17.97/6.52 YES 20.21/7.19 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 20.21/7.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.21/7.19 20.21/7.19 20.21/7.19 H-Termination with start terms of the given HASKELL could be proven: 20.21/7.19 20.21/7.19 (0) HASKELL 20.21/7.19 (1) BR [EQUIVALENT, 0 ms] 20.21/7.19 (2) HASKELL 20.21/7.19 (3) COR [EQUIVALENT, 0 ms] 20.21/7.19 (4) HASKELL 20.21/7.19 (5) Narrow [SOUND, 0 ms] 20.21/7.19 (6) AND 20.21/7.19 (7) QDP 20.21/7.19 (8) QDPOrderProof [EQUIVALENT, 17 ms] 20.21/7.19 (9) QDP 20.21/7.19 (10) DependencyGraphProof [EQUIVALENT, 0 ms] 20.21/7.19 (11) QDP 20.21/7.19 (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.21/7.19 (13) YES 20.21/7.19 (14) QDP 20.21/7.19 (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.21/7.19 (16) YES 20.21/7.19 (17) QDP 20.21/7.19 (18) DependencyGraphProof [EQUIVALENT, 0 ms] 20.21/7.19 (19) QDP 20.21/7.19 (20) QDPOrderProof [EQUIVALENT, 10 ms] 20.21/7.19 (21) QDP 20.21/7.19 (22) DependencyGraphProof [EQUIVALENT, 0 ms] 20.21/7.19 (23) QDP 20.21/7.19 (24) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.21/7.19 (25) YES 20.21/7.19 20.21/7.19 20.21/7.19 ---------------------------------------- 20.21/7.19 20.21/7.19 (0) 20.21/7.19 Obligation: 20.21/7.19 mainModule Main 20.21/7.19 module Main where { 20.21/7.19 import qualified Prelude; 20.21/7.19 data Integer = Integer MyInt ; 20.21/7.19 20.21/7.19 data MyBool = MyTrue | MyFalse ; 20.21/7.19 20.21/7.19 data MyInt = Pos Main.Nat | Neg Main.Nat ; 20.21/7.19 20.21/7.19 data Main.Nat = Succ Main.Nat | Zero ; 20.21/7.19 20.21/7.19 data Ordering = LT | EQ | GT ; 20.21/7.19 20.21/7.19 data Ratio a = CnPc a a ; 20.21/7.19 20.21/7.19 data Tup2 a b = Tup2 a b ; 20.21/7.19 20.21/7.19 ceilingCeiling0 xv MyTrue = psMyInt (ceilingN xv) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 20.21/7.19 ceilingCeiling0 xv MyFalse = ceilingN xv; 20.21/7.19 20.21/7.19 ceilingN xv = ceilingN0 xv (ceilingVu8 xv); 20.21/7.19 20.21/7.19 ceilingN0 xv (Tup2 n vw) = n; 20.21/7.19 20.21/7.19 ceilingR xv = ceilingR0 xv (ceilingVu8 xv); 20.21/7.19 20.21/7.19 ceilingR0 xv (Tup2 vv r) = r; 20.21/7.19 20.21/7.19 ceilingRatio :: Ratio MyInt -> MyInt; 20.21/7.19 ceilingRatio x = ceilingCeiling0 x (gtRatio (ceilingR x) (fromIntRatio (Main.Pos Main.Zero))); 20.21/7.19 20.21/7.19 ceilingVu8 xv = properFractionRatio xv; 20.21/7.19 20.21/7.19 compareMyInt :: MyInt -> MyInt -> Ordering; 20.21/7.19 compareMyInt = primCmpInt; 20.21/7.19 20.21/7.19 compareRatio :: Ratio MyInt -> Ratio MyInt -> Ordering; 20.21/7.19 compareRatio (CnPc x y) (CnPc x' y') = compareMyInt (srMyInt x y') (srMyInt x' y); 20.21/7.19 20.21/7.19 error :: a; 20.21/7.19 error = stop MyTrue; 20.21/7.19 20.21/7.19 esEsOrdering :: Ordering -> Ordering -> MyBool; 20.21/7.19 esEsOrdering LT LT = MyTrue; 20.21/7.19 esEsOrdering LT EQ = MyFalse; 20.21/7.19 esEsOrdering LT GT = MyFalse; 20.21/7.19 esEsOrdering EQ LT = MyFalse; 20.21/7.19 esEsOrdering EQ EQ = MyTrue; 20.21/7.19 esEsOrdering EQ GT = MyFalse; 20.21/7.19 esEsOrdering GT LT = MyFalse; 20.21/7.19 esEsOrdering GT EQ = MyFalse; 20.21/7.19 esEsOrdering GT GT = MyTrue; 20.21/7.19 20.21/7.19 fromIntMyInt :: MyInt -> MyInt; 20.21/7.19 fromIntMyInt x = x; 20.21/7.19 20.21/7.19 fromIntRatio :: MyInt -> Ratio MyInt; 20.21/7.19 fromIntRatio = intToRatio; 20.21/7.19 20.21/7.19 fromIntegerMyInt :: Integer -> MyInt; 20.21/7.19 fromIntegerMyInt (Integer x) = x; 20.21/7.19 20.21/7.19 fromIntegral = pt fromIntegerMyInt toIntegerMyInt; 20.21/7.19 20.21/7.19 gtRatio :: Ratio MyInt -> Ratio MyInt -> MyBool; 20.21/7.19 gtRatio x y = esEsOrdering (compareRatio x y) GT; 20.21/7.19 20.21/7.19 intToRatio x = CnPc (fromIntMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 20.21/7.19 20.21/7.19 primCmpInt :: MyInt -> MyInt -> Ordering; 20.21/7.19 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 20.21/7.19 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 20.21/7.19 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 20.21/7.19 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 20.21/7.19 20.21/7.19 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 20.21/7.19 primCmpNat Main.Zero Main.Zero = EQ; 20.21/7.19 primCmpNat Main.Zero (Main.Succ y) = LT; 20.21/7.19 primCmpNat (Main.Succ x) Main.Zero = GT; 20.21/7.19 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 20.21/7.19 20.21/7.19 primDivNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primDivNatS Main.Zero Main.Zero = Main.error; 20.21/7.19 primDivNatS (Main.Succ x) Main.Zero = Main.error; 20.21/7.19 primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y); 20.21/7.19 primDivNatS Main.Zero (Main.Succ x) = Main.Zero; 20.21/7.19 20.21/7.19 primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y)); 20.21/7.19 primDivNatS0 x y MyFalse = Main.Zero; 20.21/7.19 20.21/7.19 primGEqNatS :: Main.Nat -> Main.Nat -> MyBool; 20.21/7.19 primGEqNatS (Main.Succ x) Main.Zero = MyTrue; 20.21/7.19 primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y; 20.21/7.19 primGEqNatS Main.Zero (Main.Succ x) = MyFalse; 20.21/7.19 primGEqNatS Main.Zero Main.Zero = MyTrue; 20.21/7.19 20.21/7.19 primMinusNat :: Main.Nat -> Main.Nat -> MyInt; 20.21/7.19 primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero; 20.21/7.19 primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y); 20.21/7.19 primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x); 20.21/7.19 primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y; 20.21/7.19 20.21/7.19 primMinusNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y; 20.21/7.19 primMinusNatS Main.Zero (Main.Succ y) = Main.Zero; 20.21/7.19 primMinusNatS x Main.Zero = x; 20.21/7.19 20.21/7.19 primModNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primModNatS Main.Zero Main.Zero = Main.error; 20.21/7.19 primModNatS Main.Zero (Main.Succ x) = Main.Zero; 20.21/7.19 primModNatS (Main.Succ x) Main.Zero = Main.error; 20.21/7.19 primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero; 20.21/7.19 primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y)); 20.21/7.19 20.21/7.19 primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y)); 20.21/7.19 primModNatS0 x y MyFalse = Main.Succ x; 20.21/7.19 20.21/7.19 primMulInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y); 20.21/7.19 primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y); 20.21/7.19 primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y); 20.21/7.19 primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y); 20.21/7.19 20.21/7.19 primMulNat :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primMulNat Main.Zero Main.Zero = Main.Zero; 20.21/7.19 primMulNat Main.Zero (Main.Succ y) = Main.Zero; 20.21/7.19 primMulNat (Main.Succ x) Main.Zero = Main.Zero; 20.21/7.19 primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y); 20.21/7.19 20.21/7.19 primPlusInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y; 20.21/7.19 primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x; 20.21/7.19 primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y); 20.21/7.19 primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y); 20.21/7.19 20.21/7.19 primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primPlusNat Main.Zero Main.Zero = Main.Zero; 20.21/7.19 primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; 20.21/7.19 primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; 20.21/7.19 primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); 20.21/7.19 20.21/7.19 primQrmInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; 20.21/7.19 primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y); 20.21/7.19 20.21/7.19 primQuotInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primQuotInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt wx wy = Main.error; 20.21/7.19 20.21/7.19 primRemInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primRemInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt vz wu = Main.error; 20.21/7.19 20.21/7.19 properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx); 20.21/7.19 20.21/7.19 properFractionQ1 xw xx (Tup2 q vx) = q; 20.21/7.19 20.21/7.19 properFractionR xw xx = properFractionR1 xw xx (properFractionVu30 xw xx); 20.21/7.19 20.21/7.19 properFractionR1 xw xx (Tup2 vy r) = r; 20.21/7.19 20.21/7.19 properFractionRatio :: Ratio MyInt -> Tup2 MyInt (Ratio MyInt); 20.21/7.19 properFractionRatio (CnPc x y) = Tup2 (fromIntegral (properFractionQ x y)) (CnPc (properFractionR x y) y); 20.21/7.19 20.21/7.19 properFractionVu30 xw xx = quotRemMyInt xw xx; 20.21/7.19 20.21/7.19 psMyInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 psMyInt = primPlusInt; 20.21/7.19 20.21/7.19 pt :: (a -> c) -> (b -> a) -> b -> c; 20.21/7.19 pt f g x = f (g x); 20.21/7.19 20.21/7.19 quotRemMyInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; 20.21/7.19 quotRemMyInt = primQrmInt; 20.21/7.19 20.21/7.19 srMyInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 srMyInt = primMulInt; 20.21/7.19 20.21/7.19 stop :: MyBool -> a; 20.21/7.19 stop MyFalse = stop MyFalse; 20.21/7.19 20.21/7.19 toIntegerMyInt :: MyInt -> Integer; 20.21/7.19 toIntegerMyInt x = Integer x; 20.21/7.19 20.21/7.19 } 20.21/7.19 20.21/7.19 ---------------------------------------- 20.21/7.19 20.21/7.19 (1) BR (EQUIVALENT) 20.21/7.19 Replaced joker patterns by fresh variables and removed binding patterns. 20.21/7.19 ---------------------------------------- 20.21/7.19 20.21/7.19 (2) 20.21/7.19 Obligation: 20.21/7.19 mainModule Main 20.21/7.19 module Main where { 20.21/7.19 import qualified Prelude; 20.21/7.19 data Integer = Integer MyInt ; 20.21/7.19 20.21/7.19 data MyBool = MyTrue | MyFalse ; 20.21/7.19 20.21/7.19 data MyInt = Pos Main.Nat | Neg Main.Nat ; 20.21/7.19 20.21/7.19 data Main.Nat = Succ Main.Nat | Zero ; 20.21/7.19 20.21/7.19 data Ordering = LT | EQ | GT ; 20.21/7.19 20.21/7.19 data Ratio a = CnPc a a ; 20.21/7.19 20.21/7.19 data Tup2 b a = Tup2 b a ; 20.21/7.19 20.21/7.19 ceilingCeiling0 xv MyTrue = psMyInt (ceilingN xv) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 20.21/7.19 ceilingCeiling0 xv MyFalse = ceilingN xv; 20.21/7.19 20.21/7.19 ceilingN xv = ceilingN0 xv (ceilingVu8 xv); 20.21/7.19 20.21/7.19 ceilingN0 xv (Tup2 n vw) = n; 20.21/7.19 20.21/7.19 ceilingR xv = ceilingR0 xv (ceilingVu8 xv); 20.21/7.19 20.21/7.19 ceilingR0 xv (Tup2 vv r) = r; 20.21/7.19 20.21/7.19 ceilingRatio :: Ratio MyInt -> MyInt; 20.21/7.19 ceilingRatio x = ceilingCeiling0 x (gtRatio (ceilingR x) (fromIntRatio (Main.Pos Main.Zero))); 20.21/7.19 20.21/7.19 ceilingVu8 xv = properFractionRatio xv; 20.21/7.19 20.21/7.19 compareMyInt :: MyInt -> MyInt -> Ordering; 20.21/7.19 compareMyInt = primCmpInt; 20.21/7.19 20.21/7.19 compareRatio :: Ratio MyInt -> Ratio MyInt -> Ordering; 20.21/7.19 compareRatio (CnPc x y) (CnPc x' y') = compareMyInt (srMyInt x y') (srMyInt x' y); 20.21/7.19 20.21/7.19 error :: a; 20.21/7.19 error = stop MyTrue; 20.21/7.19 20.21/7.19 esEsOrdering :: Ordering -> Ordering -> MyBool; 20.21/7.19 esEsOrdering LT LT = MyTrue; 20.21/7.19 esEsOrdering LT EQ = MyFalse; 20.21/7.19 esEsOrdering LT GT = MyFalse; 20.21/7.19 esEsOrdering EQ LT = MyFalse; 20.21/7.19 esEsOrdering EQ EQ = MyTrue; 20.21/7.19 esEsOrdering EQ GT = MyFalse; 20.21/7.19 esEsOrdering GT LT = MyFalse; 20.21/7.19 esEsOrdering GT EQ = MyFalse; 20.21/7.19 esEsOrdering GT GT = MyTrue; 20.21/7.19 20.21/7.19 fromIntMyInt :: MyInt -> MyInt; 20.21/7.19 fromIntMyInt x = x; 20.21/7.19 