10.05/4.16	YES
12.11/4.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.11/4.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.11/4.73	
12.11/4.73	
12.11/4.73	H-Termination with start terms of the given HASKELL could be proven:
12.11/4.73	
12.11/4.73	(0) HASKELL
12.11/4.73	(1) BR [EQUIVALENT, 0 ms]
12.11/4.73	(2) HASKELL
12.11/4.73	(3) COR [EQUIVALENT, 0 ms]
12.11/4.73	(4) HASKELL
12.11/4.73	(5) Narrow [SOUND, 0 ms]
12.11/4.73	(6) AND
12.11/4.73	    (7) QDP
12.11/4.73	        (8) DependencyGraphProof [EQUIVALENT, 0 ms]
12.11/4.73	        (9) AND
12.11/4.73	            (10) QDP
12.11/4.73	                (11) TransformationProof [EQUIVALENT, 0 ms]
12.11/4.73	                (12) QDP
12.11/4.73	                (13) UsableRulesProof [EQUIVALENT, 0 ms]
12.11/4.73	                (14) QDP
12.11/4.73	                (15) QReductionProof [EQUIVALENT, 0 ms]
12.11/4.73	                (16) QDP
12.11/4.73	                (17) TransformationProof [EQUIVALENT, 0 ms]
12.11/4.73	                (18) QDP
12.11/4.73	                (19) UsableRulesProof [EQUIVALENT, 0 ms]
12.11/4.73	                (20) QDP
12.11/4.73	                (21) QReductionProof [EQUIVALENT, 0 ms]
12.11/4.73	                (22) QDP
12.11/4.73	                (23) TransformationProof [EQUIVALENT, 0 ms]
12.11/4.73	                (24) QDP
12.11/4.73	                (25) TransformationProof [EQUIVALENT, 0 ms]
12.11/4.73	                (26) QDP
12.11/4.73	                (27) DependencyGraphProof [EQUIVALENT, 0 ms]
12.11/4.73	                (28) QDP
12.11/4.73	                (29) UsableRulesProof [EQUIVALENT, 0 ms]
12.11/4.73	                (30) QDP
12.11/4.73	                (31) QReductionProof [EQUIVALENT, 0 ms]
12.11/4.73	                (32) QDP
12.11/4.73	                (33) TransformationProof [EQUIVALENT, 0 ms]
12.11/4.73	                (34) QDP
12.11/4.73	                (35) UsableRulesProof [EQUIVALENT, 0 ms]
12.11/4.73	                (36) QDP
12.11/4.73	                (37) QReductionProof [EQUIVALENT, 0 ms]
12.11/4.73	                (38) QDP
12.11/4.73	                (39) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.11/4.73	                (40) YES
12.11/4.73	            (41) QDP
12.11/4.73	                (42) QDPOrderProof [EQUIVALENT, 31 ms]
12.11/4.73	                (43) QDP
12.11/4.73	                (44) DependencyGraphProof [EQUIVALENT, 0 ms]
12.11/4.73	                (45) QDP
12.11/4.73	                (46) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.11/4.73	                (47) YES
12.11/4.73	    (48) QDP
12.11/4.73	        (49) DependencyGraphProof [EQUIVALENT, 0 ms]
12.11/4.73	        (50) AND
12.11/4.73	            (51) QDP
12.11/4.73	                (52) MRRProof [EQUIVALENT, 0 ms]
12.11/4.73	                (53) QDP
12.11/4.73	                (54) PisEmptyProof [EQUIVALENT, 0 ms]
12.11/4.73	                (55) YES
12.11/4.73	            (56) QDP
12.11/4.73	                (57) QDPOrderProof [EQUIVALENT, 9 ms]
12.11/4.73	                (58) QDP
12.11/4.73	                (59) DependencyGraphProof [EQUIVALENT, 0 ms]
12.11/4.73	                (60) QDP
12.11/4.73	                (61) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.11/4.73	                (62) YES
12.11/4.73	    (63) QDP
12.11/4.73	        (64) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.11/4.73	        (65) YES
12.11/4.73	
12.11/4.73	
12.11/4.73	----------------------------------------
12.11/4.73	
12.11/4.73	(0)
12.11/4.73	Obligation:
12.11/4.73	mainModule Main 
12.11/4.73	module Main where {
12.11/4.73	import qualified Prelude;
12.11/4.73	data MyBool = MyTrue  | MyFalse ;
12.11/4.73	
12.11/4.73	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
12.11/4.73	
12.11/4.73	data Main.Nat = Succ Main.Nat  | Zero ;
12.11/4.73	
12.11/4.73	data Ratio a = CnPc a a ;
12.11/4.73	
12.11/4.73	data Tup2 b a = Tup2 b a ;
12.11/4.73	
12.11/4.73	error :: a;
12.11/4.73	error = stop MyTrue;
12.11/4.73	
12.11/4.73	fst :: Tup2 a b  ->  a;
12.11/4.73	fst (Tup2 x _) = x;
12.11/4.73	
12.11/4.73	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.73	primDivNatS Main.Zero Main.Zero = Main.error;
12.11/4.73	primDivNatS (Main.Succ x) Main.Zero = Main.error;
12.11/4.73	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
12.11/4.73	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
12.11/4.73	
12.11/4.73	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
12.11/4.73	primDivNatS0 x y MyFalse = Main.Zero;
12.11/4.73	
12.11/4.73	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
12.11/4.73	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
12.11/4.73	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
12.11/4.73	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
12.11/4.73	primGEqNatS Main.Zero Main.Zero = MyTrue;
12.11/4.73	
12.11/4.73	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.73	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
12.11/4.73	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
12.11/4.73	primMinusNatS x Main.Zero = x;
12.11/4.73	
12.11/4.73	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.73	primModNatS Main.Zero Main.Zero = Main.error;
12.11/4.73	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
12.11/4.73	primModNatS (Main.Succ x) Main.Zero = Main.error;
12.11/4.73	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
12.11/4.73	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
12.11/4.73	
12.11/4.73	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
12.11/4.73	primModNatS0 x y MyFalse = Main.Succ x;
12.11/4.73	
12.11/4.73	primQrmInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
12.11/4.73	primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y);
12.11/4.73	
12.11/4.73	primQuotInt :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.73	primQuotInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
12.11/4.73	primQuotInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
12.11/4.73	primQuotInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
12.11/4.73	primQuotInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
12.11/4.73	primQuotInt vx vy = Main.error;
12.11/4.73	
12.11/4.73	primRemInt :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.73	primRemInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
12.11/4.73	primRemInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
12.11/4.73	primRemInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
12.11/4.73	primRemInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
12.11/4.73	primRemInt vv vw = Main.error;
12.11/4.73	
12.11/4.73	properFraction :: Ratio MyInt  ->  Tup2 MyInt (Ratio MyInt);
12.11/4.73	properFraction (CnPc x y) = Tup2 (qProperFraction x y) (CnPc (rProperFraction x y) y);
12.11/4.73	
12.11/4.73	qProperFraction :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.73	qProperFraction x y = fst (quotRemMyInt x y);
12.11/4.73	
12.11/4.73	quotRemMyInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
12.11/4.73	quotRemMyInt = primQrmInt;
12.11/4.73	
12.11/4.73	rProperFraction :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.73	rProperFraction x y = snd (quotRemMyInt x y);
12.11/4.73	
12.11/4.73	snd :: Tup2 a b  ->  b;
12.11/4.73	snd (Tup2 _ y) = y;
12.11/4.73	
12.11/4.73	stop :: MyBool  ->  a;
12.11/4.73	stop MyFalse = stop MyFalse;
12.11/4.73	
12.11/4.73	}
12.11/4.73	
12.11/4.73	----------------------------------------
12.11/4.73	
12.11/4.73	(1) BR (EQUIVALENT)
12.11/4.73	Replaced joker patterns by fresh variables and removed binding patterns.
