29.71/16.78	MAYBE
31.54/17.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
31.54/17.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
31.54/17.35	
31.54/17.35	
31.54/17.35	H-Termination with start terms of the given HASKELL could not be shown:
31.54/17.35	
31.54/17.35	(0) HASKELL
31.54/17.35	(1) BR [EQUIVALENT, 0 ms]
31.54/17.35	(2) HASKELL
31.54/17.35	(3) COR [EQUIVALENT, 0 ms]
31.54/17.35	(4) HASKELL
31.54/17.35	(5) Narrow [SOUND, 0 ms]
31.54/17.35	(6) AND
31.54/17.35	    (7) QDP
31.54/17.35	        (8) QDPOrderProof [EQUIVALENT, 20 ms]
31.54/17.35	        (9) QDP
31.54/17.35	        (10) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.35	        (11) QDP
31.54/17.35	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
31.54/17.35	        (13) YES
31.54/17.35	    (14) QDP
31.54/17.35	        (15) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.35	        (16) QDP
31.54/17.35	        (17) QDPOrderProof [EQUIVALENT, 0 ms]
31.54/17.35	        (18) QDP
31.54/17.35	        (19) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.35	        (20) QDP
31.54/17.35	        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
31.54/17.35	        (22) YES
31.54/17.35	    (23) QDP
31.54/17.35	        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
31.54/17.35	        (25) YES
31.54/17.35	    (26) QDP
31.54/17.35	        (27) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.35	        (28) QDP
31.54/17.35	        (29) TransformationProof [EQUIVALENT, 0 ms]
31.54/17.36	        (30) QDP
31.54/17.36	        (31) UsableRulesProof [EQUIVALENT, 0 ms]
31.54/17.36	        (32) QDP
31.54/17.36	        (33) QReductionProof [EQUIVALENT, 0 ms]
31.54/17.36	        (34) QDP
31.54/17.36	        (35) MNOCProof [EQUIVALENT, 0 ms]
31.54/17.36	        (36) QDP
31.54/17.36	        (37) InductionCalculusProof [EQUIVALENT, 0 ms]
31.54/17.36	        (38) QDP
31.54/17.36	        (39) TransformationProof [EQUIVALENT, 0 ms]
31.54/17.36	        (40) QDP
31.54/17.36	            (41) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.36	            (42) QDP
31.54/17.36	            (43) TransformationProof [EQUIVALENT, 0 ms]
31.54/17.36	            (44) QDP
31.54/17.36	            (45) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.36	            (46) QDP
31.54/17.36	            (47) TransformationProof [EQUIVALENT, 0 ms]
31.54/17.36	            (48) QDP
31.54/17.36	            (49) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.36	            (50) QDP
31.54/17.36	            (51) TransformationProof [EQUIVALENT, 0 ms]
31.54/17.36	            (52) QDP
31.54/17.36	            (53) DependencyGraphProof [EQUIVALENT, 0 ms]
31.54/17.36	            (54) QDP
31.54/17.36	            (55) MNOCProof [EQUIVALENT, 0 ms]
31.54/17.36	            (56) QDP
31.54/17.36	            (57) InductionCalculusProof [EQUIVALENT, 0 ms]
31.54/17.36	            (58) QDP
31.54/17.36	(59) Narrow [COMPLETE, 0 ms]
31.54/17.36	(60) TRUE
31.54/17.36	
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(0)
31.54/17.36	Obligation:
31.54/17.36	mainModule Main 
31.54/17.36	module Main where {
31.54/17.36	import qualified Prelude;
31.54/17.36	data Main.Char = Char MyInt ;
31.54/17.36	
31.54/17.36	data List a = Cons a (List a)  | Nil ;
31.54/17.36	
31.54/17.36	data MyBool = MyTrue  | MyFalse ;
31.54/17.36	
31.54/17.36	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
31.54/17.36	
31.54/17.36	data Main.Nat = Succ Main.Nat  | Zero ;
31.54/17.36	
31.54/17.36	divMyInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	divMyInt = primDivInt;
31.54/17.36	
31.54/17.36	error :: a;
31.54/17.36	error = stop MyTrue;
31.54/17.36	
31.54/17.36	modMyInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	modMyInt = primModInt;
31.54/17.36	
31.54/17.36	primDivInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	primDivInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
31.54/17.36	primDivInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
31.54/17.36	primDivInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
31.54/17.36	primDivInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
31.54/17.36	primDivInt vw vx = Main.error;
31.54/17.36	
31.54/17.36	primDivNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primDivNatP Main.Zero Main.Zero = Main.error;
31.54/17.36	primDivNatP (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primDivNatP (Main.Succ x) (Main.Succ y) = Main.Succ (primDivNatP (primMinusNatS x y) (Main.Succ y));
31.54/17.36	primDivNatP Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	
31.54/17.36	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primDivNatS Main.Zero Main.Zero = Main.error;
31.54/17.36	primDivNatS (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
31.54/17.36	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	
31.54/17.36	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
31.54/17.36	primDivNatS0 x y MyFalse = Main.Zero;
31.54/17.36	
31.54/17.36	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
31.54/17.36	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
31.54/17.36	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
31.54/17.36	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
31.54/17.36	primGEqNatS Main.Zero Main.Zero = MyTrue;
31.54/17.36	
31.54/17.36	primIntToChar :: MyInt  ->  Main.Char;
31.54/17.36	primIntToChar x = Main.Char x;
31.54/17.36	
31.54/17.36	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
31.54/17.36	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
31.54/17.36	primMinusNatS x Main.Zero = x;
31.54/17.36	
31.54/17.36	primModInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	primModInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
31.54/17.36	primModInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatP x (Main.Succ y));
31.54/17.36	primModInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatP x (Main.Succ y));
31.54/17.36	primModInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
31.54/17.36	primModInt vy vz = Main.error;
31.54/17.36	
31.54/17.36	primModNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primModNatP Main.Zero Main.Zero = Main.error;
31.54/17.36	primModNatP Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	primModNatP (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primModNatP (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
31.54/17.36	primModNatP (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatP0 x y (primGEqNatS x y);
31.54/17.36	
31.54/17.36	primModNatP0 x y MyTrue = primModNatP (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
31.54/17.36	primModNatP0 x y MyFalse = primMinusNatS (Main.Succ y) x;
31.54/17.36	
31.54/17.36	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primModNatS Main.Zero Main.Zero = Main.error;
31.54/17.36	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	primModNatS (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
31.54/17.36	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
31.54/17.36	
31.54/17.36	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
31.54/17.36	primModNatS0 x y MyFalse = Main.Succ x;
31.54/17.36	
31.54/17.36	primShowInt :: MyInt  ->  List Main.Char;
31.54/17.36	primShowInt (Main.Pos Main.Zero) = Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))) Nil;
31.54/17.36	primShowInt (Main.Pos (Main.Succ x)) = psPs (primShowInt (divMyInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))) (Cons (toEnumChar (modMyInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))) Nil);
31.54/17.36	primShowInt (Main.Neg x) = Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))) (primShowInt (Main.Pos x));
31.54/17.36	
31.54/17.36	psPs :: List a  ->  List a  ->  List a;
31.54/17.36	psPs Nil ys = ys;
31.54/17.36	psPs (Cons x xs) ys = Cons x (psPs xs ys);
31.54/17.36	
31.54/17.36	showMyInt :: MyInt  ->  List Main.Char;
31.54/17.36	showMyInt = primShowInt;
31.54/17.36	
31.54/17.36	showsMyInt :: MyInt  ->  List Main.Char  ->  List Main.Char;
31.54/17.36	showsMyInt = showsPrecMyInt (Main.Pos Main.Zero);
31.54/17.36	
31.54/17.36	showsPrecMyInt :: MyInt  ->  MyInt  ->  List Main.Char  ->  List Main.Char;
31.54/17.36	showsPrecMyInt vv x s = psPs (showMyInt x) s;
31.54/17.36	
31.54/17.36	stop :: MyBool  ->  a;
31.54/17.36	stop MyFalse = stop MyFalse;
31.54/17.36	
31.54/17.36	toEnumChar :: MyInt  ->  Main.Char;
31.54/17.36	toEnumChar = primIntToChar;
31.54/17.36	
31.54/17.36	}
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(1) BR (EQUIVALENT)
31.54/17.36	Replaced joker patterns by fresh variables and removed binding patterns.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(2)
31.54/17.36	Obligation:
31.54/17.36	mainModule Main 
31.54/17.36	module Main where {
31.54/17.36	import qualified Prelude;
31.54/17.36	data Main.Char = Char MyInt ;
31.54/17.36	
31.54/17.36	data List a = Cons a (List a)  | Nil ;
31.54/17.36	
31.54/17.36	data MyBool = MyTrue  | MyFalse ;
31.54/17.36	
31.54/17.36	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
31.54/17.36	
31.54/17.36	data Main.Nat = Succ Main.Nat  | Zero ;
31.54/17.36	
31.54/17.36	divMyInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	divMyInt = primDivInt;
31.54/17.36	
31.54/17.36	error :: a;
31.54/17.36	error = stop MyTrue;
31.54/17.36	
31.54/17.36	modMyInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	modMyInt = primModInt;
31.54/17.36	
31.54/17.36	primDivInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	primDivInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
31.54/17.36	primDivInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
31.54/17.36	primDivInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
31.54/17.36	primDivInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
31.54/17.36	primDivInt vw vx = Main.error;
31.54/17.36	
31.54/17.36	primDivNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primDivNatP Main.Zero Main.Zero = Main.error;
31.54/17.36	primDivNatP (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primDivNatP (Main.Succ x) (Main.Succ y) = Main.Succ (primDivNatP (primMinusNatS x y) (Main.Succ y));
31.54/17.36	primDivNatP Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	
31.54/17.36	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primDivNatS Main.Zero Main.Zero = Main.error;
31.54/17.36	primDivNatS (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
31.54/17.36	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	
31.54/17.36	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
31.54/17.36	primDivNatS0 x y MyFalse = Main.Zero;
31.54/17.36	
31.54/17.36	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
31.54/17.36	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
31.54/17.36	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
31.54/17.36	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
31.54/17.36	primGEqNatS Main.Zero Main.Zero = MyTrue;
31.54/17.36	
31.54/17.36	primIntToChar :: MyInt  ->  Main.Char;
31.54/17.36	primIntToChar x = Main.Char x;
31.54/17.36	
31.54/17.36	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
31.54/17.36	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
31.54/17.36	primMinusNatS x Main.Zero = x;
31.54/17.36	
31.54/17.36	primModInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	primModInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
31.54/17.36	primModInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatP x (Main.Succ y));
31.54/17.36	primModInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatP x (Main.Succ y));
31.54/17.36	primModInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
31.54/17.36	primModInt vy vz = Main.error;
31.54/17.36	
31.54/17.36	primModNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primModNatP Main.Zero Main.Zero = Main.error;
31.54/17.36	primModNatP Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	primModNatP (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primModNatP (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
31.54/17.36	primModNatP (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatP0 x y (primGEqNatS x y);
31.54/17.36	
31.54/17.36	primModNatP0 x y MyTrue = primModNatP (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
31.54/17.36	primModNatP0 x y MyFalse = primMinusNatS (Main.Succ y) x;
31.54/17.36	
31.54/17.36	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primModNatS Main.Zero Main.Zero = Main.error;
31.54/17.36	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	primModNatS (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
31.54/17.36	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
31.54/17.36	
31.54/17.36	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
31.54/17.36	primModNatS0 x y MyFalse = Main.Succ x;
31.54/17.36	
31.54/17.36	primShowInt :: MyInt  ->  List Main.Char;
31.54/17.36	primShowInt (Main.Pos Main.Zero) = Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))) Nil;
31.54/17.36	primShowInt (Main.Pos (Main.Succ x)) = psPs (primShowInt (divMyInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))) (Cons (toEnumChar (modMyInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))) Nil);
31.54/17.36	primShowInt (Main.Neg x) = Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))) (primShowInt (Main.Pos x));
31.54/17.36	
31.54/17.36	psPs :: List a  ->  List a  ->  List a;
31.54/17.36	psPs Nil ys = ys;
31.54/17.36	psPs (Cons x xs) ys = Cons x (psPs xs ys);
31.54/17.36	
31.54/17.36	showMyInt :: MyInt  ->  List Main.Char;
31.54/17.36	showMyInt = primShowInt;
31.54/17.36	
31.54/17.36	showsMyInt :: MyInt  ->  List Main.Char  ->  List Main.Char;
31.54/17.36	showsMyInt = showsPrecMyInt (Main.Pos Main.Zero);
31.54/17.36	
31.54/17.36	showsPrecMyInt :: MyInt  ->  MyInt  ->  List Main.Char  ->  List Main.Char;