20.21/7.19 fromIntRatio :: MyInt -> Ratio MyInt; 20.21/7.19 fromIntRatio = intToRatio; 20.21/7.19 20.21/7.19 fromIntegerMyInt :: Integer -> MyInt; 20.21/7.19 fromIntegerMyInt (Integer x) = x; 20.21/7.19 20.21/7.19 fromIntegral = pt fromIntegerMyInt toIntegerMyInt; 20.21/7.19 20.21/7.19 gtRatio :: Ratio MyInt -> Ratio MyInt -> MyBool; 20.21/7.19 gtRatio x y = esEsOrdering (compareRatio x y) GT; 20.21/7.19 20.21/7.19 intToRatio x = CnPc (fromIntMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 20.21/7.19 20.21/7.19 primCmpInt :: MyInt -> MyInt -> Ordering; 20.21/7.19 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 20.21/7.19 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 20.21/7.19 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 20.21/7.19 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 20.21/7.19 20.21/7.19 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 20.21/7.19 primCmpNat Main.Zero Main.Zero = EQ; 20.21/7.19 primCmpNat Main.Zero (Main.Succ y) = LT; 20.21/7.19 primCmpNat (Main.Succ x) Main.Zero = GT; 20.21/7.19 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 20.21/7.19 20.21/7.19 primDivNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primDivNatS Main.Zero Main.Zero = Main.error; 20.21/7.19 primDivNatS (Main.Succ x) Main.Zero = Main.error; 20.21/7.19 primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y); 20.21/7.19 primDivNatS Main.Zero (Main.Succ x) = Main.Zero; 20.21/7.19 20.21/7.19 primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y)); 20.21/7.19 primDivNatS0 x y MyFalse = Main.Zero; 20.21/7.19 20.21/7.19 primGEqNatS :: Main.Nat -> Main.Nat -> MyBool; 20.21/7.19 primGEqNatS (Main.Succ x) Main.Zero = MyTrue; 20.21/7.19 primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y; 20.21/7.19 primGEqNatS Main.Zero (Main.Succ x) = MyFalse; 20.21/7.19 primGEqNatS Main.Zero Main.Zero = MyTrue; 20.21/7.19 20.21/7.19 primMinusNat :: Main.Nat -> Main.Nat -> MyInt; 20.21/7.19 primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero; 20.21/7.19 primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y); 20.21/7.19 primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x); 20.21/7.19 primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y; 20.21/7.19 20.21/7.19 primMinusNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y; 20.21/7.19 primMinusNatS Main.Zero (Main.Succ y) = Main.Zero; 20.21/7.19 primMinusNatS x Main.Zero = x; 20.21/7.19 20.21/7.19 primModNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primModNatS Main.Zero Main.Zero = Main.error; 20.21/7.19 primModNatS Main.Zero (Main.Succ x) = Main.Zero; 20.21/7.19 primModNatS (Main.Succ x) Main.Zero = Main.error; 20.21/7.19 primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero; 20.21/7.19 primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y)); 20.21/7.19 20.21/7.19 primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y)); 20.21/7.19 primModNatS0 x y MyFalse = Main.Succ x; 20.21/7.19 20.21/7.19 primMulInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y); 20.21/7.19 primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y); 20.21/7.19 primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y); 20.21/7.19 primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y); 20.21/7.19 20.21/7.19 primMulNat :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primMulNat Main.Zero Main.Zero = Main.Zero; 20.21/7.19 primMulNat Main.Zero (Main.Succ y) = Main.Zero; 20.21/7.19 primMulNat (Main.Succ x) Main.Zero = Main.Zero; 20.21/7.19 primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y); 20.21/7.19 20.21/7.19 primPlusInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y; 20.21/7.19 primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x; 20.21/7.19 primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y); 20.21/7.19 primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y); 20.21/7.19 20.21/7.19 primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primPlusNat Main.Zero Main.Zero = Main.Zero; 20.21/7.19 primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; 20.21/7.19 primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; 20.21/7.19 primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); 20.21/7.19 20.21/7.19 primQrmInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; 20.21/7.19 primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y); 20.21/7.19 20.21/7.19 primQuotInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primQuotInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt wx wy = Main.error; 20.21/7.19 20.21/7.19 primRemInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primRemInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt vz wu = Main.error; 20.21/7.19 20.21/7.19 properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx); 20.21/7.19 20.21/7.19 properFractionQ1 xw xx (Tup2 q vx) = q; 20.21/7.19 20.21/7.19 properFractionR xw xx = properFractionR1 xw xx (properFractionVu30 xw xx); 20.21/7.19 20.21/7.19 properFractionR1 xw xx (Tup2 vy r) = r; 20.21/7.19 20.21/7.19 properFractionRatio :: Ratio MyInt -> Tup2 MyInt (Ratio MyInt); 20.21/7.19 properFractionRatio (CnPc x y) = Tup2 (fromIntegral (properFractionQ x y)) (CnPc (properFractionR x y) y); 20.21/7.19 20.21/7.19 properFractionVu30 xw xx = quotRemMyInt xw xx; 20.21/7.19 20.21/7.19 psMyInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 psMyInt = primPlusInt; 20.21/7.19 20.21/7.19 pt :: (a -> c) -> (b -> a) -> b -> c; 20.21/7.19 pt f g x = f (g x); 20.21/7.19 20.21/7.19 quotRemMyInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; 20.21/7.19 quotRemMyInt = primQrmInt; 20.21/7.19 20.21/7.19 srMyInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 srMyInt = primMulInt; 20.21/7.19 20.21/7.19 stop :: MyBool -> a; 20.21/7.19 stop MyFalse = stop MyFalse; 20.21/7.19 20.21/7.19 toIntegerMyInt :: MyInt -> Integer; 20.21/7.19 toIntegerMyInt x = Integer x; 20.21/7.19 20.21/7.19 } 20.21/7.19 20.21/7.19 ---------------------------------------- 20.21/7.19 20.21/7.19 (3) COR (EQUIVALENT) 20.21/7.19 Cond Reductions: 20.21/7.19 The following Function with conditions 20.21/7.19 "undefined |Falseundefined; 20.21/7.19 " 20.21/7.19 is transformed to 20.21/7.19 "undefined = undefined1; 20.21/7.19 " 20.21/7.19 "undefined0 True = undefined; 20.21/7.19 " 20.21/7.19 "undefined1 = undefined0 False; 20.21/7.19 " 20.21/7.19 20.21/7.19 ---------------------------------------- 20.21/7.19 20.21/7.19 (4) 20.21/7.19 Obligation: 20.21/7.19 mainModule Main 20.21/7.19 module Main where { 20.21/7.19 import qualified Prelude; 20.21/7.19 data Integer = Integer MyInt ; 20.21/7.19 20.21/7.19 data MyBool = MyTrue | MyFalse ; 20.21/7.19 20.21/7.19 data MyInt = Pos Main.Nat | Neg Main.Nat ; 20.21/7.19 20.21/7.19 data Main.Nat = Succ Main.Nat | Zero ; 20.21/7.19 20.21/7.19 data Ordering = LT | EQ | GT ; 20.21/7.19 20.21/7.19 data Ratio a = CnPc a a ; 20.21/7.19 20.21/7.19 data Tup2 b a = Tup2 b a ; 20.21/7.19 20.21/7.19 ceilingCeiling0 xv MyTrue = psMyInt (ceilingN xv) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 20.21/7.19 ceilingCeiling0 xv MyFalse = ceilingN xv; 20.21/7.19 20.21/7.19 ceilingN xv = ceilingN0 xv (ceilingVu8 xv); 20.21/7.19 20.21/7.19 ceilingN0 xv (Tup2 n vw) = n; 20.21/7.19 20.21/7.19 ceilingR xv = ceilingR0 xv (ceilingVu8 xv); 20.21/7.19 20.21/7.19 ceilingR0 xv (Tup2 vv r) = r; 20.21/7.19 20.21/7.19 ceilingRatio :: Ratio MyInt -> MyInt; 20.21/7.19 ceilingRatio x = ceilingCeiling0 x (gtRatio (ceilingR x) (fromIntRatio (Main.Pos Main.Zero))); 20.21/7.19 20.21/7.19 ceilingVu8 xv = properFractionRatio xv; 20.21/7.19 20.21/7.19 compareMyInt :: MyInt -> MyInt -> Ordering; 20.21/7.19 compareMyInt = primCmpInt; 20.21/7.19 20.21/7.19 compareRatio :: Ratio MyInt -> Ratio MyInt -> Ordering; 20.21/7.19 compareRatio (CnPc x y) (CnPc x' y') = compareMyInt (srMyInt x y') (srMyInt x' y); 20.21/7.19 20.21/7.19 error :: a; 20.21/7.19 error = stop MyTrue; 20.21/7.19 20.21/7.19 esEsOrdering :: Ordering -> Ordering -> MyBool; 20.21/7.19 esEsOrdering LT LT = MyTrue; 20.21/7.19 esEsOrdering LT EQ = MyFalse; 20.21/7.19 esEsOrdering LT GT = MyFalse; 20.21/7.19 esEsOrdering EQ LT = MyFalse; 20.21/7.19 esEsOrdering EQ EQ = MyTrue; 20.21/7.19 esEsOrdering EQ GT = MyFalse; 20.21/7.19 esEsOrdering GT LT = MyFalse; 20.21/7.19 esEsOrdering GT EQ = MyFalse; 20.21/7.19 esEsOrdering GT GT = MyTrue; 20.21/7.19 20.21/7.19 fromIntMyInt :: MyInt -> MyInt; 20.21/7.19 fromIntMyInt x = x; 20.21/7.19 20.21/7.19 fromIntRatio :: MyInt -> Ratio MyInt; 20.21/7.19 fromIntRatio = intToRatio; 20.21/7.19 20.21/7.19 fromIntegerMyInt :: Integer -> MyInt; 20.21/7.19 fromIntegerMyInt (Integer x) = x; 20.21/7.19 20.21/7.19 fromIntegral = pt fromIntegerMyInt toIntegerMyInt; 20.21/7.19 20.21/7.19 gtRatio :: Ratio MyInt -> Ratio MyInt -> MyBool; 20.21/7.19 gtRatio x y = esEsOrdering (compareRatio x y) GT; 20.21/7.19 20.21/7.19 intToRatio x = CnPc (fromIntMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 20.21/7.19 20.21/7.19 primCmpInt :: MyInt -> MyInt -> Ordering; 20.21/7.19 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 20.21/7.19 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 20.21/7.19 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 20.21/7.19 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 20.21/7.19 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 20.21/7.19 20.21/7.19 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 20.21/7.19 primCmpNat Main.Zero Main.Zero = EQ; 20.21/7.19 primCmpNat Main.Zero (Main.Succ y) = LT; 20.21/7.19 primCmpNat (Main.Succ x) Main.Zero = GT; 20.21/7.19 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 20.21/7.19 20.21/7.19 primDivNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primDivNatS Main.Zero Main.Zero = Main.error; 20.21/7.19 primDivNatS (Main.Succ x) Main.Zero = Main.error; 20.21/7.19 primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y); 20.21/7.19 primDivNatS Main.Zero (Main.Succ x) = Main.Zero; 20.21/7.19 20.21/7.19 primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y)); 20.21/7.19 primDivNatS0 x y MyFalse = Main.Zero; 20.21/7.19 20.21/7.19 primGEqNatS :: Main.Nat -> Main.Nat -> MyBool; 20.21/7.19 primGEqNatS (Main.Succ x) Main.Zero = MyTrue; 20.21/7.19 primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y; 20.21/7.19 primGEqNatS Main.Zero (Main.Succ x) = MyFalse; 20.21/7.19 primGEqNatS Main.Zero Main.Zero = MyTrue; 20.21/7.19 20.21/7.19 primMinusNat :: Main.Nat -> Main.Nat -> MyInt; 20.21/7.19 primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero; 20.21/7.19 primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y); 20.21/7.19 primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x); 20.21/7.19 primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y; 20.21/7.19 20.21/7.19 primMinusNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y; 20.21/7.19 primMinusNatS Main.Zero (Main.Succ y) = Main.Zero; 20.21/7.19 primMinusNatS x Main.Zero = x; 20.21/7.19 20.21/7.19 primModNatS :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primModNatS Main.Zero Main.Zero = Main.error; 20.21/7.19 primModNatS Main.Zero (Main.Succ x) = Main.Zero; 20.21/7.19 primModNatS (Main.Succ x) Main.Zero = Main.error; 20.21/7.19 primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero; 20.21/7.19 primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y)); 20.21/7.19 20.21/7.19 primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y)); 