78.33/60.53 YES 81.19/61.32 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 81.19/61.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 81.19/61.32 81.19/61.32 81.19/61.32 H-Termination with start terms of the given HASKELL could be proven: 81.19/61.32 81.19/61.32 (0) HASKELL 81.19/61.32 (1) BR [EQUIVALENT, 0 ms] 81.19/61.32 (2) HASKELL 81.19/61.32 (3) COR [EQUIVALENT, 0 ms] 81.19/61.32 (4) HASKELL 81.19/61.32 (5) Narrow [SOUND, 0 ms] 81.19/61.32 (6) AND 81.19/61.32 (7) QDP 81.19/61.32 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (9) YES 81.19/61.32 (10) QDP 81.19/61.32 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (12) YES 81.19/61.32 (13) QDP 81.19/61.32 (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (15) YES 81.19/61.32 (16) QDP 81.19/61.32 (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (18) YES 81.19/61.32 (19) QDP 81.19/61.32 (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (21) YES 81.19/61.32 (22) QDP 81.19/61.32 (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (24) YES 81.19/61.32 (25) QDP 81.19/61.32 (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (27) YES 81.19/61.32 (28) QDP 81.19/61.32 (29) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (30) YES 81.19/61.32 (31) QDP 81.19/61.32 (32) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (33) YES 81.19/61.32 (34) QDP 81.19/61.32 (35) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (36) YES 81.19/61.32 (37) QDP 81.19/61.32 (38) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (39) YES 81.19/61.32 (40) QDP 81.19/61.32 (41) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (42) YES 81.19/61.32 (43) QDP 81.19/61.32 (44) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (45) YES 81.19/61.32 (46) QDP 81.19/61.32 (47) QDPSizeChangeProof [EQUIVALENT, 0 ms] 81.19/61.32 (48) YES 81.19/61.32 81.19/61.32 81.19/61.32 ---------------------------------------- 81.19/61.32 81.19/61.32 (0) 81.19/61.32 Obligation: 81.19/61.32 mainModule Main 81.19/61.32 module Main where { 81.19/61.32 import qualified Prelude; 81.19/61.32 data Main.Char = Char MyInt ; 81.19/61.32 81.19/61.32 data MyBool = MyTrue | MyFalse ; 81.19/61.32 81.19/61.32 data MyInt = Pos Main.Nat | Neg Main.Nat ; 81.19/61.32 81.19/61.32 data Main.Nat = Succ Main.Nat | Zero ; 81.19/61.32 81.19/61.32 data Ordering = LT | EQ | GT ; 81.19/61.32 81.19/61.32 asAs :: MyBool -> MyBool -> MyBool; 81.19/61.32 asAs MyFalse x = MyFalse; 81.19/61.32 asAs MyTrue x = x; 81.19/61.32 81.19/61.32 compareChar :: Main.Char -> Main.Char -> Ordering; 81.19/61.32 compareChar = primCmpChar; 81.19/61.32 81.19/61.32 esEsOrdering :: Ordering -> Ordering -> MyBool; 81.19/61.32 esEsOrdering LT LT = MyTrue; 81.19/61.32 esEsOrdering LT EQ = MyFalse; 81.19/61.32 esEsOrdering LT GT = MyFalse; 81.19/61.32 esEsOrdering EQ LT = MyFalse; 81.19/61.32 esEsOrdering EQ EQ = MyTrue; 81.19/61.32 esEsOrdering EQ GT = MyFalse; 81.19/61.32 esEsOrdering GT LT = MyFalse; 81.19/61.32 esEsOrdering GT EQ = MyFalse; 81.19/61.32 esEsOrdering GT GT = MyTrue; 81.19/61.32 81.19/61.32 fsEsOrdering :: Ordering -> Ordering -> MyBool; 81.19/61.32 fsEsOrdering x y = not (esEsOrdering x y); 81.19/61.32 81.19/61.32 gtEsChar :: Main.Char -> Main.Char -> MyBool; 81.19/61.32 gtEsChar x y = fsEsOrdering (compareChar x y) LT; 81.19/61.32 81.19/61.32 isAlpha :: Main.Char -> MyBool; 81.19/61.32 isAlpha c = pePe (isUpper c) (isLower c); 81.19/61.32 81.19/61.32 isAlphaNum :: Main.Char -> MyBool; 81.19/61.32 isAlphaNum c = pePe (isAlpha c) (isDigit c); 81.19/61.32 81.19/61.32 isDigit :: Main.Char -> MyBool; 81.19/61.32 isDigit c = 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 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Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))); 81.19/61.32 81.19/61.32 ltEsChar :: Main.Char -> Main.Char -> MyBool; 81.19/61.32 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 81.19/61.32 81.19/61.32 not :: MyBool -> MyBool; 81.19/61.32 not MyTrue = MyFalse; 81.19/61.32 not MyFalse = MyTrue; 81.19/61.32 81.19/61.32 pePe :: MyBool -> MyBool -> MyBool; 81.19/61.32 pePe MyFalse x = x; 81.19/61.32 pePe MyTrue x = MyTrue; 81.19/61.32 81.19/61.32 primCmpChar :: Main.Char -> Main.Char -> Ordering; 81.19/61.32 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 81.19/61.32 81.19/61.32 primCmpInt :: MyInt -> MyInt -> Ordering; 81.19/61.32 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 81.19/61.32 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 81.19/61.32 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 81.19/61.32 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 81.19/61.32 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 81.19/61.32 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 81.19/61.32 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 81.19/61.32 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 81.19/61.32 81.19/61.32 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 81.19/61.32 primCmpNat Main.Zero Main.Zero = EQ; 81.19/61.32 primCmpNat Main.Zero (Main.Succ y) = LT; 81.19/61.32 primCmpNat (Main.Succ x) Main.Zero = GT; 81.19/61.32 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 81.19/61.32 81.19/61.32 } 81.19/61.32 81.19/61.32 ---------------------------------------- 81.19/61.32 81.19/61.32 (1) BR (EQUIVALENT) 81.19/61.32 Replaced joker patterns by fresh variables and removed binding patterns. 