------------- 80.46/62.61 80.46/62.61 (5) Narrow (SOUND) 80.46/62.61 Haskell To QDPs 80.46/62.61 80.46/62.61 digraph dp_graph { 80.46/62.61 node [outthreshold=100, inthreshold=100];1[label="isAlpha",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 80.46/62.61 3[label="isAlpha vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 80.46/62.61 4 -> 2075[label="",style="dashed", color="red", weight=0]; 80.46/62.61 4[label="pePe (isUpper vx3) (isLower vx3)",fontsize=16,color="magenta"];4 -> 2076[label="",style="dashed", color="magenta", weight=3]; 80.46/62.61 4 -> 2077[label="",style="dashed", color="magenta", weight=3]; 80.46/62.61 2076[label="isUpper vx3",fontsize=16,color="black",shape="box"];2076 -> 2457[label="",style="solid", color="black", weight=3]; 80.46/62.61 2077[label="isLower vx3",fontsize=16,color="black",shape="box"];2077 -> 2458[label="",style="solid", color="black", weight=3]; 80.46/62.61 2075[label="pePe vx309 vx264",fontsize=16,color="burlywood",shape="triangle"];2662[label="vx309/MyTrue",fontsize=10,color="white",style="solid",shape="box"];2075 -> 2662[label="",style="solid", color="burlywood", weight=9]; 80.46/62.61 2662 -> 2459[label="",style="solid", color="burlywood", weight=3]; 80.46/62.61 2663[label="vx309/MyFalse",fontsize=10,color="white",style="solid",shape="box"];2075 -> 2663[label="",style="solid", color="burlywood", weight=9]; 80.46/62.61 2663 -> 2460[label="",style="solid", color="burlywood", weight=3]; 80.46/62.61 2457 -> 2075[label="",style="dashed", color="red", weight=0]; 80.46/62.61 2457[label="pePe (asAs (gtEsChar vx3 (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ 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2666[label="vx3170/Neg vx31700",fontsize=10,color="white",style="solid",shape="box"];2506 -> 2666[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2666 -> 2508[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2507[label="asAs (not (esEsOrdering (primCmpInt (Pos vx31700) (Pos (Succ vx318))) LT)) (ltEsChar (Char (Pos vx31700)) (Char (Pos (Succ vx319))))",fontsize=16,color="burlywood",shape="box"];2667[label="vx31700/Succ vx317000",fontsize=10,color="white",style="solid",shape="box"];2507 -> 2667[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2667 -> 2509[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2668[label="vx31700/Zero",fontsize=10,color="white",style="solid",shape="box"];2507 -> 2668[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2668 -> 2510[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2508[label="asAs (not (esEsOrdering (primCmpInt (Neg vx31700) (Pos (Succ vx318))) LT)) (ltEsChar (Char (Neg vx31700)) (Char (Pos (Succ vx319))))",fontsize=16,color="burlywood",shape="box"];2669[label="vx31700/Succ vx317000",fontsize=10,color="white",style="solid",shape="box"];2508 -> 2669[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2669 -> 2511[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2670[label="vx31700/Zero",fontsize=10,color="white",style="solid",shape="box"];2508 -> 2670[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2670 -> 2512[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2509[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vx317000)) (Pos (Succ vx318))) LT)) (ltEsChar (Char (Pos (Succ vx317000))) (Char (Pos (Succ vx319))))",fontsize=16,color="black",shape="box"];2509 -> 2513[label="",style="solid", color="black", weight=3]; 80.79/62.61 2510[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vx318))) LT)) (ltEsChar (Char (Pos Zero)) (Char (Pos (Succ vx319))))",fontsize=16,color="black",shape="box"];2510 -> 2514[label="",style="solid", color="black", weight=3]; 80.79/62.61 2511[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vx317000)) (Pos (Succ vx318))) LT)) (ltEsChar (Char (Neg (Succ vx317000))) (Char (Pos (Succ vx319))))",fontsize=16,color="black",shape="box"];2511 -> 2515[label="",style="solid", color="black", weight=3]; 80.79/62.61 2512[label="asAs (not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vx318))) LT)) (ltEsChar (Char (Neg Zero)) (Char (Pos (Succ vx319))))",fontsize=16,color="black",shape="box"];2512 -> 2516[label="",style="solid", color="black", weight=3]; 80.79/62.61 2513 -> 2592[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2513[label="asAs (not (esEsOrdering (primCmpNat (Succ vx317000) (Succ vx318)) LT)) (ltEsChar (Char (Pos (Succ vx317000))) (Char (Pos (Succ vx319))))",fontsize=16,color="magenta"];2513 -> 2593[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2513 -> 2594[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2513 -> 2595[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2514 -> 2592[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2514[label="asAs (not (esEsOrdering (primCmpNat Zero (Succ vx318)) LT)) (ltEsChar (Char (Pos Zero)) (Char (Pos (Succ vx319))))",fontsize=16,color="magenta"];2514 -> 2596[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2514 -> 2597[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2514 -> 2598[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2515[label="asAs (not (esEsOrdering LT LT)) (ltEsChar (Char (Neg (Succ vx317000))) (Char (Pos (Succ vx319))))",fontsize=16,color="black",shape="box"];2515 -> 2519[label="",style="solid", color="black", weight=3]; 80.79/62.61 2516[label="asAs (not (esEsOrdering LT LT)) (ltEsChar (Char (Neg Zero)) (Char (Pos (Succ vx319))))",fontsize=16,color="black",shape="box"];2516 -> 2520[label="",style="solid", color="black", weight=3]; 80.79/62.61 2593[label="Succ vx317000",fontsize=16,color="green",shape="box"];2594[label="ltEsChar (Char (Pos (Succ vx317000))) (Char (Pos (Succ vx319)))",fontsize=16,color="black",shape="box"];2594 -> 2609[label="",style="solid", color="black", weight=3]; 80.79/62.61 2595[label="Succ vx318",fontsize=16,color="green",shape="box"];2592[label="asAs (not (esEsOrdering (primCmpNat vx317000000 vx318000) LT)) vx321",fontsize=16,color="burlywood",shape="triangle"];2671[label="vx317000000/Succ vx3170000000",fontsize=10,color="white",style="solid",shape="box"];2592 -> 2671[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2671 -> 2610[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2672[label="vx317000000/Zero",fontsize=10,color="white",style="solid",shape="box"];2592 -> 2672[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2672 -> 2611[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2596[label="Zero",fontsize=16,color="green",shape="box"];2597[label="ltEsChar (Char (Pos Zero)) (Char (Pos (Succ vx319)))",fontsize=16,color="black",shape="box"];2597 -> 2612[label="",style="solid", color="black", weight=3]; 80.79/62.61 2598[label="Succ vx318",fontsize=16,color="green",shape="box"];2519 -> 2568[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2519[label="asAs (not MyTrue) (ltEsChar (Char (Neg (Succ vx317000))) (Char (Pos (Succ vx319))))",fontsize=16,color="magenta"];2519 -> 2569[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2520 -> 2568[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2520[label="asAs (not MyTrue) (ltEsChar (Char (Neg Zero)) (Char (Pos (Succ vx319))))",fontsize=16,color="magenta"];2520 -> 2570[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2609[label="fsEsOrdering (compareChar (Char (Pos (Succ vx317000))) (Char (Pos (Succ vx319)))) GT",fontsize=16,color="black",shape="box"];2609 -> 2615[label="",style="solid", color="black", weight=3]; 80.79/62.61 2610[label="asAs (not (esEsOrdering (primCmpNat (Succ vx3170000000) vx318000) LT)) vx321",fontsize=16,color="burlywood",shape="box"];2673[label="vx318000/Succ vx3180000",fontsize=10,color="white",style="solid",shape="box"];2610 -> 2673[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2673 -> 2616[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2674[label="vx318000/Zero",fontsize=10,color="white",style="solid",shape="box"];2610 -> 2674[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2674 -> 2617[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2611[label="asAs (not (esEsOrdering (primCmpNat Zero vx318000) LT)) vx321",fontsize=16,color="burlywood",shape="box"];2675[label="vx318000/Succ vx3180000",fontsize=10,color="white",style="solid",shape="box"];2611 -> 2675[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2675 -> 2618[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2676[label="vx318000/Zero",fontsize=10,color="white",style="solid",shape="box"];2611 -> 2676[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2676 -> 2619[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2612[label="fsEsOrdering (compareChar (Char (Pos Zero)) (Char (Pos (Succ vx319)))) GT",fontsize=16,color="black",shape="box"];2612 -> 2620[label="",style="solid", color="black", weight=3]; 80.79/62.61 2569[label="ltEsChar (Char (Neg (Succ vx317000))) (Char (Pos (Succ vx319)))",fontsize=16,color="black",shape="box"];2569 -> 2574[label="",style="solid", color="black", weight=3]; 80.79/62.61 2568[label="asAs (not MyTrue) vx320",fontsize=16,color="black",shape="triangle"];2568 -> 2575[label="",style="solid", color="black", weight=3]; 80.79/62.61 2570[label="ltEsChar (Char (Neg Zero)) (Char (Pos (Succ vx319)))",fontsize=16,color="black",shape="box"];2570 -> 2576[label="",style="solid", color="black", weight=3]; 80.79/62.61 2615[label="not (esEsOrdering (compareChar (Char (Pos (Succ vx317000))) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2615 -> 2623[label="",style="solid", color="black", weight=3]; 80.79/62.61 2616[label="asAs (not (esEsOrdering (primCmpNat (Succ vx3170000000) (Succ vx3180000)) LT)) vx321",fontsize=16,color="black",shape="box"];2616 -> 2624[label="",style="solid", color="black", weight=3]; 80.79/62.61 2617[label="asAs (not (esEsOrdering (primCmpNat (Succ vx3170000000) Zero) LT)) vx321",fontsize=16,color="black",shape="box"];2617 -> 2625[label="",style="solid", color="black", weight=3]; 80.79/62.61 2618[label="asAs (not (esEsOrdering (primCmpNat Zero (Succ vx3180000)) LT)) vx321",fontsize=16,color="black",shape="box"];2618 -> 2626[label="",style="solid", color="black", weight=3]; 80.79/62.61 2619[label="asAs (not (esEsOrdering (primCmpNat Zero Zero) LT)) vx321",fontsize=16,color="black",shape="box"];2619 -> 2627[label="",style="solid", color="black", weight=3]; 80.79/62.61 2620[label="not (esEsOrdering (compareChar (Char (Pos Zero)) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2620 -> 2628[label="",style="solid", color="black", weight=3]; 80.79/62.61 2574[label="fsEsOrdering (compareChar (Char (Neg (Succ vx317000))) (Char (Pos (Succ vx319)))) GT",fontsize=16,color="black",shape="box"];2574 -> 2586[label="",style="solid", color="black", weight=3]; 80.79/62.61 2575[label="asAs MyFalse vx320",fontsize=16,color="black",shape="box"];2575 -> 2587[label="",style="solid", color="black", weight=3]; 80.79/62.61 2576[label="fsEsOrdering (compareChar (Char (Neg Zero)) (Char (Pos (Succ vx319)))) GT",fontsize=16,color="black",shape="box"];2576 -> 2588[label="",style="solid", color="black", weight=3]; 80.79/62.61 2623[label="not (esEsOrdering (primCmpChar (Char (Pos (Succ vx317000))) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2623 -> 2631[label="",style="solid", color="black", weight=3]; 80.79/62.61 2624 -> 2592[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2624[label="asAs (not (esEsOrdering (primCmpNat vx3170000000 vx3180000) LT)) vx321",fontsize=16,color="magenta"];2624 -> 2632[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2624 -> 2633[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2625[label="asAs (not (esEsOrdering GT LT)) vx321",fontsize=16,color="black",shape="box"];2625 -> 2634[label="",style="solid", color="black", weight=3]; 80.79/62.61 2626[label="asAs (not (esEsOrdering LT LT)) vx321",fontsize=16,color="black",shape="box"];2626 -> 2635[label="",style="solid", color="black", weight=3]; 80.79/62.61 2627[label="asAs (not (esEsOrdering EQ LT)) vx321",fontsize=16,color="black",shape="box"];2627 -> 2636[label="",style="solid", color="black", weight=3]; 80.79/62.61 2628[label="not (esEsOrdering (primCmpChar (Char (Pos Zero)) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2628 -> 2637[label="",style="solid", color="black", weight=3]; 80.79/62.61 2586[label="not (esEsOrdering (compareChar (Char (Neg (Succ vx317000))) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2586 -> 2613[label="",style="solid", color="black", weight=3]; 80.79/62.61 2587[label="MyFalse",fontsize=16,color="green",shape="box"];2588[label="not (esEsOrdering (compareChar (Char (Neg Zero)) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2588 -> 2614[label="",style="solid", color="black", weight=3]; 80.79/62.61 2631[label="not (esEsOrdering (primCmpInt (Pos (Succ vx317000)) (Pos (Succ vx319))) GT)",fontsize=16,color="black",shape="box"];2631 -> 2639[label="",style="solid", color="black", weight=3]; 