20.21/7.19 primModNatS0 x y MyFalse = Main.Succ x; 20.21/7.19 20.21/7.19 primMulInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y); 20.21/7.19 primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y); 20.21/7.19 primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y); 20.21/7.19 primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y); 20.21/7.19 20.21/7.19 primMulNat :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primMulNat Main.Zero Main.Zero = Main.Zero; 20.21/7.19 primMulNat Main.Zero (Main.Succ y) = Main.Zero; 20.21/7.19 primMulNat (Main.Succ x) Main.Zero = Main.Zero; 20.21/7.19 primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y); 20.21/7.19 20.21/7.19 primPlusInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y; 20.21/7.19 primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x; 20.21/7.19 primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y); 20.21/7.19 primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y); 20.21/7.19 20.21/7.19 primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; 20.21/7.19 primPlusNat Main.Zero Main.Zero = Main.Zero; 20.21/7.19 primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; 20.21/7.19 primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; 20.21/7.19 primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); 20.21/7.19 20.21/7.19 primQrmInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; 20.21/7.19 primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y); 20.21/7.19 20.21/7.19 primQuotInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primQuotInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y)); 20.21/7.19 primQuotInt wx wy = Main.error; 20.21/7.19 20.21/7.19 primRemInt :: MyInt -> MyInt -> MyInt; 20.21/7.19 primRemInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y)); 20.21/7.19 primRemInt vz wu = Main.error; 20.21/7.19 20.21/7.19 properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx); 20.21/7.19 20.21/7.19 properFractionQ1 xw xx (Tup2 q vx) = q; 20.21/7.19 20.21/7.19 properFractionR xw xx = properFractionR1 xw xx (properFractionVu30 xw xx); 20.21/7.19 20.21/7.19 properFractionR1 xw xx (Tup2 vy r) = r; 20.21/7.19 20.21/7.19 properFractionRatio :: Ratio MyInt -> Tup2 MyInt (Ratio MyInt); 20.21/7.19 properFractionRatio (CnPc x y) = Tup2 (fromIntegral (properFractionQ x y)) (CnPc (properFractionR x y) y); 20.21/7.20 20.21/7.20 properFractionVu30 xw xx = quotRemMyInt xw xx; 20.21/7.20 20.21/7.20 psMyInt :: MyInt -> MyInt -> MyInt; 20.21/7.20 psMyInt = primPlusInt; 20.21/7.20 20.21/7.20 pt :: (b -> a) -> (c -> b) -> c -> a; 20.21/7.20 pt f g x = f (g x); 20.21/7.20 20.21/7.20 quotRemMyInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; 20.21/7.20 quotRemMyInt = primQrmInt; 20.21/7.20 20.21/7.20 srMyInt :: MyInt -> MyInt -> MyInt; 20.21/7.20 srMyInt = primMulInt; 20.21/7.20 20.21/7.20 stop :: MyBool -> a; 20.21/7.20 stop MyFalse = stop MyFalse; 20.21/7.20 20.21/7.20 toIntegerMyInt :: MyInt -> Integer; 20.21/7.20 toIntegerMyInt x = Integer x; 20.21/7.20 20.21/7.20 } 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (5) Narrow (SOUND) 20.21/7.20 Haskell To QDPs 20.21/7.20 20.21/7.20 digraph dp_graph { 20.21/7.20 node [outthreshold=100, inthreshold=100];1[label="ceilingRatio",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 20.21/7.20 3[label="ceilingRatio wz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 20.21/7.20 4[label="ceilingCeiling0 wz3 (gtRatio (ceilingR wz3) (fromIntRatio (Pos Zero)))",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 20.21/7.20 5[label="ceilingCeiling0 wz3 (esEsOrdering (compareRatio (ceilingR wz3) (fromIntRatio (Pos Zero))) GT)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 20.21/7.20 6[label="ceilingCeiling0 wz3 (esEsOrdering (compareRatio (ceilingR0 wz3 (ceilingVu8 wz3)) (fromIntRatio (Pos Zero))) GT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 20.21/7.20 7[label="ceilingCeiling0 wz3 (esEsOrdering (compareRatio (ceilingR0 wz3 (properFractionRatio wz3)) (fromIntRatio (Pos Zero))) GT)",fontsize=16,color="burlywood",shape="box"];5260[label="wz3/CnPc wz30 wz31",fontsize=10,color="white",style="solid",shape="box"];7 -> 5260[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5260 -> 8[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 8[label="ceilingCeiling0 (CnPc wz30 wz31) (esEsOrdering (compareRatio (ceilingR0 (CnPc wz30 wz31) (properFractionRatio (CnPc wz30 wz31))) (fromIntRatio (Pos Zero))) GT)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 20.21/7.20 9[label="ceilingCeiling0 (CnPc wz30 wz31) (esEsOrdering (compareRatio (ceilingR0 (CnPc wz30 wz31) (Tup2 (fromIntegral (properFractionQ wz30 wz31)) (CnPc (properFractionR wz30 wz31) wz31))) (fromIntRatio (Pos Zero))) GT)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 20.21/7.20 10[label="ceilingCeiling0 (CnPc wz30 wz31) (esEsOrdering (compareRatio (CnPc (properFractionR wz30 wz31) wz31) (fromIntRatio (Pos Zero))) GT)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 20.21/7.20 11[label="ceilingCeiling0 (CnPc wz30 wz31) (esEsOrdering (compareRatio (CnPc (properFractionR wz30 wz31) wz31) (intToRatio (Pos Zero))) GT)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 20.21/7.20 12[label="ceilingCeiling0 (CnPc wz30 wz31) (esEsOrdering (compareRatio (CnPc (properFractionR wz30 wz31) wz31) (CnPc (fromIntMyInt (Pos Zero)) (fromIntMyInt (Pos (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 20.21/7.20 13[label="ceilingCeiling0 (CnPc wz30 wz31) (esEsOrdering (compareMyInt (srMyInt (properFractionR wz30 wz31) (fromIntMyInt (Pos (Succ Zero)))) (srMyInt (fromIntMyInt (Pos Zero)) wz31)) GT)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 20.21/7.20 14[label="ceilingCeiling0 (CnPc wz30 wz31) (esEsOrdering (primCmpInt (srMyInt 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140[label="",style="solid", color="black", weight=3]; 20.21/7.20 121[label="ceilingCeiling0 (CnPc (Neg (Succ wz3000)) (Neg (Succ Zero))) (esEsOrdering (primCmpInt (Neg Zero) (primMulInt (fromIntMyInt (Pos Zero)) (Neg (Succ Zero)))) GT)",fontsize=16,color="black",shape="box"];121 -> 141[label="",style="solid", color="black", weight=3]; 20.21/7.20 122[label="ceilingCeiling0 (CnPc (Neg Zero) (Neg (Succ wz3100))) (esEsOrdering (primCmpInt (Neg Zero) (primMulInt (Pos Zero) (Neg (Succ wz3100)))) GT)",fontsize=16,color="black",shape="box"];122 -> 142[label="",style="solid", color="black", weight=3]; 20.21/7.20 3193[label="primModNatS0 (Succ wz30000) wz31000 (primGEqNatS (Succ wz30000) (Succ wz31000))",fontsize=16,color="black",shape="box"];3193 -> 3792[label="",style="solid", color="black", weight=3]; 20.21/7.20 3194[label="primModNatS0 Zero wz31000 (primGEqNatS Zero (Succ wz31000))",fontsize=16,color="black",shape="box"];3194 -> 3793[label="",style="solid", color="black", weight=3]; 20.21/7.20 2539[label="primMulNat (Succ wz1860) (Succ Zero)",fontsize=16,color="black",shape="box"];2539 -> 2563[label="",style="solid", color="black", weight=3]; 20.21/7.20 2540[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];2540 -> 2564[label="",style="solid", color="black", weight=3]; 20.21/7.20 3195[label="ceilingCeiling0 (CnPc (Pos (Succ wz196)) (Pos (Succ wz197))) (esEsOrdering (primCmpInt (Pos (Succ wz2000)) (primMulInt (fromIntMyInt (Pos Zero)) (Pos (Succ wz197)))) GT)",fontsize=16,color="black",shape="box"];3195 -> 3794[label="",style="solid", color="black", weight=3]; 20.21/7.20 3196[label="ceilingCeiling0 (CnPc (Pos (Succ wz196)) (Pos (Succ wz197))) (esEsOrdering (primCmpInt (Pos Zero) (primMulInt (fromIntMyInt (Pos Zero)) (Pos (Succ wz197)))) GT)",fontsize=16,color="black",shape="box"];3196 -> 3795[label="",style="solid", color="black", weight=3]; 20.21/7.20 127[label="ceilingCeiling0 (CnPc (Pos Zero) (Pos (Succ wz3100))) (esEsOrdering 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weight=3]; 20.21/7.20 138[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ wz300000)))) (Neg (Succ (Succ wz31000)))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ (Succ wz300000)) wz31000 (primGEqNatS (Succ wz300000) wz31000)) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ wz31000))))) GT)",fontsize=16,color="burlywood",shape="box"];5305[label="wz31000/Succ wz310000",fontsize=10,color="white",style="solid",shape="box"];138 -> 5305[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5305 -> 164[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5306[label="wz31000/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 5306[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5306 -> 165[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 139[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ wz31000)))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ 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color="burlywood", weight=3]; 20.21/7.20 3814[label="primModNatS0 (Succ Zero) wz31000 (primGEqNatS Zero wz31000)",fontsize=16,color="burlywood",shape="box"];5313[label="wz31000/Succ wz310000",fontsize=10,color="white",style="solid",shape="box"];3814 -> 5313[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5313 -> 4228[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5314[label="wz31000/Zero",fontsize=10,color="white",style="solid",shape="box"];3814 -> 5314[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5314 -> 4229[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 3815[label="Succ Zero",fontsize=16,color="green",shape="box"];2637 -> 2520[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2637[label="primMulNat wz1860 (Succ Zero)",fontsize=16,color="magenta"];2637 -> 2651[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2104[label="primPlusNat wz1540 (Succ 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214[label="",style="solid", color="black", weight=3]; 20.21/7.20 4292[label="ceilingCeiling0 (CnPc (Neg (Succ wz208)) (Pos (Succ wz209))) (esEsOrdering (primCmpInt (Neg (Succ wz2120)) (Pos (primMulNat Zero (Succ wz209)))) GT)",fontsize=16,color="black",shape="box"];4292 -> 4311[label="",style="solid", color="black", weight=3]; 20.21/7.20 4293[label="ceilingCeiling0 (CnPc (Neg (Succ wz208)) (Pos (Succ wz209))) (esEsOrdering (primCmpInt (Neg Zero) (Pos (primMulNat Zero (Succ wz209)))) GT)",fontsize=16,color="black",shape="box"];4293 -> 4312[label="",style="solid", color="black", weight=3]; 20.21/7.20 191[label="ceilingCeiling0 (CnPc (Neg Zero) (Pos (Succ wz3100))) (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];191 -> 222[label="",style="solid", color="black", weight=3]; 20.21/7.20 192[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ wz300000)))) (Neg (Succ (Succ (Succ wz310000))))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ (Succ wz300000)) (Succ 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color="black", weight=3]; 20.21/7.20 194[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ (Succ wz310000))))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ Zero) (Succ wz310000) MyFalse) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ wz310000)))))) GT)",fontsize=16,color="black",shape="box"];194 -> 226[label="",style="solid", color="black", weight=3]; 20.21/7.20 195 -> 1717[label="",style="dashed", color="red", weight=0]; 20.21/7.20 195[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ Zero) Zero MyTrue) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="magenta"];195 -> 1718[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 