81.19/61.32 ---------------------------------------- 81.19/61.32 81.19/61.32 (2) 81.19/61.32 Obligation: 81.19/61.32 mainModule Main 81.19/61.32 module Main where { 81.19/61.32 import qualified Prelude; 81.19/61.32 data Main.Char = Char MyInt ; 81.19/61.32 81.19/61.32 data MyBool = MyTrue | MyFalse ; 81.19/61.32 81.19/61.32 data MyInt = Pos Main.Nat | Neg Main.Nat ; 81.19/61.32 81.19/61.32 data Main.Nat = Succ Main.Nat | Zero ; 81.19/61.32 81.19/61.32 data Ordering = LT | EQ | GT ; 81.19/61.32 81.19/61.32 asAs :: MyBool -> MyBool -> MyBool; 81.19/61.32 asAs MyFalse x = MyFalse; 81.19/61.32 asAs MyTrue x = x; 81.19/61.32 81.19/61.32 compareChar :: Main.Char -> Main.Char -> Ordering; 81.19/61.32 compareChar = primCmpChar; 81.19/61.32 81.19/61.32 esEsOrdering :: Ordering -> Ordering -> MyBool; 81.19/61.32 esEsOrdering LT LT = MyTrue; 81.19/61.32 esEsOrdering LT EQ = MyFalse; 81.19/61.32 esEsOrdering LT GT = MyFalse; 81.19/61.32 esEsOrdering EQ LT = MyFalse; 81.19/61.32 esEsOrdering EQ EQ = MyTrue; 81.19/61.32 esEsOrdering EQ GT = MyFalse; 81.19/61.32 esEsOrdering GT LT = MyFalse; 81.19/61.32 esEsOrdering GT EQ = MyFalse; 81.19/61.32 esEsOrdering GT GT = MyTrue; 81.19/61.32 81.19/61.32 fsEsOrdering :: Ordering -> Ordering -> MyBool; 81.19/61.32 fsEsOrdering x y = not (esEsOrdering x y); 81.19/61.32 81.19/61.32 gtEsChar :: Main.Char -> Main.Char -> MyBool; 81.19/61.32 gtEsChar x y = fsEsOrdering (compareChar x y) LT; 81.19/61.32 81.19/61.32 isAlpha :: Main.Char -> MyBool; 81.19/61.32 isAlpha c = pePe (isUpper c) (isLower c); 81.19/61.32 81.19/61.32 isAlphaNum :: Main.Char -> MyBool; 81.19/61.32 isAlphaNum c = pePe (isAlpha c) (isDigit c); 81.19/61.32 81.19/61.32 isDigit :: Main.Char -> MyBool; 81.19/61.32 isDigit c = 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 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81.19/61.32 isLower :: Main.Char -> MyBool; 81.19/61.32 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 (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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Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))); 81.19/61.33 81.19/61.33 ltEsChar :: Main.Char -> Main.Char -> MyBool; 81.19/61.33 ltEsChar x y = fsEsOrdering (compareChar x y) GT; 81.19/61.33 81.19/61.33 not :: MyBool -> MyBool; 81.19/61.33 not MyTrue = MyFalse; 81.19/61.33 not MyFalse = MyTrue; 81.19/61.33 81.19/61.33 pePe :: MyBool -> MyBool -> MyBool; 81.19/61.33 pePe MyFalse x = x; 81.19/61.33 pePe MyTrue x = MyTrue; 81.19/61.33 81.19/61.33 primCmpChar :: Main.Char -> Main.Char -> Ordering; 81.19/61.33 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 81.19/61.33 81.19/61.33 primCmpInt :: MyInt -> MyInt -> Ordering; 81.19/61.33 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 81.19/61.33 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 81.19/61.33 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 81.19/61.33 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 81.19/61.33 81.19/61.33 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 81.19/61.33 primCmpNat Main.Zero Main.Zero = EQ; 81.19/61.33 primCmpNat Main.Zero (Main.Succ y) = LT; 81.19/61.33 primCmpNat (Main.Succ x) Main.Zero = GT; 81.19/61.33 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 81.19/61.33 81.19/61.33 } 81.19/61.33 81.19/61.33 ---------------------------------------- 81.19/61.33 81.19/61.33 (3) COR (EQUIVALENT) 81.19/61.33 Cond Reductions: 81.19/61.33 The following Function with conditions 81.19/61.33 "undefined |Falseundefined; 81.19/61.33 " 81.19/61.33 is transformed to 81.19/61.33 "undefined = undefined1; 81.19/61.33 " 81.19/61.33 "undefined0 True = undefined; 81.19/61.33 " 81.19/61.33 "undefined1 = undefined0 False; 81.19/61.33 " 81.19/61.33 81.19/61.33 ---------------------------------------- 81.19/61.33 81.19/61.33 (4) 81.19/61.33 Obligation: 81.19/61.33 mainModule Main 81.19/61.33 module Main where { 81.19/61.33 import qualified Prelude; 81.19/61.33 data Main.Char = Char MyInt ; 81.19/61.33 81.19/61.33 data MyBool = MyTrue | MyFalse ; 81.19/61.33 81.19/61.33 data MyInt = Pos Main.Nat | Neg Main.Nat ; 81.19/61.33 81.19/61.33 data Main.Nat = Succ Main.Nat | Zero ; 81.19/61.33 81.19/61.33 data Ordering = LT | EQ | GT ; 81.19/61.33 81.19/61.33 asAs :: MyBool -> MyBool -> MyBool; 81.19/61.33 asAs MyFalse x = MyFalse; 81.19/61.33 asAs MyTrue x = x; 81.19/61.33 81.19/61.33 compareChar :: Main.Char -> Main.Char -> Ordering; 81.19/61.33 compareChar = primCmpChar; 81.19/61.33 81.19/61.33 esEsOrdering :: Ordering -> Ordering -> MyBool; 81.19/61.33 esEsOrdering LT LT = MyTrue; 81.19/61.33 esEsOrdering LT EQ = MyFalse; 81.19/61.33 esEsOrdering LT GT = MyFalse; 81.19/61.33 esEsOrdering EQ LT = MyFalse; 81.19/61.33 esEsOrdering EQ EQ = MyTrue; 81.19/61.33 esEsOrdering EQ GT = MyFalse; 81.19/61.33 esEsOrdering GT LT = MyFalse; 81.19/61.33 esEsOrdering GT EQ = MyFalse; 81.19/61.33 esEsOrdering GT GT = MyTrue; 81.19/61.33 81.19/61.33 fsEsOrdering :: Ordering -> Ordering -> MyBool; 81.19/61.33 fsEsOrdering x y = not (esEsOrdering x y); 81.19/61.33 81.19/61.33 gtEsChar :: Main.Char -> Main.Char -> MyBool; 81.19/61.33 gtEsChar x y = fsEsOrdering (compareChar x y) LT; 81.19/61.33 81.19/61.33 isAlpha :: Main.Char -> MyBool; 81.19/61.33 isAlpha c = pePe (isUpper c) (isLower c); 81.19/61.33 81.19/61.33 isAlphaNum :: Main.Char -> MyBool; 81.19/61.33 isAlphaNum c = pePe (isAlpha c) (isDigit c); 81.19/61.33 81.19/61.33 isDigit :: Main.Char -> MyBool; 81.19/61.33 isDigit c = asAs (gtEsChar c (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ 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x = x; 81.19/61.33 pePe MyTrue x = MyTrue; 81.19/61.33 81.19/61.33 primCmpChar :: Main.Char -> Main.Char -> Ordering; 81.19/61.33 primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y; 81.19/61.33 81.19/61.33 primCmpInt :: MyInt -> MyInt -> Ordering; 81.19/61.33 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 81.19/61.33 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 81.19/61.33 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 81.19/61.33 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 81.19/61.33 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 81.19/61.33 81.19/61.33 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 81.19/61.33 primCmpNat Main.Zero Main.Zero = EQ; 81.19/61.33 primCmpNat Main.Zero (Main.Succ y) = LT; 81.19/61.33 primCmpNat (Main.Succ x) Main.Zero = GT; 81.19/61.33 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 81.19/61.33 81.19/61.33 } 81.19/61.33 81.19/61.33 ---------------------------------------- 81.19/61.33 81.19/61.33 (5) Narrow (SOUND) 81.19/61.33 Haskell To QDPs 81.19/61.33 81.19/61.33 digraph dp_graph { 81.19/61.33 node [outthreshold=100, inthreshold=100];1[label="isAlphaNum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 81.19/61.33 3[label="isAlphaNum vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 81.19/61.33 4[label="pePe (isAlpha vx3) (isDigit