31.54/17.36	showsPrecMyInt vv x s = psPs (showMyInt x) s;
31.54/17.36	
31.54/17.36	stop :: MyBool  ->  a;
31.54/17.36	stop MyFalse = stop MyFalse;
31.54/17.36	
31.54/17.36	toEnumChar :: MyInt  ->  Main.Char;
31.54/17.36	toEnumChar = primIntToChar;
31.54/17.36	
31.54/17.36	}
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(3) COR (EQUIVALENT)
31.54/17.36	Cond Reductions:
31.54/17.36	The following Function with conditions
31.54/17.36	"undefined |Falseundefined;
31.54/17.36	"
31.54/17.36	is transformed to
31.54/17.36	"undefined  = undefined1;
31.54/17.36	"
31.54/17.36	"undefined0 True = undefined;
31.54/17.36	"
31.54/17.36	"undefined1  = undefined0 False;
31.54/17.36	"
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(4)
31.54/17.36	Obligation:
31.54/17.36	mainModule Main 
31.54/17.36	module Main where {
31.54/17.36	import qualified Prelude;
31.54/17.36	data Main.Char = Char MyInt ;
31.54/17.36	
31.54/17.36	data List a = Cons a (List a)  | Nil ;
31.54/17.36	
31.54/17.36	data MyBool = MyTrue  | MyFalse ;
31.54/17.36	
31.54/17.36	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
31.54/17.36	
31.54/17.36	data Main.Nat = Succ Main.Nat  | Zero ;
31.54/17.36	
31.54/17.36	divMyInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	divMyInt = primDivInt;
31.54/17.36	
31.54/17.36	error :: a;
31.54/17.36	error = stop MyTrue;
31.54/17.36	
31.54/17.36	modMyInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	modMyInt = primModInt;
31.54/17.36	
31.54/17.36	primDivInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	primDivInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
31.54/17.36	primDivInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
31.54/17.36	primDivInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
31.54/17.36	primDivInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
31.54/17.36	primDivInt vw vx = Main.error;
31.54/17.36	
31.54/17.36	primDivNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primDivNatP Main.Zero Main.Zero = Main.error;
31.54/17.36	primDivNatP (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primDivNatP (Main.Succ x) (Main.Succ y) = Main.Succ (primDivNatP (primMinusNatS x y) (Main.Succ y));
31.54/17.36	primDivNatP Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	
31.54/17.36	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primDivNatS Main.Zero Main.Zero = Main.error;
31.54/17.36	primDivNatS (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
31.54/17.36	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	
31.54/17.36	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
31.54/17.36	primDivNatS0 x y MyFalse = Main.Zero;
31.54/17.36	
31.54/17.36	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
31.54/17.36	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
31.54/17.36	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
31.54/17.36	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
31.54/17.36	primGEqNatS Main.Zero Main.Zero = MyTrue;
31.54/17.36	
31.54/17.36	primIntToChar :: MyInt  ->  Main.Char;
31.54/17.36	primIntToChar x = Main.Char x;
31.54/17.36	
31.54/17.36	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
31.54/17.36	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
31.54/17.36	primMinusNatS x Main.Zero = x;
31.54/17.36	
31.54/17.36	primModInt :: MyInt  ->  MyInt  ->  MyInt;
31.54/17.36	primModInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
31.54/17.36	primModInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatP x (Main.Succ y));
31.54/17.36	primModInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatP x (Main.Succ y));
31.54/17.36	primModInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
31.54/17.36	primModInt vy vz = Main.error;
31.54/17.36	
31.54/17.36	primModNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primModNatP Main.Zero Main.Zero = Main.error;
31.54/17.36	primModNatP Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	primModNatP (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primModNatP (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
31.54/17.36	primModNatP (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatP0 x y (primGEqNatS x y);
31.54/17.36	
31.54/17.36	primModNatP0 x y MyTrue = primModNatP (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
31.54/17.36	primModNatP0 x y MyFalse = primMinusNatS (Main.Succ y) x;
31.54/17.36	
31.54/17.36	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
31.54/17.36	primModNatS Main.Zero Main.Zero = Main.error;
31.54/17.36	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
31.54/17.36	primModNatS (Main.Succ x) Main.Zero = Main.error;
31.54/17.36	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
31.54/17.36	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
31.54/17.36	
31.54/17.36	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
31.54/17.36	primModNatS0 x y MyFalse = Main.Succ x;
31.54/17.36	
31.54/17.36	primShowInt :: MyInt  ->  List Main.Char;
31.54/17.36	primShowInt (Main.Pos Main.Zero) = Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))) Nil;
31.54/17.36	primShowInt (Main.Pos (Main.Succ x)) = psPs (primShowInt (divMyInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))) (Cons (toEnumChar (modMyInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))) Nil);
31.54/17.36	primShowInt (Main.Neg x) = Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))) (primShowInt (Main.Pos x));
31.54/17.36	
31.54/17.36	psPs :: List a  ->  List a  ->  List a;
31.54/17.36	psPs Nil ys = ys;
31.54/17.36	psPs (Cons x xs) ys = Cons x (psPs xs ys);
31.54/17.36	
31.54/17.36	showMyInt :: MyInt  ->  List Main.Char;
31.54/17.36	showMyInt = primShowInt;
31.54/17.36	
31.54/17.36	showsMyInt :: MyInt  ->  List Main.Char  ->  List Main.Char;
31.54/17.36	showsMyInt = showsPrecMyInt (Main.Pos Main.Zero);
31.54/17.36	
31.54/17.36	showsPrecMyInt :: MyInt  ->  MyInt  ->  List Main.Char  ->  List Main.Char;
31.54/17.36	showsPrecMyInt vv x s = psPs (showMyInt x) s;
31.54/17.36	
31.54/17.36	stop :: MyBool  ->  a;
31.54/17.36	stop MyFalse = stop MyFalse;
31.54/17.36	
31.54/17.36	toEnumChar :: MyInt  ->  Main.Char;
31.54/17.36	toEnumChar = primIntToChar;
31.54/17.36	
31.54/17.36	}
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(5) Narrow (SOUND)
31.54/17.36	Haskell To QDPs
31.54/17.36	
31.54/17.36	digraph dp_graph {
31.54/17.36	node [outthreshold=100, inthreshold=100];1[label="showsMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
31.54/17.36	3[label="showsMyInt ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
31.54/17.36	4[label="showsMyInt ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
31.54/17.36	5[label="showsPrecMyInt (Pos Zero) ww3 ww4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
31.54/17.36	6 -> 36[label="",style="dashed", color="red", weight=0];
31.54/17.36	6[label="psPs (showMyInt ww3) ww4",fontsize=16,color="magenta"];6 -> 37[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	6 -> 38[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	37[label="ww4",fontsize=16,color="green",shape="box"];38[label="showMyInt ww3",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
31.54/17.36	36[label="psPs ww21 ww20",fontsize=16,color="burlywood",shape="triangle"];880[label="ww21/Cons ww210 ww211",fontsize=10,color="white",style="solid",shape="box"];36 -> 880[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	880 -> 53[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	881[label="ww21/Nil",fontsize=10,color="white",style="solid",shape="box"];36 -> 881[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	881 -> 54[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	52[label="primShowInt ww3",fontsize=16,color="burlywood",shape="triangle"];882[label="ww3/Pos ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 882[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	882 -> 55[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	883[label="ww3/Neg ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 883[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	883 -> 56[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	53[label="psPs (Cons ww210 ww211) ww20",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
31.54/17.36	54[label="psPs Nil ww20",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
31.54/17.36	55[label="primShowInt (Pos ww30)",fontsize=16,color="burlywood",shape="box"];884[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];55 -> 884[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	884 -> 59[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	885[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 885[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	885 -> 60[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	56[label="primShowInt (Neg ww30)",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3];
31.54/17.36	57[label="Cons ww210 (psPs ww211 ww20)",fontsize=16,color="green",shape="box"];57 -> 62[label="",style="dashed", color="green", weight=3];
31.54/17.36	58[label="ww20",fontsize=16,color="green",shape="box"];59[label="primShowInt (Pos (Succ ww300))",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
31.54/17.36	60[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
31.54/17.36	61[label="Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))) (primShowInt (Pos ww30))",fontsize=16,color="green",shape="box"];61 -> 65[label="",style="dashed", color="green", weight=3];
31.54/17.36	62 -> 36[label="",style="dashed", color="red", weight=0];
31.54/17.36	62[label="psPs ww211 ww20",fontsize=16,color="magenta"];62 -> 66[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	63 -> 36[label="",style="dashed", color="red", weight=0];
31.54/17.36	63[label="psPs (primShowInt (divMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) (Cons (toEnumChar (modMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) Nil)",fontsize=16,color="magenta"];63 -> 67[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	63 -> 68[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	64[label="Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))) Nil",fontsize=16,color="green",shape="box"];65 -> 52[label="",style="dashed", color="red", weight=0];
31.54/17.36	65[label="primShowInt (Pos ww30)",fontsize=16,color="magenta"];65 -> 69[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	66[label="ww211",fontsize=16,color="green",shape="box"];67[label="Cons (toEnumChar (modMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) Nil",fontsize=16,color="green",shape="box"];67 -> 70[label="",style="dashed", color="green", weight=3];
31.54/17.36	68 -> 52[label="",style="dashed", color="red", weight=0];
31.54/17.36	68[label="primShowInt (divMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))",fontsize=16,color="magenta"];68 -> 71[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	69[label="Pos ww30",fontsize=16,color="green",shape="box"];70 -> 72[label="",style="dashed", color="red", weight=0];
31.54/17.36	70[label="toEnumChar (modMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))",fontsize=16,color="magenta"];70 -> 73[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	70 -> 74[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	71 -> 75[label="",style="dashed", color="red", weight=0];
31.54/17.36	71[label="divMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];71 -> 76[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	71 -> 77[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	73[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];74[label="ww300",fontsize=16,color="green",shape="box"];72[label="toEnumChar (modMyInt (Pos (Succ ww23)) (Pos (Succ ww24)))",fontsize=16,color="black",shape="triangle"];72 -> 78[label="",style="solid", color="black", weight=3];
31.54/17.36	76[label="ww300",fontsize=16,color="green",shape="box"];77[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];75[label="divMyInt (Pos (Succ ww26)) (Pos (Succ ww27))",fontsize=16,color="black",shape="triangle"];75 -> 79[label="",style="solid", color="black", weight=3];
31.54/17.36	78[label="primIntToChar (modMyInt (Pos (Succ ww23)) (Pos (Succ ww24)))",fontsize=16,color="black",shape="box"];78 -> 80[label="",style="solid", color="black", weight=3];
31.54/17.36	79[label="primDivInt (Pos (Succ ww26)) (Pos (Succ ww27))",fontsize=16,color="black",shape="box"];79 -> 81[label="",style="solid", color="black", weight=3];
31.54/17.36	80[label="Char (modMyInt (Pos (Succ ww23)) (Pos (Succ ww24)))",fontsize=16,color="green",shape="box"];80 -> 82[label="",style="dashed", color="green", weight=3];
31.54/17.36	81[label="Pos (primDivNatS (Succ ww26) (Succ ww27))",fontsize=16,color="green",shape="box"];81 -> 83[label="",style="dashed", color="green", weight=3];
31.54/17.36	82[label="modMyInt (Pos (Succ ww23)) (Pos (Succ ww24))",fontsize=16,color="black",shape="box"];82 -> 84[label="",style="solid", color="black", weight=3];
31.54/17.36	83[label="primDivNatS (Succ ww26) (Succ ww27)",fontsize=16,color="black",shape="triangle"];83 -> 85[label="",style="solid", color="black", weight=3];
31.54/17.36	84[label="primModInt (Pos (Succ ww23)) (Pos (Succ ww24))",fontsize=16,color="black",shape="box"];84 -> 86[label="",style="solid", color="black", weight=3];
31.54/17.36	85[label="primDivNatS0 ww26 ww27 (primGEqNatS ww26 ww27)",fontsize=16,color="burlywood",shape="box"];886[label="ww26/Succ ww260",fontsize=10,color="white",style="solid",shape="box"];85 -> 886[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	886 -> 87[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	887[label="ww26/Zero",fontsize=10,color="white",style="solid",shape="box"];85 -> 887[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	887 -> 88[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	86[label="Pos (primModNatS (Succ ww23) (Succ ww24))",fontsize=16,color="green",shape="box"];86 -> 89[label="",style="dashed", color="green", weight=3];
