45.97/27.80	YES
48.24/28.46	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
48.24/28.46	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
48.24/28.46	
48.24/28.46	
48.24/28.46	H-Termination with start terms of the given HASKELL could be proven:
48.24/28.46	
48.24/28.46	(0) HASKELL
48.24/28.46	(1) IFR [EQUIVALENT, 0 ms]
48.24/28.46	(2) HASKELL
48.24/28.46	(3) BR [EQUIVALENT, 0 ms]
48.24/28.46	(4) HASKELL
48.24/28.46	(5) COR [EQUIVALENT, 0 ms]
48.24/28.46	(6) HASKELL
48.24/28.46	(7) LetRed [EQUIVALENT, 0 ms]
48.24/28.46	(8) HASKELL
48.24/28.46	(9) NumRed [SOUND, 0 ms]
48.24/28.46	(10) HASKELL
48.24/28.46	(11) Narrow [SOUND, 0 ms]
48.24/28.46	(12) AND
48.24/28.46	    (13) QDP
48.24/28.46	        (14) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	        (15) QDP
48.24/28.46	        (16) QDPOrderProof [EQUIVALENT, 109 ms]
48.24/28.46	        (17) QDP
48.24/28.46	        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	        (19) QDP
48.24/28.46	        (20) TransformationProof [EQUIVALENT, 0 ms]
48.24/28.46	        (21) QDP
48.24/28.46	        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	        (23) AND
48.24/28.46	            (24) QDP
48.24/28.46	                (25) UsableRulesProof [EQUIVALENT, 0 ms]
48.24/28.46	                (26) QDP
48.24/28.46	                (27) QReductionProof [EQUIVALENT, 0 ms]
48.24/28.46	                (28) QDP
48.24/28.46	                (29) QDPOrderProof [EQUIVALENT, 0 ms]
48.24/28.46	                (30) QDP
48.24/28.46	                (31) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                (32) QDP
48.24/28.46	                (33) TransformationProof [EQUIVALENT, 0 ms]
48.24/28.46	                (34) QDP
48.24/28.46	                (35) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                (36) QDP
48.24/28.46	                (37) UsableRulesProof [EQUIVALENT, 0 ms]
48.24/28.46	                (38) QDP
48.24/28.46	                (39) QReductionProof [EQUIVALENT, 0 ms]
48.24/28.46	                (40) QDP
48.24/28.46	                (41) TransformationProof [EQUIVALENT, 0 ms]
48.24/28.46	                (42) QDP
48.24/28.46	                (43) InductionCalculusProof [EQUIVALENT, 9 ms]
48.24/28.46	                (44) QDP
48.24/28.46	                (45) NonInfProof [EQUIVALENT, 74 ms]
48.24/28.46	                (46) AND
48.24/28.46	                    (47) QDP
48.24/28.46	                        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (49) AND
48.24/28.46	                            (50) QDP
48.24/28.46	                                (51) QDPSizeChangeProof [EQUIVALENT, 0 ms]
48.24/28.46	                                (52) YES
48.24/28.46	                            (53) QDP
48.24/28.46	                                (54) QDPSizeChangeProof [EQUIVALENT, 0 ms]
48.24/28.46	                                (55) YES
48.24/28.46	                    (56) QDP
48.24/28.46	                        (57) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (58) AND
48.24/28.46	                            (59) QDP
48.24/28.46	                                (60) QDPSizeChangeProof [EQUIVALENT, 0 ms]
48.24/28.46	                                (61) YES
48.24/28.46	                            (62) QDP
48.24/28.46	                                (63) QDPSizeChangeProof [EQUIVALENT, 0 ms]
48.24/28.46	                                (64) YES
48.24/28.46	            (65) QDP
48.24/28.46	                (66) UsableRulesProof [EQUIVALENT, 0 ms]
48.24/28.46	                (67) QDP
48.24/28.46	                (68) QReductionProof [EQUIVALENT, 0 ms]
48.24/28.46	                (69) QDP
48.24/28.46	                (70) TransformationProof [EQUIVALENT, 0 ms]
48.24/28.46	                (71) QDP
48.24/28.46	                (72) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                (73) AND
48.24/28.46	                    (74) QDP
48.24/28.46	                        (75) UsableRulesProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (76) QDP
48.24/28.46	                        (77) QReductionProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (78) QDP
48.24/28.46	                        (79) MRRProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (80) QDP
48.24/28.46	                        (81) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (82) TRUE
