28.63/15.46	MAYBE
30.98/16.07	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
30.98/16.07	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
30.98/16.07	
30.98/16.07	
30.98/16.07	H-Termination with start terms of the given HASKELL could not be shown:
30.98/16.07	
30.98/16.07	(0) HASKELL
30.98/16.07	(1) BR [EQUIVALENT, 0 ms]
30.98/16.07	(2) HASKELL
30.98/16.07	(3) COR [EQUIVALENT, 0 ms]
30.98/16.07	(4) HASKELL
30.98/16.07	(5) Narrow [SOUND, 0 ms]
30.98/16.07	(6) AND
30.98/16.07	    (7) QDP
30.98/16.07	        (8) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	        (9) QDP
30.98/16.07	        (10) TransformationProof [EQUIVALENT, 0 ms]
30.98/16.07	        (11) QDP
30.98/16.07	        (12) UsableRulesProof [EQUIVALENT, 0 ms]
30.98/16.07	        (13) QDP
30.98/16.07	        (14) QReductionProof [EQUIVALENT, 0 ms]
30.98/16.07	        (15) QDP
30.98/16.07	        (16) MNOCProof [EQUIVALENT, 0 ms]
30.98/16.07	        (17) QDP
30.98/16.07	        (18) InductionCalculusProof [EQUIVALENT, 0 ms]
30.98/16.07	        (19) QDP
30.98/16.07	        (20) TransformationProof [EQUIVALENT, 0 ms]
30.98/16.07	        (21) QDP
30.98/16.07	            (22) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	            (23) QDP
30.98/16.07	            (24) TransformationProof [EQUIVALENT, 0 ms]
30.98/16.07	            (25) QDP
30.98/16.07	            (26) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	            (27) QDP
30.98/16.07	            (28) TransformationProof [EQUIVALENT, 0 ms]
30.98/16.07	            (29) QDP
30.98/16.07	            (30) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	            (31) QDP
30.98/16.07	            (32) TransformationProof [EQUIVALENT, 0 ms]
30.98/16.07	            (33) QDP
30.98/16.07	            (34) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	            (35) QDP
30.98/16.07	            (36) MNOCProof [EQUIVALENT, 0 ms]
30.98/16.07	            (37) QDP
30.98/16.07	            (38) InductionCalculusProof [EQUIVALENT, 0 ms]
30.98/16.07	            (39) QDP
30.98/16.07	    (40) QDP
30.98/16.07	        (41) QDPOrderProof [EQUIVALENT, 6 ms]
30.98/16.07	        (42) QDP
30.98/16.07	        (43) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	        (44) QDP
30.98/16.07	        (45) QDPSizeChangeProof [EQUIVALENT, 0 ms]
30.98/16.07	        (46) YES
30.98/16.07	    (47) QDP
30.98/16.07	        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	        (49) QDP
30.98/16.07	        (50) QDPOrderProof [EQUIVALENT, 0 ms]
30.98/16.07	        (51) QDP
30.98/16.07	        (52) DependencyGraphProof [EQUIVALENT, 0 ms]
30.98/16.07	        (53) QDP
30.98/16.07	        (54) QDPSizeChangeProof [EQUIVALENT, 0 ms]
30.98/16.07	        (55) YES
30.98/16.07	    (56) QDP
30.98/16.07	        (57) QDPSizeChangeProof [EQUIVALENT, 0 ms]
30.98/16.07	        (58) YES
30.98/16.07	(59) Narrow [COMPLETE, 0 ms]
30.98/16.07	(60) TRUE
30.98/16.07	
30.98/16.07	
30.98/16.07	----------------------------------------
30.98/16.07	
30.98/16.07	(0)
30.98/16.07	Obligation:
30.98/16.07	mainModule Main 
30.98/16.07	module Main where {
30.98/16.07	import qualified Prelude;
30.98/16.07	data Main.Char = Char MyInt ;
30.98/16.07	
30.98/16.07	data List a = Cons a (List a)  | Nil ;
30.98/16.07	
30.98/16.07	data MyBool = MyTrue  | MyFalse ;
30.98/16.07	
30.98/16.07	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
30.98/16.07	
30.98/16.07	data Main.Nat = Succ Main.Nat  | Zero ;
30.98/16.07	
30.98/16.07	divMyInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	divMyInt = primDivInt;
30.98/16.07	
30.98/16.07	error :: a;
30.98/16.07	error = stop MyTrue;
30.98/16.07	
30.98/16.07	modMyInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	modMyInt = primModInt;
30.98/16.07	
30.98/16.07	primDivInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	primDivInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
30.98/16.07	primDivInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
30.98/16.07	primDivInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
30.98/16.07	primDivInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
30.98/16.07	primDivInt vw vx = Main.error;
30.98/16.07	
30.98/16.07	primDivNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primDivNatP Main.Zero Main.Zero = Main.error;
30.98/16.07	primDivNatP (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primDivNatP (Main.Succ x) (Main.Succ y) = Main.Succ (primDivNatP (primMinusNatS x y) (Main.Succ y));
30.98/16.07	primDivNatP Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	
30.98/16.07	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primDivNatS Main.Zero Main.Zero = Main.error;
30.98/16.07	primDivNatS (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
30.98/16.07	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	
30.98/16.07	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
30.98/16.07	primDivNatS0 x y MyFalse = Main.Zero;
30.98/16.07	
30.98/16.07	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
30.98/16.07	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
30.98/16.07	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
30.98/16.07	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
30.98/16.07	primGEqNatS Main.Zero Main.Zero = MyTrue;
30.98/16.07	
30.98/16.07	primIntToChar :: MyInt  ->  Main.Char;
30.98/16.07	primIntToChar x = Main.Char x;
30.98/16.07	
30.98/16.07	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
30.98/16.07	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
30.98/16.07	primMinusNatS x Main.Zero = x;
30.98/16.07	
30.98/16.07	primModInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	primModInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
30.98/16.07	primModInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatP x (Main.Succ y));
30.98/16.07	primModInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatP x (Main.Succ y));
30.98/16.07	primModInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
30.98/16.07	primModInt vy vz = Main.error;
30.98/16.07	
30.98/16.07	primModNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primModNatP Main.Zero Main.Zero = Main.error;
30.98/16.07	primModNatP Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	primModNatP (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primModNatP (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
30.98/16.07	primModNatP (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatP0 x y (primGEqNatS x y);
30.98/16.07	
30.98/16.07	primModNatP0 x y MyTrue = primModNatP (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
30.98/16.07	primModNatP0 x y MyFalse = primMinusNatS (Main.Succ y) x;
30.98/16.07	
30.98/16.07	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primModNatS Main.Zero Main.Zero = Main.error;
30.98/16.07	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	primModNatS (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
30.98/16.07	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
30.98/16.07	
30.98/16.07	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
30.98/16.07	primModNatS0 x y MyFalse = Main.Succ x;
30.98/16.07	
30.98/16.07	primShowInt :: MyInt  ->  List Main.Char;
30.98/16.07	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;
30.98/16.07	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);
30.98/16.07	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));
30.98/16.07	
30.98/16.07	psPs :: List a  ->  List a  ->  List a;
30.98/16.07	psPs Nil ys = ys;
30.98/16.07	psPs (Cons x xs) ys = Cons x (psPs xs ys);
30.98/16.07	
30.98/16.07	showMyInt :: MyInt  ->  List Main.Char;
30.98/16.07	showMyInt = primShowInt;
30.98/16.07	
30.98/16.07	showsPrecMyInt :: MyInt  ->  MyInt  ->  List Main.Char  ->  List Main.Char;
30.98/16.07	showsPrecMyInt vv x s = psPs (showMyInt x) s;
30.98/16.07	
30.98/16.07	stop :: MyBool  ->  a;
30.98/16.07	stop MyFalse = stop MyFalse;
30.98/16.07	
30.98/16.07	toEnumChar :: MyInt  ->  Main.Char;
30.98/16.07	toEnumChar = primIntToChar;
30.98/16.07	
30.98/16.07	}
30.98/16.07	
30.98/16.07	----------------------------------------
30.98/16.07	
30.98/16.07	(1) BR (EQUIVALENT)
30.98/16.07	Replaced joker patterns by fresh variables and removed binding patterns.