31.54/17.36	87[label="primDivNatS0 (Succ ww260) ww27 (primGEqNatS (Succ ww260) ww27)",fontsize=16,color="burlywood",shape="box"];888[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];87 -> 888[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	888 -> 90[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	889[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 889[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	889 -> 91[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	88[label="primDivNatS0 Zero ww27 (primGEqNatS Zero ww27)",fontsize=16,color="burlywood",shape="box"];890[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];88 -> 890[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	890 -> 92[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	891[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];88 -> 891[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	891 -> 93[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	89[label="primModNatS (Succ ww23) (Succ ww24)",fontsize=16,color="burlywood",shape="triangle"];892[label="ww24/Succ ww240",fontsize=10,color="white",style="solid",shape="box"];89 -> 892[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	892 -> 94[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	893[label="ww24/Zero",fontsize=10,color="white",style="solid",shape="box"];89 -> 893[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	893 -> 95[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	90[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS (Succ ww260) (Succ ww270))",fontsize=16,color="black",shape="box"];90 -> 96[label="",style="solid", color="black", weight=3];
31.54/17.36	91[label="primDivNatS0 (Succ ww260) Zero (primGEqNatS (Succ ww260) Zero)",fontsize=16,color="black",shape="box"];91 -> 97[label="",style="solid", color="black", weight=3];
31.54/17.36	92[label="primDivNatS0 Zero (Succ ww270) (primGEqNatS Zero (Succ ww270))",fontsize=16,color="black",shape="box"];92 -> 98[label="",style="solid", color="black", weight=3];
31.54/17.36	93[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
31.54/17.36	94[label="primModNatS (Succ ww23) (Succ (Succ ww240))",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
31.54/17.36	95[label="primModNatS (Succ ww23) (Succ Zero)",fontsize=16,color="black",shape="box"];95 -> 101[label="",style="solid", color="black", weight=3];
31.54/17.36	96 -> 546[label="",style="dashed", color="red", weight=0];
31.54/17.36	96[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS ww260 ww270)",fontsize=16,color="magenta"];96 -> 547[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	96 -> 548[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	96 -> 549[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	96 -> 550[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	97[label="primDivNatS0 (Succ ww260) Zero MyTrue",fontsize=16,color="black",shape="box"];97 -> 104[label="",style="solid", color="black", weight=3];
31.54/17.36	98[label="primDivNatS0 Zero (Succ ww270) MyFalse",fontsize=16,color="black",shape="box"];98 -> 105[label="",style="solid", color="black", weight=3];
31.54/17.36	99[label="primDivNatS0 Zero Zero MyTrue",fontsize=16,color="black",shape="box"];99 -> 106[label="",style="solid", color="black", weight=3];
31.54/17.36	100[label="primModNatS0 ww23 ww240 (primGEqNatS ww23 (Succ ww240))",fontsize=16,color="burlywood",shape="box"];894[label="ww23/Succ ww230",fontsize=10,color="white",style="solid",shape="box"];100 -> 894[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	894 -> 107[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	895[label="ww23/Zero",fontsize=10,color="white",style="solid",shape="box"];100 -> 895[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	895 -> 108[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	101[label="Zero",fontsize=16,color="green",shape="box"];547[label="ww270",fontsize=16,color="green",shape="box"];548[label="ww260",fontsize=16,color="green",shape="box"];549[label="ww260",fontsize=16,color="green",shape="box"];550[label="ww270",fontsize=16,color="green",shape="box"];546[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS ww70 ww71)",fontsize=16,color="burlywood",shape="triangle"];896[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];546 -> 896[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	896 -> 587[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	897[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];546 -> 897[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	897 -> 588[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	104[label="Succ (primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];104 -> 113[label="",style="dashed", color="green", weight=3];
31.54/17.36	105[label="Zero",fontsize=16,color="green",shape="box"];106[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];106 -> 114[label="",style="dashed", color="green", weight=3];
31.54/17.36	107[label="primModNatS0 (Succ ww230) ww240 (primGEqNatS (Succ ww230) (Succ ww240))",fontsize=16,color="black",shape="box"];107 -> 115[label="",style="solid", color="black", weight=3];
31.54/17.36	108[label="primModNatS0 Zero ww240 (primGEqNatS Zero (Succ ww240))",fontsize=16,color="black",shape="box"];108 -> 116[label="",style="solid", color="black", weight=3];
31.54/17.36	587[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS (Succ ww700) ww71)",fontsize=16,color="burlywood",shape="box"];898[label="ww71/Succ ww710",fontsize=10,color="white",style="solid",shape="box"];587 -> 898[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	898 -> 594[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	899[label="ww71/Zero",fontsize=10,color="white",style="solid",shape="box"];587 -> 899[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	899 -> 595[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	588[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS Zero ww71)",fontsize=16,color="burlywood",shape="box"];900[label="ww71/Succ ww710",fontsize=10,color="white",style="solid",shape="box"];588 -> 900[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	900 -> 596[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	901[label="ww71/Zero",fontsize=10,color="white",style="solid",shape="box"];588 -> 901[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	901 -> 597[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	113 -> 780[label="",style="dashed", color="red", weight=0];
31.54/17.36	113[label="primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero)",fontsize=16,color="magenta"];113 -> 781[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	113 -> 782[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	113 -> 783[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	114 -> 780[label="",style="dashed", color="red", weight=0];
31.54/17.36	114[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];114 -> 784[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	114 -> 785[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	114 -> 786[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	115[label="primModNatS0 (Succ ww230) ww240 (primGEqNatS ww230 ww240)",fontsize=16,color="burlywood",shape="box"];902[label="ww230/Succ ww2300",fontsize=10,color="white",style="solid",shape="box"];115 -> 902[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	902 -> 123[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	903[label="ww230/Zero",fontsize=10,color="white",style="solid",shape="box"];115 -> 903[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	903 -> 124[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	116[label="primModNatS0 Zero ww240 MyFalse",fontsize=16,color="black",shape="box"];116 -> 125[label="",style="solid", color="black", weight=3];
31.54/17.36	594[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS (Succ ww700) (Succ ww710))",fontsize=16,color="black",shape="box"];594 -> 604[label="",style="solid", color="black", weight=3];
31.54/17.36	595[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS (Succ ww700) Zero)",fontsize=16,color="black",shape="box"];595 -> 605[label="",style="solid", color="black", weight=3];
31.54/17.36	596[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS Zero (Succ ww710))",fontsize=16,color="black",shape="box"];596 -> 606[label="",style="solid", color="black", weight=3];
31.54/17.36	597[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];597 -> 607[label="",style="solid", color="black", weight=3];
31.54/17.36	781[label="Succ ww260",fontsize=16,color="green",shape="box"];782[label="Zero",fontsize=16,color="green",shape="box"];783[label="Zero",fontsize=16,color="green",shape="box"];780[label="primDivNatS (primMinusNatS ww78 ww79) (Succ ww80)",fontsize=16,color="burlywood",shape="triangle"];904[label="ww78/Succ ww780",fontsize=10,color="white",style="solid",shape="box"];780 -> 904[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	904 -> 805[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	905[label="ww78/Zero",fontsize=10,color="white",style="solid",shape="box"];780 -> 905[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	905 -> 806[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	784[label="Zero",fontsize=16,color="green",shape="box"];785[label="Zero",fontsize=16,color="green",shape="box"];786[label="Zero",fontsize=16,color="green",shape="box"];123[label="primModNatS0 (Succ (Succ ww2300)) ww240 (primGEqNatS (Succ ww2300) ww240)",fontsize=16,color="burlywood",shape="box"];906[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];123 -> 906[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	906 -> 134[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	907[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];123 -> 907[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	907 -> 135[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	124[label="primModNatS0 (Succ Zero) ww240 (primGEqNatS Zero ww240)",fontsize=16,color="burlywood",shape="box"];908[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];124 -> 908[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	908 -> 136[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	909[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];124 -> 909[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	909 -> 137[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	125[label="Succ Zero",fontsize=16,color="green",shape="box"];604 -> 546[label="",style="dashed", color="red", weight=0];
31.54/17.36	604[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS ww700 ww710)",fontsize=16,color="magenta"];604 -> 618[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	604 -> 619[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	605[label="primDivNatS0 (Succ ww68) (Succ ww69) MyTrue",fontsize=16,color="black",shape="triangle"];605 -> 620[label="",style="solid", color="black", weight=3];
31.54/17.36	606[label="primDivNatS0 (Succ ww68) (Succ ww69) MyFalse",fontsize=16,color="black",shape="box"];606 -> 621[label="",style="solid", color="black", weight=3];
31.54/17.36	607 -> 605[label="",style="dashed", color="red", weight=0];
31.54/17.36	607[label="primDivNatS0 (Succ ww68) (Succ ww69) MyTrue",fontsize=16,color="magenta"];805[label="primDivNatS (primMinusNatS (Succ ww780) ww79) (Succ ww80)",fontsize=16,color="burlywood",shape="box"];910[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];805 -> 910[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	910 -> 813[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	911[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];805 -> 911[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	911 -> 814[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	806[label="primDivNatS (primMinusNatS Zero ww79) (Succ ww80)",fontsize=16,color="burlywood",shape="box"];912[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];806 -> 912[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	912 -> 815[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	913[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];806 -> 913[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	913 -> 816[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	134[label="primModNatS0 (Succ (Succ ww2300)) (Succ ww2400) (primGEqNatS (Succ ww2300) (Succ ww2400))",fontsize=16,color="black",shape="box"];134 -> 144[label="",style="solid", color="black", weight=3];
31.54/17.36	135[label="primModNatS0 (Succ (Succ ww2300)) Zero (primGEqNatS (Succ ww2300) Zero)",fontsize=16,color="black",shape="box"];135 -> 145[label="",style="solid", color="black", weight=3];
31.54/17.36	136[label="primModNatS0 (Succ Zero) (Succ ww2400) (primGEqNatS Zero (Succ ww2400))",fontsize=16,color="black",shape="box"];136 -> 146[label="",style="solid", color="black", weight=3];
31.54/17.36	137[label="primModNatS0 (Succ Zero) Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];137 -> 147[label="",style="solid", color="black", weight=3];
31.54/17.36	618[label="ww710",fontsize=16,color="green",shape="box"];619[label="ww700",fontsize=16,color="green",shape="box"];620[label="Succ (primDivNatS (primMinusNatS (Succ ww68) (Succ ww69)) (Succ (Succ ww69)))",fontsize=16,color="green",shape="box"];620 -> 629[label="",style="dashed", color="green", weight=3];
31.54/17.36	621[label="Zero",fontsize=16,color="green",shape="box"];813[label="primDivNatS (primMinusNatS (Succ ww780) (Succ ww790)) (Succ ww80)",fontsize=16,color="black",shape="box"];813 -> 821[label="",style="solid", color="black", weight=3];