12.11/4.73	----------------------------------------
12.11/4.73	
12.11/4.73	(2)
12.11/4.73	Obligation:
12.11/4.73	mainModule Main 
12.11/4.73	module Main where {
12.11/4.73	import qualified Prelude;
12.11/4.73	data MyBool = MyTrue  | MyFalse ;
12.11/4.73	
12.11/4.73	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
12.11/4.74	
12.11/4.74	data Main.Nat = Succ Main.Nat  | Zero ;
12.11/4.74	
12.11/4.74	data Ratio a = CnPc a a ;
12.11/4.74	
12.11/4.74	data Tup2 b a = Tup2 b a ;
12.11/4.74	
12.11/4.74	error :: a;
12.11/4.74	error = stop MyTrue;
12.11/4.74	
12.11/4.74	fst :: Tup2 b a  ->  b;
12.11/4.74	fst (Tup2 x wv) = x;
12.11/4.74	
12.11/4.74	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.74	primDivNatS Main.Zero Main.Zero = Main.error;
12.11/4.74	primDivNatS (Main.Succ x) Main.Zero = Main.error;
12.11/4.74	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
12.11/4.74	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
12.11/4.74	
12.11/4.74	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
12.11/4.74	primDivNatS0 x y MyFalse = Main.Zero;
12.11/4.74	
12.11/4.74	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
12.11/4.74	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
12.11/4.74	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
12.11/4.74	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
12.11/4.74	primGEqNatS Main.Zero Main.Zero = MyTrue;
12.11/4.74	
12.11/4.74	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.74	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
12.11/4.74	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
12.11/4.74	primMinusNatS x Main.Zero = x;
12.11/4.74	
12.11/4.74	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.74	primModNatS Main.Zero Main.Zero = Main.error;
12.11/4.74	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
12.11/4.74	primModNatS (Main.Succ x) Main.Zero = Main.error;
12.11/4.74	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
12.11/4.74	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
12.11/4.74	
12.11/4.74	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
12.11/4.74	primModNatS0 x y MyFalse = Main.Succ x;
12.11/4.74	
12.11/4.74	primQrmInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
12.11/4.74	primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y);
12.11/4.74	
12.11/4.74	primQuotInt :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	primQuotInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt vx vy = Main.error;
12.11/4.74	
12.11/4.74	primRemInt :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	primRemInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt vv vw = Main.error;
12.11/4.74	
12.11/4.74	properFraction :: Ratio MyInt  ->  Tup2 MyInt (Ratio MyInt);
12.11/4.74	properFraction (CnPc x y) = Tup2 (qProperFraction x y) (CnPc (rProperFraction x y) y);
12.11/4.74	
12.11/4.74	qProperFraction :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	qProperFraction x y = fst (quotRemMyInt x y);
12.11/4.74	
12.11/4.74	quotRemMyInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
12.11/4.74	quotRemMyInt = primQrmInt;
12.11/4.74	
12.11/4.74	rProperFraction :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	rProperFraction x y = snd (quotRemMyInt x y);
12.11/4.74	
12.11/4.74	snd :: Tup2 b a  ->  a;
12.11/4.74	snd (Tup2 ww y) = y;
12.11/4.74	
12.11/4.74	stop :: MyBool  ->  a;
12.11/4.74	stop MyFalse = stop MyFalse;
12.11/4.74	
12.11/4.74	}
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(3) COR (EQUIVALENT)
12.11/4.74	Cond Reductions:
12.11/4.74	The following Function with conditions
12.11/4.74	"undefined |Falseundefined;
12.11/4.74	"
12.11/4.74	is transformed to
12.11/4.74	"undefined  = undefined1;
12.11/4.74	"
12.11/4.74	"undefined0 True = undefined;
12.11/4.74	"
12.11/4.74	"undefined1  = undefined0 False;
12.11/4.74	"
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(4)
12.11/4.74	Obligation:
12.11/4.74	mainModule Main 
12.11/4.74	module Main where {
12.11/4.74	import qualified Prelude;
12.11/4.74	data MyBool = MyTrue  | MyFalse ;
12.11/4.74	
12.11/4.74	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
12.11/4.74	
12.11/4.74	data Main.Nat = Succ Main.Nat  | Zero ;
12.11/4.74	
12.11/4.74	data Ratio a = CnPc a a ;
12.11/4.74	
12.11/4.74	data Tup2 a b = Tup2 a b ;
12.11/4.74	
12.11/4.74	error :: a;
12.11/4.74	error = stop MyTrue;
12.11/4.74	
12.11/4.74	fst :: Tup2 b a  ->  b;
12.11/4.74	fst (Tup2 x wv) = x;
12.11/4.74	
12.11/4.74	primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.74	primDivNatS Main.Zero Main.Zero = Main.error;
12.11/4.74	primDivNatS (Main.Succ x) Main.Zero = Main.error;
12.11/4.74	primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
12.11/4.74	primDivNatS Main.Zero (Main.Succ x) = Main.Zero;
12.11/4.74	
12.11/4.74	primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
12.11/4.74	primDivNatS0 x y MyFalse = Main.Zero;
12.11/4.74	
12.11/4.74	primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
12.11/4.74	primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
12.11/4.74	primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
12.11/4.74	primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
12.11/4.74	primGEqNatS Main.Zero Main.Zero = MyTrue;
12.11/4.74	
12.11/4.74	primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.74	primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
12.11/4.74	primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
12.11/4.74	primMinusNatS x Main.Zero = x;
12.11/4.74	
12.11/4.74	primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
12.11/4.74	primModNatS Main.Zero Main.Zero = Main.error;
12.11/4.74	primModNatS Main.Zero (Main.Succ x) = Main.Zero;
12.11/4.74	primModNatS (Main.Succ x) Main.Zero = Main.error;
12.11/4.74	primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
12.11/4.74	primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));
12.11/4.74	
12.11/4.74	primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
12.11/4.74	primModNatS0 x y MyFalse = Main.Succ x;
12.11/4.74	
12.11/4.74	primQrmInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
12.11/4.74	primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y);
12.11/4.74	
12.11/4.74	primQuotInt :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	primQuotInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
12.11/4.74	primQuotInt vx vy = Main.error;
12.11/4.74	
12.11/4.74	primRemInt :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	primRemInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Pos (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Neg (primModNatS x (Main.Succ y));
12.11/4.74	primRemInt vv vw = Main.error;
12.11/4.74	
12.11/4.74	properFraction :: Ratio MyInt  ->  Tup2 MyInt (Ratio MyInt);
12.11/4.74	properFraction (CnPc x y) = Tup2 (qProperFraction x y) (CnPc (rProperFraction x y) y);
12.11/4.74	
12.11/4.74	qProperFraction :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	qProperFraction x y = fst (quotRemMyInt x y);
12.11/4.74	
12.11/4.74	quotRemMyInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
12.11/4.74	quotRemMyInt = primQrmInt;
12.11/4.74	
12.11/4.74	rProperFraction :: MyInt  ->  MyInt  ->  MyInt;