30.98/16.07	----------------------------------------
30.98/16.07	
30.98/16.07	(2)
30.98/16.07	Obligation:
30.98/16.07	mainModule Main 
30.98/16.07	module Main where {
30.98/16.07	import qualified Prelude;
30.98/16.07	data Main.Char = Char MyInt ;
30.98/16.07	
30.98/16.07	data List a = Cons a (List a)  | Nil ;
30.98/16.07	
30.98/16.07	data MyBool = MyTrue  | MyFalse ;
30.98/16.07	
30.98/16.07	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
30.98/16.07	
30.98/16.07	data Main.Nat = Succ Main.Nat  | Zero ;
30.98/16.07	
30.98/16.07	divMyInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	divMyInt = primDivInt;
30.98/16.07	
30.98/16.07	error :: a;
30.98/16.07	error = stop MyTrue;
30.98/16.07	
30.98/16.07	modMyInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	modMyInt = primModInt;
30.98/16.07	
30.98/16.07	primDivInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	primDivInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
30.98/16.07	primDivInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
30.98/16.07	primDivInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
30.98/16.07	primDivInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
30.98/16.07	primDivInt vw vx = Main.error;
30.98/16.07	
30.98/16.07	primDivNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primDivNatP Main.Zero Main.Zero = Main.error;
30.98/16.07	primDivNatP (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primDivNatP (Main.Succ x) (Main.Succ y) = Main.Succ (primDivNatP (primMinusNatS x y) (Main.Succ y));
30.98/16.07	primDivNatP Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	
30.98/16.07	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primDivNatS Main.Zero Main.Zero = Main.error;
30.98/16.07	primDivNatS (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
30.98/16.07	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	
30.98/16.07	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
30.98/16.07	primDivNatS0 x y MyFalse = Main.Zero;
30.98/16.07	
30.98/16.07	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
30.98/16.07	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
30.98/16.07	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
30.98/16.07	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
30.98/16.07	primGEqNatS Main.Zero Main.Zero = MyTrue;
30.98/16.07	
30.98/16.07	primIntToChar :: MyInt  ->  Main.Char;
30.98/16.07	primIntToChar x = Main.Char x;
30.98/16.07	
30.98/16.07	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
30.98/16.07	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
30.98/16.07	primMinusNatS x Main.Zero = x;
30.98/16.07	
30.98/16.07	primModInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	primModInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
30.98/16.07	primModInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatP x (Main.Succ y));
30.98/16.07	primModInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatP x (Main.Succ y));
30.98/16.07	primModInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
30.98/16.07	primModInt vy vz = Main.error;
30.98/16.07	
30.98/16.07	primModNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primModNatP Main.Zero Main.Zero = Main.error;
30.98/16.07	primModNatP Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	primModNatP (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primModNatP (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
30.98/16.07	primModNatP (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatP0 x y (primGEqNatS x y);
30.98/16.07	
30.98/16.07	primModNatP0 x y MyTrue = primModNatP (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
30.98/16.07	primModNatP0 x y MyFalse = primMinusNatS (Main.Succ y) x;
30.98/16.07	
30.98/16.07	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primModNatS Main.Zero Main.Zero = Main.error;
30.98/16.07	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	primModNatS (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
30.98/16.07	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
30.98/16.07	
30.98/16.07	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
30.98/16.07	primModNatS0 x y MyFalse = Main.Succ x;
30.98/16.07	
30.98/16.07	primShowInt :: MyInt  ->  List Main.Char;
30.98/16.07	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;
30.98/16.07	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);
30.98/16.07	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));
30.98/16.07	
30.98/16.07	psPs :: List a  ->  List a  ->  List a;
30.98/16.07	psPs Nil ys = ys;
30.98/16.07	psPs (Cons x xs) ys = Cons x (psPs xs ys);
30.98/16.07	
30.98/16.07	showMyInt :: MyInt  ->  List Main.Char;
30.98/16.07	showMyInt = primShowInt;
30.98/16.07	
30.98/16.07	showsPrecMyInt :: MyInt  ->  MyInt  ->  List Main.Char  ->  List Main.Char;
30.98/16.07	showsPrecMyInt vv x s = psPs (showMyInt x) s;
30.98/16.07	
30.98/16.07	stop :: MyBool  ->  a;
30.98/16.07	stop MyFalse = stop MyFalse;
30.98/16.07	
30.98/16.07	toEnumChar :: MyInt  ->  Main.Char;
30.98/16.07	toEnumChar = primIntToChar;
30.98/16.07	
30.98/16.07	}
30.98/16.07	
30.98/16.07	----------------------------------------
30.98/16.07	
30.98/16.07	(3) COR (EQUIVALENT)
30.98/16.07	Cond Reductions:
30.98/16.07	The following Function with conditions
30.98/16.07	"undefined |Falseundefined;
30.98/16.07	"
30.98/16.07	is transformed to
30.98/16.07	"undefined  = undefined1;
30.98/16.07	"
30.98/16.07	"undefined0 True = undefined;
30.98/16.07	"
30.98/16.07	"undefined1  = undefined0 False;
30.98/16.07	"
30.98/16.07	
30.98/16.07	----------------------------------------
30.98/16.07	
30.98/16.07	(4)
30.98/16.07	Obligation:
30.98/16.07	mainModule Main 
30.98/16.07	module Main where {
30.98/16.07	import qualified Prelude;
30.98/16.07	data Main.Char = Char MyInt ;
30.98/16.07	
30.98/16.07	data List a = Cons a (List a)  | Nil ;
30.98/16.07	
30.98/16.07	data MyBool = MyTrue  | MyFalse ;
30.98/16.07	
30.98/16.07	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
30.98/16.07	
30.98/16.07	data Main.Nat = Succ Main.Nat  | Zero ;
30.98/16.07	
30.98/16.07	divMyInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	divMyInt = primDivInt;
30.98/16.07	
30.98/16.07	error :: a;
30.98/16.07	error = stop MyTrue;
30.98/16.07	
30.98/16.07	modMyInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	modMyInt = primModInt;
30.98/16.07	
30.98/16.07	primDivInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	primDivInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
30.98/16.07	primDivInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
30.98/16.07	primDivInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatP x (Main.Succ y));
30.98/16.07	primDivInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
30.98/16.07	primDivInt vw vx = Main.error;
30.98/16.07	
30.98/16.07	primDivNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primDivNatP Main.Zero Main.Zero = Main.error;
30.98/16.07	primDivNatP (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primDivNatP (Main.Succ x) (Main.Succ y) = Main.Succ (primDivNatP (primMinusNatS x y) (Main.Succ y));
30.98/16.07	primDivNatP Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	
30.98/16.07	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primDivNatS Main.Zero Main.Zero = Main.error;
30.98/16.07	primDivNatS (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
30.98/16.07	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	
30.98/16.07	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
30.98/16.07	primDivNatS0 x y MyFalse = Main.Zero;
30.98/16.07	
30.98/16.07	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
30.98/16.07	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
30.98/16.07	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
30.98/16.07	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
30.98/16.07	primGEqNatS Main.Zero Main.Zero = MyTrue;
30.98/16.07	
30.98/16.07	primIntToChar :: MyInt  ->  Main.Char;
30.98/16.07	primIntToChar x = Main.Char x;
30.98/16.07	
30.98/16.07	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
30.98/16.07	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
30.98/16.07	primMinusNatS x Main.Zero = x;
30.98/16.07	
30.98/16.07	primModInt :: MyInt  ->  MyInt  ->  MyInt;
30.98/16.07	primModInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
30.98/16.07	primModInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatP x (Main.Succ y));
30.98/16.07	primModInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatP x (Main.Succ y));
30.98/16.07	primModInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
30.98/16.07	primModInt vy vz = Main.error;
30.98/16.07	
30.98/16.07	primModNatP :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primModNatP Main.Zero Main.Zero = Main.error;
30.98/16.07	primModNatP Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	primModNatP (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primModNatP (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
30.98/16.07	primModNatP (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatP0 x y (primGEqNatS x y);
30.98/16.07	
30.98/16.07	primModNatP0 x y MyTrue = primModNatP (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
30.98/16.07	primModNatP0 x y MyFalse = primMinusNatS (Main.Succ y) x;
30.98/16.07	
30.98/16.07	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
30.98/16.07	primModNatS Main.Zero Main.Zero = Main.error;
30.98/16.07	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
30.98/16.07	primModNatS (Main.Succ x) Main.Zero = Main.error;
30.98/16.07	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
30.98/16.07	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
30.98/16.08	
30.98/16.08	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
30.98/16.08	primModNatS0 x y MyFalse = Main.Succ x;
30.98/16.08	
30.98/16.08	primShowInt :: MyInt  ->  List Main.Char;
30.98/16.08	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;
30.98/16.08	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);
30.98/16.08	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));
30.98/16.08	
30.98/16.08	psPs :: List a  ->  List a  ->  List a;
30.98/16.08	psPs Nil ys = ys;
30.98/16.08	psPs (Cons x xs) ys = Cons x (psPs xs ys);
30.98/16.08	
30.98/16.08	showMyInt :: MyInt  ->  List Main.Char;
30.98/16.08	showMyInt = primShowInt;
30.98/16.08	
30.98/16.08	showsPrecMyInt :: MyInt  ->  MyInt  ->  List Main.Char  ->  List Main.Char;
30.98/16.08	showsPrecMyInt vv x s = psPs (showMyInt x) s;
30.98/16.08	
30.98/16.08	stop :: MyBool  ->  a;
30.98/16.08	stop MyFalse = stop MyFalse;
30.98/16.08	
30.98/16.08	toEnumChar :: MyInt  ->  Main.Char;
30.98/16.08	toEnumChar = primIntToChar;
30.98/16.08	
30.98/16.08	}
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(5) Narrow (SOUND)
30.98/16.08	Haskell To QDPs
30.98/16.08	
30.98/16.08	digraph dp_graph {
30.98/16.08	node [outthreshold=100, inthreshold=100];1[label="showsPrecMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
30.98/16.08	3[label="showsPrecMyInt ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
30.98/16.08	4[label="showsPrecMyInt ww3 ww4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
30.98/16.08	5[label="showsPrecMyInt ww3 ww4 ww5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
30.98/16.08	6 -> 36[label="",style="dashed", color="red", weight=0];
30.98/16.08	6[label="psPs (showMyInt ww4) ww5",fontsize=16,color="magenta"];6 -> 37[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	6 -> 38[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	37[label="showMyInt ww4",fontsize=16,color="black",shape="box"];37 -> 52[label="",style="solid", color="black", weight=3];
30.98/16.08	38[label="ww5",fontsize=16,color="green",shape="box"];36[label="psPs ww22 ww21",fontsize=16,color="burlywood",shape="triangle"];904[label="ww22/Cons ww220 ww221",fontsize=10,color="white",style="solid",shape="box"];36 -> 904[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	904 -> 53[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	905[label="ww22/Nil",fontsize=10,color="white",style="solid",shape="box"];36 -> 905[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	905 -> 54[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	52[label="primShowInt ww4",fontsize=16,color="burlywood",shape="triangle"];906[label="ww4/Pos ww40",fontsize=10,color="white",style="solid",shape="box"];52 -> 906[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	906 -> 55[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	907[label="ww4/Neg ww40",fontsize=10,color="white",style="solid",shape="box"];52 -> 907[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	907 -> 56[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	53[label="psPs (Cons ww220 ww221) ww21",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
30.98/16.08	54[label="psPs Nil ww21",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
30.98/16.08	55[label="primShowInt (Pos ww40)",fontsize=16,color="burlywood",shape="box"];908[label="ww40/Succ ww400",fontsize=10,color="white",style="solid",shape="box"];55 -> 908[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	908 -> 59[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	909[label="ww40/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 909[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	909 -> 60[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	56[label="primShowInt (Neg ww40)",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3];
30.98/16.08	57[label="Cons ww220 (psPs ww221 ww21)",fontsize=16,color="green",shape="box"];57 -> 62[label="",style="dashed", color="green", weight=3];
30.98/16.08	58[label="ww21",fontsize=16,color="green",shape="box"];59[label="primShowInt (Pos (Succ ww400))",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
30.98/16.08	60[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
30.98/16.08	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 ww40))",fontsize=16,color="green",shape="box"];61 -> 65[label="",style="dashed", color="green", weight=3];
30.98/16.08	62 -> 36[label="",style="dashed", color="red", weight=0];
30.98/16.08	62[label="psPs ww221 ww21",fontsize=16,color="magenta"];62 -> 66[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	63 -> 36[label="",style="dashed", color="red", weight=0];
30.98/16.08	63[label="psPs (primShowInt (divMyInt (Pos (Succ ww400)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) (Cons (toEnumChar (modMyInt (Pos (Succ ww400)) (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];
30.98/16.08	63 -> 68[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	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];
30.98/16.08	65[label="primShowInt (Pos ww40)",fontsize=16,color="magenta"];65 -> 69[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	66[label="ww221",fontsize=16,color="green",shape="box"];67 -> 52[label="",style="dashed", color="red", weight=0];
30.98/16.08	67[label="primShowInt (divMyInt (Pos (Succ ww400)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))",fontsize=16,color="magenta"];67 -> 70[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	68[label="Cons (toEnumChar (modMyInt (Pos (Succ ww400)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) Nil",fontsize=16,color="green",shape="box"];68 -> 71[label="",style="dashed", color="green", weight=3];
30.98/16.08	69[label="Pos ww40",fontsize=16,color="green",shape="box"];70 -> 72[label="",style="dashed", color="red", weight=0];
30.98/16.08	70[label="divMyInt (Pos (Succ ww400)) (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];