31.54/17.36	814[label="primDivNatS (primMinusNatS (Succ ww780) Zero) (Succ ww80)",fontsize=16,color="black",shape="box"];814 -> 822[label="",style="solid", color="black", weight=3];
31.54/17.36	815[label="primDivNatS (primMinusNatS Zero (Succ ww790)) (Succ ww80)",fontsize=16,color="black",shape="box"];815 -> 823[label="",style="solid", color="black", weight=3];
31.54/17.36	816[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww80)",fontsize=16,color="black",shape="box"];816 -> 824[label="",style="solid", color="black", weight=3];
31.54/17.36	144 -> 643[label="",style="dashed", color="red", weight=0];
31.54/17.36	144[label="primModNatS0 (Succ (Succ ww2300)) (Succ ww2400) (primGEqNatS ww2300 ww2400)",fontsize=16,color="magenta"];144 -> 644[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	144 -> 645[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	144 -> 646[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	144 -> 647[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	145[label="primModNatS0 (Succ (Succ ww2300)) Zero MyTrue",fontsize=16,color="black",shape="box"];145 -> 156[label="",style="solid", color="black", weight=3];
31.54/17.36	146[label="primModNatS0 (Succ Zero) (Succ ww2400) MyFalse",fontsize=16,color="black",shape="box"];146 -> 157[label="",style="solid", color="black", weight=3];
31.54/17.36	147[label="primModNatS0 (Succ Zero) Zero MyTrue",fontsize=16,color="black",shape="box"];147 -> 158[label="",style="solid", color="black", weight=3];
31.54/17.36	629 -> 780[label="",style="dashed", color="red", weight=0];
31.54/17.36	629[label="primDivNatS (primMinusNatS (Succ ww68) (Succ ww69)) (Succ (Succ ww69))",fontsize=16,color="magenta"];629 -> 787[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	629 -> 788[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	629 -> 789[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	821 -> 780[label="",style="dashed", color="red", weight=0];
31.54/17.36	821[label="primDivNatS (primMinusNatS ww780 ww790) (Succ ww80)",fontsize=16,color="magenta"];821 -> 829[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	821 -> 830[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	822 -> 83[label="",style="dashed", color="red", weight=0];
31.54/17.36	822[label="primDivNatS (Succ ww780) (Succ ww80)",fontsize=16,color="magenta"];822 -> 831[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	822 -> 832[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	823[label="primDivNatS Zero (Succ ww80)",fontsize=16,color="black",shape="triangle"];823 -> 833[label="",style="solid", color="black", weight=3];
31.54/17.36	824 -> 823[label="",style="dashed", color="red", weight=0];
31.54/17.36	824[label="primDivNatS Zero (Succ ww80)",fontsize=16,color="magenta"];644[label="ww2400",fontsize=16,color="green",shape="box"];645[label="ww2300",fontsize=16,color="green",shape="box"];646[label="ww2400",fontsize=16,color="green",shape="box"];647[label="Succ ww2300",fontsize=16,color="green",shape="box"];643[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww75 ww76)",fontsize=16,color="burlywood",shape="triangle"];914[label="ww75/Succ ww750",fontsize=10,color="white",style="solid",shape="box"];643 -> 914[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	914 -> 684[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	915[label="ww75/Zero",fontsize=10,color="white",style="solid",shape="box"];643 -> 915[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	915 -> 685[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	156 -> 834[label="",style="dashed", color="red", weight=0];
31.54/17.36	156[label="primModNatS (primMinusNatS (Succ (Succ ww2300)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];156 -> 835[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	156 -> 836[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	156 -> 837[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	157[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];158 -> 834[label="",style="dashed", color="red", weight=0];
31.54/17.36	158[label="primModNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];158 -> 838[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	158 -> 839[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	158 -> 840[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	787[label="Succ ww68",fontsize=16,color="green",shape="box"];788[label="Succ ww69",fontsize=16,color="green",shape="box"];789[label="Succ ww69",fontsize=16,color="green",shape="box"];829[label="ww780",fontsize=16,color="green",shape="box"];830[label="ww790",fontsize=16,color="green",shape="box"];831[label="ww780",fontsize=16,color="green",shape="box"];832[label="ww80",fontsize=16,color="green",shape="box"];833[label="Zero",fontsize=16,color="green",shape="box"];684[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) ww76)",fontsize=16,color="burlywood",shape="box"];916[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];684 -> 916[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	916 -> 688[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	917[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];684 -> 917[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	917 -> 689[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	685[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero ww76)",fontsize=16,color="burlywood",shape="box"];918[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];685 -> 918[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	918 -> 690[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	919[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];685 -> 919[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	919 -> 691[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	835[label="Succ Zero",fontsize=16,color="green",shape="box"];836[label="Succ Zero",fontsize=16,color="green",shape="box"];837[label="Succ (Succ ww2300)",fontsize=16,color="green",shape="box"];834[label="primModNatS (primMinusNatS ww82 ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="triangle"];920[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];834 -> 920[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	920 -> 865[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	921[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];834 -> 921[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	921 -> 866[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	838[label="Succ Zero",fontsize=16,color="green",shape="box"];839[label="Succ Zero",fontsize=16,color="green",shape="box"];840[label="Succ Zero",fontsize=16,color="green",shape="box"];688[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) (Succ ww760))",fontsize=16,color="black",shape="box"];688 -> 696[label="",style="solid", color="black", weight=3];
31.54/17.36	689[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) Zero)",fontsize=16,color="black",shape="box"];689 -> 697[label="",style="solid", color="black", weight=3];
31.54/17.36	690[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero (Succ ww760))",fontsize=16,color="black",shape="box"];690 -> 698[label="",style="solid", color="black", weight=3];
31.54/17.36	691[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];691 -> 699[label="",style="solid", color="black", weight=3];
31.54/17.36	865[label="primModNatS (primMinusNatS (Succ ww820) ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];922[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];865 -> 922[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	922 -> 867[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	923[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];865 -> 923[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	923 -> 868[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	866[label="primModNatS (primMinusNatS Zero ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];924[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];866 -> 924[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	924 -> 869[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	925[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];866 -> 925[label="",style="solid", color="burlywood", weight=9];
31.54/17.36	925 -> 870[label="",style="solid", color="burlywood", weight=3];
31.54/17.36	696 -> 643[label="",style="dashed", color="red", weight=0];
31.54/17.36	696[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww750 ww760)",fontsize=16,color="magenta"];696 -> 704[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	696 -> 705[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	697[label="primModNatS0 (Succ ww73) (Succ ww74) MyTrue",fontsize=16,color="black",shape="triangle"];697 -> 706[label="",style="solid", color="black", weight=3];
31.54/17.36	698[label="primModNatS0 (Succ ww73) (Succ ww74) MyFalse",fontsize=16,color="black",shape="box"];698 -> 707[label="",style="solid", color="black", weight=3];
31.54/17.36	699 -> 697[label="",style="dashed", color="red", weight=0];
31.54/17.36	699[label="primModNatS0 (Succ ww73) (Succ ww74) MyTrue",fontsize=16,color="magenta"];867[label="primModNatS (primMinusNatS (Succ ww820) (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];867 -> 871[label="",style="solid", color="black", weight=3];
31.54/17.36	868[label="primModNatS (primMinusNatS (Succ ww820) Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];868 -> 872[label="",style="solid", color="black", weight=3];
31.54/17.36	869[label="primModNatS (primMinusNatS Zero (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];869 -> 873[label="",style="solid", color="black", weight=3];
31.54/17.36	870[label="primModNatS (primMinusNatS Zero Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];870 -> 874[label="",style="solid", color="black", weight=3];
31.54/17.36	704[label="ww750",fontsize=16,color="green",shape="box"];705[label="ww760",fontsize=16,color="green",shape="box"];706 -> 834[label="",style="dashed", color="red", weight=0];
31.54/17.36	706[label="primModNatS (primMinusNatS (Succ ww73) (Succ (Succ ww74))) (Succ (Succ (Succ ww74)))",fontsize=16,color="magenta"];706 -> 847[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	706 -> 848[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	706 -> 849[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	707[label="Succ (Succ ww73)",fontsize=16,color="green",shape="box"];871 -> 834[label="",style="dashed", color="red", weight=0];
31.54/17.36	871[label="primModNatS (primMinusNatS ww820 ww830) (Succ ww84)",fontsize=16,color="magenta"];871 -> 875[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	871 -> 876[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	872 -> 89[label="",style="dashed", color="red", weight=0];
31.54/17.36	872[label="primModNatS (Succ ww820) (Succ ww84)",fontsize=16,color="magenta"];872 -> 877[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	872 -> 878[label="",style="dashed", color="magenta", weight=3];
31.54/17.36	873[label="primModNatS Zero (Succ ww84)",fontsize=16,color="black",shape="triangle"];873 -> 879[label="",style="solid", color="black", weight=3];
31.54/17.36	874 -> 873[label="",style="dashed", color="red", weight=0];
31.54/17.36	874[label="primModNatS Zero (Succ ww84)",fontsize=16,color="magenta"];847[label="Succ (Succ ww74)",fontsize=16,color="green",shape="box"];848[label="Succ (Succ ww74)",fontsize=16,color="green",shape="box"];849[label="Succ ww73",fontsize=16,color="green",shape="box"];875[label="ww830",fontsize=16,color="green",shape="box"];876[label="ww820",fontsize=16,color="green",shape="box"];877[label="ww84",fontsize=16,color="green",shape="box"];878[label="ww820",fontsize=16,color="green",shape="box"];879[label="Zero",fontsize=16,color="green",shape="box"];}
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(6)
31.54/17.36	Complex Obligation (AND)
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(7)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primModNatS0(ww73, ww74, Main.Zero, Main.Zero) -> new_primModNatS00(ww73, ww74)
31.54/17.36	   new_primModNatS1(Main.Succ(Main.Succ(ww2300)), Main.Succ(Main.Succ(ww2400))) -> new_primModNatS0(Main.Succ(ww2300), ww2400, ww2300, ww2400)
31.54/17.36	   new_primModNatS1(Main.Succ(Main.Zero), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Zero), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
31.54/17.36	   new_primModNatS0(ww73, ww74, Main.Succ(ww750), Main.Succ(ww760)) -> new_primModNatS0(ww73, ww74, ww750, ww760)
31.54/17.36	   new_primModNatS(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primModNatS(ww820, ww830, ww84)
31.54/17.36	   new_primModNatS(Main.Succ(ww820), Main.Zero, ww84) -> new_primModNatS1(ww820, ww84)
31.54/17.36	   new_primModNatS0(ww73, ww74, Main.Succ(ww750), Main.Zero) -> new_primModNatS(Main.Succ(ww73), Main.Succ(Main.Succ(ww74)), Main.Succ(Main.Succ(ww74)))
31.54/17.36	   new_primModNatS1(Main.Succ(Main.Succ(ww2300)), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Succ(ww2300)), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
31.54/17.36	   new_primModNatS00(ww73, ww74) -> new_primModNatS(Main.Succ(ww73), Main.Succ(Main.Succ(ww74)), Main.Succ(Main.Succ(ww74)))
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(8) QDPOrderProof (EQUIVALENT)
31.54/17.36	We use the reduction pair processor [LPAR04,JAR06].
31.54/17.36	
31.54/17.36	
31.54/17.36	The following pairs can be oriented strictly and are deleted.
31.54/17.36	
31.54/17.36	   new_primModNatS(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primModNatS(ww820, ww830, ww84)
31.54/17.36	   new_primModNatS(Main.Succ(ww820), Main.Zero, ww84) -> new_primModNatS1(ww820, ww84)
31.54/17.36	The remaining pairs can at least be oriented weakly.