80.79/62.61 2632[label="vx3170000000",fontsize=16,color="green",shape="box"];2633[label="vx3180000",fontsize=16,color="green",shape="box"];2634[label="asAs (not MyFalse) vx321",fontsize=16,color="black",shape="triangle"];2634 -> 2640[label="",style="solid", color="black", weight=3]; 80.79/62.61 2635 -> 2568[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2635[label="asAs (not MyTrue) vx321",fontsize=16,color="magenta"];2635 -> 2641[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2636 -> 2634[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2636[label="asAs (not MyFalse) vx321",fontsize=16,color="magenta"];2637[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vx319))) GT)",fontsize=16,color="black",shape="box"];2637 -> 2642[label="",style="solid", color="black", weight=3]; 80.79/62.61 2613[label="not (esEsOrdering (primCmpChar (Char (Neg (Succ vx317000))) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2613 -> 2621[label="",style="solid", color="black", weight=3]; 80.79/62.61 2614[label="not (esEsOrdering (primCmpChar (Char (Neg Zero)) (Char (Pos (Succ vx319)))) GT)",fontsize=16,color="black",shape="box"];2614 -> 2622[label="",style="solid", color="black", weight=3]; 80.79/62.61 2639[label="not (esEsOrdering (primCmpNat (Succ vx317000) (Succ vx319)) GT)",fontsize=16,color="black",shape="box"];2639 -> 2644[label="",style="solid", color="black", weight=3]; 80.79/62.61 2640[label="asAs MyTrue vx321",fontsize=16,color="black",shape="box"];2640 -> 2645[label="",style="solid", color="black", weight=3]; 80.79/62.61 2641[label="vx321",fontsize=16,color="green",shape="box"];2642[label="not (esEsOrdering (primCmpNat Zero (Succ vx319)) GT)",fontsize=16,color="black",shape="box"];2642 -> 2646[label="",style="solid", color="black", weight=3]; 80.79/62.61 2621[label="not (esEsOrdering (primCmpInt (Neg (Succ vx317000)) (Pos (Succ vx319))) GT)",fontsize=16,color="black",shape="box"];2621 -> 2629[label="",style="solid", color="black", weight=3]; 80.79/62.61 2622[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vx319))) GT)",fontsize=16,color="black",shape="box"];2622 -> 2630[label="",style="solid", color="black", weight=3]; 80.79/62.61 2644[label="not (esEsOrdering (primCmpNat vx317000 vx319) GT)",fontsize=16,color="burlywood",shape="triangle"];2677[label="vx317000/Succ vx3170000",fontsize=10,color="white",style="solid",shape="box"];2644 -> 2677[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2677 -> 2647[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2678[label="vx317000/Zero",fontsize=10,color="white",style="solid",shape="box"];2644 -> 2678[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2678 -> 2648[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2645[label="vx321",fontsize=16,color="green",shape="box"];2646 -> 2629[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2646[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];2629[label="not (esEsOrdering LT GT)",fontsize=16,color="black",shape="triangle"];2629 -> 2638[label="",style="solid", color="black", weight=3]; 80.79/62.61 2630 -> 2629[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2630[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];2647[label="not (esEsOrdering (primCmpNat (Succ vx3170000) vx319) GT)",fontsize=16,color="burlywood",shape="box"];2679[label="vx319/Succ vx3190",fontsize=10,color="white",style="solid",shape="box"];2647 -> 2679[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2679 -> 2649[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2680[label="vx319/Zero",fontsize=10,color="white",style="solid",shape="box"];2647 -> 2680[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2680 -> 2650[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2648[label="not (esEsOrdering (primCmpNat Zero vx319) GT)",fontsize=16,color="burlywood",shape="box"];2681[label="vx319/Succ vx3190",fontsize=10,color="white",style="solid",shape="box"];2648 -> 2681[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2681 -> 2651[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2682[label="vx319/Zero",fontsize=10,color="white",style="solid",shape="box"];2648 -> 2682[label="",style="solid", color="burlywood", weight=9]; 80.79/62.61 2682 -> 2652[label="",style="solid", color="burlywood", weight=3]; 