8.33/3.68 YES 10.13/4.20 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 10.13/4.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.13/4.20 10.13/4.20 10.13/4.20 H-Termination with start terms of the given HASKELL could be proven: 10.13/4.20 10.13/4.20 (0) HASKELL 10.13/4.20 (1) BR [EQUIVALENT, 0 ms] 10.13/4.20 (2) HASKELL 10.13/4.20 (3) COR [EQUIVALENT, 0 ms] 10.13/4.20 (4) HASKELL 10.13/4.20 (5) Narrow [SOUND, 0 ms] 10.13/4.20 (6) AND 10.13/4.20 (7) QDP 10.13/4.20 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.13/4.20 (9) YES 10.13/4.20 (10) QDP 10.13/4.20 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.13/4.20 (12) YES 10.13/4.20 (13) QDP 10.13/4.20 (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.13/4.20 (15) YES 10.13/4.20 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (0) 10.13/4.20 Obligation: 10.13/4.20 mainModule Main 10.13/4.20 module Main where { 10.13/4.20 import qualified Prelude; 10.13/4.20 data Float = Float MyInt MyInt ; 10.13/4.20 10.13/4.20 data MyBool = MyTrue | MyFalse ; 10.13/4.20 10.13/4.20 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.13/4.20 10.13/4.20 data Main.Nat = Succ Main.Nat | Zero ; 10.13/4.20 10.13/4.20 esEsFloat :: Float -> Float -> MyBool; 10.13/4.20 esEsFloat = primEqFloat; 10.13/4.20 10.13/4.20 esEsMyInt :: MyInt -> MyInt -> MyBool; 10.13/4.20 esEsMyInt = primEqInt; 10.13/4.20 10.13/4.20 primEqFloat :: Float -> Float -> MyBool; 10.13/4.20 primEqFloat (Float x1 x2) (Float y1 y2) = esEsMyInt (srMyInt x1 y1) (srMyInt x2 y2); 10.13/4.20 10.13/4.20 primEqInt :: MyInt -> MyInt -> MyBool; 10.13/4.20 primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; 10.13/4.20 primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; 10.13/4.20 primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; 10.13/4.20 primEqInt vv vw = MyFalse; 10.13/4.20 10.13/4.20 primEqNat :: Main.Nat -> Main.Nat -> MyBool; 10.13/4.20 primEqNat Main.Zero Main.Zero = MyTrue; 10.13/4.20 primEqNat Main.Zero (Main.Succ y) = MyFalse; 10.13/4.20 primEqNat (Main.Succ x) Main.Zero = MyFalse; 10.13/4.20 primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; 10.13/4.20 10.13/4.20 primMulInt :: MyInt -> MyInt -> MyInt; 10.13/4.20 primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y); 10.13/4.20 primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y); 10.13/4.20 primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y); 10.13/4.20 primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y); 10.13/4.20 10.13/4.20 primMulNat :: Main.Nat -> Main.Nat -> Main.Nat; 10.13/4.20 primMulNat Main.Zero Main.Zero = Main.Zero; 10.13/4.20 primMulNat Main.Zero (Main.Succ y) = Main.Zero; 10.13/4.20 primMulNat (Main.Succ x) Main.Zero = Main.Zero; 10.13/4.20 primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y); 10.13/4.20 10.13/4.20 primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; 10.13/4.20 primPlusNat Main.Zero Main.Zero = Main.Zero; 10.13/4.20 primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; 10.13/4.20 primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; 10.13/4.20 primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); 10.13/4.20 10.13/4.20 srMyInt :: MyInt -> MyInt -> MyInt; 10.13/4.20 srMyInt = primMulInt; 10.13/4.20 10.13/4.20 } 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (1) BR (EQUIVALENT) 10.13/4.20 Replaced joker patterns by fresh variables and removed binding patterns. 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (2) 10.13/4.20 Obligation: 10.13/4.20 mainModule Main 10.13/4.20 module Main where { 10.13/4.20 import qualified Prelude; 10.13/4.20 data Float = Float MyInt MyInt ; 10.13/4.20 10.13/4.20 data MyBool = MyTrue | MyFalse ; 10.13/4.20 10.13/4.20 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.13/4.20 10.13/4.20 data Main.Nat = Succ Main.Nat | Zero ; 10.13/4.20 10.13/4.20 esEsFloat :: Float -> Float -> MyBool; 10.13/4.20 esEsFloat = primEqFloat; 10.13/4.20 10.13/4.20 esEsMyInt :: MyInt -> MyInt -> MyBool; 10.13/4.20 esEsMyInt = primEqInt; 10.13/4.20 10.13/4.20 primEqFloat :: Float -> Float -> MyBool; 10.13/4.20 primEqFloat (Float x1 x2) (Float y1 y2) = esEsMyInt (srMyInt x1 y1) (srMyInt x2 y2); 10.13/4.20 10.13/4.20 primEqInt :: MyInt -> MyInt -> MyBool; 10.13/4.20 primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; 10.13/4.20 primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; 10.13/4.20 primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; 10.13/4.20 primEqInt vv vw = MyFalse; 10.13/4.20 10.13/4.20 primEqNat :: Main.Nat -> Main.Nat -> MyBool; 10.13/4.20 primEqNat Main.Zero Main.Zero = MyTrue; 10.13/4.20 primEqNat Main.Zero (Main.Succ y) = MyFalse; 10.13/4.20 primEqNat (Main.Succ x) Main.Zero = MyFalse; 10.13/4.20 primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; 10.13/4.20 10.13/4.20 primMulInt :: MyInt -> MyInt -> MyInt; 10.13/4.20 primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y); 10.13/4.20 primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y); 10.13/4.20 primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y); 10.13/4.20 primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y); 10.13/4.20 10.13/4.20 primMulNat :: Main.Nat -> Main.Nat -> Main.Nat; 10.13/4.20 primMulNat Main.Zero Main.Zero = Main.Zero; 10.13/4.20 primMulNat Main.Zero (Main.Succ y) = Main.Zero; 10.13/4.20 primMulNat (Main.Succ x) Main.Zero = Main.Zero; 10.13/4.20 primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y); 10.13/4.20 10.13/4.20 primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; 10.13/4.20 primPlusNat Main.Zero Main.Zero = Main.Zero; 10.13/4.20 primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; 10.13/4.20 primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; 10.13/4.20 primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); 10.13/4.20 10.13/4.20 srMyInt :: MyInt -> MyInt -> MyInt; 10.13/4.20 srMyInt = primMulInt; 10.13/4.20 10.13/4.20 } 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (3) COR (EQUIVALENT) 10.13/4.20 Cond Reductions: 10.13/4.20 The following Function with conditions 10.13/4.20 "undefined |Falseundefined; 10.13/4.20 " 10.13/4.20 is transformed to 10.13/4.20 "undefined = undefined1; 10.13/4.20 " 10.13/4.20 "undefined0 True = undefined; 10.13/4.20 " 10.13/4.20 "undefined1 = undefined0 False; 10.13/4.20 " 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (4) 10.13/4.20 Obligation: 10.13/4.20 mainModule Main 10.13/4.20 module Main where { 10.13/4.20 import qualified Prelude; 10.13/4.20 data Float = Float