31.54/17.36	Used ordering:  Polynomial interpretation [POLO]:
31.54/17.36	
31.54/17.36	   POL(Main.Succ(x_1)) = 1 + x_1
31.54/17.36	   POL(Main.Zero) = 0
31.54/17.36	   POL(new_primModNatS(x_1, x_2, x_3)) = x_1
31.54/17.36	   POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
31.54/17.36	   POL(new_primModNatS00(x_1, x_2)) = 1 + x_1
31.54/17.36	   POL(new_primModNatS1(x_1, x_2)) = x_1
31.54/17.36	
31.54/17.36	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
31.54/17.36	none
31.54/17.36	
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(9)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primModNatS0(ww73, ww74, Main.Zero, Main.Zero) -> new_primModNatS00(ww73, ww74)
31.54/17.36	   new_primModNatS1(Main.Succ(Main.Succ(ww2300)), Main.Succ(Main.Succ(ww2400))) -> new_primModNatS0(Main.Succ(ww2300), ww2400, ww2300, ww2400)
31.54/17.36	   new_primModNatS1(Main.Succ(Main.Zero), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Zero), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
31.54/17.36	   new_primModNatS0(ww73, ww74, Main.Succ(ww750), Main.Succ(ww760)) -> new_primModNatS0(ww73, ww74, ww750, ww760)
31.54/17.36	   new_primModNatS0(ww73, ww74, Main.Succ(ww750), Main.Zero) -> new_primModNatS(Main.Succ(ww73), Main.Succ(Main.Succ(ww74)), Main.Succ(Main.Succ(ww74)))
31.54/17.36	   new_primModNatS1(Main.Succ(Main.Succ(ww2300)), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Succ(ww2300)), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
31.54/17.36	   new_primModNatS00(ww73, ww74) -> new_primModNatS(Main.Succ(ww73), Main.Succ(Main.Succ(ww74)), Main.Succ(Main.Succ(ww74)))
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(10) DependencyGraphProof (EQUIVALENT)
31.54/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 6 less nodes.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(11)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primModNatS0(ww73, ww74, Main.Succ(ww750), Main.Succ(ww760)) -> new_primModNatS0(ww73, ww74, ww750, ww760)
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(12) QDPSizeChangeProof (EQUIVALENT)
31.54/17.36	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. 
31.54/17.36	
31.54/17.36	From the DPs we obtained the following set of size-change graphs:
31.54/17.36	*new_primModNatS0(ww73, ww74, Main.Succ(ww750), Main.Succ(ww760)) -> new_primModNatS0(ww73, ww74, ww750, ww760)
31.54/17.36	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
31.54/17.36	
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(13)
31.54/17.36	YES
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(14)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primDivNatS(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS(ww780, ww790, ww80)
31.54/17.36	   new_primDivNatS1(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS0(ww260, ww270, ww260, ww270)
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS0(ww68, ww69, ww700, ww710)
31.54/17.36	   new_primDivNatS1(Main.Zero, Main.Zero) -> new_primDivNatS(Main.Zero, Main.Zero, Main.Zero)
31.54/17.36	   new_primDivNatS00(ww68, ww69) -> new_primDivNatS(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69))
31.54/17.36	   new_primDivNatS(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS1(ww780, ww80)
31.54/17.36	   new_primDivNatS1(Main.Succ(ww260), Main.Zero) -> new_primDivNatS(Main.Succ(ww260), Main.Zero, Main.Zero)
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69))
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS00(ww68, ww69)
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(15) DependencyGraphProof (EQUIVALENT)
31.54/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(16)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primDivNatS(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS1(ww780, ww80)
31.54/17.36	   new_primDivNatS1(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS0(ww260, ww270, ww260, ww270)
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS0(ww68, ww69, ww700, ww710)
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69))
31.54/17.36	   new_primDivNatS(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS(ww780, ww790, ww80)
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS00(ww68, ww69)
31.54/17.36	   new_primDivNatS00(ww68, ww69) -> new_primDivNatS(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69))
31.54/17.36	   new_primDivNatS1(Main.Succ(ww260), Main.Zero) -> new_primDivNatS(Main.Succ(ww260), Main.Zero, Main.Zero)
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(17) QDPOrderProof (EQUIVALENT)
31.54/17.36	We use the reduction pair processor [LPAR04,JAR06].
31.54/17.36	
31.54/17.36	
31.54/17.36	The following pairs can be oriented strictly and are deleted.
31.54/17.36	
31.54/17.36	   new_primDivNatS(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS1(ww780, ww80)
31.54/17.36	   new_primDivNatS(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS(ww780, ww790, ww80)
31.54/17.36	The remaining pairs can at least be oriented weakly.
31.54/17.36	Used ordering:  Polynomial interpretation [POLO]:
31.54/17.36	
31.54/17.36	   POL(Main.Succ(x_1)) = 1 + x_1
31.54/17.36	   POL(Main.Zero) = 0
31.54/17.36	   POL(new_primDivNatS(x_1, x_2, x_3)) = x_1
31.54/17.36	   POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
31.54/17.36	   POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1
31.54/17.36	   POL(new_primDivNatS1(x_1, x_2)) = x_1
31.54/17.36	
31.54/17.36	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
31.54/17.36	none
31.54/17.36	
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(18)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primDivNatS1(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS0(ww260, ww270, ww260, ww270)
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS0(ww68, ww69, ww700, ww710)
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69))
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS00(ww68, ww69)
31.54/17.36	   new_primDivNatS00(ww68, ww69) -> new_primDivNatS(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69))
31.54/17.36	   new_primDivNatS1(Main.Succ(ww260), Main.Zero) -> new_primDivNatS(Main.Succ(ww260), Main.Zero, Main.Zero)
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(19) DependencyGraphProof (EQUIVALENT)
31.54/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(20)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS0(ww68, ww69, ww700, ww710)
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(21) QDPSizeChangeProof (EQUIVALENT)
31.54/17.36	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. 
31.54/17.36	
31.54/17.36	From the DPs we obtained the following set of size-change graphs:
31.54/17.36	*new_primDivNatS0(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS0(ww68, ww69, ww700, ww710)
31.54/17.36	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
31.54/17.36	
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(22)
31.54/17.36	YES
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(23)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_psPs(Cons(ww210, ww211), ww20) -> new_psPs(ww211, ww20)
31.54/17.36	
31.54/17.36	R is empty.
31.54/17.36	Q is empty.
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(24) QDPSizeChangeProof (EQUIVALENT)
31.54/17.36	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. 
31.54/17.36	
31.54/17.36	From the DPs we obtained the following set of size-change graphs:
31.54/17.36	*new_psPs(Cons(ww210, ww211), ww20) -> new_psPs(ww211, ww20)
31.54/17.36	The graph contains the following edges 1 > 1, 2 >= 2
31.54/17.36	
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(25)
31.54/17.36	YES
31.54/17.36	
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(26)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primShowInt(Main.Neg(ww30)) -> new_primShowInt(Main.Pos(ww30))
31.54/17.36	   new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(new_divMyInt(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))
31.54/17.36	
31.54/17.36	The TRS R consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.54/17.36	   new_divMyInt(ww26, ww27) -> Main.Pos(new_primDivNatS2(ww26, ww27))
31.54/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.54/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.54/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.54/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.54/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.54/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.54/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.54/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.54/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.54/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.54/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.54/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.54/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.54/17.36	
31.54/17.36	The set Q consists of the following terms:
31.54/17.36	
31.54/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.54/17.36	   new_primDivNatS02(x0, x1)
31.54/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.54/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.54/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.54/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.54/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.54/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.54/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.54/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.54/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.54/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.54/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.54/17.36	   new_primDivNatS3(x0)
31.54/17.36	   new_divMyInt(x0, x1)
31.54/17.36	
31.54/17.36	We have to consider all minimal (P,Q,R)-chains.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(27) DependencyGraphProof (EQUIVALENT)
31.54/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
31.54/17.36	----------------------------------------
31.54/17.36	
31.54/17.36	(28)
31.54/17.36	Obligation:
31.54/17.36	Q DP problem:
31.54/17.36	The TRS P consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(new_divMyInt(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))
31.54/17.36	
31.54/17.36	The TRS R consists of the following rules:
31.54/17.36	
31.54/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.54/17.36	   new_divMyInt(ww26, ww27) -> Main.Pos(new_primDivNatS2(ww26, ww27))
31.54/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.54/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.54/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.54/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.54/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.54/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.54/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.54/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.54/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	   new_divMyInt(x0, x1)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(29) TransformationProof (EQUIVALENT)
31.87/17.36	By rewriting [LPAR04] the rule new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(new_divMyInt(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]:
31.87/17.36	
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))),new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(30)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_divMyInt(ww26, ww27) -> Main.Pos(new_primDivNatS2(ww26, ww27))
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	   new_divMyInt(x0, x1)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(31) UsableRulesProof (EQUIVALENT)
31.87/17.36	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(32)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	   new_divMyInt(x0, x1)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(33) QReductionProof (EQUIVALENT)
31.87/17.36	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
31.87/17.36	
31.87/17.36	   new_divMyInt(x0, x1)
31.87/17.36	
31.87/17.36	
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(34)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(35) MNOCProof (EQUIVALENT)
31.87/17.36	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(36)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	Q is empty.
31.87/17.36	We have to consider all (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(37) InductionCalculusProof (EQUIVALENT)
31.87/17.36	Note that final constraints are written in bold face.
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	For Pair new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))) the following chains were created:
31.87/17.36	*We consider the chain new_primShowInt(Main.Pos(Main.Succ(x0))) -> new_primShowInt(Main.Pos(new_primDivNatS2(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))), new_primShowInt(Main.Pos(Main.Succ(x1))) -> new_primShowInt(Main.Pos(new_primDivNatS2(x1, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))) which results in the following constraint:
31.87/17.36	
31.87/17.36	(1)    (new_primShowInt(Main.Pos(new_primDivNatS2(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))=new_primShowInt(Main.Pos(Main.Succ(x1)))  ==>  new_primShowInt(Main.Pos(Main.Succ(x0)))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
31.87/17.36	
31.87/17.36	(2)    (Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))=x2 & new_primDivNatS2(x0, x2)=Main.Succ(x1)  ==>  new_primShowInt(Main.Pos(Main.Succ(x0)))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS2(x0, x2)=Main.Succ(x1) which results in the following new constraints:
31.87/17.36	
31.87/17.36	(3)    (new_primDivNatS01(x4, x3, x4, x3)=Main.Succ(x1) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))=Main.Succ(x3)  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x4))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(x4), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	(4)    (Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))=Main.Succ(x1) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))=Main.Zero  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Zero)))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Zero, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	(5)    (Main.Succ(new_primDivNatS4(Main.Succ(x6), Main.Zero, Main.Zero))=Main.Succ(x1) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))=Main.Zero  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x6))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(x6), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
31.87/17.36	
31.87/17.36	(6)    (x4=x7 & x3=x8 & new_primDivNatS01(x4, x3, x7, x8)=Main.Succ(x1) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x3  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x4))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(x4), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x4, x3, x7, x8)=Main.Succ(x1) which results in the following new constraints:
31.87/17.36	
31.87/17.36	(7)    (new_primDivNatS01(x12, x11, x10, x9)=Main.Succ(x1) & x12=Main.Succ(x10) & x11=Main.Succ(x9) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x11 & (\/x13:new_primDivNatS01(x12, x11, x10, x9)=Main.Succ(x13) & x12=x10 & x11=x9 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x11  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x12))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(x12), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x12))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(x12), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	(8)    (new_primDivNatS02(x15, x14)=Main.Succ(x1) & x15=Main.Zero & x14=Main.Zero & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x14  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x15))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(x15), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	(9)    (new_primDivNatS02(x21, x20)=Main.Succ(x1) & x21=Main.Succ(x19) & x20=Main.Zero & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x20  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x21))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(x21), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (7) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
31.87/17.36	
31.87/17.36	(10)    (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x10)))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(Main.Succ(x10)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We solved constraint (8) using rules (I), (II), (III).We solved constraint (9) using rules (I), (II), (III).