30.98/16.08	70 -> 74[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	71 -> 75[label="",style="dashed", color="red", weight=0];
30.98/16.08	71[label="toEnumChar (modMyInt (Pos (Succ ww400)) (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];
30.98/16.08	71 -> 77[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	73[label="ww400",fontsize=16,color="green",shape="box"];74[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];72[label="divMyInt (Pos (Succ ww24)) (Pos (Succ ww25))",fontsize=16,color="black",shape="triangle"];72 -> 78[label="",style="solid", color="black", weight=3];
30.98/16.08	76[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];77[label="ww400",fontsize=16,color="green",shape="box"];75[label="toEnumChar (modMyInt (Pos (Succ ww27)) (Pos (Succ ww28)))",fontsize=16,color="black",shape="triangle"];75 -> 79[label="",style="solid", color="black", weight=3];
30.98/16.08	78[label="primDivInt (Pos (Succ ww24)) (Pos (Succ ww25))",fontsize=16,color="black",shape="box"];78 -> 80[label="",style="solid", color="black", weight=3];
30.98/16.08	79[label="primIntToChar (modMyInt (Pos (Succ ww27)) (Pos (Succ ww28)))",fontsize=16,color="black",shape="box"];79 -> 81[label="",style="solid", color="black", weight=3];
30.98/16.08	80[label="Pos (primDivNatS (Succ ww24) (Succ ww25))",fontsize=16,color="green",shape="box"];80 -> 82[label="",style="dashed", color="green", weight=3];
30.98/16.08	81[label="Char (modMyInt (Pos (Succ ww27)) (Pos (Succ ww28)))",fontsize=16,color="green",shape="box"];81 -> 83[label="",style="dashed", color="green", weight=3];
30.98/16.08	82[label="primDivNatS (Succ ww24) (Succ ww25)",fontsize=16,color="black",shape="triangle"];82 -> 84[label="",style="solid", color="black", weight=3];
30.98/16.08	83[label="modMyInt (Pos (Succ ww27)) (Pos (Succ ww28))",fontsize=16,color="black",shape="box"];83 -> 85[label="",style="solid", color="black", weight=3];
30.98/16.08	84[label="primDivNatS0 ww24 ww25 (primGEqNatS ww24 ww25)",fontsize=16,color="burlywood",shape="box"];910[label="ww24/Succ ww240",fontsize=10,color="white",style="solid",shape="box"];84 -> 910[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	910 -> 86[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	911[label="ww24/Zero",fontsize=10,color="white",style="solid",shape="box"];84 -> 911[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	911 -> 87[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	85[label="primModInt (Pos (Succ ww27)) (Pos (Succ ww28))",fontsize=16,color="black",shape="box"];85 -> 88[label="",style="solid", color="black", weight=3];
30.98/16.08	86[label="primDivNatS0 (Succ ww240) ww25 (primGEqNatS (Succ ww240) ww25)",fontsize=16,color="burlywood",shape="box"];912[label="ww25/Succ ww250",fontsize=10,color="white",style="solid",shape="box"];86 -> 912[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	912 -> 89[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	913[label="ww25/Zero",fontsize=10,color="white",style="solid",shape="box"];86 -> 913[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	913 -> 90[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	87[label="primDivNatS0 Zero ww25 (primGEqNatS Zero ww25)",fontsize=16,color="burlywood",shape="box"];914[label="ww25/Succ ww250",fontsize=10,color="white",style="solid",shape="box"];87 -> 914[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	914 -> 91[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	915[label="ww25/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 915[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	915 -> 92[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	88[label="Pos (primModNatS (Succ ww27) (Succ ww28))",fontsize=16,color="green",shape="box"];88 -> 93[label="",style="dashed", color="green", weight=3];
30.98/16.08	89[label="primDivNatS0 (Succ ww240) (Succ ww250) (primGEqNatS (Succ ww240) (Succ ww250))",fontsize=16,color="black",shape="box"];89 -> 94[label="",style="solid", color="black", weight=3];
30.98/16.08	90[label="primDivNatS0 (Succ ww240) Zero (primGEqNatS (Succ ww240) Zero)",fontsize=16,color="black",shape="box"];90 -> 95[label="",style="solid", color="black", weight=3];
30.98/16.08	91[label="primDivNatS0 Zero (Succ ww250) (primGEqNatS Zero (Succ ww250))",fontsize=16,color="black",shape="box"];91 -> 96[label="",style="solid", color="black", weight=3];
30.98/16.08	92[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];92 -> 97[label="",style="solid", color="black", weight=3];
30.98/16.08	93[label="primModNatS (Succ ww27) (Succ ww28)",fontsize=16,color="burlywood",shape="triangle"];916[label="ww28/Succ ww280",fontsize=10,color="white",style="solid",shape="box"];93 -> 916[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	916 -> 98[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	917[label="ww28/Zero",fontsize=10,color="white",style="solid",shape="box"];93 -> 917[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	917 -> 99[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	94 -> 509[label="",style="dashed", color="red", weight=0];
30.98/16.08	94[label="primDivNatS0 (Succ ww240) (Succ ww250) (primGEqNatS ww240 ww250)",fontsize=16,color="magenta"];94 -> 510[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	94 -> 511[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	94 -> 512[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	94 -> 513[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	95[label="primDivNatS0 (Succ ww240) Zero MyTrue",fontsize=16,color="black",shape="box"];95 -> 102[label="",style="solid", color="black", weight=3];
30.98/16.08	96[label="primDivNatS0 Zero (Succ ww250) MyFalse",fontsize=16,color="black",shape="box"];96 -> 103[label="",style="solid", color="black", weight=3];
30.98/16.08	97[label="primDivNatS0 Zero Zero MyTrue",fontsize=16,color="black",shape="box"];97 -> 104[label="",style="solid", color="black", weight=3];
30.98/16.08	98[label="primModNatS (Succ ww27) (Succ (Succ ww280))",fontsize=16,color="black",shape="box"];98 -> 105[label="",style="solid", color="black", weight=3];
30.98/16.08	99[label="primModNatS (Succ ww27) (Succ Zero)",fontsize=16,color="black",shape="box"];99 -> 106[label="",style="solid", color="black", weight=3];
30.98/16.08	510[label="ww250",fontsize=16,color="green",shape="box"];511[label="ww240",fontsize=16,color="green",shape="box"];512[label="ww240",fontsize=16,color="green",shape="box"];513[label="ww250",fontsize=16,color="green",shape="box"];509[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS ww68 ww69)",fontsize=16,color="burlywood",shape="triangle"];918[label="ww68/Succ ww680",fontsize=10,color="white",style="solid",shape="box"];509 -> 918[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	918 -> 550[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	919[label="ww68/Zero",fontsize=10,color="white",style="solid",shape="box"];509 -> 919[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	919 -> 551[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	102[label="Succ (primDivNatS (primMinusNatS (Succ ww240) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];102 -> 111[label="",style="dashed", color="green", weight=3];
30.98/16.08	103[label="Zero",fontsize=16,color="green",shape="box"];104[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];104 -> 112[label="",style="dashed", color="green", weight=3];
30.98/16.08	105[label="primModNatS0 ww27 ww280 (primGEqNatS ww27 (Succ ww280))",fontsize=16,color="burlywood",shape="box"];920[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];105 -> 920[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	920 -> 113[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	921[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];105 -> 921[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	921 -> 114[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	106[label="Zero",fontsize=16,color="green",shape="box"];550[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS (Succ ww680) ww69)",fontsize=16,color="burlywood",shape="box"];922[label="ww69/Succ ww690",fontsize=10,color="white",style="solid",shape="box"];550 -> 922[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	922 -> 574[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	923[label="ww69/Zero",fontsize=10,color="white",style="solid",shape="box"];550 -> 923[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	923 -> 575[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	551[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS Zero ww69)",fontsize=16,color="burlywood",shape="box"];924[label="ww69/Succ ww690",fontsize=10,color="white",style="solid",shape="box"];551 -> 924[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	924 -> 576[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	925[label="ww69/Zero",fontsize=10,color="white",style="solid",shape="box"];551 -> 925[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	925 -> 577[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	111 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	111[label="primDivNatS (primMinusNatS (Succ ww240) Zero) (Succ Zero)",fontsize=16,color="magenta"];111 -> 801[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	111 -> 802[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	111 -> 803[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	112 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	112[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];112 -> 804[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	112 -> 805[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	112 -> 806[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	113[label="primModNatS0 (Succ ww270) ww280 (primGEqNatS (Succ ww270) (Succ ww280))",fontsize=16,color="black",shape="box"];113 -> 121[label="",style="solid", color="black", weight=3];
30.98/16.08	114[label="primModNatS0 Zero ww280 (primGEqNatS Zero (Succ ww280))",fontsize=16,color="black",shape="box"];114 -> 122[label="",style="solid", color="black", weight=3];
30.98/16.08	574[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS (Succ ww680) (Succ ww690))",fontsize=16,color="black",shape="box"];574 -> 589[label="",style="solid", color="black", weight=3];
30.98/16.08	575[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS (Succ ww680) Zero)",fontsize=16,color="black",shape="box"];575 -> 590[label="",style="solid", color="black", weight=3];
30.98/16.08	576[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS Zero (Succ ww690))",fontsize=16,color="black",shape="box"];576 -> 591[label="",style="solid", color="black", weight=3];
30.98/16.08	577[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];577 -> 592[label="",style="solid", color="black", weight=3];
30.98/16.08	801[label="Zero",fontsize=16,color="green",shape="box"];802[label="Succ ww240",fontsize=16,color="green",shape="box"];803[label="Zero",fontsize=16,color="green",shape="box"];800[label="primDivNatS (primMinusNatS ww82 ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="triangle"];926[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];800 -> 926[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	926 -> 825[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	927[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];800 -> 927[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	927 -> 826[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	804[label="Zero",fontsize=16,color="green",shape="box"];805[label="Zero",fontsize=16,color="green",shape="box"];806[label="Zero",fontsize=16,color="green",shape="box"];121[label="primModNatS0 (Succ ww270) ww280 (primGEqNatS ww270 ww280)",fontsize=16,color="burlywood",shape="box"];928[label="ww270/Succ ww2700",fontsize=10,color="white",style="solid",shape="box"];121 -> 928[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	928 -> 131[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	929[label="ww270/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 929[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	929 -> 132[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	122[label="primModNatS0 Zero ww280 MyFalse",fontsize=16,color="black",shape="box"];122 -> 133[label="",style="solid", color="black", weight=3];
30.98/16.08	589 -> 509[label="",style="dashed", color="red", weight=0];
30.98/16.08	589[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS ww680 ww690)",fontsize=16,color="magenta"];589 -> 604[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	589 -> 605[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	590[label="primDivNatS0 (Succ ww66) (Succ ww67) MyTrue",fontsize=16,color="black",shape="triangle"];590 -> 606[label="",style="solid", color="black", weight=3];
30.98/16.08	591[label="primDivNatS0 (Succ ww66) (Succ ww67) MyFalse",fontsize=16,color="black",shape="box"];591 -> 607[label="",style="solid", color="black", weight=3];
30.98/16.08	592 -> 590[label="",style="dashed", color="red", weight=0];
30.98/16.08	592[label="primDivNatS0 (Succ ww66) (Succ ww67) MyTrue",fontsize=16,color="magenta"];825[label="primDivNatS (primMinusNatS (Succ ww820) ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];930[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];825 -> 930[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	930 -> 831[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	931[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];825 -> 931[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	931 -> 832[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	826[label="primDivNatS (primMinusNatS Zero ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];932[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];826 -> 932[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	932 -> 833[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	933[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];826 -> 933[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	933 -> 834[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	131[label="primModNatS0 (Succ (Succ ww2700)) ww280 (primGEqNatS (Succ ww2700) ww280)",fontsize=16,color="burlywood",shape="box"];934[label="ww280/Succ ww2800",fontsize=10,color="white",style="solid",shape="box"];131 -> 934[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	934 -> 140[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	935[label="ww280/Zero",fontsize=10,color="white",style="solid",shape="box"];131 -> 935[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	935 -> 141[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	132[label="primModNatS0 (Succ Zero) ww280 (primGEqNatS Zero ww280)",fontsize=16,color="burlywood",shape="box"];936[label="ww280/Succ ww2800",fontsize=10,color="white",style="solid",shape="box"];132 -> 936[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	936 -> 142[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	937[label="ww280/Zero",fontsize=10,color="white",style="solid",shape="box"];132 -> 937[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	937 -> 143[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	133[label="Succ Zero",fontsize=16,color="green",shape="box"];604[label="ww680",fontsize=16,color="green",shape="box"];605[label="ww690",fontsize=16,color="green",shape="box"];606[label="Succ (primDivNatS (primMinusNatS (Succ ww66) (Succ ww67)) (Succ (Succ ww67)))",fontsize=16,color="green",shape="box"];606 -> 650[label="",style="dashed", color="green", weight=3];
30.98/16.08	607[label="Zero",fontsize=16,color="green",shape="box"];831[label="primDivNatS (primMinusNatS (Succ ww820) (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];831 -> 841[label="",style="solid", color="black", weight=3];