vx3)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 81.19/61.33 5[label="pePe (pePe (isUpper vx3) (isLower vx3)) (isDigit vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 81.19/61.33 6 -> 50[label="",style="dashed", color="red", weight=0]; 81.19/61.33 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188[label="",style="solid", color="black", weight=3]; 81.19/61.34 176[label="pePe (pePe (pePe (asAs MyFalse (ltEsChar (Char (Neg Zero)) (Char (Pos (Succ vx34))))) (asAs (gtEsChar (Char (Neg Zero)) (Char (Pos (Succ vx35)))) (ltEsChar (Char (Neg Zero)) (Char (Pos (Succ vx36)))))) (isLower (Char (Neg Zero)))) (isDigit (Char (Neg Zero)))",fontsize=16,color="black",shape="box"];176 -> 189[label="",style="solid", color="black", weight=3]; 81.19/61.34 869 -> 1389[label="",style="dashed", color="red", weight=0]; 81.19/61.34 869[label="pePe (pePe (pePe (not (esEsOrdering (primCmpNat (Succ vx120) (Succ vx121)) GT)) (pePe (asAs (gtEsChar (Char (Pos (Succ vx120))) (Char (Pos (Succ vx122)))) (ltEsChar (Char (Pos (Succ vx120))) (Char (Pos (Succ vx123))))) (asAs (gtEsChar (Char (Pos (Succ vx120))) (Char (Pos (Succ vx124)))) (ltEsChar (Char (Pos (Succ vx120))) (Char (Pos (Succ vx125))))))) (isLower (Char (Pos (Succ vx120))))) (isDigit (Char (Pos (Succ vx120))))",fontsize=16,color="magenta"];869 -> 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308[label="",style="solid", color="black", weight=3]; 81.19/61.34 294[label="pePe (pePe (asAs (not (esEsOrdering (primCmpInt (Neg (Succ vx30000)) (Pos (Succ vx35))) LT)) (ltEsChar (Char (Neg (Succ vx30000))) (Char (Pos (Succ vx36))))) (isLower (Char (Neg (Succ vx30000))))) (isDigit (Char (Neg (Succ vx30000))))",fontsize=16,color="black",shape="box"];294 -> 309[label="",style="solid", color="black", weight=3]; 81.19/61.34 295[label="pePe (pePe (asAs (not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vx35))) LT)) (ltEsChar (Char (Neg Zero)) (Char (Pos (Succ vx36))))) (isLower (Char (Neg Zero)))) (isDigit (Char (Neg Zero)))",fontsize=16,color="black",shape="box"];295 -> 310[label="",style="solid", color="black", weight=3]; 81.19/61.34 1584 -> 827[label="",style="dashed", color="red", weight=0]; 81.19/61.34 1584[label="pePe (pePe (pePe MyFalse (pePe (asAs (gtEsChar (Char (Pos (Succ vx179))) (Char (Pos (Succ vx180)))) (ltEsChar (Char (Pos (Succ vx179))) (Char (Pos (Succ vx181))))) (asAs 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2833[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 2817 -> 2834[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 2818[label="pePe (pePe (not (esEsOrdering GT GT)) (isLower (Char (Pos (Succ vx362))))) (isDigit (Char (Pos (Succ vx362))))",fontsize=16,color="black",shape="box"];2818 -> 2835[label="",style="solid", color="black", weight=3]; 81.19/61.34 2819[label="pePe (pePe (not (esEsOrdering LT GT)) (isLower (Char (Pos (Succ vx362))))) (isDigit (Char (Pos (Succ vx362))))",fontsize=16,color="black",shape="box"];2819 -> 2836[label="",style="solid", color="black", weight=3]; 81.19/61.34 2820[label="pePe (pePe (not (esEsOrdering EQ GT)) (isLower (Char (Pos (Succ vx362))))) (isDigit (Char (Pos (Succ vx362))))",fontsize=16,color="black",shape="box"];2820 -> 2837[label="",style="solid", color="black", weight=3]; 81.19/61.34 2848[label="vx346",fontsize=16,color="green",shape="box"];2849[label="Succ 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2937[label="",style="solid", color="black", weight=3]; 81.19/61.34 2933[label="pePe (pePe (asAs (not (esEsOrdering EQ LT)) (ltEsChar (Char (Pos (Succ vx373))) (Char (Pos (Succ vx374))))) (pePe (asAs (gtEsChar (Char (Pos (Succ vx373))) (Char (Pos (Succ vx375)))) (ltEsChar (Char (Pos (Succ vx373))) (Char (Pos (Succ vx376))))) (asAs (gtEsChar (Char (Pos (Succ vx373))) (Char (Pos (Succ vx377)))) (ltEsChar (Char (Pos (Succ vx373))) (Char (Pos (Succ vx378))))))) (isDigit (Char (Pos (Succ vx373))))",fontsize=16,color="black",shape="box"];2933 -> 2938[label="",style="solid", color="black", weight=3]; 81.19/61.34 1065[label="pePe (pePe (asAs MyFalse (ltEsChar (Char (Pos Zero)) (Char (Pos (Succ vx150))))) (asAs (gtEsChar (Char (Pos Zero)) (Char (Pos (Succ vx151)))) (ltEsChar (Char (Pos Zero)) (Char (Pos (Succ vx152)))))) (isDigit (Char (Pos Zero)))",fontsize=16,color="black",shape="box"];1065 -> 1086[label="",style="solid", color="black", weight=3]; 81.19/61.34 1066[label="pePe (asAs (not 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81.19/61.34 3912[label="not (esEsOrdering LT LT)",fontsize=16,color="magenta"];3497[label="vx392",fontsize=16,color="green",shape="box"];3498[label="vx393",fontsize=16,color="green",shape="box"];3499[label="Succ vx390",fontsize=16,color="green",shape="box"];3500[label="vx390",fontsize=16,color="green",shape="box"];3501[label="Succ vx391",fontsize=16,color="green",shape="box"];3496[label="pePe (pePe (not (esEsOrdering (primCmpNat vx406 vx407) GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="burlywood",shape="triangle"];4010[label="vx406/Succ vx4060",fontsize=10,color="white",style="solid",shape="box"];3496 -> 4010[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4010 -> 3532[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4011[label="vx406/Zero",fontsize=10,color="white",style="solid",shape="box"];3496 -> 4011[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4011 -> 3533[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3300 -> 3552[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3300[label="pePe (asAs (not (esEsOrdering (primCmpNat (Succ vx390) (Succ vx392)) LT)) (ltEsChar (Char (Pos (Succ vx390))) (Char (Pos (Succ vx393))))) (isDigit (Char (Pos (Succ vx390))))",fontsize=16,color="magenta"];3300 -> 3553[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3300 -> 3554[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3300 -> 3555[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3300 -> 3556[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3532[label="pePe (pePe (not (esEsOrdering (primCmpNat (Succ vx4060) vx407) GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ 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3543[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4015[label="vx407/Zero",fontsize=10,color="white",style="solid",shape="box"];3533 -> 4015[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4015 -> 3544[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3553[label="vx393",fontsize=16,color="green",shape="box"];3554[label="Succ vx392",fontsize=16,color="green",shape="box"];3555[label="Succ vx390",fontsize=16,color="green",shape="box"];3556[label="vx390",fontsize=16,color="green",shape="box"];3552[label="pePe (asAs (not (esEsOrdering (primCmpNat vx414 vx415) LT)) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="burlywood",shape="triangle"];4016[label="vx414/Succ vx4140",fontsize=10,color="white",style="solid",shape="box"];3552 -> 4016[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4016 -> 3581[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4017[label="vx414/Zero",fontsize=10,color="white",style="solid",shape="box"];3552 -> 4017[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4017 -> 3582[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3541[label="pePe (pePe (not (esEsOrdering (primCmpNat (Succ vx4060) (Succ vx4070)) GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="black",shape="box"];3541 -> 3583[label="",style="solid", color="black", weight=3]; 81.19/61.34 3542[label="pePe (pePe (not (esEsOrdering (primCmpNat (Succ vx4060) Zero) GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="black",shape="box"];3542 -> 3584[label="",style="solid", color="black", weight=3]; 81.19/61.34 3543[label="pePe 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vx4150",fontsize=10,color="white",style="solid",shape="box"];3581 -> 4018[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4018 -> 3587[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4019[label="vx415/Zero",fontsize=10,color="white",style="solid",shape="box"];3581 -> 4019[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4019 -> 3588[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3582[label="pePe (asAs (not (esEsOrdering (primCmpNat Zero vx415) LT)) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="burlywood",shape="box"];4020[label="vx415/Succ vx4150",fontsize=10,color="white",style="solid",shape="box"];3582 -> 4020[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4020 -> 3589[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4021[label="vx415/Zero",fontsize=10,color="white",style="solid",shape="box"];3582 -> 4021[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4021 -> 3590[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3583 -> 3496[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3583[label="pePe (pePe (not (esEsOrdering (primCmpNat vx4060 vx4070) GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="magenta"];3583 -> 3591[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3583 -> 3592[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3584[label="pePe (pePe (not (esEsOrdering GT GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="black",shape="box"];3584 -> 3593[label="",style="solid", color="black", weight=3]; 81.19/61.34 3585[label="pePe (pePe (not (esEsOrdering LT GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="black",shape="box"];3585 -> 3594[label="",style="solid", color="black", weight=3]; 81.19/61.34 3586[label="pePe (pePe (not (esEsOrdering EQ GT)) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="black",shape="box"];3586 -> 3595[label="",style="solid", color="black", weight=3]; 81.19/61.34 3587[label="pePe (asAs (not (esEsOrdering (primCmpNat (Succ vx4140) (Succ vx4150)) LT)) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3587 -> 3596[label="",style="solid", color="black", weight=3]; 81.19/61.34 3588[label="pePe (asAs (not 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(asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="black",shape="box"];3593 -> 3600[label="",style="solid", color="black", weight=3]; 81.19/61.34 3594[label="pePe (pePe (not MyFalse) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="black",shape="triangle"];3594 -> 3601[label="",style="solid", color="black", weight=3]; 81.19/61.34 3595 -> 3594[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3595[label="pePe (pePe (not MyFalse) (asAs (gtEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx409)))) (ltEsChar (Char (Pos (Succ vx408))) (Char (Pos (Succ vx410)))))) (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="magenta"];3596 -> 3552[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3596[label="pePe (asAs (not (esEsOrdering (primCmpNat vx4140 vx4150) LT)) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="magenta"];3596 -> 3602[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3596 -> 3603[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3597[label="pePe (asAs (not (esEsOrdering GT LT)) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3597 -> 3604[label="",style="solid", color="black", weight=3]; 81.19/61.34 3598[label="pePe (asAs (not (esEsOrdering LT LT)) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3598 -> 3605[label="",style="solid", color="black", weight=3]; 81.19/61.34 3599[label="pePe (asAs (not (esEsOrdering EQ LT)) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ 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weight=3]; 81.19/61.34 3602[label="vx4150",fontsize=16,color="green",shape="box"];3603[label="vx4140",fontsize=16,color="green",shape="box"];3604[label="pePe (asAs (not MyFalse) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="triangle"];3604 -> 3611[label="",style="solid", color="black", weight=3]; 81.19/61.34 3605[label="pePe (asAs (not MyTrue) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3605 -> 3612[label="",style="solid", color="black", weight=3]; 81.19/61.34 3606 -> 3604[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3606[label="pePe (asAs (not MyFalse) (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="magenta"];3607[label="vx410",fontsize=16,color="green",shape="box"];3608[label="vx408",fontsize=16,color="green",shape="box"];3609[label="vx409",fontsize=16,color="green",shape="box"];3610 -> 1605[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3610[label="pePe MyTrue (isDigit (Char (Pos (Succ vx408))))",fontsize=16,color="magenta"];3610 -> 3613[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3611[label="pePe (asAs MyTrue (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3611 -> 3614[label="",style="solid", color="black", weight=3]; 81.19/61.34 3612[label="pePe (asAs MyFalse (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417))))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3612 -> 3615[label="",style="solid", color="black", weight=3]; 81.19/61.34 3613[label="vx408",fontsize=16,color="green",shape="box"];3614[label="pePe (ltEsChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417)))) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3614 -> 3616[label="",style="solid", color="black", weight=3]; 81.19/61.34 3615[label="pePe MyFalse (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3615 -> 3617[label="",style="solid", color="black", weight=3]; 81.19/61.34 3616[label="pePe (fsEsOrdering (compareChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417)))) GT) (isDigit (Char (Pos (Succ vx416))))",fontsize=16,color="black",shape="box"];3616 -> 3618[label="",style="solid", color="black", weight=3]; 81.19/61.34 3617[label="isDigit (Char (Pos (Succ vx416)))",fontsize=16,color="black",shape="triangle"];3617 -> 3619[label="",style="solid", color="black", weight=3]; 81.19/61.34 3618 -> 3620[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3618[label="pePe (not (esEsOrdering 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(Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="magenta"];3619 -> 3833[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3619 -> 3834[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3621 -> 3617[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3621[label="isDigit (Char (Pos (Succ vx416)))",fontsize=16,color="magenta"];3620[label="pePe (not (esEsOrdering (compareChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417)))) GT)) vx418",fontsize=16,color="black",shape="triangle"];3620 -> 3625[label="",style="solid", color="black", weight=3]; 81.19/61.34 3833 -> 3879[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3833[label="ltEsChar (Char (Pos (Succ vx416))) (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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="magenta"];3833 -> 3880[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3833 -> 3881[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3834 -> 3888[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3834[label="gtEsChar (Char (Pos (Succ vx416))) (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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="magenta"];3834 -> 3889[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3834 -> 3890[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3625[label="pePe (not (esEsOrdering (primCmpChar (Char (Pos (Succ vx416))) (Char (Pos (Succ vx417)))) GT)) vx418",fontsize=16,color="black",shape="box"];3625 -> 3634[label="",style="solid", color="black", weight=3]; 81.19/61.34 3880[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];3881[label="vx416",fontsize=16,color="green",shape="box"];3879[label="ltEsChar (Char (Pos (Succ vx444))) (Char (Pos (Succ vx445)))",fontsize=16,color="black",shape="triangle"];3879 -> 3897[label="",style="solid", color="black", weight=3]; 81.19/61.34 3889[label="vx416",fontsize=16,color="green",shape="box"];3890[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];3888[label="gtEsChar (Char (Pos (Succ vx447))) (Char (Pos (Succ vx448)))",fontsize=16,color="black",shape="triangle"];3888 -> 3898[label="",style="solid", color="black", weight=3]; 81.19/61.34 3634[label="pePe (not (esEsOrdering (primCmpInt (Pos (Succ vx416)) (Pos (Succ vx417))) GT)) vx418",fontsize=16,color="black",shape="box"];3634 -> 3636[label="",style="solid", color="black", weight=3]; 81.19/61.34 3897[label="fsEsOrdering (compareChar (Char (Pos (Succ vx444))) (Char (Pos (Succ vx445)))) GT",fontsize=16,color="black",shape="box"];3897 -> 3903[label="",style="solid", color="black", weight=3]; 81.19/61.34 3898[label="fsEsOrdering (compareChar (Char (Pos (Succ vx447))) (Char (Pos (Succ vx448)))) LT",fontsize=16,color="black",shape="box"];3898 -> 3904[label="",style="solid", color="black", weight=3]; 81.19/61.34 3636[label="pePe (not (esEsOrdering (primCmpNat (Succ vx416) (Succ vx417)) GT)) vx418",fontsize=16,color="black",shape="box"];3636 -> 3638[label="",style="solid", color="black", weight=3]; 81.19/61.34 3903[label="not (esEsOrdering (compareChar (Char (Pos (Succ vx444))) (Char (Pos (Succ vx445)))) GT)",fontsize=16,color="black",shape="box"];3903 -> 3909[label="",style="solid", color="black", weight=3]; 81.19/61.34 3904[label="not (esEsOrdering (compareChar (Char (Pos (Succ vx447))) (Char (Pos (Succ vx448)))) LT)",fontsize=16,color="black",shape="box"];3904 -> 3910[label="",style="solid", color="black", weight=3]; 81.19/61.34 3638[label="pePe (not (esEsOrdering (primCmpNat vx416 vx417) GT)) vx418",fontsize=16,color="burlywood",shape="triangle"];4022[label="vx416/Succ vx4160",fontsize=10,color="white",style="solid",shape="box"];3638 -> 4022[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4022 -> 3640[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4023[label="vx416/Zero",fontsize=10,color="white",style="solid",shape="box"];3638 -> 4023[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4023 -> 3641[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3909[label="not (esEsOrdering (primCmpChar (Char (Pos (Succ vx444))) (Char (Pos (Succ vx445)))) GT)",fontsize=16,color="black",shape="box"];3909 -> 3913[label="",style="solid", color="black", weight=3]; 81.19/61.34 3910[label="not (esEsOrdering (primCmpChar (Char (Pos (Succ vx447))) (Char (Pos (Succ vx448)))) LT)",fontsize=16,color="black",shape="box"];3910 -> 3914[label="",style="solid", color="black", weight=3]; 81.19/61.34 3640[label="pePe (not (esEsOrdering (primCmpNat (Succ vx4160) vx417) GT)) vx418",fontsize=16,color="burlywood",shape="box"];4024[label="vx417/Succ vx4170",fontsize=10,color="white",style="solid",shape="box"];3640 -> 4024[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4024 -> 