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	To summarize, we get the following constraints P__>=_ for the following pairs.
31.87/17.36	
31.87/17.36	*new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
31.87/17.36	
31.87/17.36	*(new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x10)))))_>=_new_primShowInt(Main.Pos(new_primDivNatS2(Main.Succ(Main.Succ(x10)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by  "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(38)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(39) TransformationProof (EQUIVALENT)
31.87/17.36	By narrowing [LPAR04] the rule new_primShowInt(Main.Pos(Main.Succ(ww300))) -> new_primShowInt(Main.Pos(new_primDivNatS2(ww300, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
31.87/17.36	
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x0)))) -> new_primShowInt(Main.Pos(new_primDivNatS01(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))),new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x0)))) -> new_primShowInt(Main.Pos(new_primDivNatS01(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Zero))) -> new_primShowInt(Main.Pos(Main.Zero)),new_primShowInt(Main.Pos(Main.Succ(Main.Zero))) -> new_primShowInt(Main.Pos(Main.Zero)))
31.87/17.36	
31.87/17.36	
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(40)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x0)))) -> new_primShowInt(Main.Pos(new_primDivNatS01(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Zero))) -> new_primShowInt(Main.Pos(Main.Zero))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(41) DependencyGraphProof (EQUIVALENT)
31.87/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(42)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x0)))) -> new_primShowInt(Main.Pos(new_primDivNatS01(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(43) TransformationProof (EQUIVALENT)
31.87/17.36	By narrowing [LPAR04] the rule new_primShowInt(Main.Pos(Main.Succ(Main.Succ(x0)))) -> new_primShowInt(Main.Pos(new_primDivNatS01(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
31.87/17.36	
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x2))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(x2), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))),new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x2))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(x2), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Zero)))) -> new_primShowInt(Main.Pos(Main.Zero)),new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Zero)))) -> new_primShowInt(Main.Pos(Main.Zero)))
31.87/17.36	
31.87/17.36	
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(44)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x2))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(x2), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Zero)))) -> new_primShowInt(Main.Pos(Main.Zero))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(45) DependencyGraphProof (EQUIVALENT)
31.87/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(46)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x2))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(x2), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(47) TransformationProof (EQUIVALENT)
31.87/17.36	By narrowing [LPAR04] the rule new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x2))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(x2), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
31.87/17.36	
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2)))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(x2)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))),new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2)))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(x2)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))) -> new_primShowInt(Main.Pos(Main.Zero)),new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))) -> new_primShowInt(Main.Pos(Main.Zero)))
31.87/17.36	
31.87/17.36	
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(48)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2)))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(x2)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))) -> new_primShowInt(Main.Pos(Main.Zero))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(49) DependencyGraphProof (EQUIVALENT)
31.87/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(50)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2)))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(x2)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(51) TransformationProof (EQUIVALENT)
31.87/17.36	By narrowing [LPAR04] the rule new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2)))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(x2)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
31.87/17.36	
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))),new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	   (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))) -> new_primShowInt(Main.Pos(Main.Zero)),new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))) -> new_primShowInt(Main.Pos(Main.Zero)))
31.87/17.36	
31.87/17.36	
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(52)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))) -> new_primShowInt(Main.Pos(Main.Zero))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(53) DependencyGraphProof (EQUIVALENT)
31.87/17.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(54)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(55) MNOCProof (EQUIVALENT)
31.87/17.36	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(56)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	Q is empty.
31.87/17.36	We have to consider all (P,Q,R)-chains.
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(57) InductionCalculusProof (EQUIVALENT)
31.87/17.36	Note that final constraints are written in bold face.
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	For Pair new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))) the following chains were created:
31.87/17.36	*We consider the chain new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x0))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x0))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x1))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x1, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))) which results in the following constraint:
31.87/17.36	
31.87/17.36	(1)    (new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x0))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1)))))))  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x0)))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x0))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
31.87/17.36	
31.87/17.36	(2)    (Main.Succ(Main.Succ(Main.Succ(x0)))=x2 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x3 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))=x4 & new_primDivNatS01(x2, x3, x0, x4)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1)))))  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x0)))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x0))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x2, x3, x0, x4)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) which results in the following new constraints:
31.87/17.36	
31.87/17.36	(3)    (new_primDivNatS01(x8, x7, x6, x5)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(x6))))=x8 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x7 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))=Main.Succ(x5) & (\/x9:new_primDivNatS01(x8, x7, x6, x5)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x9))))) & Main.Succ(Main.Succ(Main.Succ(x6)))=x8 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x7 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))=x5  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x6)))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x6))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x6, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x6))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x6)))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(x6), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	(4)    (new_primDivNatS02(x11, x10)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) & Main.Succ(Main.Succ(Main.Succ(Main.Zero)))=x11 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x10 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))=Main.Zero  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Zero))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Zero, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	(5)    (new_primDivNatS02(x17, x16)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(x15))))=x17 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x16 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))=Main.Zero  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x15))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x15)))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(x15), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
31.87/17.36	
31.87/17.36	(6)    (new_primDivNatS01(x8, x7, x6, x5)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(x6))))=x8 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x7 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))=x5  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x6))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x6)))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(x6), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x8, x7, x6, x5)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) which results in the following new constraints:
31.87/17.36	
31.87/17.36	(7)    (new_primDivNatS01(x21, x20, x19, x18)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19)))))=x21 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x20 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))=Main.Succ(x18) & (\/x22:new_primDivNatS01(x21, x20, x19, x18)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x22))))) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19))))=x21 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x20 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))=x18  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19)))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(x19), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19)))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19))))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(Main.Succ(x19)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	(8)    (new_primDivNatS02(x24, x23)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))=x24 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x23 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))=Main.Zero  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(Main.Zero), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	(9)    (new_primDivNatS02(x30, x29)=Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x1))))) & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x28)))))=x30 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))=x29 & Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))=Main.Zero  ==>  new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x28)))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x28))))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(Main.Succ(x28)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We simplified constraint (7) using rules (I), (II), (III), (IV) which results in the following new constraint:
31.87/17.36	
31.87/17.36	(10)    (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19)))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19))))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(Main.Succ(x19)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II).
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	To summarize, we get the following constraints P__>=_ for the following pairs.
31.87/17.36	
31.87/17.36	*new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))
31.87/17.36	
31.87/17.36	*(new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19)))))))))_>=_new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x19))))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), Main.Succ(Main.Succ(x19)), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	
31.87/17.36	The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by  "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 
31.87/17.36	----------------------------------------
31.87/17.36	
31.87/17.36	(58)
31.87/17.36	Obligation:
31.87/17.36	Q DP problem:
31.87/17.36	The TRS P consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(x2))))))) -> new_primShowInt(Main.Pos(new_primDivNatS01(Main.Succ(Main.Succ(Main.Succ(x2))), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))), x2, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))
31.87/17.36	
31.87/17.36	The TRS R consists of the following rules:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(ww270)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Succ(ww710)) -> new_primDivNatS01(ww68, ww69, ww700, ww710)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Zero, Main.Succ(ww710)) -> Main.Zero
31.87/17.36	   new_primDivNatS01(ww68, ww69, Main.Succ(ww700), Main.Zero) -> new_primDivNatS02(ww68, ww69)
31.87/17.36	   new_primDivNatS02(ww68, ww69) -> Main.Succ(new_primDivNatS4(Main.Succ(ww68), Main.Succ(ww69), Main.Succ(ww69)))
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Succ(ww790), ww80) -> new_primDivNatS4(ww780, ww790, ww80)
31.87/17.36	   new_primDivNatS4(Main.Succ(ww780), Main.Zero, ww80) -> new_primDivNatS2(ww780, ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(ww790), ww80) -> new_primDivNatS3(ww80)
31.87/17.36	   new_primDivNatS3(ww80) -> Main.Zero
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Zero, Main.Zero, Main.Zero))
31.87/17.36	   new_primDivNatS2(Main.Succ(ww260), Main.Zero) -> Main.Succ(new_primDivNatS4(Main.Succ(ww260), Main.Zero, Main.Zero))
31.87/17.36	
31.87/17.36	The set Q consists of the following terms:
31.87/17.36	
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Succ(x0))
31.87/17.36	   new_primDivNatS02(x0, x1)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Zero, x1)
31.87/17.36	   new_primDivNatS2(Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Zero)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Zero, x0)
31.87/17.36	   new_primDivNatS4(Main.Succ(x0), Main.Succ(x1), x2)
31.87/17.36	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
31.87/17.36	   new_primDivNatS4(Main.Zero, Main.Succ(x0), x1)
31.87/17.36	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1))
31.87/17.36	   new_primDivNatS3(x0)
31.87/17.36	
31.87/17.36	We have to consider all minimal (P,Q,R)-chains.