30.98/16.08	832[label="primDivNatS (primMinusNatS (Succ ww820) Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];832 -> 842[label="",style="solid", color="black", weight=3];
30.98/16.08	833[label="primDivNatS (primMinusNatS Zero (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];833 -> 843[label="",style="solid", color="black", weight=3];
30.98/16.08	834[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];834 -> 844[label="",style="solid", color="black", weight=3];
30.98/16.08	140[label="primModNatS0 (Succ (Succ ww2700)) (Succ ww2800) (primGEqNatS (Succ ww2700) (Succ ww2800))",fontsize=16,color="black",shape="box"];140 -> 150[label="",style="solid", color="black", weight=3];
30.98/16.08	141[label="primModNatS0 (Succ (Succ ww2700)) Zero (primGEqNatS (Succ ww2700) Zero)",fontsize=16,color="black",shape="box"];141 -> 151[label="",style="solid", color="black", weight=3];
30.98/16.08	142[label="primModNatS0 (Succ Zero) (Succ ww2800) (primGEqNatS Zero (Succ ww2800))",fontsize=16,color="black",shape="box"];142 -> 152[label="",style="solid", color="black", weight=3];
30.98/16.08	143[label="primModNatS0 (Succ Zero) Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];143 -> 153[label="",style="solid", color="black", weight=3];
30.98/16.08	650 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	650[label="primDivNatS (primMinusNatS (Succ ww66) (Succ ww67)) (Succ (Succ ww67))",fontsize=16,color="magenta"];650 -> 807[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	650 -> 808[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	650 -> 809[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	841 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	841[label="primDivNatS (primMinusNatS ww820 ww830) (Succ ww84)",fontsize=16,color="magenta"];841 -> 849[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	841 -> 850[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	842 -> 82[label="",style="dashed", color="red", weight=0];
30.98/16.08	842[label="primDivNatS (Succ ww820) (Succ ww84)",fontsize=16,color="magenta"];842 -> 851[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	842 -> 852[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	843[label="primDivNatS Zero (Succ ww84)",fontsize=16,color="black",shape="triangle"];843 -> 853[label="",style="solid", color="black", weight=3];
30.98/16.08	844 -> 843[label="",style="dashed", color="red", weight=0];
30.98/16.08	844[label="primDivNatS Zero (Succ ww84)",fontsize=16,color="magenta"];150 -> 668[label="",style="dashed", color="red", weight=0];
30.98/16.08	150[label="primModNatS0 (Succ (Succ ww2700)) (Succ ww2800) (primGEqNatS ww2700 ww2800)",fontsize=16,color="magenta"];150 -> 669[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	150 -> 670[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	150 -> 671[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	150 -> 672[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	151[label="primModNatS0 (Succ (Succ ww2700)) Zero MyTrue",fontsize=16,color="black",shape="box"];151 -> 163[label="",style="solid", color="black", weight=3];
30.98/16.08	152 -> 555[label="",style="dashed", color="red", weight=0];
30.98/16.08	152[label="primModNatS0 (Succ Zero) (Succ ww2800) MyFalse",fontsize=16,color="magenta"];152 -> 556[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	152 -> 557[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	153[label="primModNatS0 (Succ Zero) Zero MyTrue",fontsize=16,color="black",shape="box"];153 -> 165[label="",style="solid", color="black", weight=3];
30.98/16.08	807[label="Succ ww67",fontsize=16,color="green",shape="box"];808[label="Succ ww66",fontsize=16,color="green",shape="box"];809[label="Succ ww67",fontsize=16,color="green",shape="box"];849[label="ww830",fontsize=16,color="green",shape="box"];850[label="ww820",fontsize=16,color="green",shape="box"];851[label="ww820",fontsize=16,color="green",shape="box"];852[label="ww84",fontsize=16,color="green",shape="box"];853[label="Zero",fontsize=16,color="green",shape="box"];669[label="ww2800",fontsize=16,color="green",shape="box"];670[label="ww2700",fontsize=16,color="green",shape="box"];671[label="Succ ww2700",fontsize=16,color="green",shape="box"];672[label="ww2800",fontsize=16,color="green",shape="box"];668[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS ww79 ww80)",fontsize=16,color="burlywood",shape="triangle"];938[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];668 -> 938[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	938 -> 709[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	939[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];668 -> 939[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	939 -> 710[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	163 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	163[label="primModNatS (primMinusNatS (Succ (Succ ww2700)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];163 -> 859[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	163 -> 860[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	163 -> 861[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	556[label="Zero",fontsize=16,color="green",shape="box"];557[label="ww2800",fontsize=16,color="green",shape="box"];555[label="primModNatS0 (Succ ww71) (Succ ww72) MyFalse",fontsize=16,color="black",shape="triangle"];555 -> 578[label="",style="solid", color="black", weight=3];
30.98/16.08	165 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	165[label="primModNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];165 -> 862[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	165 -> 863[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	165 -> 864[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	709[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS (Succ ww790) ww80)",fontsize=16,color="burlywood",shape="box"];940[label="ww80/Succ ww800",fontsize=10,color="white",style="solid",shape="box"];709 -> 940[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	940 -> 715[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	941[label="ww80/Zero",fontsize=10,color="white",style="solid",shape="box"];709 -> 941[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	941 -> 716[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	710[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS Zero ww80)",fontsize=16,color="burlywood",shape="box"];942[label="ww80/Succ ww800",fontsize=10,color="white",style="solid",shape="box"];710 -> 942[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	942 -> 717[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	943[label="ww80/Zero",fontsize=10,color="white",style="solid",shape="box"];710 -> 943[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	943 -> 718[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	859[label="Succ Zero",fontsize=16,color="green",shape="box"];860[label="Succ Zero",fontsize=16,color="green",shape="box"];861[label="Succ (Succ ww2700)",fontsize=16,color="green",shape="box"];858[label="primModNatS (primMinusNatS ww86 ww87) (Succ ww88)",fontsize=16,color="burlywood",shape="triangle"];944[label="ww86/Succ ww860",fontsize=10,color="white",style="solid",shape="box"];858 -> 944[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	944 -> 889[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	945[label="ww86/Zero",fontsize=10,color="white",style="solid",shape="box"];858 -> 945[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	945 -> 890[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	578[label="Succ (Succ ww71)",fontsize=16,color="green",shape="box"];862[label="Succ Zero",fontsize=16,color="green",shape="box"];863[label="Succ Zero",fontsize=16,color="green",shape="box"];864[label="Succ Zero",fontsize=16,color="green",shape="box"];715[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS (Succ ww790) (Succ ww800))",fontsize=16,color="black",shape="box"];715 -> 723[label="",style="solid", color="black", weight=3];
30.98/16.08	716[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS (Succ ww790) Zero)",fontsize=16,color="black",shape="box"];716 -> 724[label="",style="solid", color="black", weight=3];
30.98/16.08	717[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS Zero (Succ ww800))",fontsize=16,color="black",shape="box"];717 -> 725[label="",style="solid", color="black", weight=3];
30.98/16.08	718[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];718 -> 726[label="",style="solid", color="black", weight=3];
30.98/16.08	889[label="primModNatS (primMinusNatS (Succ ww860) ww87) (Succ ww88)",fontsize=16,color="burlywood",shape="box"];946[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];889 -> 946[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	946 -> 891[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	947[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];889 -> 947[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	947 -> 892[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	890[label="primModNatS (primMinusNatS Zero ww87) (Succ ww88)",fontsize=16,color="burlywood",shape="box"];948[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];890 -> 948[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	948 -> 893[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	949[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];890 -> 949[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	949 -> 894[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	723 -> 668[label="",style="dashed", color="red", weight=0];
30.98/16.08	723[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS ww790 ww800)",fontsize=16,color="magenta"];723 -> 733[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	723 -> 734[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	724[label="primModNatS0 (Succ ww77) (Succ ww78) MyTrue",fontsize=16,color="black",shape="triangle"];724 -> 735[label="",style="solid", color="black", weight=3];
30.98/16.08	725 -> 555[label="",style="dashed", color="red", weight=0];
30.98/16.08	725[label="primModNatS0 (Succ ww77) (Succ ww78) MyFalse",fontsize=16,color="magenta"];725 -> 736[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	725 -> 737[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	726 -> 724[label="",style="dashed", color="red", weight=0];
30.98/16.08	726[label="primModNatS0 (Succ ww77) (Succ ww78) MyTrue",fontsize=16,color="magenta"];891[label="primModNatS (primMinusNatS (Succ ww860) (Succ ww870)) (Succ ww88)",fontsize=16,color="black",shape="box"];891 -> 895[label="",style="solid", color="black", weight=3];
30.98/16.08	892[label="primModNatS (primMinusNatS (Succ ww860) Zero) (Succ ww88)",fontsize=16,color="black",shape="box"];892 -> 896[label="",style="solid", color="black", weight=3];
30.98/16.08	893[label="primModNatS (primMinusNatS Zero (Succ ww870)) (Succ ww88)",fontsize=16,color="black",shape="box"];893 -> 897[label="",style="solid", color="black", weight=3];
30.98/16.08	894[label="primModNatS (primMinusNatS Zero Zero) (Succ ww88)",fontsize=16,color="black",shape="box"];894 -> 898[label="",style="solid", color="black", weight=3];
30.98/16.08	733[label="ww790",fontsize=16,color="green",shape="box"];734[label="ww800",fontsize=16,color="green",shape="box"];735 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	735[label="primModNatS (primMinusNatS (Succ ww77) (Succ (Succ ww78))) (Succ (Succ (Succ ww78)))",fontsize=16,color="magenta"];735 -> 871[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	735 -> 872[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	735 -> 873[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	736[label="ww77",fontsize=16,color="green",shape="box"];737[label="ww78",fontsize=16,color="green",shape="box"];895 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	895[label="primModNatS (primMinusNatS ww860 ww870) (Succ ww88)",fontsize=16,color="magenta"];895 -> 899[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	895 -> 900[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	896 -> 93[label="",style="dashed", color="red", weight=0];
30.98/16.08	896[label="primModNatS (Succ ww860) (Succ ww88)",fontsize=16,color="magenta"];896 -> 901[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	896 -> 902[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	897[label="primModNatS Zero (Succ ww88)",fontsize=16,color="black",shape="triangle"];897 -> 903[label="",style="solid", color="black", weight=3];
30.98/16.08	898 -> 897[label="",style="dashed", color="red", weight=0];
30.98/16.08	898[label="primModNatS Zero (Succ ww88)",fontsize=16,color="magenta"];871[label="Succ (Succ ww78)",fontsize=16,color="green",shape="box"];872[label="Succ (Succ ww78)",fontsize=16,color="green",shape="box"];873[label="Succ ww77",fontsize=16,color="green",shape="box"];899[label="ww870",fontsize=16,color="green",shape="box"];900[label="ww860",fontsize=16,color="green",shape="box"];901[label="ww88",fontsize=16,color="green",shape="box"];902[label="ww860",fontsize=16,color="green",shape="box"];903[label="Zero",fontsize=16,color="green",shape="box"];}
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(6)
30.98/16.08	Complex Obligation (AND)
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(7)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primShowInt(Main.Neg(ww40)) -> new_primShowInt(Main.Pos(ww40))
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(new_divMyInt(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_divMyInt(ww24, ww25) -> Main.Pos(new_primDivNatS3(ww24, ww25))
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_divMyInt(x0, x1)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(8) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(9)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(new_divMyInt(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_divMyInt(ww24, ww25) -> Main.Pos(new_primDivNatS3(ww24, ww25))
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_divMyInt(x0, x1)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(10) TransformationProof (EQUIVALENT)
30.98/16.08	By rewriting [LPAR04] the rule new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(new_divMyInt(ww400, 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]:
30.98/16.08	
30.98/16.08	   (new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, 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(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(11)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_divMyInt(ww24, ww25) -> Main.Pos(new_primDivNatS3(ww24, ww25))
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_divMyInt(x0, x1)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(12) UsableRulesProof (EQUIVALENT)
30.98/16.08	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.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(13)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_divMyInt(x0, x1)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(14) QReductionProof (EQUIVALENT)
30.98/16.08	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
30.98/16.08	
30.98/16.08	   new_divMyInt(x0, x1)
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(15)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(16) MNOCProof (EQUIVALENT)
30.98/16.08	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(17)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(18) InductionCalculusProof (EQUIVALENT)
30.98/16.08	Note that final constraints are written in bold face.