12.11/4.74	rProperFraction x y = snd (quotRemMyInt x y);
12.11/4.74	
12.11/4.74	snd :: Tup2 b a  ->  a;
12.11/4.74	snd (Tup2 ww y) = y;
12.11/4.74	
12.11/4.74	stop :: MyBool  ->  a;
12.11/4.74	stop MyFalse = stop MyFalse;
12.11/4.74	
12.11/4.74	}
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(5) Narrow (SOUND)
12.11/4.74	Haskell To QDPs
12.11/4.74	
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12.11/4.74	704[label="wx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 704[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	704 -> 92[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	88[label="primDivNatS0 Zero wx3100 (primGEqNatS Zero wx3100)",fontsize=16,color="burlywood",shape="box"];705[label="wx3100/Succ wx31000",fontsize=10,color="white",style="solid",shape="box"];88 -> 705[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	705 -> 93[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	706[label="wx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];88 -> 706[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	706 -> 94[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	89[label="primModNatS0 wx3000 wx31000 (primGEqNatS wx3000 (Succ wx31000))",fontsize=16,color="burlywood",shape="box"];707[label="wx3000/Succ wx30000",fontsize=10,color="white",style="solid",shape="box"];89 -> 707[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	707 -> 95[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	708[label="wx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];89 -> 708[label="",style="solid", color="burlywood", weight=9];
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12.11/4.74	92[label="primDivNatS0 (Succ wx30000) Zero (primGEqNatS (Succ wx30000) Zero)",fontsize=16,color="black",shape="box"];92 -> 98[label="",style="solid", color="black", weight=3];
12.11/4.74	93[label="primDivNatS0 Zero (Succ wx31000) (primGEqNatS Zero (Succ wx31000))",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
12.11/4.74	94[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
12.11/4.74	95[label="primModNatS0 (Succ wx30000) wx31000 (primGEqNatS (Succ wx30000) (Succ wx31000))",fontsize=16,color="black",shape="box"];95 -> 101[label="",style="solid", color="black", weight=3];
12.11/4.74	96[label="primModNatS0 Zero wx31000 (primGEqNatS Zero (Succ wx31000))",fontsize=16,color="black",shape="box"];96 -> 102[label="",style="solid", color="black", weight=3];
12.11/4.74	97 -> 548[label="",style="dashed", color="red", weight=0];
12.11/4.74	97[label="primDivNatS0 (Succ wx30000) (Succ wx31000) (primGEqNatS wx30000 wx31000)",fontsize=16,color="magenta"];97 -> 549[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	97 -> 550[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	97 -> 551[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	97 -> 552[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	98[label="primDivNatS0 (Succ wx30000) Zero MyTrue",fontsize=16,color="black",shape="box"];98 -> 105[label="",style="solid", color="black", weight=3];
12.11/4.74	99[label="primDivNatS0 Zero (Succ wx31000) MyFalse",fontsize=16,color="black",shape="box"];99 -> 106[label="",style="solid", color="black", weight=3];
12.11/4.74	100[label="primDivNatS0 Zero Zero MyTrue",fontsize=16,color="black",shape="box"];100 -> 107[label="",style="solid", color="black", weight=3];
12.11/4.74	101[label="primModNatS0 (Succ wx30000) wx31000 (primGEqNatS wx30000 wx31000)",fontsize=16,color="burlywood",shape="box"];709[label="wx30000/Succ wx300000",fontsize=10,color="white",style="solid",shape="box"];101 -> 709[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	709 -> 108[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	710[label="wx30000/Zero",fontsize=10,color="white",style="solid",shape="box"];101 -> 710[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	710 -> 109[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	102[label="primModNatS0 Zero wx31000 MyFalse",fontsize=16,color="black",shape="box"];102 -> 110[label="",style="solid", color="black", weight=3];
12.11/4.74	549[label="wx31000",fontsize=16,color="green",shape="box"];550[label="wx31000",fontsize=16,color="green",shape="box"];551[label="wx30000",fontsize=16,color="green",shape="box"];552[label="wx30000",fontsize=16,color="green",shape="box"];548[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS wx44 wx45)",fontsize=16,color="burlywood",shape="triangle"];711[label="wx44/Succ wx440",fontsize=10,color="white",style="solid",shape="box"];548 -> 711[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	711 -> 589[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	712[label="wx44/Zero",fontsize=10,color="white",style="solid",shape="box"];548 -> 712[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	712 -> 590[label="",style="solid", color="burlywood", weight=3];
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12.11/4.74	106[label="Zero",fontsize=16,color="green",shape="box"];107[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];107 -> 116[label="",style="dashed", color="green", weight=3];
12.11/4.74	108[label="primModNatS0 (Succ (Succ wx300000)) wx31000 (primGEqNatS (Succ wx300000) wx31000)",fontsize=16,color="burlywood",shape="box"];713[label="wx31000/Succ wx310000",fontsize=10,color="white",style="solid",shape="box"];108 -> 713[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	713 -> 117[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	714[label="wx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];108 -> 714[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	714 -> 118[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	109[label="primModNatS0 (Succ Zero) wx31000 (primGEqNatS Zero wx31000)",fontsize=16,color="burlywood",shape="box"];715[label="wx31000/Succ wx310000",fontsize=10,color="white",style="solid",shape="box"];109 -> 715[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	715 -> 119[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	716[label="wx31000/Zero",fontsize=10,color="white",style="solid",shape="box"];109 -> 716[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	716 -> 120[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	110[label="Succ Zero",fontsize=16,color="green",shape="box"];589[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS (Succ wx440) wx45)",fontsize=16,color="burlywood",shape="box"];717[label="wx45/Succ wx450",fontsize=10,color="white",style="solid",shape="box"];589 -> 717[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	717 -> 630[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	718[label="wx45/Zero",fontsize=10,color="white",style="solid",shape="box"];589 -> 718[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	718 -> 631[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	590[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS Zero wx45)",fontsize=16,color="burlywood",shape="box"];719[label="wx45/Succ wx450",fontsize=10,color="white",style="solid",shape="box"];590 -> 719[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	719 -> 632[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	720[label="wx45/Zero",fontsize=10,color="white",style="solid",shape="box"];590 -> 720[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	720 -> 633[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	115 -> 60[label="",style="dashed", color="red", weight=0];