31.87/17.37	----------------------------------------
31.87/17.37	
31.87/17.37	(59) Narrow (COMPLETE)
31.87/17.37	Haskell To QDPs
31.87/17.37	
31.87/17.37	digraph dp_graph {
31.87/17.37	node [outthreshold=100, inthreshold=100];1[label="showsMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
31.87/17.37	3[label="showsMyInt ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
31.87/17.37	4[label="showsMyInt ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
31.87/17.37	5[label="showsPrecMyInt (Pos Zero) ww3 ww4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
31.87/17.37	6 -> 36[label="",style="dashed", color="red", weight=0];
31.87/17.37	6[label="psPs (showMyInt ww3) ww4",fontsize=16,color="magenta"];6 -> 37[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	6 -> 38[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	37[label="ww4",fontsize=16,color="green",shape="box"];38[label="showMyInt ww3",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
31.87/17.37	36[label="psPs ww21 ww20",fontsize=16,color="burlywood",shape="triangle"];880[label="ww21/Cons ww210 ww211",fontsize=10,color="white",style="solid",shape="box"];36 -> 880[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	880 -> 53[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	881[label="ww21/Nil",fontsize=10,color="white",style="solid",shape="box"];36 -> 881[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	881 -> 54[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	52[label="primShowInt ww3",fontsize=16,color="burlywood",shape="triangle"];882[label="ww3/Pos ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 882[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	882 -> 55[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	883[label="ww3/Neg ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 883[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	883 -> 56[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	53[label="psPs (Cons ww210 ww211) ww20",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
31.87/17.37	54[label="psPs Nil ww20",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
31.87/17.37	55[label="primShowInt (Pos ww30)",fontsize=16,color="burlywood",shape="box"];884[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];55 -> 884[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	884 -> 59[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	885[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 885[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	885 -> 60[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	56[label="primShowInt (Neg ww30)",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3];
31.87/17.37	57[label="Cons ww210 (psPs ww211 ww20)",fontsize=16,color="green",shape="box"];57 -> 62[label="",style="dashed", color="green", weight=3];
31.87/17.37	58[label="ww20",fontsize=16,color="green",shape="box"];59[label="primShowInt (Pos (Succ ww300))",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
31.87/17.37	60[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
31.87/17.37	61[label="Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))) (primShowInt (Pos ww30))",fontsize=16,color="green",shape="box"];61 -> 65[label="",style="dashed", color="green", weight=3];
31.87/17.37	62 -> 36[label="",style="dashed", color="red", weight=0];
31.87/17.37	62[label="psPs ww211 ww20",fontsize=16,color="magenta"];62 -> 66[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	63 -> 36[label="",style="dashed", color="red", weight=0];
31.87/17.37	63[label="psPs (primShowInt (divMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) (Cons (toEnumChar (modMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) Nil)",fontsize=16,color="magenta"];63 -> 67[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	63 -> 68[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	64[label="Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))) Nil",fontsize=16,color="green",shape="box"];65 -> 52[label="",style="dashed", color="red", weight=0];
31.87/17.37	65[label="primShowInt (Pos ww30)",fontsize=16,color="magenta"];65 -> 69[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	66[label="ww211",fontsize=16,color="green",shape="box"];67[label="Cons (toEnumChar (modMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) Nil",fontsize=16,color="green",shape="box"];67 -> 70[label="",style="dashed", color="green", weight=3];
31.87/17.37	68 -> 52[label="",style="dashed", color="red", weight=0];
31.87/17.37	68[label="primShowInt (divMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))",fontsize=16,color="magenta"];68 -> 71[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	69[label="Pos ww30",fontsize=16,color="green",shape="box"];70 -> 72[label="",style="dashed", color="red", weight=0];
31.87/17.37	70[label="toEnumChar (modMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))",fontsize=16,color="magenta"];70 -> 73[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	70 -> 74[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	71 -> 75[label="",style="dashed", color="red", weight=0];
31.87/17.37	71[label="divMyInt (Pos (Succ ww300)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];71 -> 76[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	71 -> 77[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	73[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];74[label="ww300",fontsize=16,color="green",shape="box"];72[label="toEnumChar (modMyInt (Pos (Succ ww23)) (Pos (Succ ww24)))",fontsize=16,color="black",shape="triangle"];72 -> 78[label="",style="solid", color="black", weight=3];
31.87/17.37	76[label="ww300",fontsize=16,color="green",shape="box"];77[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];75[label="divMyInt (Pos (Succ ww26)) (Pos (Succ ww27))",fontsize=16,color="black",shape="triangle"];75 -> 79[label="",style="solid", color="black", weight=3];
31.87/17.37	78[label="primIntToChar (modMyInt (Pos (Succ ww23)) (Pos (Succ ww24)))",fontsize=16,color="black",shape="box"];78 -> 80[label="",style="solid", color="black", weight=3];
31.87/17.37	79[label="primDivInt (Pos (Succ ww26)) (Pos (Succ ww27))",fontsize=16,color="black",shape="box"];79 -> 81[label="",style="solid", color="black", weight=3];
31.87/17.37	80[label="Char (modMyInt (Pos (Succ ww23)) (Pos (Succ ww24)))",fontsize=16,color="green",shape="box"];80 -> 82[label="",style="dashed", color="green", weight=3];
31.87/17.37	81[label="Pos (primDivNatS (Succ ww26) (Succ ww27))",fontsize=16,color="green",shape="box"];81 -> 83[label="",style="dashed", color="green", weight=3];
31.87/17.37	82[label="modMyInt (Pos (Succ ww23)) (Pos (Succ ww24))",fontsize=16,color="black",shape="box"];82 -> 84[label="",style="solid", color="black", weight=3];
31.87/17.37	83[label="primDivNatS (Succ ww26) (Succ ww27)",fontsize=16,color="black",shape="triangle"];83 -> 85[label="",style="solid", color="black", weight=3];
31.87/17.37	84[label="primModInt (Pos (Succ ww23)) (Pos (Succ ww24))",fontsize=16,color="black",shape="box"];84 -> 86[label="",style="solid", color="black", weight=3];
31.87/17.37	85[label="primDivNatS0 ww26 ww27 (primGEqNatS ww26 ww27)",fontsize=16,color="burlywood",shape="box"];886[label="ww26/Succ ww260",fontsize=10,color="white",style="solid",shape="box"];85 -> 886[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	886 -> 87[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	887[label="ww26/Zero",fontsize=10,color="white",style="solid",shape="box"];85 -> 887[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	887 -> 88[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	86[label="Pos (primModNatS (Succ ww23) (Succ ww24))",fontsize=16,color="green",shape="box"];86 -> 89[label="",style="dashed", color="green", weight=3];
31.87/17.37	87[label="primDivNatS0 (Succ ww260) ww27 (primGEqNatS (Succ ww260) ww27)",fontsize=16,color="burlywood",shape="box"];888[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];87 -> 888[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	888 -> 90[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	889[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 889[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	889 -> 91[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	88[label="primDivNatS0 Zero ww27 (primGEqNatS Zero ww27)",fontsize=16,color="burlywood",shape="box"];890[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];88 -> 890[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	890 -> 92[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	891[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];88 -> 891[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	891 -> 93[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	89[label="primModNatS (Succ ww23) (Succ ww24)",fontsize=16,color="burlywood",shape="triangle"];892[label="ww24/Succ ww240",fontsize=10,color="white",style="solid",shape="box"];89 -> 892[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	892 -> 94[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	893[label="ww24/Zero",fontsize=10,color="white",style="solid",shape="box"];89 -> 893[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	893 -> 95[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	90[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS (Succ ww260) (Succ ww270))",fontsize=16,color="black",shape="box"];90 -> 96[label="",style="solid", color="black", weight=3];
31.87/17.37	91[label="primDivNatS0 (Succ ww260) Zero (primGEqNatS (Succ ww260) Zero)",fontsize=16,color="black",shape="box"];91 -> 97[label="",style="solid", color="black", weight=3];
31.87/17.37	92[label="primDivNatS0 Zero (Succ ww270) (primGEqNatS Zero (Succ ww270))",fontsize=16,color="black",shape="box"];92 -> 98[label="",style="solid", color="black", weight=3];
31.87/17.37	93[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
31.87/17.37	94[label="primModNatS (Succ ww23) (Succ (Succ ww240))",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
31.87/17.37	95[label="primModNatS (Succ ww23) (Succ Zero)",fontsize=16,color="black",shape="box"];95 -> 101[label="",style="solid", color="black", weight=3];
31.87/17.37	96 -> 546[label="",style="dashed", color="red", weight=0];
31.87/17.37	96[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS ww260 ww270)",fontsize=16,color="magenta"];96 -> 547[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	96 -> 548[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	96 -> 549[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	96 -> 550[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	97[label="primDivNatS0 (Succ ww260) Zero MyTrue",fontsize=16,color="black",shape="box"];97 -> 104[label="",style="solid", color="black", weight=3];
31.87/17.37	98[label="primDivNatS0 Zero (Succ ww270) MyFalse",fontsize=16,color="black",shape="box"];98 -> 105[label="",style="solid", color="black", weight=3];
31.87/17.37	99[label="primDivNatS0 Zero Zero MyTrue",fontsize=16,color="black",shape="box"];99 -> 106[label="",style="solid", color="black", weight=3];
31.87/17.37	100[label="primModNatS0 ww23 ww240 (primGEqNatS ww23 (Succ ww240))",fontsize=16,color="burlywood",shape="box"];894[label="ww23/Succ ww230",fontsize=10,color="white",style="solid",shape="box"];100 -> 894[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	894 -> 107[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	895[label="ww23/Zero",fontsize=10,color="white",style="solid",shape="box"];100 -> 895[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	895 -> 108[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	101[label="Zero",fontsize=16,color="green",shape="box"];547[label="ww270",fontsize=16,color="green",shape="box"];548[label="ww260",fontsize=16,color="green",shape="box"];549[label="ww260",fontsize=16,color="green",shape="box"];550[label="ww270",fontsize=16,color="green",shape="box"];546[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS ww70 ww71)",fontsize=16,color="burlywood",shape="triangle"];896[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];546 -> 896[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	896 -> 587[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	897[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];546 -> 897[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	897 -> 588[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	104[label="Succ (primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];104 -> 113[label="",style="dashed", color="green", weight=3];
31.87/17.37	105[label="Zero",fontsize=16,color="green",shape="box"];106[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];106 -> 114[label="",style="dashed", color="green", weight=3];
31.87/17.37	107[label="primModNatS0 (Succ ww230) ww240 (primGEqNatS (Succ ww230) (Succ ww240))",fontsize=16,color="black",shape="box"];107 -> 115[label="",style="solid", color="black", weight=3];
31.87/17.37	108[label="primModNatS0 Zero ww240 (primGEqNatS Zero (Succ ww240))",fontsize=16,color="black",shape="box"];108 -> 116[label="",style="solid", color="black", weight=3];
31.87/17.37	587[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS (Succ ww700) ww71)",fontsize=16,color="burlywood",shape="box"];898[label="ww71/Succ ww710",fontsize=10,color="white",style="solid",shape="box"];587 -> 898[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	898 -> 594[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	899[label="ww71/Zero",fontsize=10,color="white",style="solid",shape="box"];587 -> 899[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	899 -> 595[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	588[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS Zero ww71)",fontsize=16,color="burlywood",shape="box"];900[label="ww71/Succ ww710",fontsize=10,color="white",style="solid",shape="box"];588 -> 900[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	900 -> 596[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	901[label="ww71/Zero",fontsize=10,color="white",style="solid",shape="box"];588 -> 901[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	901 -> 597[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	113 -> 780[label="",style="dashed", color="red", weight=0];
31.87/17.37	113[label="primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero)",fontsize=16,color="magenta"];113 -> 781[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	113 -> 782[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	113 -> 783[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	114 -> 780[label="",style="dashed", color="red", weight=0];
31.87/17.37	114[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];114 -> 784[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	114 -> 785[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	114 -> 786[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	115[label="primModNatS0 (Succ ww230) ww240 (primGEqNatS ww230 ww240)",fontsize=16,color="burlywood",shape="box"];902[label="ww230/Succ ww2300",fontsize=10,color="white",style="solid",shape="box"];115 -> 902[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	902 -> 123[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	903[label="ww230/Zero",fontsize=10,color="white",style="solid",shape="box"];115 -> 903[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	903 -> 124[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	116[label="primModNatS0 Zero ww240 MyFalse",fontsize=16,color="black",shape="box"];116 -> 125[label="",style="solid", color="black", weight=3];
31.87/17.37	594[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS (Succ ww700) (Succ ww710))",fontsize=16,color="black",shape="box"];594 -> 604[label="",style="solid", color="black", weight=3];
31.87/17.37	595[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS (Succ ww700) Zero)",fontsize=16,color="black",shape="box"];595 -> 605[label="",style="solid", color="black", weight=3];
31.87/17.37	596[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS Zero (Succ ww710))",fontsize=16,color="black",shape="box"];596 -> 606[label="",style="solid", color="black", weight=3];
31.87/17.37	597[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];597 -> 607[label="",style="solid", color="black", weight=3];