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	For Pair new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, 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:
30.98/16.08	*We consider the chain new_primShowInt(Main.Pos(Main.Succ(x0))) -> new_primShowInt(Main.Pos(new_primDivNatS3(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_primDivNatS3(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:
30.98/16.08	
30.98/16.08	(1)    (new_primShowInt(Main.Pos(new_primDivNatS3(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_primDivNatS3(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
30.98/16.08	
30.98/16.08	(2)    (Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))=x2 & new_primDivNatS3(x0, x2)=Main.Succ(x1)  ==>  new_primShowInt(Main.Pos(Main.Succ(x0)))_>=_new_primShowInt(Main.Pos(new_primDivNatS3(x0, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS3(x0, x2)=Main.Succ(x1) which results in the following new constraints:
30.98/16.08	
30.98/16.08	(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_primDivNatS3(Main.Succ(x4), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	(4)    (Main.Succ(new_primDivNatS2(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_primDivNatS3(Main.Succ(x6), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	(5)    (Main.Succ(new_primDivNatS2(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_primDivNatS3(Main.Zero, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
30.98/16.08	
30.98/16.08	(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_primDivNatS3(Main.Succ(x4), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	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:
30.98/16.08	
30.98/16.08	(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_primDivNatS3(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_primDivNatS3(Main.Succ(x12), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	(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_primDivNatS3(Main.Succ(x15), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	(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_primDivNatS3(Main.Succ(x21), Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We simplified constraint (7) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
30.98/16.08	
30.98/16.08	(10)    (new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x10)))))_>=_new_primShowInt(Main.Pos(new_primDivNatS3(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)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We solved constraint (8) using rules (I), (II), (III).We solved constraint (9) using rules (I), (II), (III).
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	To summarize, we get the following constraints P__>=_ for the following pairs.
30.98/16.08	
30.98/16.08	*new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
30.98/16.08	
30.98/16.08	*(new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(x10)))))_>=_new_primShowInt(Main.Pos(new_primDivNatS3(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)))))))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	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. 
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(19)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(20) TransformationProof (EQUIVALENT)
30.98/16.08	By narrowing [LPAR04] the rule new_primShowInt(Main.Pos(Main.Succ(ww400))) -> new_primShowInt(Main.Pos(new_primDivNatS3(ww400, 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]:
30.98/16.08	
30.98/16.08	   (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))))))))))))
30.98/16.08	   (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)))
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(21)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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)))))))))))
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(Main.Zero))) -> new_primShowInt(Main.Pos(Main.Zero))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(22) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(23)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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)))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(24) TransformationProof (EQUIVALENT)
30.98/16.08	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]:
30.98/16.08	
30.98/16.08	   (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)))))))))))
30.98/16.08	   (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)))
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(25)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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))))))))))
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Zero)))) -> new_primShowInt(Main.Pos(Main.Zero))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(26) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(27)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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))))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(28) TransformationProof (EQUIVALENT)
30.98/16.08	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]:
30.98/16.08	
30.98/16.08	   (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))))))))))
30.98/16.08	   (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)))
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(29)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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)))))))))
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Zero))))) -> new_primShowInt(Main.Pos(Main.Zero))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(30) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(31)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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)))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(32) TransformationProof (EQUIVALENT)
30.98/16.08	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]:
30.98/16.08	
30.98/16.08	   (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)))))))))
30.98/16.08	   (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)))
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(33)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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))))))))
30.98/16.08	   new_primShowInt(Main.Pos(Main.Succ(Main.Succ(Main.Succ(Main.Succ(Main.Zero)))))) -> new_primShowInt(Main.Pos(Main.Zero))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(34) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(35)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(36) MNOCProof (EQUIVALENT)
30.98/16.08	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(37)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(38) InductionCalculusProof (EQUIVALENT)
30.98/16.08	Note that final constraints are written in bold face.
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	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:
30.98/16.08	*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:
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	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:
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	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:
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We simplified constraint (7) using rules (I), (II), (III), (IV) which results in the following new constraint:
30.98/16.08	
30.98/16.08	(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)))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II).
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	To summarize, we get the following constraints P__>=_ for the following pairs.
30.98/16.08	
30.98/16.08	*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))))))))
30.98/16.08	
30.98/16.08	*(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)))))))))
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	
30.98/16.08	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. 
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(39)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   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))))))))
30.98/16.08	
30.98/16.08	The TRS R consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS01(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(ww250)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS01(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Zero, Main.Succ(ww690)) -> Main.Zero
30.98/16.08	   new_primDivNatS01(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS02(ww66, ww67)
30.98/16.08	   new_primDivNatS02(ww66, ww67) -> Main.Succ(new_primDivNatS2(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67)))
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS2(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(ww830), ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, ww84) -> new_primDivNatS4(ww84)
30.98/16.08	   new_primDivNatS2(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS3(ww820, ww84)
30.98/16.08	   new_primDivNatS3(Main.Succ(ww240), Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Succ(ww240), Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero) -> Main.Succ(new_primDivNatS2(Main.Zero, Main.Zero, Main.Zero))
30.98/16.08	   new_primDivNatS4(ww84) -> Main.Zero
30.98/16.08	
30.98/16.08	The set Q consists of the following terms:
30.98/16.08	
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Succ(x2))
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Succ(x1), x2)
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Succ(x0), x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Succ(x0))
30.98/16.08	   new_primDivNatS2(Main.Zero, Main.Zero, x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Zero)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Succ(x3))
30.98/16.08	   new_primDivNatS02(x0, x1)
30.98/16.08	   new_primDivNatS3(Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS2(Main.Succ(x0), Main.Zero, x1)
30.98/16.08	   new_primDivNatS01(x0, x1, Main.Succ(x2), Main.Zero)
30.98/16.08	   new_primDivNatS4(x0)
30.98/16.08	   new_primDivNatS3(Main.Succ(x0), Main.Succ(x1))
30.98/16.08	
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(40)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primModNatS0(ww77, ww78, Main.Zero, Main.Zero) -> new_primModNatS00(ww77, ww78)
30.98/16.08	   new_primModNatS1(Main.Succ(Main.Succ(ww2700)), Main.Succ(Main.Succ(ww2800))) -> new_primModNatS0(Main.Succ(ww2700), ww2800, ww2700, ww2800)
30.98/16.08	   new_primModNatS1(Main.Succ(Main.Zero), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Zero), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
30.98/16.08	   new_primModNatS0(ww77, ww78, Main.Succ(ww790), Main.Succ(ww800)) -> new_primModNatS0(ww77, ww78, ww790, ww800)
30.98/16.08	   new_primModNatS(Main.Succ(ww860), Main.Succ(ww870), ww88) -> new_primModNatS(ww860, ww870, ww88)
30.98/16.08	   new_primModNatS(Main.Succ(ww860), Main.Zero, ww88) -> new_primModNatS1(ww860, ww88)
30.98/16.08	   new_primModNatS0(ww77, ww78, Main.Succ(ww790), Main.Zero) -> new_primModNatS(Main.Succ(ww77), Main.Succ(Main.Succ(ww78)), Main.Succ(Main.Succ(ww78)))
30.98/16.08	   new_primModNatS1(Main.Succ(Main.Succ(ww2700)), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Succ(ww2700)), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
30.98/16.08	   new_primModNatS00(ww77, ww78) -> new_primModNatS(Main.Succ(ww77), Main.Succ(Main.Succ(ww78)), Main.Succ(Main.Succ(ww78)))
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(41) QDPOrderProof (EQUIVALENT)
30.98/16.08	We use the reduction pair processor [LPAR04,JAR06].
30.98/16.08	
30.98/16.08	
30.98/16.08	The following pairs can be oriented strictly and are deleted.
30.98/16.08	
30.98/16.08	   new_primModNatS(Main.Succ(ww860), Main.Succ(ww870), ww88) -> new_primModNatS(ww860, ww870, ww88)
30.98/16.08	   new_primModNatS(Main.Succ(ww860), Main.Zero, ww88) -> new_primModNatS1(ww860, ww88)
30.98/16.08	The remaining pairs can at least be oriented weakly.
30.98/16.08	Used ordering:  Polynomial interpretation [POLO]:
30.98/16.08	
30.98/16.08	   POL(Main.Succ(x_1)) = 1 + x_1
30.98/16.08	   POL(Main.Zero) = 0
30.98/16.08	   POL(new_primModNatS(x_1, x_2, x_3)) = x_1
30.98/16.08	   POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
30.98/16.08	   POL(new_primModNatS00(x_1, x_2)) = 1 + x_1
30.98/16.08	   POL(new_primModNatS1(x_1, x_2)) = x_1
30.98/16.08	
30.98/16.08	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
30.98/16.08	none
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(42)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primModNatS0(ww77, ww78, Main.Zero, Main.Zero) -> new_primModNatS00(ww77, ww78)
30.98/16.08	   new_primModNatS1(Main.Succ(Main.Succ(ww2700)), Main.Succ(Main.Succ(ww2800))) -> new_primModNatS0(Main.Succ(ww2700), ww2800, ww2700, ww2800)
30.98/16.08	   new_primModNatS1(Main.Succ(Main.Zero), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Zero), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
30.98/16.08	   new_primModNatS0(ww77, ww78, Main.Succ(ww790), Main.Succ(ww800)) -> new_primModNatS0(ww77, ww78, ww790, ww800)
30.98/16.08	   new_primModNatS0(ww77, ww78, Main.Succ(ww790), Main.Zero) -> new_primModNatS(Main.Succ(ww77), Main.Succ(Main.Succ(ww78)), Main.Succ(Main.Succ(ww78)))
30.98/16.08	   new_primModNatS1(Main.Succ(Main.Succ(ww2700)), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(Main.Succ(ww2700)), Main.Succ(Main.Zero), Main.Succ(Main.Zero))
30.98/16.08	   new_primModNatS00(ww77, ww78) -> new_primModNatS(Main.Succ(ww77), Main.Succ(Main.Succ(ww78)), Main.Succ(Main.Succ(ww78)))
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(43) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 6 less nodes.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(44)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primModNatS0(ww77, ww78, Main.Succ(ww790), Main.Succ(ww800)) -> new_primModNatS0(ww77, ww78, ww790, ww800)
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(45) QDPSizeChangeProof (EQUIVALENT)
30.98/16.08	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. 