12.11/4.74	115[label="primDivNatS (primMinusNatS (Succ wx30000) Zero) (Succ Zero)",fontsize=16,color="magenta"];115 -> 125[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	115 -> 126[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	116 -> 60[label="",style="dashed", color="red", weight=0];
12.11/4.74	116[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];116 -> 127[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	116 -> 128[label="",style="dashed", color="magenta", weight=3];
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12.11/4.74	118[label="primModNatS0 (Succ (Succ wx300000)) Zero (primGEqNatS (Succ wx300000) Zero)",fontsize=16,color="black",shape="box"];118 -> 130[label="",style="solid", color="black", weight=3];
12.11/4.74	119[label="primModNatS0 (Succ Zero) (Succ wx310000) (primGEqNatS Zero (Succ wx310000))",fontsize=16,color="black",shape="box"];119 -> 131[label="",style="solid", color="black", weight=3];
12.11/4.74	120[label="primModNatS0 (Succ Zero) Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];120 -> 132[label="",style="solid", color="black", weight=3];
12.11/4.74	630[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS (Succ wx440) (Succ wx450))",fontsize=16,color="black",shape="box"];630 -> 636[label="",style="solid", color="black", weight=3];
12.11/4.74	631[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS (Succ wx440) Zero)",fontsize=16,color="black",shape="box"];631 -> 637[label="",style="solid", color="black", weight=3];
12.11/4.74	632[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS Zero (Succ wx450))",fontsize=16,color="black",shape="box"];632 -> 638[label="",style="solid", color="black", weight=3];
12.11/4.74	633[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];633 -> 639[label="",style="solid", color="black", weight=3];
12.11/4.74	125[label="primMinusNatS (Succ wx30000) Zero",fontsize=16,color="black",shape="triangle"];125 -> 138[label="",style="solid", color="black", weight=3];
12.11/4.74	126[label="Zero",fontsize=16,color="green",shape="box"];127[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];127 -> 139[label="",style="solid", color="black", weight=3];
12.11/4.74	128[label="Zero",fontsize=16,color="green",shape="box"];129 -> 593[label="",style="dashed", color="red", weight=0];
12.11/4.74	129[label="primModNatS0 (Succ (Succ wx300000)) (Succ wx310000) (primGEqNatS wx300000 wx310000)",fontsize=16,color="magenta"];129 -> 594[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	129 -> 595[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	129 -> 596[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	129 -> 597[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	130[label="primModNatS0 (Succ (Succ wx300000)) Zero MyTrue",fontsize=16,color="black",shape="box"];130 -> 142[label="",style="solid", color="black", weight=3];
12.11/4.74	131 -> 399[label="",style="dashed", color="red", weight=0];
12.11/4.74	131[label="primModNatS0 (Succ Zero) (Succ wx310000) MyFalse",fontsize=16,color="magenta"];131 -> 400[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	131 -> 401[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	132[label="primModNatS0 (Succ Zero) Zero MyTrue",fontsize=16,color="black",shape="box"];132 -> 144[label="",style="solid", color="black", weight=3];
12.11/4.74	636 -> 548[label="",style="dashed", color="red", weight=0];
12.11/4.74	636[label="primDivNatS0 (Succ wx42) (Succ wx43) (primGEqNatS wx440 wx450)",fontsize=16,color="magenta"];636 -> 644[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	636 -> 645[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	637[label="primDivNatS0 (Succ wx42) (Succ wx43) MyTrue",fontsize=16,color="black",shape="triangle"];637 -> 646[label="",style="solid", color="black", weight=3];
12.11/4.74	638[label="primDivNatS0 (Succ wx42) (Succ wx43) MyFalse",fontsize=16,color="black",shape="box"];638 -> 647[label="",style="solid", color="black", weight=3];
12.11/4.74	639 -> 637[label="",style="dashed", color="red", weight=0];
12.11/4.74	639[label="primDivNatS0 (Succ wx42) (Succ wx43) MyTrue",fontsize=16,color="magenta"];138[label="Succ wx30000",fontsize=16,color="green",shape="box"];139[label="Zero",fontsize=16,color="green",shape="box"];594[label="wx310000",fontsize=16,color="green",shape="box"];595[label="wx310000",fontsize=16,color="green",shape="box"];596[label="wx300000",fontsize=16,color="green",shape="box"];597[label="Succ wx300000",fontsize=16,color="green",shape="box"];593[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS wx49 wx50)",fontsize=16,color="burlywood",shape="triangle"];721[label="wx49/Succ wx490",fontsize=10,color="white",style="solid",shape="box"];593 -> 721[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	721 -> 634[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	722[label="wx49/Zero",fontsize=10,color="white",style="solid",shape="box"];593 -> 722[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	722 -> 635[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	142 -> 65[label="",style="dashed", color="red", weight=0];
12.11/4.74	142[label="primModNatS (primMinusNatS (Succ (Succ wx300000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];142 -> 155[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	142 -> 156[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	400[label="Zero",fontsize=16,color="green",shape="box"];401[label="wx310000",fontsize=16,color="green",shape="box"];399[label="primModNatS0 (Succ wx33) (Succ wx34) MyFalse",fontsize=16,color="black",shape="triangle"];399 -> 414[label="",style="solid", color="black", weight=3];
12.11/4.74	144 -> 65[label="",style="dashed", color="red", weight=0];
12.11/4.74	144[label="primModNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];144 -> 157[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	144 -> 158[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	644[label="wx450",fontsize=16,color="green",shape="box"];645[label="wx440",fontsize=16,color="green",shape="box"];646[label="Succ (primDivNatS (primMinusNatS (Succ wx42) (Succ wx43)) (Succ (Succ wx43)))",fontsize=16,color="green",shape="box"];646 -> 652[label="",style="dashed", color="green", weight=3];
12.11/4.74	647[label="Zero",fontsize=16,color="green",shape="box"];634[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS (Succ wx490) wx50)",fontsize=16,color="burlywood",shape="box"];723[label="wx50/Succ wx500",fontsize=10,color="white",style="solid",shape="box"];634 -> 723[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	723 -> 640[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	724[label="wx50/Zero",fontsize=10,color="white",style="solid",shape="box"];634 -> 724[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	724 -> 641[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	635[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS Zero wx50)",fontsize=16,color="burlywood",shape="box"];725[label="wx50/Succ wx500",fontsize=10,color="white",style="solid",shape="box"];635 -> 725[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	725 -> 642[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	726[label="wx50/Zero",fontsize=10,color="white",style="solid",shape="box"];635 -> 726[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	726 -> 643[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	155 -> 440[label="",style="dashed", color="red", weight=0];