3643[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4025[label="vx417/Zero",fontsize=10,color="white",style="solid",shape="box"];3640 -> 4025[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4025 -> 3644[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3641[label="pePe (not (esEsOrdering (primCmpNat Zero vx417) GT)) vx418",fontsize=16,color="burlywood",shape="box"];4026[label="vx417/Succ vx4170",fontsize=10,color="white",style="solid",shape="box"];3641 -> 4026[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4026 -> 3645[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4027[label="vx417/Zero",fontsize=10,color="white",style="solid",shape="box"];3641 -> 4027[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4027 -> 3646[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3913[label="not (esEsOrdering (primCmpInt (Pos (Succ vx444)) (Pos (Succ vx445))) GT)",fontsize=16,color="black",shape="box"];3913 -> 3915[label="",style="solid", color="black", weight=3]; 81.19/61.34 3914[label="not (esEsOrdering (primCmpInt (Pos (Succ vx447)) (Pos (Succ vx448))) LT)",fontsize=16,color="black",shape="box"];3914 -> 3916[label="",style="solid", color="black", weight=3]; 81.19/61.34 3643[label="pePe (not (esEsOrdering (primCmpNat (Succ vx4160) (Succ vx4170)) GT)) vx418",fontsize=16,color="black",shape="box"];3643 -> 3648[label="",style="solid", color="black", weight=3]; 81.19/61.34 3644[label="pePe (not (esEsOrdering (primCmpNat (Succ vx4160) Zero) GT)) vx418",fontsize=16,color="black",shape="box"];3644 -> 3649[label="",style="solid", color="black", weight=3]; 81.19/61.34 3645[label="pePe (not (esEsOrdering (primCmpNat Zero (Succ vx4170)) GT)) vx418",fontsize=16,color="black",shape="box"];3645 -> 3650[label="",style="solid", color="black", weight=3]; 81.19/61.34 3646[label="pePe (not (esEsOrdering (primCmpNat Zero Zero) GT)) vx418",fontsize=16,color="black",shape="box"];3646 -> 3651[label="",style="solid", color="black", weight=3]; 81.19/61.34 3915[label="not (esEsOrdering (primCmpNat (Succ vx444) (Succ vx445)) GT)",fontsize=16,color="black",shape="box"];3915 -> 3917[label="",style="solid", color="black", weight=3]; 81.19/61.34 3916[label="not (esEsOrdering (primCmpNat (Succ vx447) (Succ vx448)) LT)",fontsize=16,color="black",shape="box"];3916 -> 3918[label="",style="solid", color="black", weight=3]; 81.19/61.34 3648 -> 3638[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3648[label="pePe (not (esEsOrdering (primCmpNat vx4160 vx4170) GT)) vx418",fontsize=16,color="magenta"];3648 -> 3654[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3648 -> 3655[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3649[label="pePe (not (esEsOrdering GT GT)) vx418",fontsize=16,color="black",shape="box"];3649 -> 3656[label="",style="solid", color="black", weight=3]; 81.19/61.34 3650[label="pePe (not (esEsOrdering LT GT)) vx418",fontsize=16,color="black",shape="box"];3650 -> 3657[label="",style="solid", color="black", weight=3]; 81.19/61.34 3651[label="pePe (not (esEsOrdering EQ GT)) vx418",fontsize=16,color="black",shape="box"];3651 -> 3658[label="",style="solid", color="black", weight=3]; 81.19/61.34 3917[label="not (esEsOrdering (primCmpNat vx444 vx445) GT)",fontsize=16,color="burlywood",shape="triangle"];4028[label="vx444/Succ vx4440",fontsize=10,color="white",style="solid",shape="box"];3917 -> 4028[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4028 -> 3919[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4029[label="vx444/Zero",fontsize=10,color="white",style="solid",shape="box"];3917 -> 4029[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4029 -> 3920[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3918[label="not (esEsOrdering (primCmpNat vx447 vx448) LT)",fontsize=16,color="burlywood",shape="triangle"];4030[label="vx447/Succ vx4470",fontsize=10,color="white",style="solid",shape="box"];3918 -> 4030[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4030 -> 3921[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4031[label="vx447/Zero",fontsize=10,color="white",style="solid",shape="box"];3918 -> 4031[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4031 -> 3922[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3654[label="vx4170",fontsize=16,color="green",shape="box"];3655[label="vx4160",fontsize=16,color="green",shape="box"];3656[label="pePe (not MyTrue) vx418",fontsize=16,color="black",shape="box"];3656 -> 3663[label="",style="solid", color="black", weight=3]; 81.19/61.34 3657[label="pePe (not MyFalse) vx418",fontsize=16,color="black",shape="triangle"];3657 -> 3664[label="",style="solid", color="black", weight=3]; 81.19/61.34 3658 -> 3657[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3658[label="pePe (not MyFalse) vx418",fontsize=16,color="magenta"];3919[label="not (esEsOrdering (primCmpNat (Succ vx4440) vx445) GT)",fontsize=16,color="burlywood",shape="box"];4032[label="vx445/Succ vx4450",fontsize=10,color="white",style="solid",shape="box"];3919 -> 4032[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4032 -> 3923[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4033[label="vx445/Zero",fontsize=10,color="white",style="solid",shape="box"];3919 -> 4033[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4033 -> 3924[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3920[label="not (esEsOrdering (primCmpNat Zero vx445) GT)",fontsize=16,color="burlywood",shape="box"];4034[label="vx445/Succ vx4450",fontsize=10,color="white",style="solid",shape="box"];3920 -> 4034[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4034 -> 3925[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4035[label="vx445/Zero",fontsize=10,color="white",style="solid",shape="box"];3920 -> 4035[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4035 -> 3926[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3921[label="not (esEsOrdering (primCmpNat (Succ vx4470) vx448) LT)",fontsize=16,color="burlywood",shape="box"];4036[label="vx448/Succ vx4480",fontsize=10,color="white",style="solid",shape="box"];3921 -> 4036[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4036 -> 3927[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4037[label="vx448/Zero",fontsize=10,color="white",style="solid",shape="box"];3921 -> 4037[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4037 -> 3928[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3922[label="not (esEsOrdering (primCmpNat Zero vx448) LT)",fontsize=16,color="burlywood",shape="box"];4038[label="vx448/Succ vx4480",fontsize=10,color="white",style="solid",shape="box"];3922 -> 4038[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4038 -> 3929[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 4039[label="vx448/Zero",fontsize=10,color="white",style="solid",shape="box"];3922 -> 4039[label="",style="solid", color="burlywood", weight=9]; 81.19/61.34 4039 -> 3930[label="",style="solid", color="burlywood", weight=3]; 81.19/61.34 3663[label="pePe MyFalse vx418",fontsize=16,color="black",shape="box"];3663 -> 3669[label="",style="solid", color="black", weight=3]; 81.19/61.34 3664[label="pePe MyTrue vx418",fontsize=16,color="black",shape="box"];3664 -> 3670[label="",style="solid", color="black", weight=3]; 81.19/61.34 3923[label="not (esEsOrdering (primCmpNat (Succ vx4440) (Succ vx4450)) GT)",fontsize=16,color="black",shape="box"];3923 -> 3931[label="",style="solid", color="black", weight=3]; 81.19/61.34 3924[label="not (esEsOrdering (primCmpNat (Succ vx4440) Zero) GT)",fontsize=16,color="black",shape="box"];3924 -> 3932[label="",style="solid", color="black", weight=3]; 81.19/61.34 3925[label="not (esEsOrdering (primCmpNat Zero (Succ vx4450)) GT)",fontsize=16,color="black",shape="box"];3925 -> 3933[label="",style="solid", color="black", weight=3]; 81.19/61.34 3926[label="not (esEsOrdering (primCmpNat Zero Zero) GT)",fontsize=16,color="black",shape="box"];3926 -> 3934[label="",style="solid", color="black", weight=3]; 81.19/61.34 3927[label="not (esEsOrdering (primCmpNat (Succ vx4470) (Succ vx4480)) LT)",fontsize=16,color="black",shape="box"];3927 -> 3935[label="",style="solid", color="black", weight=3]; 81.19/61.34 3928[label="not (esEsOrdering (primCmpNat (Succ vx4470) Zero) LT)",fontsize=16,color="black",shape="box"];3928 -> 3936[label="",style="solid", color="black", weight=3]; 81.19/61.34 3929[label="not (esEsOrdering (primCmpNat Zero (Succ vx4480)) LT)",fontsize=16,color="black",shape="box"];3929 -> 3937[label="",style="solid", color="black", weight=3]; 81.19/61.34 3930[label="not (esEsOrdering (primCmpNat Zero Zero) LT)",fontsize=16,color="black",shape="box"];3930 -> 3938[label="",style="solid", color="black", weight=3]; 81.19/61.34 3669[label="vx418",fontsize=16,color="green",shape="box"];3670[label="MyTrue",fontsize=16,color="green",shape="box"];3931 -> 3917[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3931[label="not (esEsOrdering (primCmpNat vx4440 vx4450) GT)",fontsize=16,color="magenta"];3931 -> 3939[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3931 -> 3940[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3932[label="not (esEsOrdering GT GT)",fontsize=16,color="black",shape="box"];3932 -> 3941[label="",style="solid", color="black", weight=3]; 81.19/61.34 3933 -> 3891[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3933[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];3934[label="not (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];3934 -> 3942[label="",style="solid", color="black", weight=3]; 81.19/61.34 3935 -> 3918[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3935[label="not (esEsOrdering (primCmpNat vx4470 vx4480) LT)",fontsize=16,color="magenta"];3935 -> 3943[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3935 -> 3944[label="",style="dashed", color="magenta", weight=3]; 81.19/61.34 3936[label="not (esEsOrdering GT LT)",fontsize=16,color="black",shape="box"];3936 -> 3945[label="",style="solid", color="black", weight=3]; 81.19/61.34 3937 -> 3892[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3937[label="not (esEsOrdering LT LT)",fontsize=16,color="magenta"];3938[label="not (esEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];3938 -> 3946[label="",style="solid", color="black", weight=3]; 81.19/61.34 3939[label="vx4450",fontsize=16,color="green",shape="box"];3940[label="vx4440",fontsize=16,color="green",shape="box"];3941 -> 3900[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3941[label="not MyTrue",fontsize=16,color="magenta"];3942 -> 3899[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3942[label="not MyFalse",fontsize=16,color="magenta"];3943[label="vx4470",fontsize=16,color="green",shape="box"];3944[label="vx4480",fontsize=16,color="green",shape="box"];3945 -> 3899[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3945[label="not MyFalse",fontsize=16,color="magenta"];3946 -> 3899[label="",style="dashed", color="red", weight=0]; 81.19/61.34 3946[label="not MyFalse",fontsize=16,color="magenta"];} 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (6) 81.19/61.34 Complex Obligation (AND) 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (7) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe5(Main.Succ(vx3600), Main.Succ(vx3610), vx362) -> new_pePe5(vx3600, vx3610, vx362) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (8) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe5(Main.Succ(vx3600), Main.Succ(vx3610), vx362) -> new_pePe5(vx3600, vx3610, vx362) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (9) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (10) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe2(Main.Succ(vx3880), Main.Succ(vx3890), vx390, vx391, vx392, vx393) -> new_pePe2(vx3880, vx3890, vx390, vx391, vx392, vx393) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (11) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe2(Main.Succ(vx3880), Main.Succ(vx3890), vx390, vx391, vx392, vx393) -> new_pePe2(vx3880, vx3890, vx390, vx391, vx392, vx393) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (12) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (13) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe3(Main.Succ(vx3800), Main.Succ(vx3810), vx382, vx383, vx384, vx385, vx386) -> new_pePe3(vx3800, vx3810, vx382, vx383, vx384, vx385, vx386) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (14) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe3(Main.Succ(vx3800), Main.Succ(vx3810), vx382, vx383, vx384, vx385, vx386) -> new_pePe3(vx3800, vx3810, vx382, vx383, vx384, vx385, vx386) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (15) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (16) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe10(Main.Succ(vx1180), Main.Succ(vx1190), vx120, vx121, vx122, vx123, vx124, vx125) -> new_pePe10(vx1180, vx1190, vx120, vx121, vx122, vx123, vx124, vx125) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (17) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe10(Main.Succ(vx1180), Main.Succ(vx1190), vx120, vx121, vx122, vx123, vx124, vx125) -> new_pePe10(vx1180, vx1190, vx120, vx121, vx122, vx123, vx124, vx125) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (18) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (19) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe(Main.Succ(vx4160), Main.Succ(vx4170), vx418) -> new_pePe(vx4160, vx4170, vx418) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (20) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe(Main.Succ(vx4160), Main.Succ(vx4170), vx418) -> new_pePe(vx4160, vx4170, vx418) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (21) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (22) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe0(Main.Succ(vx4140), Main.Succ(vx4150), vx416, vx417) -> new_pePe0(vx4140, vx4150, vx416, vx417) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (23) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe0(Main.Succ(vx4140), Main.Succ(vx4150), vx416, vx417) -> new_pePe0(vx4140, vx4150, vx416, vx417) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (24) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (25) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe8(Main.Succ(vx1890), Main.Succ(vx1900), vx191, vx192, vx193, vx194) -> new_pePe8(vx1890, vx1900, vx191, vx192, vx193, vx194) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (26) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe8(Main.Succ(vx1890), Main.Succ(vx1900), vx191, vx192, vx193, vx194) -> new_pePe8(vx1890, vx1900, vx191, vx192, vx193, vx194) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (27) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (28) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe1(Main.Succ(vx4060), Main.Succ(vx4070), vx408, vx409, vx410) -> new_pePe1(vx4060, vx4070, vx408, vx409, vx410) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (29) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe1(Main.Succ(vx4060), Main.Succ(vx4070), vx408, vx409, vx410) -> new_pePe1(vx4060, vx4070, vx408, vx409, vx410) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (30) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (31) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_not0(Main.Succ(vx4440), Main.Succ(vx4450)) -> new_not0(vx4440, vx4450) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (32) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_not0(Main.Succ(vx4440), Main.Succ(vx4450)) -> new_not0(vx4440, vx4450) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (33) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (34) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe9(Main.Succ(vx1770), Main.Succ(vx1780), vx179, vx180, vx181, vx182, vx183) -> new_pePe9(vx1770, vx1780, vx179, vx180, vx181, vx182, vx183) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (35) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe9(Main.Succ(vx1770), Main.Succ(vx1780), vx179, vx180, vx181, vx182, vx183) -> new_pePe9(vx1770, vx1780, vx179, vx180, vx181, vx182, vx183) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (36) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (37) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe6(Main.Succ(vx3110), Main.Succ(vx3120), vx313, vx314) -> new_pePe6(vx3110, vx3120, vx313, vx314) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (38) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe6(Main.Succ(vx3110), Main.Succ(vx3120), vx313, vx314) -> new_pePe6(vx3110, vx3120, vx313, vx314) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (39) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (40) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe4(Main.Succ(vx3710), Main.Succ(vx3720), vx373, vx374, vx375, vx376, vx377, vx378) -> new_pePe4(vx3710, vx3720, vx373, vx374, vx375, vx376, vx377, vx378) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (41) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe4(Main.Succ(vx3710), Main.Succ(vx3720), vx373, vx374, vx375, vx376, vx377, vx378) -> new_pePe4(vx3710, vx3720, vx373, vx374, vx375, vx376, vx377, vx378) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (42) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (43) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_pePe7(Main.Succ(vx3050), Main.Succ(vx3060), vx307, vx308, vx309) -> new_pePe7(vx3050, vx3060, vx307, vx308, vx309) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (44) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_pePe7(Main.Succ(vx3050), Main.Succ(vx3060), vx307, vx308, vx309) -> new_pePe7(vx3050, vx3060, vx307, vx308, vx309) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (45) 81.19/61.34 YES 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (46) 81.19/61.34 Obligation: 81.19/61.34 Q DP problem: 81.19/61.34 The TRS P consists of the following rules: 81.19/61.34 81.19/61.34 new_not(Main.Succ(vx4470), Main.Succ(vx4480)) -> new_not(vx4470, vx4480) 81.19/61.34 81.19/61.34 R is empty. 81.19/61.34 Q is empty. 81.19/61.34 We have to consider all minimal (P,Q,R)-chains. 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (47) QDPSizeChangeProof (EQUIVALENT) 81.19/61.34 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. 81.19/61.34 81.19/61.34 From the DPs we obtained the following set of size-change graphs: 81.19/61.34 *new_not(Main.Succ(vx4470), Main.Succ(vx4480)) -> new_not(vx4470, vx4480) 81.19/61.34 The graph contains the following edges 1 > 1, 2 > 2 81.19/61.34 81.19/61.34 81.19/61.34 ---------------------------------------- 81.19/61.34 81.19/61.34 (48) 81.19/61.34 YES 81.51/61.46 EOF