30.98/16.08	
30.98/16.08	From the DPs we obtained the following set of size-change graphs:
30.98/16.08	*new_primModNatS0(ww77, ww78, Main.Succ(ww790), Main.Succ(ww800)) -> new_primModNatS0(ww77, ww78, ww790, ww800)
30.98/16.08	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(46)
30.98/16.08	YES
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(47)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS1(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS0(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS0(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS1(Main.Zero, Main.Zero) -> new_primDivNatS(Main.Zero, Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS00(ww66, ww67) -> new_primDivNatS(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67))
30.98/16.08	   new_primDivNatS(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS1(ww820, ww84)
30.98/16.08	   new_primDivNatS1(Main.Succ(ww240), Main.Zero) -> new_primDivNatS(Main.Succ(ww240), Main.Zero, Main.Zero)
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67))
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS00(ww66, ww67)
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(48) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(49)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS1(ww820, ww84)
30.98/16.08	   new_primDivNatS1(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS0(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS0(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67))
30.98/16.08	   new_primDivNatS(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS(ww820, ww830, ww84)
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS00(ww66, ww67)
30.98/16.08	   new_primDivNatS00(ww66, ww67) -> new_primDivNatS(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67))
30.98/16.08	   new_primDivNatS1(Main.Succ(ww240), Main.Zero) -> new_primDivNatS(Main.Succ(ww240), Main.Zero, Main.Zero)
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(50) QDPOrderProof (EQUIVALENT)
30.98/16.08	We use the reduction pair processor [LPAR04,JAR06].
30.98/16.08	
30.98/16.08	
30.98/16.08	The following pairs can be oriented strictly and are deleted.
30.98/16.08	
30.98/16.08	   new_primDivNatS(Main.Succ(ww820), Main.Zero, ww84) -> new_primDivNatS1(ww820, ww84)
30.98/16.08	   new_primDivNatS(Main.Succ(ww820), Main.Succ(ww830), ww84) -> new_primDivNatS(ww820, ww830, ww84)
30.98/16.08	The remaining pairs can at least be oriented weakly.
30.98/16.08	Used ordering:  Polynomial interpretation [POLO]:
30.98/16.08	
30.98/16.08	   POL(Main.Succ(x_1)) = 1 + x_1
30.98/16.08	   POL(Main.Zero) = 0
30.98/16.08	   POL(new_primDivNatS(x_1, x_2, x_3)) = x_1
30.98/16.08	   POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
30.98/16.08	   POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1
30.98/16.08	   POL(new_primDivNatS1(x_1, x_2)) = x_1
30.98/16.08	
30.98/16.08	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
30.98/16.08	none
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(51)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS1(Main.Succ(ww240), Main.Succ(ww250)) -> new_primDivNatS0(ww240, ww250, ww240, ww250)
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS0(ww66, ww67, ww680, ww690)
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Zero) -> new_primDivNatS(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67))
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Zero, Main.Zero) -> new_primDivNatS00(ww66, ww67)
30.98/16.08	   new_primDivNatS00(ww66, ww67) -> new_primDivNatS(Main.Succ(ww66), Main.Succ(ww67), Main.Succ(ww67))
30.98/16.08	   new_primDivNatS1(Main.Succ(ww240), Main.Zero) -> new_primDivNatS(Main.Succ(ww240), Main.Zero, Main.Zero)
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(52) DependencyGraphProof (EQUIVALENT)
30.98/16.08	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(53)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS0(ww66, ww67, ww680, ww690)
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(54) QDPSizeChangeProof (EQUIVALENT)
30.98/16.08	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. 
30.98/16.08	
30.98/16.08	From the DPs we obtained the following set of size-change graphs:
30.98/16.08	*new_primDivNatS0(ww66, ww67, Main.Succ(ww680), Main.Succ(ww690)) -> new_primDivNatS0(ww66, ww67, ww680, ww690)
30.98/16.08	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(55)
30.98/16.08	YES
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(56)
30.98/16.08	Obligation:
30.98/16.08	Q DP problem:
30.98/16.08	The TRS P consists of the following rules:
30.98/16.08	
30.98/16.08	   new_psPs(Cons(ww220, ww221), ww21) -> new_psPs(ww221, ww21)
30.98/16.08	
30.98/16.08	R is empty.
30.98/16.08	Q is empty.
30.98/16.08	We have to consider all minimal (P,Q,R)-chains.
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(57) QDPSizeChangeProof (EQUIVALENT)
30.98/16.08	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. 
30.98/16.08	
30.98/16.08	From the DPs we obtained the following set of size-change graphs:
30.98/16.08	*new_psPs(Cons(ww220, ww221), ww21) -> new_psPs(ww221, ww21)
30.98/16.08	The graph contains the following edges 1 > 1, 2 >= 2
30.98/16.08	
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(58)
30.98/16.08	YES
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(59) Narrow (COMPLETE)
30.98/16.08	Haskell To QDPs
30.98/16.08	
30.98/16.08	digraph dp_graph {
30.98/16.08	node [outthreshold=100, inthreshold=100];1[label="showsPrecMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
30.98/16.08	3[label="showsPrecMyInt ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
30.98/16.08	4[label="showsPrecMyInt ww3 ww4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
30.98/16.08	5[label="showsPrecMyInt ww3 ww4 ww5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
30.98/16.08	6 -> 36[label="",style="dashed", color="red", weight=0];
30.98/16.08	6[label="psPs (showMyInt ww4) ww5",fontsize=16,color="magenta"];6 -> 37[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	6 -> 38[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	37[label="showMyInt ww4",fontsize=16,color="black",shape="box"];37 -> 52[label="",style="solid", color="black", weight=3];
30.98/16.08	38[label="ww5",fontsize=16,color="green",shape="box"];36[label="psPs ww22 ww21",fontsize=16,color="burlywood",shape="triangle"];904[label="ww22/Cons ww220 ww221",fontsize=10,color="white",style="solid",shape="box"];36 -> 904[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	904 -> 53[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	905[label="ww22/Nil",fontsize=10,color="white",style="solid",shape="box"];36 -> 905[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	905 -> 54[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	52[label="primShowInt ww4",fontsize=16,color="burlywood",shape="triangle"];906[label="ww4/Pos ww40",fontsize=10,color="white",style="solid",shape="box"];52 -> 906[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	906 -> 55[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	907[label="ww4/Neg ww40",fontsize=10,color="white",style="solid",shape="box"];52 -> 907[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	907 -> 56[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	53[label="psPs (Cons ww220 ww221) ww21",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
30.98/16.08	54[label="psPs Nil ww21",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
30.98/16.08	55[label="primShowInt (Pos ww40)",fontsize=16,color="burlywood",shape="box"];908[label="ww40/Succ ww400",fontsize=10,color="white",style="solid",shape="box"];55 -> 908[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	908 -> 59[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	909[label="ww40/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 909[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	909 -> 60[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	56[label="primShowInt (Neg ww40)",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3];
30.98/16.08	57[label="Cons ww220 (psPs ww221 ww21)",fontsize=16,color="green",shape="box"];57 -> 62[label="",style="dashed", color="green", weight=3];
30.98/16.08	58[label="ww21",fontsize=16,color="green",shape="box"];59[label="primShowInt (Pos (Succ ww400))",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
30.98/16.08	60[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
30.98/16.08	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 ww40))",fontsize=16,color="green",shape="box"];61 -> 65[label="",style="dashed", color="green", weight=3];
30.98/16.08	62 -> 36[label="",style="dashed", color="red", weight=0];
30.98/16.08	62[label="psPs ww221 ww21",fontsize=16,color="magenta"];62 -> 66[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	63 -> 36[label="",style="dashed", color="red", weight=0];
30.98/16.08	63[label="psPs (primShowInt (divMyInt (Pos (Succ ww400)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) (Cons (toEnumChar (modMyInt (Pos (Succ ww400)) (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];
30.98/16.08	63 -> 68[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	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];
30.98/16.08	65[label="primShowInt (Pos ww40)",fontsize=16,color="magenta"];65 -> 69[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	66[label="ww221",fontsize=16,color="green",shape="box"];67 -> 52[label="",style="dashed", color="red", weight=0];
30.98/16.08	67[label="primShowInt (divMyInt (Pos (Succ ww400)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))",fontsize=16,color="magenta"];67 -> 70[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	68[label="Cons (toEnumChar (modMyInt (Pos (Succ ww400)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) Nil",fontsize=16,color="green",shape="box"];68 -> 71[label="",style="dashed", color="green", weight=3];
30.98/16.08	69[label="Pos ww40",fontsize=16,color="green",shape="box"];70 -> 72[label="",style="dashed", color="red", weight=0];
30.98/16.08	70[label="divMyInt (Pos (Succ ww400)) (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];
30.98/16.08	70 -> 74[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	71 -> 75[label="",style="dashed", color="red", weight=0];
30.98/16.08	71[label="toEnumChar (modMyInt (Pos (Succ ww400)) (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];
30.98/16.08	71 -> 77[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	73[label="ww400",fontsize=16,color="green",shape="box"];74[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];72[label="divMyInt (Pos (Succ ww24)) (Pos (Succ ww25))",fontsize=16,color="black",shape="triangle"];72 -> 78[label="",style="solid", color="black", weight=3];
30.98/16.08	76[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];77[label="ww400",fontsize=16,color="green",shape="box"];75[label="toEnumChar (modMyInt (Pos (Succ ww27)) (Pos (Succ ww28)))",fontsize=16,color="black",shape="triangle"];75 -> 79[label="",style="solid", color="black", weight=3];
30.98/16.08	78[label="primDivInt (Pos (Succ ww24)) (Pos (Succ ww25))",fontsize=16,color="black",shape="box"];78 -> 80[label="",style="solid", color="black", weight=3];
30.98/16.08	79[label="primIntToChar (modMyInt (Pos (Succ ww27)) (Pos (Succ ww28)))",fontsize=16,color="black",shape="box"];79 -> 81[label="",style="solid", color="black", weight=3];
30.98/16.08	80[label="Pos (primDivNatS (Succ ww24) (Succ ww25))",fontsize=16,color="green",shape="box"];80 -> 82[label="",style="dashed", color="green", weight=3];
30.98/16.08	81[label="Char (modMyInt (Pos (Succ ww27)) (Pos (Succ ww28)))",fontsize=16,color="green",shape="box"];81 -> 83[label="",style="dashed", color="green", weight=3];
30.98/16.08	82[label="primDivNatS (Succ ww24) (Succ ww25)",fontsize=16,color="black",shape="triangle"];82 -> 84[label="",style="solid", color="black", weight=3];
30.98/16.08	83[label="modMyInt (Pos (Succ ww27)) (Pos (Succ ww28))",fontsize=16,color="black",shape="box"];83 -> 85[label="",style="solid", color="black", weight=3];
30.98/16.08	84[label="primDivNatS0 ww24 ww25 (primGEqNatS ww24 ww25)",fontsize=16,color="burlywood",shape="box"];910[label="ww24/Succ ww240",fontsize=10,color="white",style="solid",shape="box"];84 -> 910[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	910 -> 86[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	911[label="ww24/Zero",fontsize=10,color="white",style="solid",shape="box"];84 -> 911[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	911 -> 87[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	85[label="primModInt (Pos (Succ ww27)) (Pos (Succ ww28))",fontsize=16,color="black",shape="box"];85 -> 88[label="",style="solid", color="black", weight=3];