48.24/28.46	                    (83) QDP
48.24/28.46	                        (84) UsableRulesProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (85) QDP
48.24/28.46	                        (86) QReductionProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (87) QDP
48.24/28.46	                        (88) QDPOrderProof [EQUIVALENT, 13 ms]
48.24/28.46	                        (89) QDP
48.24/28.46	                        (90) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (91) QDP
48.24/28.46	                        (92) InductionCalculusProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (93) QDP
48.24/28.46	                        (94) NonInfProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (95) QDP
48.24/28.46	                        (96) DependencyGraphProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (97) QDP
48.24/28.46	                        (98) QDPSizeChangeProof [EQUIVALENT, 0 ms]
48.24/28.46	                        (99) YES
48.24/28.46	    (100) QDP
48.24/28.46	        (101) QDPSizeChangeProof [EQUIVALENT, 0 ms]
48.24/28.46	        (102) YES
48.24/28.46	
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(0)
48.24/28.46	Obligation:
48.24/28.46	mainModule Main 
48.24/28.46	module Main where {
48.24/28.46	import qualified Prelude;
48.24/28.46	}
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(1) IFR (EQUIVALENT)
48.24/28.46	If Reductions:
48.24/28.46	The following If expression
48.24/28.46	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
48.24/28.46	is transformed to
48.24/28.46	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
48.24/28.46	primModNatS0 x y False = Succ x;
48.24/28.46	"
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(2)
48.24/28.46	Obligation:
48.24/28.46	mainModule Main 
48.24/28.46	module Main where {
48.24/28.46	import qualified Prelude;
48.24/28.46	}
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(3) BR (EQUIVALENT)
48.24/28.46	Replaced joker patterns by fresh variables and removed binding patterns.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(4)
48.24/28.46	Obligation:
48.24/28.46	mainModule Main 
48.24/28.46	module Main where {
48.24/28.46	import qualified Prelude;
48.24/28.46	}
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(5) COR (EQUIVALENT)
48.24/28.46	Cond Reductions:
48.24/28.46	The following Function with conditions
48.24/28.46	"absReal x|x >= 0x|otherwise`negate` x;
48.24/28.46	"
48.24/28.46	is transformed to
48.24/28.46	"absReal x = absReal2 x;
48.24/28.46	"
48.24/28.46	"absReal0 x True = `negate` x;
48.24/28.46	"
48.24/28.46	"absReal1 x True = x;
48.24/28.46	absReal1 x False = absReal0 x otherwise;
48.24/28.46	"
48.24/28.46	"absReal2 x = absReal1 x (x >= 0);
48.24/28.46	"
48.24/28.46	The following Function with conditions
48.24/28.46	"gcd' x 0 = x;
48.24/28.46	gcd' x y = gcd' y (x `rem` y);
48.24/28.46	"
48.24/28.46	is transformed to
48.24/28.46	"gcd' x xx = gcd'2 x xx;
48.24/28.46	gcd' x y = gcd'0 x y;
48.24/28.46	"
48.24/28.46	"gcd'0 x y = gcd' y (x `rem` y);
48.24/28.46	"
48.24/28.46	"gcd'1 True x xx = x;
48.24/28.46	gcd'1 xy xz yu = gcd'0 xz yu;
48.24/28.46	"
48.24/28.46	"gcd'2 x xx = gcd'1 (xx == 0) x xx;
48.24/28.46	gcd'2 yv yw = gcd'0 yv yw;
48.24/28.46	"
48.24/28.46	The following Function with conditions
48.24/28.46	"gcd 0 0 = error [];
48.24/28.46	gcd x y = gcd' (abs x) (abs y) where {
48.24/28.46	gcd' x 0 = x;
48.24/28.46	gcd' x y = gcd' y (x `rem` y);
48.24/28.46	} 
48.24/28.46	;
48.24/28.46	"
48.24/28.46	is transformed to
48.24/28.46	"gcd yx yy = gcd3 yx yy;
48.24/28.46	gcd x y = gcd0 x y;
48.24/28.46	"
48.24/28.46	"gcd0 x y = gcd' (abs x) (abs y) where {
48.24/28.46	gcd' x xx = gcd'2 x xx;
48.24/28.46	gcd' x y = gcd'0 x y;
48.24/28.46	;
48.24/28.46	gcd'0 x y = gcd' y (x `rem` y);
48.24/28.46	;
48.24/28.46	gcd'1 True x xx = x;
48.24/28.46	gcd'1 xy xz yu = gcd'0 xz yu;
48.24/28.46	;
48.24/28.46	gcd'2 x xx = gcd'1 (xx == 0) x xx;
48.24/28.46	gcd'2 yv yw = gcd'0 yv yw;
48.24/28.46	} 
48.24/28.46	;
48.24/28.46	"
48.24/28.46	"gcd1 True yx yy = error [];
48.24/28.46	gcd1 yz zu zv = gcd0 zu zv;
48.24/28.46	"
48.24/28.46	"gcd2 True yx yy = gcd1 (yy == 0) yx yy;
48.24/28.46	gcd2 zw zx zy = gcd0 zx zy;
48.24/28.46	"
48.24/28.46	"gcd3 yx yy = gcd2 (yx == 0) yx yy;
48.24/28.46	gcd3 zz vuu = gcd0 zz vuu;
48.24/28.46	"
48.24/28.46	The following Function with conditions