196[label="ceilingCeiling0 (CnPc (Neg (Succ Zero)) (Neg (Succ (Succ wz31000)))) (esEsOrdering (primCmpInt (Neg (primPlusNat Zero (Succ Zero))) 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4227[label="primModNatS0 (Succ (Succ wz300000)) Zero (primGEqNatS (Succ wz300000) Zero)",fontsize=16,color="black",shape="box"];4227 -> 4249[label="",style="solid", color="black", weight=3]; 20.21/7.20 4228[label="primModNatS0 (Succ Zero) (Succ wz310000) (primGEqNatS Zero (Succ wz310000))",fontsize=16,color="black",shape="box"];4228 -> 4250[label="",style="solid", color="black", weight=3]; 20.21/7.20 4229[label="primModNatS0 (Succ Zero) Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4229 -> 4251[label="",style="solid", color="black", weight=3]; 20.21/7.20 2651[label="wz1860",fontsize=16,color="green",shape="box"];2120[label="primPlusNat (Succ wz15400) (Succ Zero)",fontsize=16,color="black",shape="box"];2120 -> 2182[label="",style="solid", color="black", weight=3]; 20.21/7.20 2121[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];2121 -> 2183[label="",style="solid", color="black", weight=3]; 20.21/7.20 4230[label="ceilingCeiling0 (CnPc 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GT)",fontsize=16,color="black",shape="box"];4270 -> 4295[label="",style="solid", color="black", weight=3]; 20.21/7.20 214[label="ceilingCeiling0 (CnPc (Pos Zero) (Neg (Succ wz3100))) MyFalse",fontsize=16,color="black",shape="box"];214 -> 250[label="",style="solid", color="black", weight=3]; 20.21/7.20 4311[label="ceilingCeiling0 (CnPc (Neg (Succ wz208)) (Pos (Succ wz209))) (esEsOrdering LT GT)",fontsize=16,color="black",shape="box"];4311 -> 4330[label="",style="solid", color="black", weight=3]; 20.21/7.20 4312[label="ceilingCeiling0 (CnPc (Neg (Succ wz208)) (Pos (Succ wz209))) (esEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) GT)",fontsize=16,color="black",shape="box"];4312 -> 4331[label="",style="solid", color="black", weight=3]; 20.21/7.20 222[label="ceilingCeiling0 (CnPc (Neg Zero) (Pos (Succ wz3100))) MyFalse",fontsize=16,color="black",shape="box"];222 -> 260[label="",style="solid", color="black", weight=3]; 20.21/7.20 223[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ 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265[label="",style="solid", color="black", weight=3]; 20.21/7.20 226[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ (Succ wz310000))))) (esEsOrdering (primCmpInt (Neg (primMulNat (Succ (Succ Zero)) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ wz310000)))))) GT)",fontsize=16,color="black",shape="box"];226 -> 266[label="",style="solid", color="black", weight=3]; 20.21/7.20 1718[label="Succ Zero",fontsize=16,color="green",shape="box"];1717[label="ceilingCeiling0 (CnPc (Neg (Succ wz120)) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ Zero) Zero MyTrue) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="triangle"];1717 -> 1721[label="",style="solid", color="black", weight=3]; 20.21/7.20 228[label="ceilingCeiling0 (CnPc (Neg (Succ Zero)) (Neg (Succ (Succ wz31000)))) (esEsOrdering (primCmpInt (Neg (Succ Zero)) (srMyInt (fromIntMyInt (Pos 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4672[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4248 -> 4673[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4248 -> 4674[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4249 -> 2656[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4249[label="primModNatS0 (Succ (Succ wz300000)) Zero MyTrue",fontsize=16,color="magenta"];4249 -> 4273[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4250 -> 4387[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4250[label="primModNatS0 (Succ Zero) (Succ wz310000) MyFalse",fontsize=16,color="magenta"];4250 -> 4388[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4250 -> 4389[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4251[label="primModNatS0 (Succ Zero) Zero MyTrue",fontsize=16,color="black",shape="box"];4251 -> 4275[label="",style="solid", color="black", weight=3]; 20.21/7.20 2182[label="Succ (Succ (primPlusNat wz15400 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4295[label="ceilingCeiling0 (CnPc (Pos (Succ wz202)) (Neg (Succ wz203))) (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];4295 -> 4314[label="",style="solid", color="black", weight=3]; 20.21/7.20 250[label="ceilingN (CnPc (Pos Zero) (Neg (Succ wz3100)))",fontsize=16,color="black",shape="box"];250 -> 290[label="",style="solid", color="black", weight=3]; 20.21/7.20 4330[label="ceilingCeiling0 (CnPc (Neg (Succ wz208)) (Pos (Succ wz209))) MyFalse",fontsize=16,color="black",shape="triangle"];4330 -> 4338[label="",style="solid", color="black", weight=3]; 20.21/7.20 4331[label="ceilingCeiling0 (CnPc (Neg (Succ wz208)) (Pos (Succ wz209))) (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];4331 -> 4339[label="",style="solid", color="black", weight=3]; 20.21/7.20 260[label="ceilingN (CnPc (Neg Zero) (Pos (Succ wz3100)))",fontsize=16,color="black",shape="box"];260 -> 300[label="",style="solid", color="black", weight=3]; 20.21/7.20 261[label="ceilingCeiling0 (CnPc (Neg (Succ 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2288[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 4276[label="ceilingCeiling0 (CnPc (Pos (Succ wz196)) (Pos (Succ wz197))) (esEsOrdering GT GT)",fontsize=16,color="black",shape="box"];4276 -> 4301[label="",style="solid", color="black", weight=3]; 20.21/7.20 4277[label="ceilingCeiling0 (CnPc (Pos (Succ wz196)) (Pos (Succ wz197))) MyFalse",fontsize=16,color="black",shape="box"];4277 -> 4302[label="",style="solid", color="black", weight=3]; 20.21/7.20 280[label="ceilingN0 (CnPc (Pos Zero) (Pos (Succ wz3100))) (ceilingVu8 (CnPc (Pos Zero) (Pos (Succ wz3100))))",fontsize=16,color="black",shape="box"];280 -> 321[label="",style="solid", color="black", weight=3]; 20.21/7.20 4313 -> 4345[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4313[label="psMyInt (ceilingN (CnPc (Pos (Succ wz202)) (Neg (Succ wz203)))) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="magenta"];4313 -> 4346[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4314[label="ceilingCeiling0 (CnPc (Pos (Succ wz202)) (Neg (Succ wz203))) MyFalse",fontsize=16,color="black",shape="box"];4314 -> 4333[label="",style="solid", color="black", weight=3]; 20.21/7.20 290[label="ceilingN0 (CnPc (Pos Zero) (Neg (Succ wz3100))) (ceilingVu8 (CnPc (Pos Zero) (Neg (Succ wz3100))))",fontsize=16,color="black",shape="box"];290 -> 332[label="",style="solid", color="black", weight=3]; 20.21/7.20 4338[label="ceilingN (CnPc (Neg (Succ wz208)) (Pos (Succ wz209)))",fontsize=16,color="black",shape="box"];4338 -> 4348[label="",style="solid", color="black", weight=3]; 20.21/7.20 4339 -> 4330[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4339[label="ceilingCeiling0 (CnPc (Neg (Succ wz208)) (Pos (Succ wz209))) MyFalse",fontsize=16,color="magenta"];300[label="ceilingN0 (CnPc (Neg Zero) (Pos (Succ wz3100))) (ceilingVu8 (CnPc (Neg Zero) (Pos (Succ wz3100))))",fontsize=16,color="black",shape="box"];300 -> 343[label="",style="solid", color="black", weight=3]; 20.21/7.20 301[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ wz3000000))))) (Neg (Succ (Succ (Succ (Succ wz3100000)))))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ (Succ (Succ wz3000000))) (Succ (Succ wz3100000)) (primGEqNatS wz3000000 wz3100000)) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ (Succ wz3100000))))))) GT)",fontsize=16,color="burlywood",shape="box"];5327[label="wz3000000/Succ wz30000000",fontsize=10,color="white",style="solid",shape="box"];301 -> 5327[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5327 -> 344[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5328[label="wz3000000/Zero",fontsize=10,color="white",style="solid",shape="box"];301 -> 5328[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5328 -> 345[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 302 -> 2579[label="",style="dashed", color="red", weight=0]; 20.21/7.20 302[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ wz3000000))))) (Neg (Succ (Succ (Succ Zero))))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ (Succ (Succ wz3000000))) (Succ Zero) MyTrue) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ Zero)))))) GT)",fontsize=16,color="magenta"];302 -> 2580[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 302 -> 2581[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 303[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ Zero)))) (Neg (Succ (Succ (Succ (Succ wz3100000)))))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ (Succ Zero)) (Succ (Succ wz3100000)) MyFalse) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ (Succ wz3100000))))))) GT)",fontsize=16,color="black",shape="box"];303 -> 347[label="",style="solid", color="black", weight=3]; 20.21/7.20 304 -> 2579[label="",style="dashed", color="red", weight=0]; 20.21/7.20 304[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ Zero)))) (Neg (Succ (Succ (Succ Zero))))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ (Succ Zero)) (Succ Zero) MyTrue) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ Zero)))))) GT)",fontsize=16,color="magenta"];304 -> 2582[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 304 -> 2583[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 305[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ wz300000)))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS (Succ wz300000) (Succ (Succ Zero))) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];305 -> 349[label="",style="solid", color="black", weight=3]; 20.21/7.20 306[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ (Succ wz310000))))) (esEsOrdering (primCmpInt (Neg (primPlusNat (primPlusNat 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2288[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];2288 -> 2306[label="",style="solid", color="black", weight=3]; 20.21/7.20 4301[label="ceilingCeiling0 (CnPc (Pos (Succ wz196)) (Pos (Succ wz197))) MyTrue",fontsize=16,color="black",shape="box"];4301 -> 4320[label="",style="solid", color="black", weight=3]; 20.21/7.20 4302[label="ceilingN (CnPc (Pos (Succ wz196)) (Pos (Succ wz197)))",fontsize=16,color="black",shape="triangle"];4302 -> 4321[label="",style="solid", color="black", weight=3]; 20.21/7.20 321[label="ceilingN0 (CnPc (Pos Zero) (Pos (Succ wz3100))) (properFractionRatio (CnPc (Pos Zero) (Pos (Succ wz3100))))",fontsize=16,color="black",shape="box"];321 -> 370[label="",style="solid", color="black", weight=3]; 20.21/7.20 4346 -> 4333[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4346[label="ceilingN (CnPc (Pos (Succ wz202)) (Neg (Succ wz203)))",fontsize=16,color="magenta"];4345[label="psMyInt wz230 (fromIntMyInt (Pos (Succ 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weight=3]; 20.21/7.20 344[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ wz30000000)))))) (Neg (Succ (Succ (Succ (Succ wz3100000)))))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ (Succ (Succ (Succ wz30000000)))) (Succ (Succ wz3100000)) (primGEqNatS (Succ wz30000000) wz3100000)) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ (Succ wz3100000))))))) GT)",fontsize=16,color="burlywood",shape="box"];5335[label="wz3100000/Succ wz31000000",fontsize=10,color="white",style="solid",shape="box"];344 -> 5335[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5335 -> 