30.98/16.08	86[label="primDivNatS0 (Succ ww240) ww25 (primGEqNatS (Succ ww240) ww25)",fontsize=16,color="burlywood",shape="box"];912[label="ww25/Succ ww250",fontsize=10,color="white",style="solid",shape="box"];86 -> 912[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	912 -> 89[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	913[label="ww25/Zero",fontsize=10,color="white",style="solid",shape="box"];86 -> 913[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	913 -> 90[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	87[label="primDivNatS0 Zero ww25 (primGEqNatS Zero ww25)",fontsize=16,color="burlywood",shape="box"];914[label="ww25/Succ ww250",fontsize=10,color="white",style="solid",shape="box"];87 -> 914[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	914 -> 91[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	915[label="ww25/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 915[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	915 -> 92[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	88[label="Pos (primModNatS (Succ ww27) (Succ ww28))",fontsize=16,color="green",shape="box"];88 -> 93[label="",style="dashed", color="green", weight=3];
30.98/16.08	89[label="primDivNatS0 (Succ ww240) (Succ ww250) (primGEqNatS (Succ ww240) (Succ ww250))",fontsize=16,color="black",shape="box"];89 -> 94[label="",style="solid", color="black", weight=3];
30.98/16.08	90[label="primDivNatS0 (Succ ww240) Zero (primGEqNatS (Succ ww240) Zero)",fontsize=16,color="black",shape="box"];90 -> 95[label="",style="solid", color="black", weight=3];
30.98/16.08	91[label="primDivNatS0 Zero (Succ ww250) (primGEqNatS Zero (Succ ww250))",fontsize=16,color="black",shape="box"];91 -> 96[label="",style="solid", color="black", weight=3];
30.98/16.08	92[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];92 -> 97[label="",style="solid", color="black", weight=3];
30.98/16.08	93[label="primModNatS (Succ ww27) (Succ ww28)",fontsize=16,color="burlywood",shape="triangle"];916[label="ww28/Succ ww280",fontsize=10,color="white",style="solid",shape="box"];93 -> 916[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	916 -> 98[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	917[label="ww28/Zero",fontsize=10,color="white",style="solid",shape="box"];93 -> 917[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	917 -> 99[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	94 -> 509[label="",style="dashed", color="red", weight=0];
30.98/16.08	94[label="primDivNatS0 (Succ ww240) (Succ ww250) (primGEqNatS ww240 ww250)",fontsize=16,color="magenta"];94 -> 510[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	94 -> 511[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	94 -> 512[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	94 -> 513[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	95[label="primDivNatS0 (Succ ww240) Zero MyTrue",fontsize=16,color="black",shape="box"];95 -> 102[label="",style="solid", color="black", weight=3];
30.98/16.08	96[label="primDivNatS0 Zero (Succ ww250) MyFalse",fontsize=16,color="black",shape="box"];96 -> 103[label="",style="solid", color="black", weight=3];
30.98/16.08	97[label="primDivNatS0 Zero Zero MyTrue",fontsize=16,color="black",shape="box"];97 -> 104[label="",style="solid", color="black", weight=3];
30.98/16.08	98[label="primModNatS (Succ ww27) (Succ (Succ ww280))",fontsize=16,color="black",shape="box"];98 -> 105[label="",style="solid", color="black", weight=3];
30.98/16.08	99[label="primModNatS (Succ ww27) (Succ Zero)",fontsize=16,color="black",shape="box"];99 -> 106[label="",style="solid", color="black", weight=3];
30.98/16.08	510[label="ww250",fontsize=16,color="green",shape="box"];511[label="ww240",fontsize=16,color="green",shape="box"];512[label="ww240",fontsize=16,color="green",shape="box"];513[label="ww250",fontsize=16,color="green",shape="box"];509[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS ww68 ww69)",fontsize=16,color="burlywood",shape="triangle"];918[label="ww68/Succ ww680",fontsize=10,color="white",style="solid",shape="box"];509 -> 918[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	918 -> 550[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	919[label="ww68/Zero",fontsize=10,color="white",style="solid",shape="box"];509 -> 919[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	919 -> 551[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	102[label="Succ (primDivNatS (primMinusNatS (Succ ww240) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];102 -> 111[label="",style="dashed", color="green", weight=3];
30.98/16.08	103[label="Zero",fontsize=16,color="green",shape="box"];104[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];104 -> 112[label="",style="dashed", color="green", weight=3];
30.98/16.08	105[label="primModNatS0 ww27 ww280 (primGEqNatS ww27 (Succ ww280))",fontsize=16,color="burlywood",shape="box"];920[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];105 -> 920[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	920 -> 113[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	921[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];105 -> 921[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	921 -> 114[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	106[label="Zero",fontsize=16,color="green",shape="box"];550[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS (Succ ww680) ww69)",fontsize=16,color="burlywood",shape="box"];922[label="ww69/Succ ww690",fontsize=10,color="white",style="solid",shape="box"];550 -> 922[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	922 -> 574[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	923[label="ww69/Zero",fontsize=10,color="white",style="solid",shape="box"];550 -> 923[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	923 -> 575[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	551[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS Zero ww69)",fontsize=16,color="burlywood",shape="box"];924[label="ww69/Succ ww690",fontsize=10,color="white",style="solid",shape="box"];551 -> 924[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	924 -> 576[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	925[label="ww69/Zero",fontsize=10,color="white",style="solid",shape="box"];551 -> 925[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	925 -> 577[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	111 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	111[label="primDivNatS (primMinusNatS (Succ ww240) Zero) (Succ Zero)",fontsize=16,color="magenta"];111 -> 801[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	111 -> 802[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	111 -> 803[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	112 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	112[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];112 -> 804[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	112 -> 805[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	112 -> 806[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	113[label="primModNatS0 (Succ ww270) ww280 (primGEqNatS (Succ ww270) (Succ ww280))",fontsize=16,color="black",shape="box"];113 -> 121[label="",style="solid", color="black", weight=3];
30.98/16.08	114[label="primModNatS0 Zero ww280 (primGEqNatS Zero (Succ ww280))",fontsize=16,color="black",shape="box"];114 -> 122[label="",style="solid", color="black", weight=3];
30.98/16.08	574[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS (Succ ww680) (Succ ww690))",fontsize=16,color="black",shape="box"];574 -> 589[label="",style="solid", color="black", weight=3];
30.98/16.08	575[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS (Succ ww680) Zero)",fontsize=16,color="black",shape="box"];575 -> 590[label="",style="solid", color="black", weight=3];
30.98/16.08	576[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS Zero (Succ ww690))",fontsize=16,color="black",shape="box"];576 -> 591[label="",style="solid", color="black", weight=3];
30.98/16.08	577[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];577 -> 592[label="",style="solid", color="black", weight=3];
30.98/16.08	801[label="Zero",fontsize=16,color="green",shape="box"];802[label="Succ ww240",fontsize=16,color="green",shape="box"];803[label="Zero",fontsize=16,color="green",shape="box"];800[label="primDivNatS (primMinusNatS ww82 ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="triangle"];926[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];800 -> 926[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	926 -> 825[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	927[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];800 -> 927[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	927 -> 826[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	804[label="Zero",fontsize=16,color="green",shape="box"];805[label="Zero",fontsize=16,color="green",shape="box"];806[label="Zero",fontsize=16,color="green",shape="box"];121[label="primModNatS0 (Succ ww270) ww280 (primGEqNatS ww270 ww280)",fontsize=16,color="burlywood",shape="box"];928[label="ww270/Succ ww2700",fontsize=10,color="white",style="solid",shape="box"];121 -> 928[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	928 -> 131[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	929[label="ww270/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 929[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	929 -> 132[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	122[label="primModNatS0 Zero ww280 MyFalse",fontsize=16,color="black",shape="box"];122 -> 133[label="",style="solid", color="black", weight=3];
30.98/16.08	589 -> 509[label="",style="dashed", color="red", weight=0];
30.98/16.08	589[label="primDivNatS0 (Succ ww66) (Succ ww67) (primGEqNatS ww680 ww690)",fontsize=16,color="magenta"];589 -> 604[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	589 -> 605[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	590[label="primDivNatS0 (Succ ww66) (Succ ww67) MyTrue",fontsize=16,color="black",shape="triangle"];590 -> 606[label="",style="solid", color="black", weight=3];
30.98/16.08	591[label="primDivNatS0 (Succ ww66) (Succ ww67) MyFalse",fontsize=16,color="black",shape="box"];591 -> 607[label="",style="solid", color="black", weight=3];
30.98/16.08	592 -> 590[label="",style="dashed", color="red", weight=0];
30.98/16.08	592[label="primDivNatS0 (Succ ww66) (Succ ww67) MyTrue",fontsize=16,color="magenta"];825[label="primDivNatS (primMinusNatS (Succ ww820) ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];930[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];825 -> 930[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	930 -> 831[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	931[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];825 -> 931[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	931 -> 832[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	826[label="primDivNatS (primMinusNatS Zero ww83) (Succ ww84)",fontsize=16,color="burlywood",shape="box"];932[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];826 -> 932[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	932 -> 833[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	933[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];826 -> 933[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	933 -> 834[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	131[label="primModNatS0 (Succ (Succ ww2700)) ww280 (primGEqNatS (Succ ww2700) ww280)",fontsize=16,color="burlywood",shape="box"];934[label="ww280/Succ ww2800",fontsize=10,color="white",style="solid",shape="box"];131 -> 934[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	934 -> 140[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	935[label="ww280/Zero",fontsize=10,color="white",style="solid",shape="box"];131 -> 935[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	935 -> 141[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	132[label="primModNatS0 (Succ Zero) ww280 (primGEqNatS Zero ww280)",fontsize=16,color="burlywood",shape="box"];936[label="ww280/Succ ww2800",fontsize=10,color="white",style="solid",shape="box"];132 -> 936[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	936 -> 142[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	937[label="ww280/Zero",fontsize=10,color="white",style="solid",shape="box"];132 -> 937[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	937 -> 143[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	133[label="Succ Zero",fontsize=16,color="green",shape="box"];604[label="ww680",fontsize=16,color="green",shape="box"];605[label="ww690",fontsize=16,color="green",shape="box"];606[label="Succ (primDivNatS (primMinusNatS (Succ ww66) (Succ ww67)) (Succ (Succ ww67)))",fontsize=16,color="green",shape="box"];606 -> 650[label="",style="dashed", color="green", weight=3];
30.98/16.08	607[label="Zero",fontsize=16,color="green",shape="box"];831[label="primDivNatS (primMinusNatS (Succ ww820) (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];831 -> 841[label="",style="solid", color="black", weight=3];
30.98/16.08	832[label="primDivNatS (primMinusNatS (Succ ww820) Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];832 -> 842[label="",style="solid", color="black", weight=3];