MyInt MyInt ; 10.13/4.20 10.13/4.20 data MyBool = MyTrue | MyFalse ; 10.13/4.20 10.13/4.20 data MyInt = Pos Main.Nat | Neg Main.Nat ; 10.13/4.20 10.13/4.20 data Main.Nat = Succ Main.Nat | Zero ; 10.13/4.20 10.13/4.20 esEsFloat :: Float -> Float -> MyBool; 10.13/4.20 esEsFloat = primEqFloat; 10.13/4.20 10.13/4.20 esEsMyInt :: MyInt -> MyInt -> MyBool; 10.13/4.20 esEsMyInt = primEqInt; 10.13/4.20 10.13/4.20 primEqFloat :: Float -> Float -> MyBool; 10.13/4.20 primEqFloat (Float x1 x2) (Float y1 y2) = esEsMyInt (srMyInt x1 y1) (srMyInt x2 y2); 10.13/4.20 10.13/4.20 primEqInt :: MyInt -> MyInt -> MyBool; 10.13/4.20 primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; 10.13/4.20 primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; 10.13/4.20 primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; 10.13/4.20 primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; 10.13/4.20 primEqInt vv vw = MyFalse; 10.13/4.20 10.13/4.20 primEqNat :: Main.Nat -> Main.Nat -> MyBool; 10.13/4.20 primEqNat Main.Zero Main.Zero = MyTrue; 10.13/4.20 primEqNat Main.Zero (Main.Succ y) = MyFalse; 10.13/4.20 primEqNat (Main.Succ x) Main.Zero = MyFalse; 10.13/4.20 primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; 10.13/4.20 10.13/4.20 primMulInt :: MyInt -> MyInt -> MyInt; 10.13/4.20 primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y); 10.13/4.20 primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y); 10.13/4.20 primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y); 10.13/4.20 primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y); 10.13/4.20 10.13/4.20 primMulNat :: Main.Nat -> Main.Nat -> Main.Nat; 10.13/4.20 primMulNat Main.Zero Main.Zero = Main.Zero; 10.13/4.20 primMulNat Main.Zero (Main.Succ y) = Main.Zero; 10.13/4.20 primMulNat (Main.Succ x) Main.Zero = Main.Zero; 10.13/4.20 primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y); 10.13/4.20 10.13/4.20 primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; 10.13/4.20 primPlusNat Main.Zero Main.Zero = Main.Zero; 10.13/4.20 primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; 10.13/4.20 primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; 10.13/4.20 primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); 10.13/4.20 10.13/4.20 srMyInt :: MyInt -> MyInt -> MyInt; 10.13/4.20 srMyInt = primMulInt; 10.13/4.20 10.13/4.20 } 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (5) Narrow (SOUND) 10.13/4.20 Haskell To QDPs 10.13/4.20 10.13/4.20 digraph dp_graph { 10.13/4.20 node [outthreshold=100, inthreshold=100];1[label="esEsFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.13/4.20 3[label="esEsFloat vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 10.13/4.20 4[label="esEsFloat vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 10.13/4.20 5[label="primEqFloat vz3 vz4",fontsize=16,color="burlywood",shape="box"];505[label="vz3/Float vz30 vz31",fontsize=10,color="white",style="solid",shape="box"];5 -> 505[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 505 -> 6[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 6[label="primEqFloat (Float vz30 vz31) vz4",fontsize=16,color="burlywood",shape="box"];506[label="vz4/Float vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];6 -> 506[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 506 -> 7[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 7[label="primEqFloat (Float vz30 vz31) (Float vz40 vz41)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 10.13/4.20 8[label="esEsMyInt (srMyInt vz30 vz40) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 10.13/4.20 9[label="primEqInt (srMyInt vz30 vz40) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 10.13/4.20 10[label="primEqInt (primMulInt vz30 vz40) (srMyInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];507[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];10 -> 507[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 507 -> 11[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 508[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];10 -> 508[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 508 -> 12[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 11[label="primEqInt (primMulInt (Pos vz300) vz40) (srMyInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];509[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];11 -> 509[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 509 -> 13[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 510[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];11 -> 510[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 510 -> 14[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 12[label="primEqInt (primMulInt (Neg vz300) vz40) (srMyInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];511[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 511[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 511 -> 15[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 512[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 512[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 512 -> 16[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 13[label="primEqInt (primMulInt (Pos vz300) (Pos vz400)) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 10.13/4.20 14[label="primEqInt (primMulInt (Pos vz300) (Neg vz400)) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 10.13/4.20 15[label="primEqInt (primMulInt (Neg vz300) (Pos vz400)) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 10.13/4.20 16[label="primEqInt (primMulInt (Neg vz300) (Neg vz400)) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 10.13/4.20 17 -> 270[label="",style="dashed", color="red", weight=0]; 10.13/4.20 17[label="primEqInt (Pos (primMulNat vz300 vz400)) (srMyInt vz31 vz41)",fontsize=16,color="magenta"];17 -> 271[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 18 -> 346[label="",style="dashed", color="red", weight=0]; 10.13/4.20 18[label="primEqInt (Neg (primMulNat vz300 vz400)) (srMyInt vz31 vz41)",fontsize=16,color="magenta"];18 -> 347[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 19 -> 346[label="",style="dashed", color="red", weight=0]; 10.13/4.20 19[label="primEqInt (Neg (primMulNat vz300 vz400)) (srMyInt vz31 vz41)",fontsize=16,color="magenta"];19 -> 348[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 20 -> 270[label="",style="dashed", color="red", weight=0]; 10.13/4.20 20[label="primEqInt (Pos (primMulNat vz300 vz400)) (srMyInt vz31 vz41)",fontsize=16,color="magenta"];20 -> 272[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 271[label="primMulNat vz300 vz400",fontsize=16,color="burlywood",shape="triangle"];513[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];271 -> 513[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 513 -> 283[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 514[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];271 -> 514[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 514 -> 284[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 270[label="primEqInt (Pos vz10) (srMyInt vz31 vz41)",fontsize=16,color="burlywood",shape="triangle"];515[label="vz10/Succ vz100",fontsize=10,color="white",style="solid",shape="box"];270 -> 515[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 515 -> 285[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 516[label="vz10/Zero",fontsize=10,color="white",style="solid",shape="box"];270 -> 516[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 516 -> 286[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 347 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 347[label="primMulNat vz300 vz400",fontsize=16,color="magenta"];347 -> 359[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 346[label="primEqInt (Neg vz15) (srMyInt vz31 vz41)",fontsize=16,color="burlywood",shape="triangle"];517[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];346 -> 517[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 517 -> 360[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 518[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];346 -> 518[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 518 -> 361[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 348 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 348[label="primMulNat vz300 vz400",fontsize=16,color="magenta"];348 -> 362[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 272 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 272[label="primMulNat vz300 vz400",fontsize=16,color="magenta"];272 -> 287[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 272 -> 288[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 283[label="primMulNat (Succ vz3000) vz400",fontsize=16,color="burlywood",shape="box"];519[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];283 -> 519[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 519 -> 303[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 520[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];283 -> 520[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 520 -> 304[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 284[label="primMulNat Zero vz400",fontsize=16,color="burlywood",shape="box"];521[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];284 -> 521[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 521 -> 305[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 522[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];284 -> 522[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 522 -> 306[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 285[label="primEqInt (Pos (Succ vz100)) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];285 -> 307[label="",style="solid", color="black", weight=3]; 10.13/4.20 286[label="primEqInt (Pos Zero) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];286 -> 308[label="",style="solid", color="black", weight=3]; 10.13/4.20 359[label="vz400",fontsize=16,color="green",shape="box"];360[label="primEqInt (Neg (Succ vz150)) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];360 -> 373[label="",style="solid", color="black", weight=3]; 10.13/4.20 361[label="primEqInt (Neg Zero) (srMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];361 -> 374[label="",style="solid", color="black", weight=3]; 10.13/4.20 362[label="vz300",fontsize=16,color="green",shape="box"];287[label="vz400",fontsize=16,color="green",shape="box"];288[label="vz300",fontsize=16,color="green",shape="box"];303[label="primMulNat (Succ vz3000) (Succ vz4000)",fontsize=16,color="black",shape="box"];303 -> 319[label="",style="solid", color="black", weight=3]; 10.13/4.20 304[label="primMulNat (Succ vz3000) Zero",fontsize=16,color="black",shape="box"];304 -> 320[label="",style="solid", color="black", weight=3]; 10.13/4.20 305[label="primMulNat Zero (Succ vz4000)",fontsize=16,color="black",shape="box"];305 -> 321[label="",style="solid", color="black", weight=3]; 10.13/4.20 306[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];306 -> 322[label="",style="solid", color="black", weight=3]; 10.13/4.20 307[label="primEqInt (Pos (Succ vz100)) (primMulInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];523[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];307 -> 523[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 523 -> 323[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 524[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];307 -> 524[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 524 -> 324[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 308[label="primEqInt (Pos Zero) (primMulInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];525[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];308 -> 525[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 525 -> 325[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 526[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];308 -> 526[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 526 -> 326[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 373[label="primEqInt (Neg (Succ vz150)) (primMulInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];527[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];373 -> 527[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 527 -> 378[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 528[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];373 -> 528[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 528 -> 379[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 374[label="primEqInt (Neg Zero) (primMulInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];529[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];374 -> 529[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 529 -> 380[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 530[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];374 -> 530[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 530 -> 381[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 319 -> 332[label="",style="dashed", color="red", weight=0]; 10.13/4.20 