48.24/28.46	"undefined |Falseundefined;
48.24/28.46	"
48.24/28.46	is transformed to
48.24/28.46	"undefined  = undefined1;
48.24/28.46	"
48.24/28.46	"undefined0 True = undefined;
48.24/28.46	"
48.24/28.46	"undefined1  = undefined0 False;
48.24/28.46	"
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(6)
48.24/28.46	Obligation:
48.24/28.46	mainModule Main 
48.24/28.46	module Main where {
48.24/28.46	import qualified Prelude;
48.24/28.46	}
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(7) LetRed (EQUIVALENT)
48.24/28.46	Let/Where Reductions:
48.24/28.46	The bindings of the following Let/Where expression
48.24/28.46	"gcd' (abs x) (abs y) where {
48.24/28.46	gcd' x xx = gcd'2 x xx;
48.24/28.46	gcd' x y = gcd'0 x y;
48.24/28.46	;
48.24/28.46	gcd'0 x y = gcd' y (x `rem` y);
48.24/28.46	;
48.24/28.46	gcd'1 True x xx = x;
48.24/28.46	gcd'1 xy xz yu = gcd'0 xz yu;
48.24/28.46	;
48.24/28.46	gcd'2 x xx = gcd'1 (xx == 0) x xx;
48.24/28.46	gcd'2 yv yw = gcd'0 yv yw;
48.24/28.46	} 
48.24/28.46	"
48.24/28.46	are unpacked to the following functions on top level
48.24/28.46	"gcd0Gcd'2 x xx = gcd0Gcd'1 (xx == 0) x xx;
48.24/28.46	gcd0Gcd'2 yv yw = gcd0Gcd'0 yv yw;
48.24/28.46	"
48.24/28.46	"gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y);
48.24/28.46	"
48.24/28.46	"gcd0Gcd'1 True x xx = x;
48.24/28.46	gcd0Gcd'1 xy xz yu = gcd0Gcd'0 xz yu;
48.24/28.46	"
48.24/28.46	"gcd0Gcd' x xx = gcd0Gcd'2 x xx;
48.24/28.46	gcd0Gcd' x y = gcd0Gcd'0 x y;
48.24/28.46	"
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(8)
48.24/28.46	Obligation:
48.24/28.46	mainModule Main 
48.24/28.46	module Main where {
48.24/28.46	import qualified Prelude;
48.24/28.46	}
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(9) NumRed (SOUND)
48.24/28.46	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(10)
48.24/28.46	Obligation:
48.24/28.46	mainModule Main 
48.24/28.46	module Main where {
48.24/28.46	import qualified Prelude;
48.24/28.46	}
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(11) Narrow (SOUND)
48.24/28.46	Haskell To QDPs
48.24/28.46	
48.24/28.46	digraph dp_graph {
48.24/28.46	node [outthreshold=100, inthreshold=100];1[label="gcd",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
48.24/28.46	3[label="gcd vuv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
48.24/28.46	4[label="gcd vuv3 vuv4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
48.24/28.46	5[label="gcd3 vuv3 vuv4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
48.24/28.46	6[label="gcd2 (vuv3 == fromInt (Pos Zero)) vuv3 vuv4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
48.24/28.46	7[label="gcd2 (primEqInt vuv3 (fromInt (Pos Zero))) vuv3 vuv4",fontsize=16,color="burlywood",shape="box"];1509[label="vuv3/Pos vuv30",fontsize=10,color="white",style="solid",shape="box"];7 -> 1509[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1509 -> 8[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1510[label="vuv3/Neg vuv30",fontsize=10,color="white",style="solid",shape="box"];7 -> 1510[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1510 -> 9[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	8[label="gcd2 (primEqInt (Pos vuv30) (fromInt (Pos Zero))) (Pos vuv30) vuv4",fontsize=16,color="burlywood",shape="box"];1511[label="vuv30/Succ vuv300",fontsize=10,color="white",style="solid",shape="box"];8 -> 1511[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1511 -> 10[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1512[label="vuv30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 1512[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1512 -> 11[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	9[label="gcd2 (primEqInt (Neg vuv30) (fromInt (Pos Zero))) (Neg vuv30) vuv4",fontsize=16,color="burlywood",shape="box"];1513[label="vuv30/Succ vuv300",fontsize=10,color="white",style="solid",shape="box"];9 -> 1513[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1513 -> 12[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1514[label="vuv30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 1514[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1514 -> 13[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	10[label="gcd2 (primEqInt (Pos (Succ vuv300)) (fromInt (Pos Zero))) (Pos (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