12.11/4.74	155[label="primMinusNatS (Succ (Succ wx300000)) (Succ Zero)",fontsize=16,color="magenta"];155 -> 441[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	155 -> 442[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	156[label="Succ Zero",fontsize=16,color="green",shape="box"];414[label="Succ (Succ wx33)",fontsize=16,color="green",shape="box"];157 -> 440[label="",style="dashed", color="red", weight=0];
12.11/4.74	157[label="primMinusNatS (Succ Zero) (Succ Zero)",fontsize=16,color="magenta"];157 -> 443[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	157 -> 444[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	158[label="Succ Zero",fontsize=16,color="green",shape="box"];652 -> 60[label="",style="dashed", color="red", weight=0];
12.11/4.74	652[label="primDivNatS (primMinusNatS (Succ wx42) (Succ wx43)) (Succ (Succ wx43))",fontsize=16,color="magenta"];652 -> 658[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	652 -> 659[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	640[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS (Succ wx490) (Succ wx500))",fontsize=16,color="black",shape="box"];640 -> 648[label="",style="solid", color="black", weight=3];
12.11/4.74	641[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS (Succ wx490) Zero)",fontsize=16,color="black",shape="box"];641 -> 649[label="",style="solid", color="black", weight=3];
12.11/4.74	642[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS Zero (Succ wx500))",fontsize=16,color="black",shape="box"];642 -> 650[label="",style="solid", color="black", weight=3];
12.11/4.74	643[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];643 -> 651[label="",style="solid", color="black", weight=3];
12.11/4.74	441[label="Zero",fontsize=16,color="green",shape="box"];442[label="Succ wx300000",fontsize=16,color="green",shape="box"];440[label="primMinusNatS (Succ wx36) (Succ wx37)",fontsize=16,color="black",shape="triangle"];440 -> 475[label="",style="solid", color="black", weight=3];
12.11/4.74	443[label="Zero",fontsize=16,color="green",shape="box"];444[label="Zero",fontsize=16,color="green",shape="box"];658 -> 475[label="",style="dashed", color="red", weight=0];
12.11/4.74	658[label="primMinusNatS (Succ wx42) (Succ wx43)",fontsize=16,color="magenta"];658 -> 662[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	658 -> 663[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	659[label="Succ wx43",fontsize=16,color="green",shape="box"];648 -> 593[label="",style="dashed", color="red", weight=0];
12.11/4.74	648[label="primModNatS0 (Succ wx47) (Succ wx48) (primGEqNatS wx490 wx500)",fontsize=16,color="magenta"];648 -> 653[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	648 -> 654[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	649[label="primModNatS0 (Succ wx47) (Succ wx48) MyTrue",fontsize=16,color="black",shape="triangle"];649 -> 655[label="",style="solid", color="black", weight=3];
12.11/4.74	650 -> 399[label="",style="dashed", color="red", weight=0];
12.11/4.74	650[label="primModNatS0 (Succ wx47) (Succ wx48) MyFalse",fontsize=16,color="magenta"];650 -> 656[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	650 -> 657[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	651 -> 649[label="",style="dashed", color="red", weight=0];
12.11/4.74	651[label="primModNatS0 (Succ wx47) (Succ wx48) MyTrue",fontsize=16,color="magenta"];475[label="primMinusNatS wx36 wx37",fontsize=16,color="burlywood",shape="triangle"];727[label="wx36/Succ wx360",fontsize=10,color="white",style="solid",shape="box"];475 -> 727[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	727 -> 516[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	728[label="wx36/Zero",fontsize=10,color="white",style="solid",shape="box"];475 -> 728[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	728 -> 517[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	662[label="Succ wx43",fontsize=16,color="green",shape="box"];663[label="Succ wx42",fontsize=16,color="green",shape="box"];653[label="wx500",fontsize=16,color="green",shape="box"];654[label="wx490",fontsize=16,color="green",shape="box"];655 -> 65[label="",style="dashed", color="red", weight=0];
12.11/4.74	655[label="primModNatS (primMinusNatS (Succ wx47) (Succ (Succ wx48))) (Succ (Succ (Succ wx48)))",fontsize=16,color="magenta"];655 -> 660[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	655 -> 661[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	656[label="wx47",fontsize=16,color="green",shape="box"];657[label="wx48",fontsize=16,color="green",shape="box"];516[label="primMinusNatS (Succ wx360) wx37",fontsize=16,color="burlywood",shape="box"];729[label="wx37/Succ wx370",fontsize=10,color="white",style="solid",shape="box"];516 -> 729[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	729 -> 530[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	730[label="wx37/Zero",fontsize=10,color="white",style="solid",shape="box"];516 -> 730[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	730 -> 531[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	517[label="primMinusNatS Zero wx37",fontsize=16,color="burlywood",shape="box"];731[label="wx37/Succ wx370",fontsize=10,color="white",style="solid",shape="box"];517 -> 731[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	731 -> 532[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	732[label="wx37/Zero",fontsize=10,color="white",style="solid",shape="box"];517 -> 732[label="",style="solid", color="burlywood", weight=9];
12.11/4.74	732 -> 533[label="",style="solid", color="burlywood", weight=3];
12.11/4.74	660 -> 475[label="",style="dashed", color="red", weight=0];
12.11/4.74	660[label="primMinusNatS (Succ wx47) (Succ (Succ wx48))",fontsize=16,color="magenta"];660 -> 664[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	660 -> 665[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	661[label="Succ (Succ wx48)",fontsize=16,color="green",shape="box"];530[label="primMinusNatS (Succ wx360) (Succ wx370)",fontsize=16,color="black",shape="box"];530 -> 544[label="",style="solid", color="black", weight=3];
12.11/4.74	531[label="primMinusNatS (Succ wx360) Zero",fontsize=16,color="black",shape="box"];531 -> 545[label="",style="solid", color="black", weight=3];
12.11/4.74	532[label="primMinusNatS Zero (Succ wx370)",fontsize=16,color="black",shape="box"];532 -> 546[label="",style="solid", color="black", weight=3];
12.11/4.74	533[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];533 -> 547[label="",style="solid", color="black", weight=3];
12.11/4.74	664[label="Succ (Succ wx48)",fontsize=16,color="green",shape="box"];665[label="Succ wx47",fontsize=16,color="green",shape="box"];544 -> 475[label="",style="dashed", color="red", weight=0];