30.98/16.08	833[label="primDivNatS (primMinusNatS Zero (Succ ww830)) (Succ ww84)",fontsize=16,color="black",shape="box"];833 -> 843[label="",style="solid", color="black", weight=3];
30.98/16.08	834[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww84)",fontsize=16,color="black",shape="box"];834 -> 844[label="",style="solid", color="black", weight=3];
30.98/16.08	140[label="primModNatS0 (Succ (Succ ww2700)) (Succ ww2800) (primGEqNatS (Succ ww2700) (Succ ww2800))",fontsize=16,color="black",shape="box"];140 -> 150[label="",style="solid", color="black", weight=3];
30.98/16.08	141[label="primModNatS0 (Succ (Succ ww2700)) Zero (primGEqNatS (Succ ww2700) Zero)",fontsize=16,color="black",shape="box"];141 -> 151[label="",style="solid", color="black", weight=3];
30.98/16.08	142[label="primModNatS0 (Succ Zero) (Succ ww2800) (primGEqNatS Zero (Succ ww2800))",fontsize=16,color="black",shape="box"];142 -> 152[label="",style="solid", color="black", weight=3];
30.98/16.08	143[label="primModNatS0 (Succ Zero) Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];143 -> 153[label="",style="solid", color="black", weight=3];
30.98/16.08	650 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	650[label="primDivNatS (primMinusNatS (Succ ww66) (Succ ww67)) (Succ (Succ ww67))",fontsize=16,color="magenta"];650 -> 807[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	650 -> 808[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	650 -> 809[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	841 -> 800[label="",style="dashed", color="red", weight=0];
30.98/16.08	841[label="primDivNatS (primMinusNatS ww820 ww830) (Succ ww84)",fontsize=16,color="magenta"];841 -> 849[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	841 -> 850[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	842 -> 82[label="",style="dashed", color="red", weight=0];
30.98/16.08	842[label="primDivNatS (Succ ww820) (Succ ww84)",fontsize=16,color="magenta"];842 -> 851[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	842 -> 852[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	843[label="primDivNatS Zero (Succ ww84)",fontsize=16,color="black",shape="triangle"];843 -> 853[label="",style="solid", color="black", weight=3];
30.98/16.08	844 -> 843[label="",style="dashed", color="red", weight=0];
30.98/16.08	844[label="primDivNatS Zero (Succ ww84)",fontsize=16,color="magenta"];150 -> 668[label="",style="dashed", color="red", weight=0];
30.98/16.08	150[label="primModNatS0 (Succ (Succ ww2700)) (Succ ww2800) (primGEqNatS ww2700 ww2800)",fontsize=16,color="magenta"];150 -> 669[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	150 -> 670[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	150 -> 671[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	150 -> 672[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	151[label="primModNatS0 (Succ (Succ ww2700)) Zero MyTrue",fontsize=16,color="black",shape="box"];151 -> 163[label="",style="solid", color="black", weight=3];
30.98/16.08	152 -> 555[label="",style="dashed", color="red", weight=0];
30.98/16.08	152[label="primModNatS0 (Succ Zero) (Succ ww2800) MyFalse",fontsize=16,color="magenta"];152 -> 556[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	152 -> 557[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	153[label="primModNatS0 (Succ Zero) Zero MyTrue",fontsize=16,color="black",shape="box"];153 -> 165[label="",style="solid", color="black", weight=3];
30.98/16.08	807[label="Succ ww67",fontsize=16,color="green",shape="box"];808[label="Succ ww66",fontsize=16,color="green",shape="box"];809[label="Succ ww67",fontsize=16,color="green",shape="box"];849[label="ww830",fontsize=16,color="green",shape="box"];850[label="ww820",fontsize=16,color="green",shape="box"];851[label="ww820",fontsize=16,color="green",shape="box"];852[label="ww84",fontsize=16,color="green",shape="box"];853[label="Zero",fontsize=16,color="green",shape="box"];669[label="ww2800",fontsize=16,color="green",shape="box"];670[label="ww2700",fontsize=16,color="green",shape="box"];671[label="Succ ww2700",fontsize=16,color="green",shape="box"];672[label="ww2800",fontsize=16,color="green",shape="box"];668[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS ww79 ww80)",fontsize=16,color="burlywood",shape="triangle"];938[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];668 -> 938[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	938 -> 709[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	939[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];668 -> 939[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	939 -> 710[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	163 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	163[label="primModNatS (primMinusNatS (Succ (Succ ww2700)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];163 -> 859[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	163 -> 860[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	163 -> 861[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	556[label="Zero",fontsize=16,color="green",shape="box"];557[label="ww2800",fontsize=16,color="green",shape="box"];555[label="primModNatS0 (Succ ww71) (Succ ww72) MyFalse",fontsize=16,color="black",shape="triangle"];555 -> 578[label="",style="solid", color="black", weight=3];
30.98/16.08	165 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	165[label="primModNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];165 -> 862[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	165 -> 863[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	165 -> 864[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	709[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS (Succ ww790) ww80)",fontsize=16,color="burlywood",shape="box"];940[label="ww80/Succ ww800",fontsize=10,color="white",style="solid",shape="box"];709 -> 940[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	940 -> 715[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	941[label="ww80/Zero",fontsize=10,color="white",style="solid",shape="box"];709 -> 941[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	941 -> 716[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	710[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS Zero ww80)",fontsize=16,color="burlywood",shape="box"];942[label="ww80/Succ ww800",fontsize=10,color="white",style="solid",shape="box"];710 -> 942[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	942 -> 717[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	943[label="ww80/Zero",fontsize=10,color="white",style="solid",shape="box"];710 -> 943[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	943 -> 718[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	859[label="Succ Zero",fontsize=16,color="green",shape="box"];860[label="Succ Zero",fontsize=16,color="green",shape="box"];861[label="Succ (Succ ww2700)",fontsize=16,color="green",shape="box"];858[label="primModNatS (primMinusNatS ww86 ww87) (Succ ww88)",fontsize=16,color="burlywood",shape="triangle"];944[label="ww86/Succ ww860",fontsize=10,color="white",style="solid",shape="box"];858 -> 944[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	944 -> 889[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	945[label="ww86/Zero",fontsize=10,color="white",style="solid",shape="box"];858 -> 945[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	945 -> 890[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	578[label="Succ (Succ ww71)",fontsize=16,color="green",shape="box"];862[label="Succ Zero",fontsize=16,color="green",shape="box"];863[label="Succ Zero",fontsize=16,color="green",shape="box"];864[label="Succ Zero",fontsize=16,color="green",shape="box"];715[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS (Succ ww790) (Succ ww800))",fontsize=16,color="black",shape="box"];715 -> 723[label="",style="solid", color="black", weight=3];
30.98/16.08	716[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS (Succ ww790) Zero)",fontsize=16,color="black",shape="box"];716 -> 724[label="",style="solid", color="black", weight=3];
30.98/16.08	717[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS Zero (Succ ww800))",fontsize=16,color="black",shape="box"];717 -> 725[label="",style="solid", color="black", weight=3];
30.98/16.08	718[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];718 -> 726[label="",style="solid", color="black", weight=3];
30.98/16.08	889[label="primModNatS (primMinusNatS (Succ ww860) ww87) (Succ ww88)",fontsize=16,color="burlywood",shape="box"];946[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];889 -> 946[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	946 -> 891[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	947[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];889 -> 947[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	947 -> 892[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	890[label="primModNatS (primMinusNatS Zero ww87) (Succ ww88)",fontsize=16,color="burlywood",shape="box"];948[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];890 -> 948[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	948 -> 893[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	949[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];890 -> 949[label="",style="solid", color="burlywood", weight=9];
30.98/16.08	949 -> 894[label="",style="solid", color="burlywood", weight=3];
30.98/16.08	723 -> 668[label="",style="dashed", color="red", weight=0];
30.98/16.08	723[label="primModNatS0 (Succ ww77) (Succ ww78) (primGEqNatS ww790 ww800)",fontsize=16,color="magenta"];723 -> 733[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	723 -> 734[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	724[label="primModNatS0 (Succ ww77) (Succ ww78) MyTrue",fontsize=16,color="black",shape="triangle"];724 -> 735[label="",style="solid", color="black", weight=3];
30.98/16.08	725 -> 555[label="",style="dashed", color="red", weight=0];
30.98/16.08	725[label="primModNatS0 (Succ ww77) (Succ ww78) MyFalse",fontsize=16,color="magenta"];725 -> 736[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	725 -> 737[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	726 -> 724[label="",style="dashed", color="red", weight=0];
30.98/16.08	726[label="primModNatS0 (Succ ww77) (Succ ww78) MyTrue",fontsize=16,color="magenta"];891[label="primModNatS (primMinusNatS (Succ ww860) (Succ ww870)) (Succ ww88)",fontsize=16,color="black",shape="box"];891 -> 895[label="",style="solid", color="black", weight=3];
30.98/16.08	892[label="primModNatS (primMinusNatS (Succ ww860) Zero) (Succ ww88)",fontsize=16,color="black",shape="box"];892 -> 896[label="",style="solid", color="black", weight=3];
30.98/16.08	893[label="primModNatS (primMinusNatS Zero (Succ ww870)) (Succ ww88)",fontsize=16,color="black",shape="box"];893 -> 897[label="",style="solid", color="black", weight=3];
30.98/16.08	894[label="primModNatS (primMinusNatS Zero Zero) (Succ ww88)",fontsize=16,color="black",shape="box"];894 -> 898[label="",style="solid", color="black", weight=3];
30.98/16.08	733[label="ww790",fontsize=16,color="green",shape="box"];734[label="ww800",fontsize=16,color="green",shape="box"];735 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	735[label="primModNatS (primMinusNatS (Succ ww77) (Succ (Succ ww78))) (Succ (Succ (Succ ww78)))",fontsize=16,color="magenta"];735 -> 871[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	735 -> 872[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	735 -> 873[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	736[label="ww77",fontsize=16,color="green",shape="box"];737[label="ww78",fontsize=16,color="green",shape="box"];895 -> 858[label="",style="dashed", color="red", weight=0];
30.98/16.08	895[label="primModNatS (primMinusNatS ww860 ww870) (Succ ww88)",fontsize=16,color="magenta"];895 -> 899[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	895 -> 900[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	896 -> 93[label="",style="dashed", color="red", weight=0];
30.98/16.08	896[label="primModNatS (Succ ww860) (Succ ww88)",fontsize=16,color="magenta"];896 -> 901[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	896 -> 902[label="",style="dashed", color="magenta", weight=3];
30.98/16.08	897[label="primModNatS Zero (Succ ww88)",fontsize=16,color="black",shape="triangle"];897 -> 903[label="",style="solid", color="black", weight=3];
30.98/16.08	898 -> 897[label="",style="dashed", color="red", weight=0];
30.98/16.08	898[label="primModNatS Zero (Succ ww88)",fontsize=16,color="magenta"];871[label="Succ (Succ ww78)",fontsize=16,color="green",shape="box"];872[label="Succ (Succ ww78)",fontsize=16,color="green",shape="box"];873[label="Succ ww77",fontsize=16,color="green",shape="box"];899[label="ww870",fontsize=16,color="green",shape="box"];900[label="ww860",fontsize=16,color="green",shape="box"];901[label="ww88",fontsize=16,color="green",shape="box"];902[label="ww860",fontsize=16,color="green",shape="box"];903[label="Zero",fontsize=16,color="green",shape="box"];}
30.98/16.08	
30.98/16.08	----------------------------------------
30.98/16.08	
30.98/16.08	(60)
30.98/16.08	TRUE
31.17/16.14	EOF