399[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5336[label="wz3100000/Zero",fontsize=10,color="white",style="solid",shape="box"];344 -> 5336[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5336 -> 400[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 345[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ 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410[label="ceilingCeiling0 (CnPc (Neg (Succ Zero)) (Neg (Succ (Succ wz31000)))) (esEsOrdering (primCmpNat (primMulNat Zero (Succ (Succ wz31000))) (Succ Zero)) GT)",fontsize=16,color="black",shape="box"];410 -> 466[label="",style="solid", color="black", weight=3]; 20.21/7.20 2005[label="ceilingN0 (CnPc (Neg (Succ wz146)) (Neg (Succ wz147))) (ceilingVu8 (CnPc (Neg (Succ wz146)) (Neg (Succ wz147))))",fontsize=16,color="black",shape="box"];2005 -> 2054[label="",style="solid", color="black", weight=3]; 20.21/7.20 412[label="ceilingN0 (CnPc (Neg Zero) (Neg (Succ wz3100))) (Tup2 (fromIntegral (properFractionQ (Neg Zero) (Neg (Succ wz3100)))) (CnPc (properFractionR (Neg Zero) (Neg (Succ wz3100))) (Neg (Succ wz3100))))",fontsize=16,color="black",shape="box"];412 -> 468[label="",style="solid", color="black", weight=3]; 20.21/7.20 4752 -> 4670[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4752[label="primModNatS0 (Succ wz250) (Succ wz251) (primGEqNatS wz2520 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4776[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4755 -> 4777[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4930[label="primModNatS (primMinusNatS (Succ wz2550) (Succ wz2560)) (Succ wz257)",fontsize=16,color="black",shape="box"];4930 -> 4939[label="",style="solid", color="black", weight=3]; 20.21/7.20 4931[label="primModNatS (primMinusNatS (Succ wz2550) Zero) (Succ wz257)",fontsize=16,color="black",shape="box"];4931 -> 4940[label="",style="solid", color="black", weight=3]; 20.21/7.20 4932[label="primModNatS (primMinusNatS Zero (Succ wz2560)) (Succ wz257)",fontsize=16,color="black",shape="box"];4932 -> 4941[label="",style="solid", color="black", weight=3]; 20.21/7.20 4933[label="primModNatS (primMinusNatS Zero Zero) (Succ wz257)",fontsize=16,color="black",shape="box"];4933 -> 4942[label="",style="solid", color="black", weight=3]; 20.21/7.20 4347 -> 4302[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4347[label="ceilingN (CnPc (Pos (Succ 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4770[label="wz2530",fontsize=16,color="green",shape="box"];4771[label="wz2520",fontsize=16,color="green",shape="box"];4772[label="wz251",fontsize=16,color="green",shape="box"];4773[label="wz250",fontsize=16,color="green",shape="box"];4774[label="wz251",fontsize=16,color="green",shape="box"];4775[label="wz250",fontsize=16,color="green",shape="box"];4776[label="wz251",fontsize=16,color="green",shape="box"];4777[label="wz250",fontsize=16,color="green",shape="box"];4939 -> 4871[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4939[label="primModNatS (primMinusNatS wz2550 wz2560) (Succ wz257)",fontsize=16,color="magenta"];4939 -> 4945[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4939 -> 4946[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4940[label="primModNatS (Succ wz2550) (Succ wz257)",fontsize=16,color="burlywood",shape="box"];5353[label="wz257/Succ wz2570",fontsize=10,color="white",style="solid",shape="box"];4940 -> 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528[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ (Succ wz310000))))) (esEsOrdering (primCmpInt (Neg (Succ (Succ (primPlusNat Zero Zero)))) (primMulInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ wz310000)))))) GT)",fontsize=16,color="black",shape="box"];528 -> 600[label="",style="solid", color="black", weight=3]; 20.21/7.20 1898[label="ceilingCeiling0 (CnPc (Neg (Succ wz120)) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg Zero) (primMulInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="triangle"];1898 -> 1906[label="",style="solid", color="black", weight=3]; 20.21/7.20 530[label="ceilingCeiling0 (CnPc (Neg (Succ Zero)) (Neg (Succ (Succ wz31000)))) (esEsOrdering LT GT)",fontsize=16,color="black",shape="box"];530 -> 602[label="",style="solid", color="black", weight=3]; 20.21/7.20 2069[label="ceilingN0 (CnPc (Neg (Succ wz146)) (Neg (Succ wz147))) (Tup2 (fromIntegral (properFractionQ (Neg (Succ wz146)) 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5374[label="wz310000000/Zero",fontsize=10,color="white",style="solid",shape="box"];2368 -> 5374[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5374 -> 2388[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 2369[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ wz23000))))) (Neg (Succ (Succ (Succ (Succ (Succ (Succ wz24)))))))) (esEsOrdering (primCmpInt (Neg (Succ wz1730)) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ (Succ (Succ (Succ wz24))))))))) GT)",fontsize=16,color="black",shape="box"];2369 -> 2389[label="",style="solid", color="black", weight=3]; 20.21/7.20 2370[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ wz23000))))) (Neg (Succ (Succ (Succ (Succ (Succ (Succ wz24)))))))) (esEsOrdering (primCmpInt (Neg Zero) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ (Succ (Succ (Succ wz24))))))))) GT)",fontsize=16,color="black",shape="box"];2370 -> 2390[label="",style="solid", color="black", weight=3]; 20.21/7.20 4278 -> 4566[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4278[label="primModNatS0 (Succ (Succ (Succ (Succ (Succ wz300000000))))) (Succ (Succ (Succ Zero))) MyTrue",fontsize=16,color="magenta"];4278 -> 4583[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4278 -> 4584[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4279[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ wz340000)))))) (Neg (Succ (Succ (Succ (Succ (Succ Zero))))))) (esEsOrdering (primCmpInt (Neg (Succ wz2150)) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))))) GT)",fontsize=16,color="black",shape="box"];4279 -> 4323[label="",style="solid", color="black", weight=3]; 20.21/7.20 4280[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ wz340000)))))) (Neg (Succ (Succ (Succ (Succ (Succ Zero))))))) (esEsOrdering (primCmpInt (Neg Zero) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))))) GT)",fontsize=16,color="black",shape="box"];4280 -> 4324[label="",style="solid", color="black", weight=3]; 20.21/7.20 2371 -> 2492[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2371[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="magenta"];2371 -> 2493[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4281 -> 4566[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4281[label="primModNatS0 (Succ (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero))) MyTrue",fontsize=16,color="magenta"];4281 -> 4585[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4281 -> 4586[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2280[label="primMulNat (primModNatS (primMinusNatS (Succ (Succ wz30000000)) (Succ Zero)) (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="black",shape="box"];2280 -> 2297[label="",style="solid", color="black", weight=3]; 20.21/7.20 2497[label="ceilingCeiling0 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863[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ wz30000000)))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS (Succ wz30000000) (Succ (Succ Zero))) (Succ Zero))) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];863 -> 959[label="",style="solid", color="black", weight=3]; 20.21/7.20 1443[label="ceilingCeiling0 (CnPc (Neg (Succ wz87)) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (Succ Zero)) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];1443 -> 1483[label="",style="solid", color="black", weight=3]; 20.21/7.20 866[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ (Succ wz310000))))) (esEsOrdering (primCmpNat Zero (Succ (Succ (primPlusNat Zero Zero)))) GT)",fontsize=16,color="black",shape="box"];866 -> 962[label="",style="solid", color="black", weight=3]; 20.21/7.20 1963[label="Succ 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894[label="properFractionQ1 (Pos Zero) (Pos (Succ wz3100)) (quotRemMyInt (Pos Zero) (Pos (Succ wz3100)))",fontsize=16,color="black",shape="box"];894 -> 997[label="",style="solid", color="black", weight=3]; 20.21/7.20 4539[label="Neg (Succ wz230000)",fontsize=16,color="green",shape="box"];4540[label="Pos Zero",fontsize=16,color="green",shape="box"];4514[label="properFractionQ (Pos (Succ wz202)) (Neg (Succ wz203))",fontsize=16,color="black",shape="box"];4514 -> 4545[label="",style="solid", color="black", weight=3]; 20.21/7.20 918[label="properFractionQ1 (Pos Zero) (Neg (Succ wz3100)) (quotRemMyInt (Pos Zero) (Neg (Succ wz3100)))",fontsize=16,color="black",shape="box"];918 -> 1029[label="",style="solid", color="black", weight=3]; 20.21/7.20 4604[label="properFractionQ1 (Neg (Succ wz208)) (Pos (Succ wz209)) (properFractionVu30 (Neg (Succ wz208)) (Pos (Succ wz209)))",fontsize=16,color="black",shape="box"];4604 -> 4629[label="",style="solid", color="black", weight=3]; 20.21/7.20 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2473[label="",style="solid", color="black", weight=3]; 20.21/7.20 2454 -> 2474[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2454[label="primMulNat (primModNatS0 (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ (Succ Zero)))) MyTrue) (Succ Zero)",fontsize=16,color="magenta"];2454 -> 2476[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2455[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ wz23000))))) (Neg (Succ (Succ (Succ (Succ (Succ (Succ wz24)))))))) (esEsOrdering (primCmpInt (Neg (Succ wz1730)) (primMulInt (Pos Zero) (Neg (Succ (Succ (Succ (Succ (Succ (Succ wz24))))))))) GT)",fontsize=16,color="black",shape="box"];2455 -> 2482[label="",style="solid", color="black", weight=3]; 20.21/7.20 2457[label="Succ (Succ (Succ (Succ (Succ wz24))))",fontsize=16,color="green",shape="box"];2458[label="wz23000",fontsize=16,color="green",shape="box"];2456[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ wz181))))) (Neg (Succ wz182))) 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1197[label="",style="solid", color="black", weight=3]; 20.21/7.20 2374[label="primMulNat (primModNatS Zero (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="black",shape="box"];2374 -> 2394[label="",style="solid", color="black", weight=3]; 20.21/7.20 4255[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];4256[label="wz59",fontsize=16,color="green",shape="box"];1083[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ Zero)))) (Neg (Succ (Succ (Succ (Succ wz3100000)))))) (esEsOrdering (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)))) (primMulInt (Pos Zero) (Neg (Succ (Succ (Succ (Succ wz3100000))))))) GT)",fontsize=16,color="black",shape="box"];1083 -> 1203[label="",style="solid", color="black", weight=3]; 20.21/7.20 1085[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ wz300000000))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (primMulNat (primModNatS0 (Succ wz300000000) Zero (primGEqNatS 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20.21/7.20 1210[label="ceilingN (CnPc (Neg (Succ (Succ Zero))) (Neg (Succ (Succ (Succ wz310000)))))",fontsize=16,color="black",shape="box"];1210 -> 1377[label="",style="solid", color="black", weight=3]; 20.21/7.20 1212[label="pt fromIntegerMyInt toIntegerMyInt (properFractionQ (Neg (Succ Zero)) (Neg (Succ (Succ wz31000))))",fontsize=16,color="black",shape="box"];1212 -> 1379[label="",style="solid", color="black", weight=3]; 20.21/7.20 2302[label="properFractionQ1 (Neg (Succ wz146)) (Neg (Succ wz147)) (quotRemMyInt (Neg (Succ wz146)) (Neg (Succ wz147)))",fontsize=16,color="black",shape="box"];2302 -> 2375[label="",style="solid", color="black", weight=3]; 20.21/7.20 1214[label="properFractionQ1 (Neg Zero) (Neg (Succ wz3100)) (Tup2 (primQuotInt (Neg Zero) (Neg (Succ wz3100))) (primRemInt (Neg Zero) (Neg (Succ wz3100))))",fontsize=16,color="black",shape="box"];1214 -> 1381[label="",style="solid", color="black", weight=3]; 20.21/7.20 4630[label="properFractionQ1 (Pos (Succ wz196)) (Pos 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2643[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2657[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (Succ wz1940)) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];2657 -> 2680[label="",style="solid", color="black", weight=3]; 20.21/7.20 2658[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg Zero) (srMyInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];2658 -> 2681[label="",style="solid", color="black", weight=3]; 20.21/7.20 1874 -> 1976[label="",style="dashed", color="red", weight=0]; 20.21/7.20 1874[label="ceilingCeiling0 (CnPc (Neg (Succ wz87)) (Neg (Succ (Succ Zero)))) MyFalse",fontsize=16,color="magenta"];1874 -> 2659[label="",style="dashed", 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2665[label="",style="dashed", color="green", weight=3]; 20.21/7.20 1878[label="wz3100",fontsize=16,color="green",shape="box"];4761 -> 2665[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4761[label="primDivNatS (Succ wz196) (Succ wz197)",fontsize=16,color="magenta"];4761 -> 4783[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4761 -> 4784[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4762 -> 2665[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4762[label="primDivNatS (Succ wz202) (Succ wz203)",fontsize=16,color="magenta"];4762 -> 4785[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4762 -> 4786[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4802[label="wz209",fontsize=16,color="green",shape="box"];4803[label="wz208",fontsize=16,color="green",shape="box"];2665[label="primDivNatS (Succ wz146) (Succ wz147)",fontsize=16,color="black",shape="triangle"];2665 -> 4287[label="",style="solid", color="black", weight=3]; 20.21/7.20 2574 -> 2520[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2574[label="primMulNat (primModNatS0 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz300000000000)))))))) (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz310000000000))))))) (primGEqNatS wz300000000000 wz310000000000)) (Succ Zero)",fontsize=16,color="magenta"];2574 -> 4233[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2575 -> 2520[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2575[label="primMulNat (primModNatS0 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz300000000000)))))))) (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) MyTrue) (Succ Zero)",fontsize=16,color="magenta"];2575 -> 4234[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2576 -> 2520[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2576[label="primMulNat (primModNatS0 (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) (Succ (Succ (Succ (Succ (Succ (Succ 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4534[label="wz241",fontsize=16,color="green",shape="box"];4535[label="Zero",fontsize=16,color="green",shape="box"];2545 -> 4670[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2545[label="primModNatS0 (Succ (Succ wz3000000000)) (Succ (Succ Zero)) (primGEqNatS wz3000000000 (Succ Zero))",fontsize=16,color="magenta"];2545 -> 4695[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2545 -> 4696[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2545 -> 4697[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2545 -> 4698[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2546 -> 4387[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2546[label="primModNatS0 (Succ Zero) (Succ (Succ Zero)) MyFalse",fontsize=16,color="magenta"];2546 -> 4392[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2546 -> 4393[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2514 -> 2260[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2514[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];2514 -> 4282[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2513[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ Zero))))) (Neg (Succ (Succ (Succ (Succ (Succ wz31000000))))))) (esEsOrdering (primCmpInt (Neg (Succ (Succ wz187))) (primMulInt (Pos Zero) (Neg (Succ (Succ (Succ (Succ (Succ wz31000000)))))))) GT)",fontsize=16,color="black",shape="triangle"];2513 -> 4283[label="",style="solid", color="black", weight=3]; 20.21/7.20 2642[label="Succ (Succ (Succ wz3100000))",fontsize=16,color="green",shape="box"];2643[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];2680[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (Succ wz1940)) (primMulInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];2680 -> 4285[label="",style="solid", color="black", weight=3]; 20.21/7.20 2681 -> 1898[label="",style="dashed", color="red", weight=0]; 20.21/7.20 2681[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg Zero) (primMulInt (fromIntMyInt (Pos Zero)) (Neg (Succ (Succ Zero))))) GT)",fontsize=16,color="magenta"];2681 -> 4286[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 2659[label="Succ Zero",fontsize=16,color="green",shape="box"];2660[label="wz87",fontsize=16,color="green",shape="box"];2661[label="Succ (Succ wz310000)",fontsize=16,color="green",shape="box"];2662[label="Succ Zero",fontsize=16,color="green",shape="box"];2663[label="Succ 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4233[label="primModNatS0 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz300000000000)))))))) (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz310000000000))))))) (primGEqNatS wz300000000000 wz310000000000)",fontsize=16,color="magenta"];4233 -> 4699[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4233 -> 4700[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4233 -> 4701[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4233 -> 4702[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4234 -> 4566[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4234[label="primModNatS0 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz300000000000)))))))) (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) MyTrue",fontsize=16,color="magenta"];4234 -> 4595[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4234 -> 4596[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4235 -> 4387[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4235[label="primModNatS0 (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz310000000000))))))) MyFalse",fontsize=16,color="magenta"];4235 -> 4394[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4235 -> 4395[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4236 -> 4566[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4236[label="primModNatS0 (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) MyTrue",fontsize=16,color="magenta"];4236 -> 4597[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4236 -> 4598[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4611[label="Succ (Succ (Succ (Succ wz245)))",fontsize=16,color="green",shape="box"];4612[label="wz244",fontsize=16,color="green",shape="box"];4695[label="Succ Zero",fontsize=16,color="green",shape="box"];4696[label="Succ 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wz147)",fontsize=16,color="burlywood",shape="box"];5401[label="wz147/Succ wz1470",fontsize=10,color="white",style="solid",shape="box"];4384 -> 5401[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5401 -> 4450[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5402[label="wz147/Zero",fontsize=10,color="white",style="solid",shape="box"];4384 -> 5402[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5402 -> 4451[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 4699[label="wz310000000000",fontsize=16,color="green",shape="box"];4700[label="Succ (Succ (Succ (Succ (Succ (Succ wz310000000000)))))",fontsize=16,color="green",shape="box"];4701[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ wz300000000000))))))",fontsize=16,color="green",shape="box"];4702[label="wz300000000000",fontsize=16,color="green",shape="box"];4595[label="Succ (Succ (Succ (Succ (Succ Zero))))",fontsize=16,color="green",shape="box"];4596[label="Succ (Succ (Succ 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GT)",fontsize=16,color="black",shape="box"];4381 -> 4446[label="",style="solid", color="black", weight=3]; 20.21/7.20 4382[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpInt (Neg (Succ wz1940)) (Neg (primMulNat Zero (Succ (Succ Zero))))) GT)",fontsize=16,color="black",shape="box"];4382 -> 4447[label="",style="solid", color="black", weight=3]; 20.21/7.20 4448[label="primDivNatS0 (Succ wz1460) (Succ wz1470) (primGEqNatS (Succ wz1460) (Succ wz1470))",fontsize=16,color="black",shape="box"];4448 -> 4497[label="",style="solid", color="black", weight=3]; 20.21/7.20 4449[label="primDivNatS0 (Succ wz1460) Zero (primGEqNatS (Succ wz1460) Zero)",fontsize=16,color="black",shape="box"];4449 -> 4498[label="",style="solid", color="black", weight=3]; 20.21/7.20 4450[label="primDivNatS0 Zero (Succ wz1470) (primGEqNatS Zero (Succ wz1470))",fontsize=16,color="black",shape="box"];4450 -> 4499[label="",style="solid", color="black", weight=3]; 20.21/7.20 4451[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4451 -> 4500[label="",style="solid", color="black", weight=3]; 20.21/7.20 4445[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];4445 -> 4494[label="",style="dashed", color="green", weight=3]; 20.21/7.20 4446[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ Zero))))) (Neg (Succ (Succ (Succ (Succ (Succ wz31000000))))))) (esEsOrdering (primCmpNat Zero (Succ (Succ wz187))) GT)",fontsize=16,color="black",shape="box"];4446 -> 4495[label="",style="solid", color="black", weight=3]; 20.21/7.20 4447[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpNat (primMulNat Zero (Succ (Succ Zero))) (Succ wz1940)) GT)",fontsize=16,color="black",shape="box"];4447 -> 4496[label="",style="solid", color="black", weight=3]; 20.21/7.20 4497 -> 5107[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4497[label="primDivNatS0 (Succ wz1460) (Succ wz1470) (primGEqNatS wz1460 wz1470)",fontsize=16,color="magenta"];4497 -> 5108[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4497 -> 5109[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4497 -> 5110[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4497 -> 5111[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4498[label="primDivNatS0 (Succ wz1460) Zero MyTrue",fontsize=16,color="black",shape="box"];4498 -> 4561[label="",style="solid", color="black", weight=3]; 20.21/7.20 4499[label="primDivNatS0 Zero (Succ wz1470) MyFalse",fontsize=16,color="black",shape="box"];4499 -> 4562[label="",style="solid", color="black", weight=3]; 20.21/7.20 4500[label="primDivNatS0 Zero Zero MyTrue",fontsize=16,color="black",shape="box"];4500 -> 4563[label="",style="solid", color="black", weight=3]; 20.21/7.20 4494 -> 