319[label="primPlusNat (primMulNat vz3000 (Succ vz4000)) (Succ vz4000)",fontsize=16,color="magenta"];319 -> 333[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 320[label="Zero",fontsize=16,color="green",shape="box"];321[label="Zero",fontsize=16,color="green",shape="box"];322[label="Zero",fontsize=16,color="green",shape="box"];323[label="primEqInt (Pos (Succ vz100)) (primMulInt (Pos vz310) vz41)",fontsize=16,color="burlywood",shape="box"];531[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];323 -> 531[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 531 -> 334[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 532[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];323 -> 532[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 532 -> 335[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 324[label="primEqInt (Pos (Succ vz100)) (primMulInt (Neg vz310) vz41)",fontsize=16,color="burlywood",shape="box"];533[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];324 -> 533[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 533 -> 336[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 534[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];324 -> 534[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 534 -> 337[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 325[label="primEqInt (Pos Zero) (primMulInt (Pos vz310) vz41)",fontsize=16,color="burlywood",shape="box"];535[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];325 -> 535[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 535 -> 338[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 536[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];325 -> 536[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 536 -> 339[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 326[label="primEqInt (Pos Zero) (primMulInt (Neg vz310) vz41)",fontsize=16,color="burlywood",shape="box"];537[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];326 -> 537[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 537 -> 340[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 538[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];326 -> 538[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 538 -> 341[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 378[label="primEqInt (Neg (Succ vz150)) (primMulInt (Pos vz310) vz41)",fontsize=16,color="burlywood",shape="box"];539[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];378 -> 539[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 539 -> 385[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 540[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];378 -> 540[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 540 -> 386[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 379[label="primEqInt (Neg (Succ vz150)) (primMulInt (Neg vz310) vz41)",fontsize=16,color="burlywood",shape="box"];541[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];379 -> 541[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 541 -> 387[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 542[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];379 -> 542[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 542 -> 388[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 380[label="primEqInt (Neg Zero) (primMulInt (Pos vz310) vz41)",fontsize=16,color="burlywood",shape="box"];543[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];380 -> 543[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 543 -> 389[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 544[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];380 -> 544[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 544 -> 390[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 381[label="primEqInt (Neg Zero) (primMulInt (Neg vz310) vz41)",fontsize=16,color="burlywood",shape="box"];545[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];381 -> 545[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 545 -> 391[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 546[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];381 -> 546[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 546 -> 392[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 333 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 333[label="primMulNat vz3000 (Succ vz4000)",fontsize=16,color="magenta"];333 -> 342[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 333 -> 343[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 332[label="primPlusNat vz14 (Succ vz4000)",fontsize=16,color="burlywood",shape="triangle"];547[label="vz14/Succ vz140",fontsize=10,color="white",style="solid",shape="box"];332 -> 547[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 547 -> 344[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 548[label="vz14/Zero",fontsize=10,color="white",style="solid",shape="box"];332 -> 548[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 548 -> 345[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 334[label="primEqInt (Pos (Succ vz100)) (primMulInt (Pos vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];334 -> 363[label="",style="solid", color="black", weight=3]; 10.13/4.20 335[label="primEqInt (Pos (Succ vz100)) (primMulInt (Pos vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];335 -> 364[label="",style="solid", color="black", weight=3]; 10.13/4.20 336[label="primEqInt (Pos (Succ vz100)) (primMulInt (Neg vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];336 -> 365[label="",style="solid", color="black", weight=3]; 10.13/4.20 337[label="primEqInt (Pos (Succ vz100)) (primMulInt (Neg vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];337 -> 366[label="",style="solid", color="black", weight=3]; 10.13/4.20 338[label="primEqInt (Pos Zero) (primMulInt (Pos vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];338 -> 367[label="",style="solid", color="black", weight=3]; 10.13/4.20 339[label="primEqInt (Pos Zero) (primMulInt (Pos vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];339 -> 368[label="",style="solid", color="black", weight=3]; 10.13/4.20 340[label="primEqInt (Pos Zero) (primMulInt (Neg vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];340 -> 369[label="",style="solid", color="black", weight=3]; 10.13/4.20 341[label="primEqInt (Pos Zero) (primMulInt (Neg vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];341 -> 370[label="",style="solid", color="black", weight=3]; 10.13/4.20 385[label="primEqInt (Neg (Succ vz150)) (primMulInt (Pos vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];385 -> 396[label="",style="solid", color="black", weight=3]; 10.13/4.20 386[label="primEqInt (Neg (Succ vz150)) (primMulInt (Pos vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];386 -> 397[label="",style="solid", color="black", weight=3]; 10.13/4.20 387[label="primEqInt (Neg (Succ vz150)) (primMulInt (Neg vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];387 -> 398[label="",style="solid", color="black", weight=3]; 10.13/4.20 388[label="primEqInt (Neg (Succ vz150)) (primMulInt (Neg vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];388 -> 399[label="",style="solid", color="black", weight=3]; 10.13/4.20 389[label="primEqInt (Neg Zero) (primMulInt (Pos vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];389 -> 400[label="",style="solid", color="black", weight=3]; 10.13/4.20 390[label="primEqInt (Neg Zero) (primMulInt (Pos vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];390 -> 401[label="",style="solid", color="black", weight=3]; 10.13/4.20 391[label="primEqInt (Neg Zero) (primMulInt (Neg vz310) (Pos vz410))",fontsize=16,color="black",shape="box"];391 -> 402[label="",style="solid", color="black", weight=3]; 10.13/4.20 392[label="primEqInt (Neg Zero) (primMulInt (Neg vz310) (Neg vz410))",fontsize=16,color="black",shape="box"];392 -> 403[label="",style="solid", color="black", weight=3]; 10.13/4.20 342[label="Succ vz4000",fontsize=16,color="green",shape="box"];343[label="vz3000",fontsize=16,color="green",shape="box"];344[label="primPlusNat (Succ vz140) (Succ vz4000)",fontsize=16,color="black",shape="box"];344 -> 371[label="",style="solid", color="black", weight=3]; 10.13/4.20 345[label="primPlusNat Zero (Succ vz4000)",fontsize=16,color="black",shape="box"];345 -> 372[label="",style="solid", color="black", weight=3]; 10.13/4.20 363 -> 375[label="",style="dashed", color="red", weight=0]; 10.13/4.20 363[label="primEqInt (Pos (Succ vz100)) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];363 -> 376[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 364 -> 382[label="",style="dashed", color="red", weight=0]; 10.13/4.20 364[label="primEqInt (Pos (Succ vz100)) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];364 -> 383[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 365 -> 382[label="",style="dashed", color="red", weight=0]; 10.13/4.20 365[label="primEqInt (Pos (Succ vz100)) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];365 -> 384[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 366 -> 375[label="",style="dashed", color="red", weight=0]; 10.13/4.20 366[label="primEqInt (Pos (Succ vz100)) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];366 -> 377[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 367 -> 393[label="",style="dashed", color="red", weight=0]; 10.13/4.20 367[label="primEqInt (Pos Zero) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];367 -> 394[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 368 -> 404[label="",style="dashed", color="red", weight=0]; 10.13/4.20 368[label="primEqInt (Pos Zero) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];368 -> 405[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 369 -> 404[label="",style="dashed", color="red", weight=0]; 10.13/4.20 369[label="primEqInt (Pos Zero) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];369 -> 406[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 370 -> 393[label="",style="dashed", color="red", weight=0]; 10.13/4.20 370[label="primEqInt (Pos Zero) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];370 -> 395[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 396 -> 407[label="",style="dashed", color="red", weight=0]; 10.13/4.20 396[label="primEqInt (Neg (Succ vz150)) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];396 -> 408[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 397 -> 410[label="",style="dashed", color="red", weight=0]; 10.13/4.20 397[label="primEqInt (Neg (Succ vz150)) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];397 -> 411[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 398 -> 410[label="",style="dashed", color="red", weight=0]; 10.13/4.20 398[label="primEqInt (Neg (Succ vz150)) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];398 -> 412[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 399 -> 407[label="",style="dashed", color="red", weight=0]; 10.13/4.20 399[label="primEqInt (Neg (Succ vz150)) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];399 -> 409[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 400 -> 413[label="",style="dashed", color="red", weight=0]; 10.13/4.20 400[label="primEqInt (Neg Zero) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];400 -> 414[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 401 -> 416[label="",style="dashed", color="red", weight=0]; 10.13/4.20 401[label="primEqInt (Neg Zero) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];401 -> 417[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 402 -> 416[label="",style="dashed", color="red", weight=0]; 10.13/4.20 402[label="primEqInt (Neg Zero) (Neg (primMulNat vz310 vz410))",fontsize=16,color="magenta"];402 -> 418[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 403 -> 413[label="",style="dashed", color="red", weight=0]; 10.13/4.20 403[label="primEqInt (Neg Zero) (Pos (primMulNat vz310 vz410))",fontsize=16,color="magenta"];403 -> 415[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 371[label="Succ (Succ (primPlusNat vz140 vz4000))",fontsize=16,color="green",shape="box"];371 -> 419[label="",style="dashed", color="green", weight=3]; 10.13/4.20 372[label="Succ vz4000",fontsize=16,color="green",shape="box"];376 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 376[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];376 -> 420[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 376 -> 421[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 375[label="primEqInt (Pos (Succ vz100)) (Pos vz16)",fontsize=16,color="burlywood",shape="triangle"];549[label="vz16/Succ vz160",fontsize=10,color="white",style="solid",shape="box"];375 -> 549[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 549 -> 422[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 550[label="vz16/Zero",fontsize=10,color="white",style="solid",shape="box"];375 -> 550[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 550 -> 423[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 383 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 