31.87/17.37	781[label="Succ ww260",fontsize=16,color="green",shape="box"];782[label="Zero",fontsize=16,color="green",shape="box"];783[label="Zero",fontsize=16,color="green",shape="box"];780[label="primDivNatS (primMinusNatS ww78 ww79) (Succ ww80)",fontsize=16,color="burlywood",shape="triangle"];904[label="ww78/Succ ww780",fontsize=10,color="white",style="solid",shape="box"];780 -> 904[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	904 -> 805[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	905[label="ww78/Zero",fontsize=10,color="white",style="solid",shape="box"];780 -> 905[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	905 -> 806[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	784[label="Zero",fontsize=16,color="green",shape="box"];785[label="Zero",fontsize=16,color="green",shape="box"];786[label="Zero",fontsize=16,color="green",shape="box"];123[label="primModNatS0 (Succ (Succ ww2300)) ww240 (primGEqNatS (Succ ww2300) ww240)",fontsize=16,color="burlywood",shape="box"];906[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];123 -> 906[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	906 -> 134[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	907[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];123 -> 907[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	907 -> 135[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	124[label="primModNatS0 (Succ Zero) ww240 (primGEqNatS Zero ww240)",fontsize=16,color="burlywood",shape="box"];908[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];124 -> 908[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	908 -> 136[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	909[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];124 -> 909[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	909 -> 137[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	125[label="Succ Zero",fontsize=16,color="green",shape="box"];604 -> 546[label="",style="dashed", color="red", weight=0];
31.87/17.37	604[label="primDivNatS0 (Succ ww68) (Succ ww69) (primGEqNatS ww700 ww710)",fontsize=16,color="magenta"];604 -> 618[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	604 -> 619[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	605[label="primDivNatS0 (Succ ww68) (Succ ww69) MyTrue",fontsize=16,color="black",shape="triangle"];605 -> 620[label="",style="solid", color="black", weight=3];
31.87/17.37	606[label="primDivNatS0 (Succ ww68) (Succ ww69) MyFalse",fontsize=16,color="black",shape="box"];606 -> 621[label="",style="solid", color="black", weight=3];
31.87/17.37	607 -> 605[label="",style="dashed", color="red", weight=0];
31.87/17.37	607[label="primDivNatS0 (Succ ww68) (Succ ww69) MyTrue",fontsize=16,color="magenta"];805[label="primDivNatS (primMinusNatS (Succ ww780) ww79) (Succ ww80)",fontsize=16,color="burlywood",shape="box"];910[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];805 -> 910[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	910 -> 813[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	911[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];805 -> 911[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	911 -> 814[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	806[label="primDivNatS (primMinusNatS Zero ww79) (Succ ww80)",fontsize=16,color="burlywood",shape="box"];912[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];806 -> 912[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	912 -> 815[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	913[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];806 -> 913[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	913 -> 816[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	134[label="primModNatS0 (Succ (Succ ww2300)) (Succ ww2400) (primGEqNatS (Succ ww2300) (Succ ww2400))",fontsize=16,color="black",shape="box"];134 -> 144[label="",style="solid", color="black", weight=3];
31.87/17.37	135[label="primModNatS0 (Succ (Succ ww2300)) Zero (primGEqNatS (Succ ww2300) Zero)",fontsize=16,color="black",shape="box"];135 -> 145[label="",style="solid", color="black", weight=3];
31.87/17.37	136[label="primModNatS0 (Succ Zero) (Succ ww2400) (primGEqNatS Zero (Succ ww2400))",fontsize=16,color="black",shape="box"];136 -> 146[label="",style="solid", color="black", weight=3];
31.87/17.37	137[label="primModNatS0 (Succ Zero) Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];137 -> 147[label="",style="solid", color="black", weight=3];
31.87/17.37	618[label="ww710",fontsize=16,color="green",shape="box"];619[label="ww700",fontsize=16,color="green",shape="box"];620[label="Succ (primDivNatS (primMinusNatS (Succ ww68) (Succ ww69)) (Succ (Succ ww69)))",fontsize=16,color="green",shape="box"];620 -> 629[label="",style="dashed", color="green", weight=3];
31.87/17.37	621[label="Zero",fontsize=16,color="green",shape="box"];813[label="primDivNatS (primMinusNatS (Succ ww780) (Succ ww790)) (Succ ww80)",fontsize=16,color="black",shape="box"];813 -> 821[label="",style="solid", color="black", weight=3];
31.87/17.37	814[label="primDivNatS (primMinusNatS (Succ ww780) Zero) (Succ ww80)",fontsize=16,color="black",shape="box"];814 -> 822[label="",style="solid", color="black", weight=3];
31.87/17.37	815[label="primDivNatS (primMinusNatS Zero (Succ ww790)) (Succ ww80)",fontsize=16,color="black",shape="box"];815 -> 823[label="",style="solid", color="black", weight=3];
31.87/17.37	816[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww80)",fontsize=16,color="black",shape="box"];816 -> 824[label="",style="solid", color="black", weight=3];
31.87/17.37	144 -> 643[label="",style="dashed", color="red", weight=0];
31.87/17.37	144[label="primModNatS0 (Succ (Succ ww2300)) (Succ ww2400) (primGEqNatS ww2300 ww2400)",fontsize=16,color="magenta"];144 -> 644[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	144 -> 645[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	144 -> 646[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	144 -> 647[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	145[label="primModNatS0 (Succ (Succ ww2300)) Zero MyTrue",fontsize=16,color="black",shape="box"];145 -> 156[label="",style="solid", color="black", weight=3];
31.87/17.37	146[label="primModNatS0 (Succ Zero) (Succ ww2400) MyFalse",fontsize=16,color="black",shape="box"];146 -> 157[label="",style="solid", color="black", weight=3];
31.87/17.37	147[label="primModNatS0 (Succ Zero) Zero MyTrue",fontsize=16,color="black",shape="box"];147 -> 158[label="",style="solid", color="black", weight=3];
31.87/17.37	629 -> 780[label="",style="dashed", color="red", weight=0];
31.87/17.37	629[label="primDivNatS (primMinusNatS (Succ ww68) (Succ ww69)) (Succ (Succ ww69))",fontsize=16,color="magenta"];629 -> 787[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	629 -> 788[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	629 -> 789[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	821 -> 780[label="",style="dashed", color="red", weight=0];
31.87/17.37	821[label="primDivNatS (primMinusNatS ww780 ww790) (Succ ww80)",fontsize=16,color="magenta"];821 -> 829[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	821 -> 830[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	822 -> 83[label="",style="dashed", color="red", weight=0];
31.87/17.37	822[label="primDivNatS (Succ ww780) (Succ ww80)",fontsize=16,color="magenta"];822 -> 831[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	822 -> 832[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	823[label="primDivNatS Zero (Succ ww80)",fontsize=16,color="black",shape="triangle"];823 -> 833[label="",style="solid", color="black", weight=3];
31.87/17.37	824 -> 823[label="",style="dashed", color="red", weight=0];
31.87/17.37	824[label="primDivNatS Zero (Succ ww80)",fontsize=16,color="magenta"];644[label="ww2400",fontsize=16,color="green",shape="box"];645[label="ww2300",fontsize=16,color="green",shape="box"];646[label="ww2400",fontsize=16,color="green",shape="box"];647[label="Succ ww2300",fontsize=16,color="green",shape="box"];643[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww75 ww76)",fontsize=16,color="burlywood",shape="triangle"];914[label="ww75/Succ ww750",fontsize=10,color="white",style="solid",shape="box"];643 -> 914[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	914 -> 684[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	915[label="ww75/Zero",fontsize=10,color="white",style="solid",shape="box"];643 -> 915[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	915 -> 685[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	156 -> 834[label="",style="dashed", color="red", weight=0];
31.87/17.37	156[label="primModNatS (primMinusNatS (Succ (Succ ww2300)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];156 -> 835[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	156 -> 836[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	156 -> 837[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	157[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];158 -> 834[label="",style="dashed", color="red", weight=0];
31.87/17.37	158[label="primModNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];158 -> 838[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	158 -> 839[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	158 -> 840[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	787[label="Succ ww68",fontsize=16,color="green",shape="box"];788[label="Succ ww69",fontsize=16,color="green",shape="box"];789[label="Succ ww69",fontsize=16,color="green",shape="box"];829[label="ww780",fontsize=16,color="green",shape="box"];830[label="ww790",fontsize=16,color="green",shape="box"];831[label="ww780",fontsize=16,color="green",shape="box"];832[label="ww80",fontsize=16,color="green",shape="box"];833[label="Zero",fontsize=16,color="green",shape="box"];684[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) ww76)",fontsize=16,color="burlywood",shape="box"];916[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];684 -> 916[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	916 -> 688[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	917[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];684 -> 917[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	917 -> 689[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	685[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero ww76)",fontsize=16,color="burlywood",shape="box"];918[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];685 -> 918[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	918 -> 690[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	919[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];685 -> 919[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	919 -> 691[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	835[label="Succ Zero",fontsize=16,color="green",shape="box"];836[label="Succ Zero",fontsize=16,color="green",shape="box"];837[label="Succ (Succ ww2300)",fontsize=16,color="green",shape="box"];834[label="primModNatS (primMinusNatS ww82 ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="triangle"];920[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];834 -> 920[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	920 -> 865[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	921[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];834 -> 921[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	921 -> 866[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	838[label="Succ Zero",fontsize=16,color="green",shape="box"];839[label="Succ Zero",fontsize=16,color="green",shape="box"];840[label="Succ Zero",fontsize=16,color="green",shape="box"];688[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) (Succ ww760))",fontsize=16,color="black",shape="box"];688 -> 696[label="",style="solid", color="black", weight=3];
31.87/17.37	689[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) Zero)",fontsize=16,color="black",shape="box"];689 -> 697[label="",style="solid", color="black", weight=3];
31.87/17.37	690[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero (Succ ww760))",fontsize=16,color="black",shape="box"];690 -> 698[label="",style="solid", color="black", weight=3];
31.87/17.37	691[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];691 -> 699[label="",style="solid", color="black", weight=3];
31.87/17.37	865[label="primModNatS (primMinusNatS (Succ ww820) ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];922[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];865 -> 922[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	922 -> 867[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	923[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];865 -> 923[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	923 -> 868[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	866[label="primModNatS (primMinusNatS Zero ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];924[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];866 -> 924[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	924 -> 869[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	925[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];866 -> 925[label="",style="solid", color="burlywood", weight=9];
31.87/17.37	925 -> 870[label="",style="solid", color="burlywood", weight=3];
31.87/17.37	696 -> 643[label="",style="dashed", color="red", weight=0];
31.87/17.37	696[label="primModNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww750 ww760)",fontsize=16,color="magenta"];696 -> 704[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	696 -> 705[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	697[label="primModNatS0 (Succ ww73) (Succ ww74) MyTrue",fontsize=16,color="black",shape="triangle"];697 -> 706[label="",style="solid", color="black", weight=3];
31.87/17.37	698[label="primModNatS0 (Succ ww73) (Succ ww74) MyFalse",fontsize=16,color="black",shape="box"];698 -> 707[label="",style="solid", color="black", weight=3];
31.87/17.37	699 -> 697[label="",style="dashed", color="red", weight=0];
31.87/17.37	699[label="primModNatS0 (Succ ww73) (Succ ww74) MyTrue",fontsize=16,color="magenta"];867[label="primModNatS (primMinusNatS (Succ ww820) (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];867 -> 871[label="",style="solid", color="black", weight=3];
31.87/17.37	868[label="primModNatS (primMinusNatS (Succ ww820) Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];868 -> 872[label="",style="solid", color="black", weight=3];
31.87/17.37	869[label="primModNatS (primMinusNatS Zero (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];869 -> 873[label="",style="solid", color="black", weight=3];
31.87/17.37	870[label="primModNatS (primMinusNatS Zero Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];870 -> 874[label="",style="solid", color="black", weight=3];
31.87/17.37	704[label="ww750",fontsize=16,color="green",shape="box"];705[label="ww760",fontsize=16,color="green",shape="box"];706 -> 834[label="",style="dashed", color="red", weight=0];
31.87/17.37	706[label="primModNatS (primMinusNatS (Succ ww73) (Succ (Succ ww74))) (Succ (Succ (Succ ww74)))",fontsize=16,color="magenta"];706 -> 847[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	706 -> 848[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	706 -> 849[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	707[label="Succ (Succ ww73)",fontsize=16,color="green",shape="box"];871 -> 834[label="",style="dashed", color="red", weight=0];
31.87/17.37	871[label="primModNatS (primMinusNatS ww820 ww830) (Succ ww84)",fontsize=16,color="magenta"];871 -> 875[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	871 -> 876[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	872 -> 89[label="",style="dashed", color="red", weight=0];
31.87/17.37	872[label="primModNatS (Succ ww820) (Succ ww84)",fontsize=16,color="magenta"];872 -> 877[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	872 -> 878[label="",style="dashed", color="magenta", weight=3];
31.87/17.37	873[label="primModNatS Zero (Succ ww84)",fontsize=16,color="black",shape="triangle"];873 -> 879[label="",style="solid", color="black", weight=3];
31.87/17.37	874 -> 873[label="",style="dashed", color="red", weight=0];
31.87/17.37	874[label="primModNatS Zero (Succ ww84)",fontsize=16,color="magenta"];847[label="Succ (Succ ww74)",fontsize=16,color="green",shape="box"];848[label="Succ (Succ ww74)",fontsize=16,color="green",shape="box"];849[label="Succ ww73",fontsize=16,color="green",shape="box"];875[label="ww830",fontsize=16,color="green",shape="box"];876[label="ww820",fontsize=16,color="green",shape="box"];877[label="ww84",fontsize=16,color="green",shape="box"];878[label="ww820",fontsize=16,color="green",shape="box"];879[label="Zero",fontsize=16,color="green",shape="box"];}
31.87/17.37	
31.87/17.37	----------------------------------------
31.87/17.37	
31.87/17.37	(60)
31.87/17.37	TRUE
31.90/17.40	EOF