12.11/4.74	544[label="primMinusNatS wx360 wx370",fontsize=16,color="magenta"];544 -> 591[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	544 -> 592[label="",style="dashed", color="magenta", weight=3];
12.11/4.74	545[label="Succ wx360",fontsize=16,color="green",shape="box"];546[label="Zero",fontsize=16,color="green",shape="box"];547[label="Zero",fontsize=16,color="green",shape="box"];591[label="wx370",fontsize=16,color="green",shape="box"];592[label="wx360",fontsize=16,color="green",shape="box"];}
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(6)
12.11/4.74	Complex Obligation (AND)
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(7)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Zero, Main.Zero) -> new_primModNatS00(wx47, wx48)
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Zero) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx47), Main.Succ(Main.Succ(wx48))), Main.Succ(Main.Succ(wx48)))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS1, Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Succ(wx500)) -> new_primModNatS0(wx47, wx48, wx490, wx500)
12.11/4.74	   new_primModNatS00(wx47, wx48) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx47), Main.Succ(Main.Succ(wx48))), Main.Succ(Main.Succ(wx48)))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS0(wx300000), Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Succ(wx310000))) -> new_primModNatS0(Main.Succ(wx300000), wx310000, wx300000, wx310000)
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS0(wx300000) -> new_primMinusNatS3(Main.Succ(wx300000), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(8) DependencyGraphProof (EQUIVALENT)
12.11/4.74	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(9)
12.11/4.74	Complex Obligation (AND)
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(10)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS0(wx300000), Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS1, Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS0(wx300000) -> new_primMinusNatS3(Main.Succ(wx300000), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(11) TransformationProof (EQUIVALENT)
12.11/4.74	By rewriting [LPAR04] the rule new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS0(wx300000), Main.Succ(Main.Zero)) at position [0] we obtained the following new rules [LPAR04]:
12.11/4.74	
12.11/4.74	   (new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero)),new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero)))
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(12)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS1, Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS0(wx300000) -> new_primMinusNatS3(Main.Succ(wx300000), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(13) UsableRulesProof (EQUIVALENT)
12.11/4.74	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.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(14)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS1, Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(15) QReductionProof (EQUIVALENT)
12.11/4.74	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
12.11/4.74	
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(16)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS1, Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(17) TransformationProof (EQUIVALENT)
12.11/4.74	By rewriting [LPAR04] the rule new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS1, Main.Succ(Main.Zero)) at position [0] we obtained the following new rules [LPAR04]:
12.11/4.74	
12.11/4.74	   (new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Zero, Main.Zero), Main.Succ(Main.Zero)),new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Zero, Main.Zero), Main.Succ(Main.Zero)))
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(18)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Zero, Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(19) UsableRulesProof (EQUIVALENT)
12.11/4.74	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.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(20)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Zero, Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(21) QReductionProof (EQUIVALENT)
12.11/4.74	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
12.11/4.74	
12.11/4.74	   new_primMinusNatS1
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(22)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Zero, Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(23) TransformationProof (EQUIVALENT)
12.11/4.74	By rewriting [LPAR04] the rule new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero)) at position [0] we obtained the following new rules [LPAR04]:
12.11/4.74	
12.11/4.74	   (new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero)),new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero)))
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(24)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Zero, Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(25) TransformationProof (EQUIVALENT)
12.11/4.74	By rewriting [LPAR04] the rule new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS3(Main.Zero, Main.Zero), Main.Succ(Main.Zero)) at position [0] we obtained the following new rules [LPAR04]:
12.11/4.74	
12.11/4.74	   (new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Zero, Main.Zero), Main.Succ(Main.Zero)),new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Zero, Main.Zero), Main.Succ(Main.Zero)))
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(26)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Zero)), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Zero, Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(27) DependencyGraphProof (EQUIVALENT)
12.11/4.74	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(28)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(29) UsableRulesProof (EQUIVALENT)
12.11/4.74	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.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(30)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(31) QReductionProof (EQUIVALENT)
12.11/4.74	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(32)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(33) TransformationProof (EQUIVALENT)
12.11/4.74	By rewriting [LPAR04] the rule new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx300000), Main.Zero), Main.Succ(Main.Zero)) at position [0] we obtained the following new rules [LPAR04]:
12.11/4.74	
12.11/4.74	   (new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(wx300000), Main.Succ(Main.Zero)),new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(wx300000), Main.Succ(Main.Zero)))
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(34)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(wx300000), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(35) UsableRulesProof (EQUIVALENT)
12.11/4.74	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.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(36)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(wx300000), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	R is empty.