383[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];383 -> 424[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 383 -> 425[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 382[label="primEqInt (Pos (Succ vz100)) (Neg vz17)",fontsize=16,color="black",shape="triangle"];382 -> 426[label="",style="solid", color="black", weight=3]; 10.13/4.20 384 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 384[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];384 -> 427[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 384 -> 428[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 377 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 377[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];377 -> 429[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 377 -> 430[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 394 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 394[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];394 -> 431[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 394 -> 432[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 393[label="primEqInt (Pos Zero) (Pos vz18)",fontsize=16,color="burlywood",shape="triangle"];551[label="vz18/Succ vz180",fontsize=10,color="white",style="solid",shape="box"];393 -> 551[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 551 -> 433[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 552[label="vz18/Zero",fontsize=10,color="white",style="solid",shape="box"];393 -> 552[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 552 -> 434[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 405 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 405[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];405 -> 435[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 405 -> 436[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 404[label="primEqInt (Pos Zero) (Neg vz19)",fontsize=16,color="burlywood",shape="triangle"];553[label="vz19/Succ vz190",fontsize=10,color="white",style="solid",shape="box"];404 -> 553[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 553 -> 437[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 554[label="vz19/Zero",fontsize=10,color="white",style="solid",shape="box"];404 -> 554[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 554 -> 438[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 406 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 406[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];406 -> 439[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 406 -> 440[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 395 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 395[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];395 -> 441[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 395 -> 442[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 408 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 408[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];408 -> 443[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 408 -> 444[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 407[label="primEqInt (Neg (Succ vz150)) (Pos vz20)",fontsize=16,color="black",shape="triangle"];407 -> 445[label="",style="solid", color="black", weight=3]; 10.13/4.20 411 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 411[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];411 -> 446[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 411 -> 447[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 410[label="primEqInt (Neg (Succ vz150)) (Neg vz21)",fontsize=16,color="burlywood",shape="triangle"];555[label="vz21/Succ vz210",fontsize=10,color="white",style="solid",shape="box"];410 -> 555[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 555 -> 448[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 556[label="vz21/Zero",fontsize=10,color="white",style="solid",shape="box"];410 -> 556[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 556 -> 449[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 412 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 412[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];412 -> 450[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 412 -> 451[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 409 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 409[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];409 -> 452[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 409 -> 453[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 414 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 414[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];414 -> 454[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 414 -> 455[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 413[label="primEqInt (Neg Zero) (Pos vz22)",fontsize=16,color="burlywood",shape="triangle"];557[label="vz22/Succ vz220",fontsize=10,color="white",style="solid",shape="box"];413 -> 557[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 557 -> 456[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 558[label="vz22/Zero",fontsize=10,color="white",style="solid",shape="box"];413 -> 558[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 558 -> 457[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 417 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 417[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];417 -> 458[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 417 -> 459[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 416[label="primEqInt (Neg Zero) (Neg vz23)",fontsize=16,color="burlywood",shape="triangle"];559[label="vz23/Succ vz230",fontsize=10,color="white",style="solid",shape="box"];416 -> 559[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 559 -> 460[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 560[label="vz23/Zero",fontsize=10,color="white",style="solid",shape="box"];416 -> 560[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 560 -> 461[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 418 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 418[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];418 -> 462[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 418 -> 463[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 415 -> 271[label="",style="dashed", color="red", weight=0]; 10.13/4.20 415[label="primMulNat vz310 vz410",fontsize=16,color="magenta"];415 -> 464[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 415 -> 