80.79/62.61 2638[label="not MyFalse",fontsize=16,color="black",shape="triangle"];2638 -> 2643[label="",style="solid", color="black", weight=3]; 80.79/62.61 2649[label="not (esEsOrdering (primCmpNat (Succ vx3170000) (Succ vx3190)) GT)",fontsize=16,color="black",shape="box"];2649 -> 2653[label="",style="solid", color="black", weight=3]; 80.79/62.61 2650[label="not (esEsOrdering (primCmpNat (Succ vx3170000) Zero) GT)",fontsize=16,color="black",shape="box"];2650 -> 2654[label="",style="solid", color="black", weight=3]; 80.79/62.61 2651[label="not (esEsOrdering (primCmpNat Zero (Succ vx3190)) GT)",fontsize=16,color="black",shape="box"];2651 -> 2655[label="",style="solid", color="black", weight=3]; 80.79/62.61 2652[label="not (esEsOrdering (primCmpNat Zero Zero) GT)",fontsize=16,color="black",shape="box"];2652 -> 2656[label="",style="solid", color="black", weight=3]; 80.79/62.61 2643[label="MyTrue",fontsize=16,color="green",shape="box"];2653 -> 2644[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2653[label="not (esEsOrdering (primCmpNat vx3170000 vx3190) GT)",fontsize=16,color="magenta"];2653 -> 2657[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2653 -> 2658[label="",style="dashed", color="magenta", weight=3]; 80.79/62.61 2654[label="not (esEsOrdering GT GT)",fontsize=16,color="black",shape="box"];2654 -> 2659[label="",style="solid", color="black", weight=3]; 80.79/62.61 2655 -> 2629[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2655[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];2656[label="not (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];2656 -> 2660[label="",style="solid", color="black", weight=3]; 80.79/62.61 2657[label="vx3190",fontsize=16,color="green",shape="box"];2658[label="vx3170000",fontsize=16,color="green",shape="box"];2659[label="not MyTrue",fontsize=16,color="black",shape="box"];2659 -> 2661[label="",style="solid", color="black", weight=3]; 80.79/62.61 2660 -> 2638[label="",style="dashed", color="red", weight=0]; 80.79/62.61 2660[label="not MyFalse",fontsize=16,color="magenta"];2661[label="MyFalse",fontsize=16,color="green",shape="box"];} 80.79/62.61 80.79/62.61 ---------------------------------------- 80.79/62.61 80.79/62.61 (6) 80.79/62.61 Complex Obligation (AND) 80.79/62.61 80.79/62.61 ---------------------------------------- 80.79/62.61 80.79/62.61 (7) 80.79/62.61 Obligation: 80.79/62.61 Q DP problem: 80.79/62.61 The TRS P consists of the following rules: 80.79/62.61 80.79/62.61 new_asAs(Main.Succ(vx3170000000), Main.Succ(vx3180000), vx321) -> new_asAs(vx3170000000, vx3180000, vx321) 80.79/62.61 80.79/62.61 R is empty. 80.79/62.61 Q is empty. 80.79/62.61 We have to consider all minimal (P,Q,R)-chains. 80.79/62.61 ---------------------------------------- 80.79/62.61 80.79/62.61 (8) QDPSizeChangeProof (EQUIVALENT) 80.79/62.61 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 80.79/62.61 80.79/62.61 From the DPs we obtained the following set of size-change graphs: 80.79/62.61 *new_asAs(Main.Succ(vx3170000000), Main.Succ(vx3180000), vx321) -> new_asAs(vx3170000000, vx3180000, vx321) 80.79/62.61 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 80.79/62.61 80.79/62.61 80.79/62.61 ---------------------------------------- 80.79/62.61 80.79/62.61 (9) 80.79/62.61 YES 80.79/62.61 80.79/62.61 ---------------------------------------- 80.79/62.61 80.79/62.61 (10) 80.79/62.61 Obligation: 80.79/62.61 Q DP problem: 80.79/62.61 The TRS P consists of the following rules: 80.79/62.61 80.79/62.61 new_not(Main.Succ(vx3170000), Main.Succ(vx3190)) -> new_not(vx3170000, vx3190) 80.79/62.61 80.79/62.61 R is empty. 80.79/62.61 Q is empty. 80.79/62.61 We have to consider all minimal (P,Q,R)-chains. 80.79/62.61 ---------------------------------------- 80.79/62.61 80.79/62.61 (11) QDPSizeChangeProof (EQUIVALENT) 80.79/62.61 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 80.79/62.61 80.79/62.61 From the DPs we obtained the following set of size-change graphs: 80.79/62.61 *new_not(Main.Succ(vx3170000), Main.Succ(vx3190)) -> new_not(vx3170000, vx3190) 80.79/62.61 The graph contains the following edges 1 > 1, 2 > 2 80.79/62.61 80.79/62.61 80.79/62.61 ---------------------------------------- 80.79/62.61 80.79/62.61 (12) 80.79/62.61 YES 80.79/62.65 EOF