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(37) QReductionProof (EQUIVALENT)
12.11/4.74	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(38)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(wx300000), Main.Succ(Main.Zero))
12.11/4.74	
12.11/4.74	R is empty.
12.11/4.74	Q is empty.
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(39) QDPSizeChangeProof (EQUIVALENT)
12.11/4.74	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. 
12.11/4.74	
12.11/4.74	From the DPs we obtained the following set of size-change graphs:
12.11/4.74	*new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Zero)) -> new_primModNatS(Main.Succ(wx300000), Main.Succ(Main.Zero))
12.11/4.74	The graph contains the following edges 1 > 1, 2 >= 2
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(40)
12.11/4.74	YES
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(41)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS00(wx47, wx48) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx47), Main.Succ(Main.Succ(wx48))), Main.Succ(Main.Succ(wx48)))
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Succ(wx310000))) -> new_primModNatS0(Main.Succ(wx300000), wx310000, wx300000, wx310000)
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Zero, Main.Zero) -> new_primModNatS00(wx47, wx48)
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Zero) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx47), Main.Succ(Main.Succ(wx48))), Main.Succ(Main.Succ(wx48)))
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Succ(wx500)) -> new_primModNatS0(wx47, wx48, wx490, wx500)
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS0(wx300000) -> new_primMinusNatS3(Main.Succ(wx300000), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(42) QDPOrderProof (EQUIVALENT)
12.11/4.74	We use the reduction pair processor [LPAR04,JAR06].
12.11/4.74	
12.11/4.74	
12.11/4.74	The following pairs can be oriented strictly and are deleted.
12.11/4.74	
12.11/4.74	   new_primModNatS(Main.Succ(Main.Succ(Main.Succ(wx300000))), Main.Succ(Main.Succ(wx310000))) -> new_primModNatS0(Main.Succ(wx300000), wx310000, wx300000, wx310000)
12.11/4.74	The remaining pairs can at least be oriented weakly.
12.11/4.74	Used ordering:  Polynomial interpretation [POLO]:
12.11/4.74	
12.11/4.74	   POL(Main.Succ(x_1)) = 1 + x_1
12.11/4.74	   POL(Main.Zero) = 0
12.11/4.74	   POL(new_primMinusNatS2(x_1, x_2)) = x_1
12.11/4.74	   POL(new_primModNatS(x_1, x_2)) = x_1
12.11/4.74	   POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
12.11/4.74	   POL(new_primModNatS00(x_1, x_2)) = 1 + x_1
12.11/4.74	
12.11/4.74	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(43)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS00(wx47, wx48) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx47), Main.Succ(Main.Succ(wx48))), Main.Succ(Main.Succ(wx48)))
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Zero, Main.Zero) -> new_primModNatS00(wx47, wx48)
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Zero) -> new_primModNatS(new_primMinusNatS2(Main.Succ(wx47), Main.Succ(Main.Succ(wx48))), Main.Succ(Main.Succ(wx48)))
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Succ(wx500)) -> new_primModNatS0(wx47, wx48, wx490, wx500)
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS0(wx300000) -> new_primMinusNatS3(Main.Succ(wx300000), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(44) DependencyGraphProof (EQUIVALENT)
12.11/4.74	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(45)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Succ(wx500)) -> new_primModNatS0(wx47, wx48, wx490, wx500)
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS3(wx36, wx37) -> new_primMinusNatS2(wx36, wx37)
12.11/4.74	   new_primMinusNatS1 -> new_primMinusNatS3(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS0(wx300000) -> new_primMinusNatS3(Main.Succ(wx300000), Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS0(x0)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS1
12.11/4.74	   new_primMinusNatS3(x0, x1)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(46) QDPSizeChangeProof (EQUIVALENT)
12.11/4.74	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. 
12.11/4.74	
12.11/4.74	From the DPs we obtained the following set of size-change graphs:
12.11/4.74	*new_primModNatS0(wx47, wx48, Main.Succ(wx490), Main.Succ(wx500)) -> new_primModNatS0(wx47, wx48, wx490, wx500)
12.11/4.74	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(47)
12.11/4.74	YES
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(48)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Succ(wx450)) -> new_primDivNatS0(wx42, wx43, wx440, wx450)
12.11/4.74	   new_primDivNatS00(wx42, wx43) -> new_primDivNatS(new_primMinusNatS2(Main.Succ(wx42), Main.Succ(wx43)), Main.Succ(wx43))
12.11/4.74	   new_primDivNatS(Main.Succ(Main.Zero), Main.Zero) -> new_primDivNatS(new_primMinusNatS5, Main.Zero)
12.11/4.74	   new_primDivNatS(Main.Succ(Main.Succ(wx30000)), Main.Zero) -> new_primDivNatS(new_primMinusNatS4(wx30000), Main.Zero)
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Zero, Main.Zero) -> new_primDivNatS00(wx42, wx43)
12.11/4.74	   new_primDivNatS(Main.Succ(Main.Succ(wx30000)), Main.Succ(wx31000)) -> new_primDivNatS0(wx30000, wx31000, wx30000, wx31000)
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Zero) -> new_primDivNatS(new_primMinusNatS2(Main.Succ(wx42), Main.Succ(wx43)), Main.Succ(wx43))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS5 -> Main.Zero
12.11/4.74	   new_primMinusNatS4(wx30000) -> Main.Succ(wx30000)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS4(x0)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS5
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(49) DependencyGraphProof (EQUIVALENT)
12.11/4.74	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(50)
12.11/4.74	Complex Obligation (AND)
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(51)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primDivNatS(Main.Succ(Main.Succ(wx30000)), Main.Zero) -> new_primDivNatS(new_primMinusNatS4(wx30000), Main.Zero)
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS5 -> Main.Zero
12.11/4.74	   new_primMinusNatS4(wx30000) -> Main.Succ(wx30000)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS4(x0)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS5
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(52) MRRProof (EQUIVALENT)
12.11/4.74	By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
12.11/4.74	
12.11/4.74	Strictly oriented dependency pairs:
12.11/4.74	
12.11/4.74	   new_primDivNatS(Main.Succ(Main.Succ(wx30000)), Main.Zero) -> new_primDivNatS(new_primMinusNatS4(wx30000), Main.Zero)
12.11/4.74	
12.11/4.74	Strictly oriented rules of the TRS R:
12.11/4.74	
12.11/4.74	   new_primMinusNatS4(wx30000) -> Main.Succ(wx30000)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	Used ordering: Polynomial interpretation [POLO]:
12.11/4.74	
12.11/4.74	   POL(Main.Succ(x_1)) = 1 + 2*x_1
12.11/4.74	   POL(Main.Zero) = 2
12.11/4.74	   POL(new_primDivNatS(x_1, x_2)) = x_1 + x_2
12.11/4.74	   POL(new_primMinusNatS2(x_1, x_2)) = x_1 + 2*x_2
12.11/4.74	   POL(new_primMinusNatS4(x_1)) = 2 + 2*x_1
12.11/4.74	   POL(new_primMinusNatS5) = 2
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(53)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	P is empty.