465[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 419[label="primPlusNat vz140 vz4000",fontsize=16,color="burlywood",shape="triangle"];561[label="vz140/Succ vz1400",fontsize=10,color="white",style="solid",shape="box"];419 -> 561[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 561 -> 466[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 562[label="vz140/Zero",fontsize=10,color="white",style="solid",shape="box"];419 -> 562[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 562 -> 467[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 420[label="vz410",fontsize=16,color="green",shape="box"];421[label="vz310",fontsize=16,color="green",shape="box"];422[label="primEqInt (Pos (Succ vz100)) (Pos (Succ vz160))",fontsize=16,color="black",shape="box"];422 -> 468[label="",style="solid", color="black", weight=3]; 10.13/4.20 423[label="primEqInt (Pos (Succ vz100)) (Pos Zero)",fontsize=16,color="black",shape="box"];423 -> 469[label="",style="solid", color="black", weight=3]; 10.13/4.20 424[label="vz410",fontsize=16,color="green",shape="box"];425[label="vz310",fontsize=16,color="green",shape="box"];426[label="MyFalse",fontsize=16,color="green",shape="box"];427[label="vz410",fontsize=16,color="green",shape="box"];428[label="vz310",fontsize=16,color="green",shape="box"];429[label="vz410",fontsize=16,color="green",shape="box"];430[label="vz310",fontsize=16,color="green",shape="box"];431[label="vz410",fontsize=16,color="green",shape="box"];432[label="vz310",fontsize=16,color="green",shape="box"];433[label="primEqInt (Pos Zero) (Pos (Succ vz180))",fontsize=16,color="black",shape="box"];433 -> 470[label="",style="solid", color="black", weight=3]; 10.13/4.20 434[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];434 -> 471[label="",style="solid", color="black", weight=3]; 10.13/4.20 435[label="vz410",fontsize=16,color="green",shape="box"];436[label="vz310",fontsize=16,color="green",shape="box"];437[label="primEqInt (Pos Zero) (Neg (Succ vz190))",fontsize=16,color="black",shape="box"];437 -> 472[label="",style="solid", color="black", weight=3]; 10.13/4.20 438[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];438 -> 473[label="",style="solid", color="black", weight=3]; 10.13/4.20 439[label="vz410",fontsize=16,color="green",shape="box"];440[label="vz310",fontsize=16,color="green",shape="box"];441[label="vz410",fontsize=16,color="green",shape="box"];442[label="vz310",fontsize=16,color="green",shape="box"];443[label="vz410",fontsize=16,color="green",shape="box"];444[label="vz310",fontsize=16,color="green",shape="box"];445[label="MyFalse",fontsize=16,color="green",shape="box"];446[label="vz410",fontsize=16,color="green",shape="box"];447[label="vz310",fontsize=16,color="green",shape="box"];448[label="primEqInt (Neg (Succ vz150)) (Neg (Succ vz210))",fontsize=16,color="black",shape="box"];448 -> 474[label="",style="solid", color="black", weight=3]; 10.13/4.20 449[label="primEqInt (Neg (Succ vz150)) (Neg Zero)",fontsize=16,color="black",shape="box"];449 -> 475[label="",style="solid", color="black", weight=3]; 10.13/4.20 450[label="vz410",fontsize=16,color="green",shape="box"];451[label="vz310",fontsize=16,color="green",shape="box"];452[label="vz410",fontsize=16,color="green",shape="box"];453[label="vz310",fontsize=16,color="green",shape="box"];454[label="vz410",fontsize=16,color="green",shape="box"];455[label="vz310",fontsize=16,color="green",shape="box"];456[label="primEqInt (Neg Zero) (Pos (Succ vz220))",fontsize=16,color="black",shape="box"];456 -> 476[label="",style="solid", color="black", weight=3]; 10.13/4.20 457[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];457 -> 477[label="",style="solid", color="black", weight=3]; 10.13/4.20 458[label="vz410",fontsize=16,color="green",shape="box"];459[label="vz310",fontsize=16,color="green",shape="box"];460[label="primEqInt (Neg Zero) (Neg (Succ vz230))",fontsize=16,color="black",shape="box"];460 -> 478[label="",style="solid", color="black", weight=3]; 10.13/4.20 461[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];461 -> 479[label="",style="solid", color="black", weight=3]; 10.13/4.20 462[label="vz410",fontsize=16,color="green",shape="box"];463[label="vz310",fontsize=16,color="green",shape="box"];464[label="vz410",fontsize=16,color="green",shape="box"];465[label="vz310",fontsize=16,color="green",shape="box"];466[label="primPlusNat (Succ vz1400) vz4000",fontsize=16,color="burlywood",shape="box"];563[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];466 -> 563[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 563 -> 480[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 564[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];466 -> 564[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 564 -> 481[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 467[label="primPlusNat Zero vz4000",fontsize=16,color="burlywood",shape="box"];565[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];467 -> 565[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 565 -> 482[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 566[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];467 -> 566[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 566 -> 483[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 468[label="primEqNat vz100 vz160",fontsize=16,color="burlywood",shape="triangle"];567[label="vz100/Succ vz1000",fontsize=10,color="white",style="solid",shape="box"];468 -> 567[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 567 -> 484[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 568[label="vz100/Zero",fontsize=10,color="white",style="solid",shape="box"];468 -> 568[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 568 -> 485[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 469[label="MyFalse",fontsize=16,color="green",shape="box"];470[label="MyFalse",fontsize=16,color="green",shape="box"];471[label="MyTrue",fontsize=16,color="green",shape="box"];472[label="MyFalse",fontsize=16,color="green",shape="box"];473[label="MyTrue",fontsize=16,color="green",shape="box"];474 -> 468[label="",style="dashed", color="red", weight=0]; 10.13/4.20 474[label="primEqNat vz150 vz210",fontsize=16,color="magenta"];474 -> 486[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 474 -> 487[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 475[label="MyFalse",fontsize=16,color="green",shape="box"];476[label="MyFalse",fontsize=16,color="green",shape="box"];477[label="MyTrue",fontsize=16,color="green",shape="box"];478[label="MyFalse",fontsize=16,color="green",shape="box"];479[label="MyTrue",fontsize=16,color="green",shape="box"];480[label="primPlusNat (Succ vz1400) (Succ vz40000)",fontsize=16,color="black",shape="box"];480 -> 488[label="",style="solid", color="black", weight=3]; 10.13/4.20 481[label="primPlusNat (Succ vz1400) Zero",fontsize=16,color="black",shape="box"];481 -> 489[label="",style="solid", color="black", weight=3]; 10.13/4.20 482[label="primPlusNat Zero (Succ vz40000)",fontsize=16,color="black",shape="box"];482 -> 490[label="",style="solid", color="black", weight=3]; 10.13/4.20 483[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];483 -> 491[label="",style="solid", color="black", weight=3]; 10.13/4.20 484[label="primEqNat (Succ vz1000) vz160",fontsize=16,color="burlywood",shape="box"];569[label="vz160/Succ vz1600",fontsize=10,color="white",style="solid",shape="box"];484 -> 569[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 569 -> 492[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 570[label="vz160/Zero",fontsize=10,color="white",style="solid",shape="box"];484 -> 570[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 570 -> 493[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 485[label="primEqNat Zero vz160",fontsize=16,color="burlywood",shape="box"];571[label="vz160/Succ vz1600",fontsize=10,color="white",style="solid",shape="box"];485 -> 571[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 571 -> 494[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 572[label="vz160/Zero",fontsize=10,color="white",style="solid",shape="box"];485 -> 572[label="",style="solid", color="burlywood", weight=9]; 10.13/4.20 572 -> 495[label="",style="solid", color="burlywood", weight=3]; 10.13/4.20 486[label="vz210",fontsize=16,color="green",shape="box"];487[label="vz150",fontsize=16,color="green",shape="box"];488[label="Succ (Succ (primPlusNat vz1400 vz40000))",fontsize=16,color="green",shape="box"];488 -> 496[label="",style="dashed", color="green", weight=3]; 10.13/4.20 489[label="Succ vz1400",fontsize=16,color="green",shape="box"];490[label="Succ vz40000",fontsize=16,color="green",shape="box"];491[label="Zero",fontsize=16,color="green",shape="box"];492[label="primEqNat (Succ vz1000) (Succ vz1600)",fontsize=16,color="black",shape="box"];492 -> 497[label="",style="solid", color="black", weight=3]; 10.13/4.20 493[label="primEqNat (Succ vz1000) Zero",fontsize=16,color="black",shape="box"];493 -> 498[label="",style="solid", color="black", weight=3]; 10.13/4.20 494[label="primEqNat Zero (Succ vz1600)",fontsize=16,color="black",shape="box"];494 -> 499[label="",style="solid", color="black", weight=3]; 10.13/4.20 495[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];495 -> 500[label="",style="solid", color="black", weight=3]; 10.13/4.20 496 -> 419[label="",style="dashed", color="red", weight=0]; 10.13/4.20 496[label="primPlusNat vz1400 vz40000",fontsize=16,color="magenta"];496 -> 501[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 496 -> 502[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 497 -> 468[label="",style="dashed", color="red", weight=0]; 10.13/4.20 497[label="primEqNat vz1000 vz1600",fontsize=16,color="magenta"];497 -> 503[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 497 -> 504[label="",style="dashed", color="magenta", weight=3]; 10.13/4.20 498[label="MyFalse",fontsize=16,color="green",shape="box"];499[label="MyFalse",fontsize=16,color="green",shape="box"];500[label="MyTrue",fontsize=16,color="green",shape="box"];501[label="vz1400",fontsize=16,color="green",shape="box"];502[label="vz40000",fontsize=16,color="green",shape="box"];503[label="vz1600",fontsize=16,color="green",shape="box"];504[label="vz1000",fontsize=16,color="green",shape="box"];} 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (6) 10.13/4.20 Complex Obligation (AND) 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (7) 10.13/4.20 Obligation: 10.13/4.20 Q DP problem: 10.13/4.20 The TRS P consists of the following rules: 10.13/4.20 10.13/4.20 new_primEqNat(Main.Succ(vz1000), Main.Succ(vz1600)) -> new_primEqNat(vz1000, vz1600) 10.13/4.20 10.13/4.20 R is empty. 10.13/4.20 Q is empty. 10.13/4.20 We have to consider all minimal (P,Q,R)-chains. 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (8) QDPSizeChangeProof (EQUIVALENT) 10.13/4.20 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. 10.13/4.20 10.13/4.20 From the DPs we obtained the following set of size-change graphs: 10.13/4.20 *new_primEqNat(Main.Succ(vz1000), Main.Succ(vz1600)) -> new_primEqNat(vz1000, vz1600) 10.13/4.20 The graph contains the following edges 1 > 1, 2 > 2 10.13/4.20 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (9) 10.13/4.20 YES 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (10) 10.13/4.20 Obligation: 10.13/4.20 Q DP problem: 10.13/4.20 The TRS P consists of the following rules: 10.13/4.20 10.13/4.20 new_primMulNat(Main.Succ(vz3000), Main.Succ(vz4000)) -> new_primMulNat(vz3000, Main.Succ(vz4000)) 10.13/4.20 10.13/4.20 R is empty. 10.13/4.20 Q is empty. 10.13/4.20 We have to consider all minimal (P,Q,R)-chains. 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (11) QDPSizeChangeProof (EQUIVALENT) 10.13/4.20 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. 10.13/4.20 10.13/4.20 From the DPs we obtained the following set of size-change graphs: 10.13/4.20 *new_primMulNat(Main.Succ(vz3000), Main.Succ(vz4000)) -> new_primMulNat(vz3000, Main.Succ(vz4000)) 10.13/4.20 The graph contains the following edges 1 > 1, 2 >= 2 10.13/4.20 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (12) 10.13/4.20 YES 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (13) 10.13/4.20 Obligation: 10.13/4.20 Q DP problem: 10.13/4.20 The TRS P consists of the following rules: 10.13/4.20 10.13/4.20 new_primPlusNat(Main.Succ(vz1400), Main.Succ(vz40000)) -> new_primPlusNat(vz1400, vz40000) 10.13/4.20 10.13/4.20 R is empty. 10.13/4.20 Q is empty. 10.13/4.20 We have to consider all minimal (P,Q,R)-chains. 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (14) QDPSizeChangeProof (EQUIVALENT) 10.13/4.20 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. 10.13/4.20 10.13/4.20 From the DPs we obtained the following set of size-change graphs: 10.13/4.20 *new_primPlusNat(Main.Succ(vz1400), Main.Succ(vz40000)) -> new_primPlusNat(vz1400, vz40000) 10.13/4.20 The graph contains the following edges 1 > 1, 2 > 2 10.13/4.20 10.13/4.20 10.13/4.20 ---------------------------------------- 10.13/4.20 10.13/4.20 (15) 10.13/4.20 YES 10.13/4.24 EOF