2260[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4494[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];4494 -> 4530[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4495 -> 4531[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4495[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ Zero))))) (Neg (Succ (Succ (Succ (Succ (Succ wz31000000))))))) (esEsOrdering LT GT)",fontsize=16,color="magenta"];4495 -> 4536[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4495 -> 4537[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4496[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering (primCmpNat Zero (Succ wz1940)) GT)",fontsize=16,color="black",shape="box"];4496 -> 4558[label="",style="solid", color="black", weight=3]; 20.21/7.20 5108[label="wz1470",fontsize=16,color="green",shape="box"];5109[label="wz1460",fontsize=16,color="green",shape="box"];5110[label="wz1470",fontsize=16,color="green",shape="box"];5111[label="wz1460",fontsize=16,color="green",shape="box"];5107[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS wz292 wz293)",fontsize=16,color="burlywood",shape="triangle"];5403[label="wz292/Succ wz2920",fontsize=10,color="white",style="solid",shape="box"];5107 -> 5403[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5403 -> 5148[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5404[label="wz292/Zero",fontsize=10,color="white",style="solid",shape="box"];5107 -> 5404[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5404 -> 5149[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 4561[label="Succ (primDivNatS (primMinusNatS (Succ wz1460) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4561 -> 4620[label="",style="dashed", color="green", weight=3]; 20.21/7.20 4562[label="Zero",fontsize=16,color="green",shape="box"];4563[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4563 -> 4621[label="",style="dashed", color="green", weight=3]; 20.21/7.20 4530[label="Zero",fontsize=16,color="green",shape="box"];4536[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];4537[label="wz31000000",fontsize=16,color="green",shape="box"];4558 -> 1724[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4558[label="ceilingCeiling0 (CnPc (Neg (Succ (Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))))) (Neg (Succ (Succ Zero)))) (esEsOrdering LT GT)",fontsize=16,color="magenta"];4558 -> 4615[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5148[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS (Succ wz2920) wz293)",fontsize=16,color="burlywood",shape="box"];5405[label="wz293/Succ wz2930",fontsize=10,color="white",style="solid",shape="box"];5148 -> 5405[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5405 -> 5150[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5406[label="wz293/Zero",fontsize=10,color="white",style="solid",shape="box"];5148 -> 5406[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5406 -> 5151[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5149[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS Zero wz293)",fontsize=16,color="burlywood",shape="box"];5407[label="wz293/Succ wz2930",fontsize=10,color="white",style="solid",shape="box"];5149 -> 5407[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5407 -> 5152[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5408[label="wz293/Zero",fontsize=10,color="white",style="solid",shape="box"];5149 -> 5408[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5408 -> 5153[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 4620 -> 5216[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4620[label="primDivNatS (primMinusNatS (Succ wz1460) Zero) (Succ Zero)",fontsize=16,color="magenta"];4620 -> 5217[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4620 -> 5218[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4620 -> 5219[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4621 -> 5216[label="",style="dashed", color="red", weight=0]; 20.21/7.20 4621[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];4621 -> 5220[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4621 -> 5221[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4621 -> 5222[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 4615[label="Succ (Succ (Succ (Succ (Succ (Succ wz3000000000)))))",fontsize=16,color="green",shape="box"];5150[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS (Succ wz2920) (Succ wz2930))",fontsize=16,color="black",shape="box"];5150 -> 5154[label="",style="solid", color="black", weight=3]; 20.21/7.20 5151[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS (Succ wz2920) Zero)",fontsize=16,color="black",shape="box"];5151 -> 5155[label="",style="solid", color="black", weight=3]; 20.21/7.20 5152[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS Zero (Succ wz2930))",fontsize=16,color="black",shape="box"];5152 -> 5156[label="",style="solid", color="black", weight=3]; 20.21/7.20 5153[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];5153 -> 5157[label="",style="solid", color="black", weight=3]; 20.21/7.20 5217[label="Zero",fontsize=16,color="green",shape="box"];5218[label="Zero",fontsize=16,color="green",shape="box"];5219[label="Succ wz1460",fontsize=16,color="green",shape="box"];5216[label="primDivNatS (primMinusNatS wz295 wz296) (Succ wz297)",fontsize=16,color="burlywood",shape="triangle"];5409[label="wz295/Succ wz2950",fontsize=10,color="white",style="solid",shape="box"];5216 -> 5409[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5409 -> 5244[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5410[label="wz295/Zero",fontsize=10,color="white",style="solid",shape="box"];5216 -> 5410[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5410 -> 5245[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5220[label="Zero",fontsize=16,color="green",shape="box"];5221[label="Zero",fontsize=16,color="green",shape="box"];5222[label="Zero",fontsize=16,color="green",shape="box"];5154 -> 5107[label="",style="dashed", color="red", weight=0]; 20.21/7.20 5154[label="primDivNatS0 (Succ wz290) (Succ wz291) (primGEqNatS wz2920 wz2930)",fontsize=16,color="magenta"];5154 -> 5158[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5154 -> 5159[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5155[label="primDivNatS0 (Succ wz290) (Succ wz291) MyTrue",fontsize=16,color="black",shape="triangle"];5155 -> 5160[label="",style="solid", color="black", weight=3]; 20.21/7.20 5156[label="primDivNatS0 (Succ wz290) (Succ wz291) MyFalse",fontsize=16,color="black",shape="box"];5156 -> 5161[label="",style="solid", color="black", weight=3]; 20.21/7.20 5157 -> 5155[label="",style="dashed", color="red", weight=0]; 20.21/7.20 5157[label="primDivNatS0 (Succ wz290) (Succ wz291) MyTrue",fontsize=16,color="magenta"];5244[label="primDivNatS (primMinusNatS (Succ wz2950) wz296) (Succ wz297)",fontsize=16,color="burlywood",shape="box"];5411[label="wz296/Succ wz2960",fontsize=10,color="white",style="solid",shape="box"];5244 -> 5411[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5411 -> 5246[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5412[label="wz296/Zero",fontsize=10,color="white",style="solid",shape="box"];5244 -> 5412[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5412 -> 5247[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5245[label="primDivNatS (primMinusNatS Zero wz296) (Succ wz297)",fontsize=16,color="burlywood",shape="box"];5413[label="wz296/Succ wz2960",fontsize=10,color="white",style="solid",shape="box"];5245 -> 5413[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5413 -> 5248[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5414[label="wz296/Zero",fontsize=10,color="white",style="solid",shape="box"];5245 -> 5414[label="",style="solid", color="burlywood", weight=9]; 20.21/7.20 5414 -> 5249[label="",style="solid", color="burlywood", weight=3]; 20.21/7.20 5158[label="wz2920",fontsize=16,color="green",shape="box"];5159[label="wz2930",fontsize=16,color="green",shape="box"];5160[label="Succ (primDivNatS (primMinusNatS (Succ wz290) (Succ wz291)) (Succ (Succ wz291)))",fontsize=16,color="green",shape="box"];5160 -> 5162[label="",style="dashed", color="green", weight=3]; 20.21/7.20 5161[label="Zero",fontsize=16,color="green",shape="box"];5246[label="primDivNatS (primMinusNatS (Succ wz2950) (Succ wz2960)) (Succ wz297)",fontsize=16,color="black",shape="box"];5246 -> 5250[label="",style="solid", color="black", weight=3]; 20.21/7.20 5247[label="primDivNatS (primMinusNatS (Succ wz2950) Zero) (Succ wz297)",fontsize=16,color="black",shape="box"];5247 -> 5251[label="",style="solid", color="black", weight=3]; 20.21/7.20 5248[label="primDivNatS (primMinusNatS Zero (Succ wz2960)) (Succ wz297)",fontsize=16,color="black",shape="box"];5248 -> 5252[label="",style="solid", color="black", weight=3]; 20.21/7.20 5249[label="primDivNatS (primMinusNatS Zero Zero) (Succ wz297)",fontsize=16,color="black",shape="box"];5249 -> 5253[label="",style="solid", color="black", weight=3]; 20.21/7.20 5162 -> 5216[label="",style="dashed", color="red", weight=0]; 20.21/7.20 5162[label="primDivNatS (primMinusNatS (Succ wz290) (Succ wz291)) (Succ (Succ wz291))",fontsize=16,color="magenta"];5162 -> 5226[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5162 -> 5227[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5162 -> 5228[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5250 -> 5216[label="",style="dashed", color="red", weight=0]; 20.21/7.20 5250[label="primDivNatS (primMinusNatS wz2950 wz2960) (Succ wz297)",fontsize=16,color="magenta"];5250 -> 5254[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5250 -> 5255[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5251 -> 2665[label="",style="dashed", color="red", weight=0]; 20.21/7.20 5251[label="primDivNatS (Succ wz2950) (Succ wz297)",fontsize=16,color="magenta"];5251 -> 5256[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5251 -> 5257[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5252 -> 1594[label="",style="dashed", color="red", weight=0]; 20.21/7.20 5252[label="primDivNatS Zero (Succ wz297)",fontsize=16,color="magenta"];5252 -> 5258[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5253 -> 1594[label="",style="dashed", color="red", weight=0]; 20.21/7.20 5253[label="primDivNatS Zero (Succ wz297)",fontsize=16,color="magenta"];5253 -> 5259[label="",style="dashed", color="magenta", weight=3]; 20.21/7.20 5226[label="Succ wz291",fontsize=16,color="green",shape="box"];5227[label="Succ wz291",fontsize=16,color="green",shape="box"];5228[label="Succ wz290",fontsize=16,color="green",shape="box"];5254[label="wz2960",fontsize=16,color="green",shape="box"];5255[label="wz2950",fontsize=16,color="green",shape="box"];5256[label="wz297",fontsize=16,color="green",shape="box"];5257[label="wz2950",fontsize=16,color="green",shape="box"];5258[label="wz297",fontsize=16,color="green",shape="box"];5259[label="wz297",fontsize=16,color="green",shape="box"];} 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (6) 20.21/7.20 Complex Obligation (AND) 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (7) 20.21/7.20 Obligation: 20.21/7.20 Q DP problem: 20.21/7.20 The TRS P consists of the following rules: 20.21/7.20 20.21/7.20 new_primModNatS0(wz250, wz251, Main.Zero, Main.Zero) -> new_primModNatS00(wz250, wz251) 20.21/7.20 new_primModNatS0(wz250, wz251, Main.Succ(wz2520), Main.Succ(wz2530)) -> new_primModNatS0(wz250, wz251, wz2520, wz2530) 20.21/7.20 new_primModNatS(Main.Succ(wz2550), Main.Succ(wz2560), wz257) -> new_primModNatS(wz2550, wz2560, wz257) 20.21/7.20 new_primModNatS01(Main.Succ(Main.Succ(wz300000)), Main.Zero) -> new_primModNatS02(wz300000) 20.21/7.20 new_primModNatS(Main.Succ(wz2550), Main.Zero, Main.Succ(wz2570)) -> new_primModNatS01(wz2550, wz2570) 20.21/7.20 new_primModNatS02(wz3000000000) -> new_primModNatS(Main.Succ(Main.Succ(wz3000000000)), Main.Succ(Main.Zero), Main.Succ(Main.Zero)) 20.21/7.20 new_primModNatS00(wz247, wz248) -> new_primModNatS(Main.Succ(wz247), Main.Succ(Main.Succ(wz248)), Main.Succ(Main.Succ(wz248))) 20.21/7.20 new_primModNatS0(wz250, wz251, Main.Succ(wz2520), Main.Zero) -> new_primModNatS00(wz250, wz251) 20.21/7.20 new_primModNatS01(Main.Succ(Main.Succ(wz300000)), Main.Succ(wz310000)) -> new_primModNatS0(Main.Succ(wz300000), wz310000, wz300000, wz310000) 20.21/7.20 new_primModNatS01(Main.Succ(Main.Zero), Main.Zero) -> new_primModNatS(Main.Succ(Main.Zero), Main.Succ(Main.Zero), Main.Succ(Main.Zero)) 20.21/7.20 20.21/7.20 R is empty. 