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS5 -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS4(x0)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS5
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(54) PisEmptyProof (EQUIVALENT)
12.11/4.74	The TRS P is empty. Hence, there is no (P,Q,R) chain.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(55)
12.11/4.74	YES
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(56)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Zero, Main.Zero) -> new_primDivNatS00(wx42, wx43)
12.11/4.74	   new_primDivNatS00(wx42, wx43) -> new_primDivNatS(new_primMinusNatS2(Main.Succ(wx42), Main.Succ(wx43)), Main.Succ(wx43))
12.11/4.74	   new_primDivNatS(Main.Succ(Main.Succ(wx30000)), Main.Succ(wx31000)) -> new_primDivNatS0(wx30000, wx31000, wx30000, wx31000)
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Succ(wx450)) -> new_primDivNatS0(wx42, wx43, wx440, wx450)
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Zero) -> new_primDivNatS(new_primMinusNatS2(Main.Succ(wx42), Main.Succ(wx43)), Main.Succ(wx43))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS5 -> Main.Zero
12.11/4.74	   new_primMinusNatS4(wx30000) -> Main.Succ(wx30000)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS4(x0)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS5
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(57) QDPOrderProof (EQUIVALENT)
12.11/4.74	We use the reduction pair processor [LPAR04,JAR06].
12.11/4.74	
12.11/4.74	
12.11/4.74	The following pairs can be oriented strictly and are deleted.
12.11/4.74	
12.11/4.74	   new_primDivNatS(Main.Succ(Main.Succ(wx30000)), Main.Succ(wx31000)) -> new_primDivNatS0(wx30000, wx31000, wx30000, wx31000)
12.11/4.74	The remaining pairs can at least be oriented weakly.
12.11/4.74	Used ordering:  Polynomial interpretation [POLO]:
12.11/4.74	
12.11/4.74	   POL(Main.Succ(x_1)) = 1 + x_1
12.11/4.74	   POL(Main.Zero) = 1
12.11/4.74	   POL(new_primDivNatS(x_1, x_2)) = x_1
12.11/4.74	   POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
12.11/4.74	   POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1
12.11/4.74	   POL(new_primMinusNatS2(x_1, x_2)) = x_1
12.11/4.74	
12.11/4.74	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
12.11/4.74	
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(58)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Zero, Main.Zero) -> new_primDivNatS00(wx42, wx43)
12.11/4.74	   new_primDivNatS00(wx42, wx43) -> new_primDivNatS(new_primMinusNatS2(Main.Succ(wx42), Main.Succ(wx43)), Main.Succ(wx43))
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Succ(wx450)) -> new_primDivNatS0(wx42, wx43, wx440, wx450)
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Zero) -> new_primDivNatS(new_primMinusNatS2(Main.Succ(wx42), Main.Succ(wx43)), Main.Succ(wx43))
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS5 -> Main.Zero
12.11/4.74	   new_primMinusNatS4(wx30000) -> Main.Succ(wx30000)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS4(x0)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS5
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(59) DependencyGraphProof (EQUIVALENT)
12.11/4.74	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(60)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Succ(wx450)) -> new_primDivNatS0(wx42, wx43, wx440, wx450)
12.11/4.74	
12.11/4.74	The TRS R consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS5 -> Main.Zero
12.11/4.74	   new_primMinusNatS4(wx30000) -> Main.Succ(wx30000)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero) -> Main.Zero
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS2(wx360, wx370)
12.11/4.74	   new_primMinusNatS2(Main.Succ(wx360), Main.Zero) -> Main.Succ(wx360)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(wx370)) -> Main.Zero
12.11/4.74	
12.11/4.74	The set Q consists of the following terms:
12.11/4.74	
12.11/4.74	   new_primMinusNatS4(x0)
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Succ(x0))
12.11/4.74	   new_primMinusNatS2(Main.Zero, Main.Zero)
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Zero)
12.11/4.74	   new_primMinusNatS5
12.11/4.74	   new_primMinusNatS2(Main.Succ(x0), Main.Succ(x1))
12.11/4.74	
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(61) QDPSizeChangeProof (EQUIVALENT)
12.11/4.74	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. 
12.11/4.74	
12.11/4.74	From the DPs we obtained the following set of size-change graphs:
12.11/4.74	*new_primDivNatS0(wx42, wx43, Main.Succ(wx440), Main.Succ(wx450)) -> new_primDivNatS0(wx42, wx43, wx440, wx450)
12.11/4.74	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(62)
12.11/4.74	YES
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(63)
12.11/4.74	Obligation:
12.11/4.74	Q DP problem:
12.11/4.74	The TRS P consists of the following rules:
12.11/4.74	
12.11/4.74	   new_primMinusNatS(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS(wx360, wx370)
12.11/4.74	
12.11/4.74	R is empty.
12.11/4.74	Q is empty.
12.11/4.74	We have to consider all minimal (P,Q,R)-chains.
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(64) QDPSizeChangeProof (EQUIVALENT)
12.11/4.74	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. 
12.11/4.74	
12.11/4.74	From the DPs we obtained the following set of size-change graphs:
12.11/4.74	*new_primMinusNatS(Main.Succ(wx360), Main.Succ(wx370)) -> new_primMinusNatS(wx360, wx370)
12.11/4.74	The graph contains the following edges 1 > 1, 2 > 2
12.11/4.74	
12.11/4.74	
12.11/4.74	----------------------------------------
12.11/4.74	
12.11/4.74	(65)
12.11/4.74	YES
12.27/4.79	EOF