20.21/7.20 Q is empty. 20.21/7.20 We have to consider all minimal (P,Q,R)-chains. 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (8) QDPOrderProof (EQUIVALENT) 20.21/7.20 We use the reduction pair processor [LPAR04,JAR06]. 20.21/7.20 20.21/7.20 20.21/7.20 The following pairs can be oriented strictly and are deleted. 20.21/7.20 20.21/7.20 new_primModNatS(Main.Succ(wz2550), Main.Succ(wz2560), wz257) -> new_primModNatS(wz2550, wz2560, wz257) 20.21/7.20 new_primModNatS(Main.Succ(wz2550), Main.Zero, Main.Succ(wz2570)) -> new_primModNatS01(wz2550, wz2570) 20.21/7.20 The remaining pairs can at least be oriented weakly. 20.21/7.20 Used ordering: Polynomial interpretation [POLO]: 20.21/7.20 20.21/7.20 POL(Main.Succ(x_1)) = 1 + x_1 20.21/7.20 POL(Main.Zero) = 0 20.21/7.20 POL(new_primModNatS(x_1, x_2, x_3)) = x_1 20.21/7.20 POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 20.21/7.20 POL(new_primModNatS00(x_1, x_2)) = 1 + x_1 20.21/7.20 POL(new_primModNatS01(x_1, x_2)) = x_1 20.21/7.20 POL(new_primModNatS02(x_1)) = 2 + x_1 20.21/7.20 20.21/7.20 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 20.21/7.20 none 20.21/7.20 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (9) 20.21/7.20 Obligation: 20.21/7.20 Q DP problem: 20.21/7.20 The TRS P consists of the following rules: 20.21/7.20 20.21/7.20 new_primModNatS0(wz250, wz251, Main.Zero, Main.Zero) -> new_primModNatS00(wz250, wz251) 20.21/7.20 new_primModNatS0(wz250, wz251, Main.Succ(wz2520), Main.Succ(wz2530)) -> new_primModNatS0(wz250, wz251, wz2520, wz2530) 20.21/7.20 new_primModNatS01(Main.Succ(Main.Succ(wz300000)), Main.Zero) -> new_primModNatS02(wz300000) 20.21/7.20 new_primModNatS02(wz3000000000) -> new_primModNatS(Main.Succ(Main.Succ(wz3000000000)), Main.Succ(Main.Zero), Main.Succ(Main.Zero)) 20.21/7.20 new_primModNatS00(wz247, wz248) -> new_primModNatS(Main.Succ(wz247), Main.Succ(Main.Succ(wz248)), Main.Succ(Main.Succ(wz248))) 20.21/7.20 new_primModNatS0(wz250, wz251, Main.Succ(wz2520), Main.Zero) -> new_primModNatS00(wz250, wz251) 20.21/7.20 new_primModNatS01(Main.Succ(Main.Succ(wz300000)), Main.Succ(wz310000)) -> new_primModNatS0(Main.Succ(wz300000), wz310000, wz300000, wz310000) 20.21/7.20 new_primModNatS01(Main.Succ(Main.Zero), Main.Zero) -> new_primModNatS(Main.Succ(Main.Zero), Main.Succ(Main.Zero), Main.Succ(Main.Zero)) 20.21/7.20 20.21/7.20 R is empty. 20.21/7.20 Q is empty. 20.21/7.20 We have to consider all minimal (P,Q,R)-chains. 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (10) DependencyGraphProof (EQUIVALENT) 20.21/7.20 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 7 less nodes. 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (11) 20.21/7.20 Obligation: 20.21/7.20 Q DP problem: 20.21/7.20 The TRS P consists of the following rules: 20.21/7.20 20.21/7.20 new_primModNatS0(wz250, wz251, Main.Succ(wz2520), Main.Succ(wz2530)) -> new_primModNatS0(wz250, wz251, wz2520, wz2530) 20.21/7.20 20.21/7.20 R is empty. 20.21/7.20 Q is empty. 20.21/7.20 We have to consider all minimal (P,Q,R)-chains. 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (12) QDPSizeChangeProof (EQUIVALENT) 20.21/7.20 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. 20.21/7.20 20.21/7.20 From the DPs we obtained the following set of size-change graphs: 20.21/7.20 *new_primModNatS0(wz250, wz251, Main.Succ(wz2520), Main.Succ(wz2530)) -> new_primModNatS0(wz250, wz251, wz2520, wz2530) 20.21/7.20 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 20.21/7.20 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (13) 20.21/7.20 YES 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (14) 20.21/7.20 Obligation: 20.21/7.20 Q DP problem: 20.21/7.20 The TRS P consists of the following rules: 20.21/7.20 20.21/7.20 new_primMulNat(Main.Succ(wz1860)) -> new_primMulNat(wz1860) 20.21/7.20 20.21/7.20 R is empty. 20.21/7.20 Q is empty. 20.21/7.20 We have to consider all minimal (P,Q,R)-chains. 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (15) QDPSizeChangeProof (EQUIVALENT) 20.21/7.20 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. 20.21/7.20 20.21/7.20 From the DPs we obtained the following set of size-change graphs: 20.21/7.20 *new_primMulNat(Main.Succ(wz1860)) -> new_primMulNat(wz1860) 20.21/7.20 The graph contains the following edges 1 > 1 20.21/7.20 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (16) 20.21/7.20 YES 20.21/7.20 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (17) 20.21/7.20 Obligation: 20.21/7.20 Q DP problem: 20.21/7.20 The TRS P consists of the following rules: 20.21/7.20 20.21/7.20 new_primDivNatS(Main.Succ(wz2950), Main.Succ(wz2960), wz297) -> new_primDivNatS(wz2950, wz2960, wz297) 20.21/7.20 new_primDivNatS1(Main.Succ(wz1460), Main.Succ(wz1470)) -> new_primDivNatS0(wz1460, wz1470, wz1460, wz1470) 20.21/7.20 new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Succ(wz2930)) -> new_primDivNatS0(wz290, wz291, wz2920, wz2930) 20.21/7.20 new_primDivNatS1(Main.Zero, Main.Zero) -> new_primDivNatS(Main.Zero, Main.Zero, Main.Zero) 20.21/7.20 new_primDivNatS00(wz290, wz291) -> new_primDivNatS(Main.Succ(wz290), Main.Succ(wz291), Main.Succ(wz291)) 20.21/7.20 new_primDivNatS(Main.Succ(wz2950), Main.Zero, wz297) -> new_primDivNatS1(wz2950, wz297) 20.21/7.20 new_primDivNatS1(Main.Succ(wz1460), Main.Zero) -> new_primDivNatS(Main.Succ(wz1460), Main.Zero, Main.Zero) 20.21/7.20 new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Zero) -> new_primDivNatS(Main.Succ(wz290), Main.Succ(wz291), Main.Succ(wz291)) 20.21/7.20 new_primDivNatS0(wz290, wz291, Main.Zero, Main.Zero) -> new_primDivNatS00(wz290, wz291) 20.21/7.20 20.21/7.20 R is empty. 20.21/7.20 Q is empty. 20.21/7.20 We have to consider all minimal (P,Q,R)-chains. 20.21/7.20 ---------------------------------------- 20.21/7.20 20.21/7.20 (18) DependencyGraphProof (EQUIVALENT) 20.21/7.20 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 20.53/7.20 ---------------------------------------- 20.53/7.20 20.53/7.20 (19) 20.53/7.20 Obligation: 20.53/7.20 Q DP problem: 20.53/7.20 The TRS P consists of the following rules: 20.53/7.20 20.53/7.20 new_primDivNatS(Main.Succ(wz2950), Main.Zero, wz297) -> new_primDivNatS1(wz2950, wz297) 20.53/7.20 new_primDivNatS1(Main.Succ(wz1460), Main.Succ(wz1470)) -> new_primDivNatS0(wz1460, wz1470, wz1460, wz1470) 20.53/7.20 new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Succ(wz2930)) -> new_primDivNatS0(wz290, wz291, wz2920, wz2930) 20.53/7.20 new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Zero) -> new_primDivNatS(Main.Succ(wz290), Main.Succ(wz291), Main.Succ(wz291)) 20.53/7.20 new_primDivNatS(Main.Succ(wz2950), Main.Succ(wz2960), wz297) -> new_primDivNatS(wz2950, wz2960, wz297) 20.53/7.20 new_primDivNatS0(wz290, wz291, Main.Zero, Main.Zero) -> new_primDivNatS00(wz290, wz291) 20.53/7.20 new_primDivNatS00(wz290, wz291) -> new_primDivNatS(Main.Succ(wz290), Main.Succ(wz291), Main.Succ(wz291)) 20.53/7.20 new_primDivNatS1(Main.Succ(wz1460), Main.Zero) -> new_primDivNatS(Main.Succ(wz1460), Main.Zero, Main.Zero) 20.53/7.20 20.53/7.20 R is empty. 20.53/7.20 Q is empty. 20.53/7.20 We have to consider all minimal (P,Q,R)-chains. 20.53/7.20 ---------------------------------------- 20.53/7.20 20.53/7.20 (20) QDPOrderProof (EQUIVALENT) 20.53/7.20 We use the reduction pair processor [LPAR04,JAR06]. 20.53/7.20 20.53/7.20 20.53/7.20 The following pairs can be oriented strictly and are deleted. 20.53/7.20 20.53/7.20 new_primDivNatS(Main.Succ(wz2950), Main.Zero, wz297) -> new_primDivNatS1(wz2950, wz297) 20.53/7.20 new_primDivNatS(Main.Succ(wz2950), Main.Succ(wz2960), wz297) -> new_primDivNatS(wz2950, wz2960, wz297) 20.53/7.20 The remaining pairs can at least be oriented weakly. 20.53/7.20 Used ordering: Polynomial interpretation [POLO]: 20.53/7.20 20.53/7.20 POL(Main.Succ(x_1)) = 1 + x_1 20.53/7.20 POL(Main.Zero) = 0 20.53/7.20 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 20.53/7.20 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 20.53/7.20 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 20.53/7.20 POL(new_primDivNatS1(x_1, x_2)) = x_1 20.53/7.20 20.53/7.20 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 20.53/7.20 none 20.53/7.20 20.53/7.20 20.53/7.20 ---------------------------------------- 20.53/7.20 20.53/7.20 (21) 20.53/7.20 Obligation: 20.53/7.20 Q DP problem: 20.53/7.20 The TRS P consists of the following rules: 20.53/7.20 20.53/7.20 new_primDivNatS1(Main.Succ(wz1460), Main.Succ(wz1470)) -> new_primDivNatS0(wz1460, wz1470, wz1460, wz1470) 20.53/7.20 new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Succ(wz2930)) -> new_primDivNatS0(wz290, wz291, wz2920, wz2930) 20.53/7.20 new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Zero) -> new_primDivNatS(Main.Succ(wz290), Main.Succ(wz291), Main.Succ(wz291)) 20.53/7.20 new_primDivNatS0(wz290, wz291, Main.Zero, Main.Zero) -> new_primDivNatS00(wz290, wz291) 20.53/7.20 new_primDivNatS00(wz290, wz291) -> new_primDivNatS(Main.Succ(wz290), Main.Succ(wz291), Main.Succ(wz291)) 20.53/7.20 new_primDivNatS1(Main.Succ(wz1460), Main.Zero) -> new_primDivNatS(Main.Succ(wz1460), Main.Zero, Main.Zero) 20.53/7.20 20.53/7.20 R is empty. 20.53/7.20 Q is empty. 20.53/7.20 We have to consider all minimal (P,Q,R)-chains. 20.53/7.20 ---------------------------------------- 20.53/7.20 20.53/7.20 (22) DependencyGraphProof (EQUIVALENT) 20.53/7.20 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 20.53/7.20 ---------------------------------------- 20.53/7.20 20.53/7.20 (23) 20.53/7.20 Obligation: 20.53/7.20 Q DP problem: 20.53/7.20 The TRS P consists of the following rules: 20.53/7.20 20.53/7.20 new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Succ(wz2930)) -> new_primDivNatS0(wz290, wz291, wz2920, wz2930) 20.53/7.20 20.53/7.20 R is empty. 20.53/7.20 Q is empty. 20.53/7.20 We have to consider all minimal (P,Q,R)-chains. 20.53/7.20 ---------------------------------------- 20.53/7.20 20.53/7.20 (24) QDPSizeChangeProof (EQUIVALENT) 20.53/7.20 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. 20.53/7.20 20.53/7.20 From the DPs we obtained the following set of size-change graphs: 20.53/7.20 *new_primDivNatS0(wz290, wz291, Main.Succ(wz2920), Main.Succ(wz2930)) -> new_primDivNatS0(wz290, wz291, wz2920, wz2930) 20.53/7.20 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 20.53/7.20 20.53/7.20 20.53/7.20 ---------------------------------------- 20.53/7.20 20.53/7.20 (25) 20.53/7.20 YES 20.53/7.24 EOF