48.24/28.46	11[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) vuv4",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
48.24/28.46	12[label="gcd2 (primEqInt (Neg (Succ vuv300)) (fromInt (Pos Zero))) (Neg (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
48.24/28.46	13[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) vuv4",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
48.24/28.46	14[label="gcd2 (primEqInt (Pos (Succ vuv300)) (Pos Zero)) (Pos (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
48.24/28.46	15[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) vuv4",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
48.24/28.46	16[label="gcd2 (primEqInt (Neg (Succ vuv300)) (Pos Zero)) (Neg (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
48.24/28.46	17[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) vuv4",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
48.24/28.46	18[label="gcd2 False (Pos (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
48.24/28.46	19[label="gcd2 True (Pos Zero) vuv4",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
48.24/28.46	20[label="gcd2 False (Neg (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
48.24/28.46	21[label="gcd2 True (Neg Zero) vuv4",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
48.24/28.46	22[label="gcd0 (Pos (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
48.24/28.46	23[label="gcd1 (vuv4 == fromInt (Pos Zero)) (Pos Zero) vuv4",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
48.24/28.46	24[label="gcd0 (Neg (Succ vuv300)) vuv4",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
48.24/28.46	25[label="gcd1 (vuv4 == fromInt (Pos Zero)) (Neg Zero) vuv4",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
48.24/28.46	26[label="gcd0Gcd' (abs (Pos (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
48.24/28.46	27[label="gcd1 (primEqInt vuv4 (fromInt (Pos Zero))) (Pos Zero) vuv4",fontsize=16,color="burlywood",shape="box"];1515[label="vuv4/Pos vuv40",fontsize=10,color="white",style="solid",shape="box"];27 -> 1515[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1515 -> 31[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1516[label="vuv4/Neg vuv40",fontsize=10,color="white",style="solid",shape="box"];27 -> 1516[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1516 -> 32[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	28[label="gcd0Gcd' (abs (Neg (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];28 -> 33[label="",style="solid", color="black", weight=3];
48.24/28.46	29[label="gcd1 (primEqInt vuv4 (fromInt (Pos Zero))) (Neg Zero) vuv4",fontsize=16,color="burlywood",shape="box"];1517[label="vuv4/Pos vuv40",fontsize=10,color="white",style="solid",shape="box"];29 -> 1517[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1517 -> 34[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1518[label="vuv4/Neg vuv40",fontsize=10,color="white",style="solid",shape="box"];29 -> 1518[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1518 -> 35[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	30[label="gcd0Gcd'2 (abs (Pos (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];30 -> 36[label="",style="solid", color="black", weight=3];
48.24/28.46	31[label="gcd1 (primEqInt (Pos vuv40) (fromInt (Pos Zero))) (Pos Zero) (Pos vuv40)",fontsize=16,color="burlywood",shape="box"];1519[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];31 -> 1519[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1519 -> 37[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1520[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];31 -> 1520[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1520 -> 38[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	32[label="gcd1 (primEqInt (Neg vuv40) (fromInt (Pos Zero))) (Pos Zero) (Neg vuv40)",fontsize=16,color="burlywood",shape="box"];1521[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];32 -> 1521[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1521 -> 39[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1522[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 1522[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1522 -> 40[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	33[label="gcd0Gcd'2 (abs (Neg (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3];
48.24/28.46	34[label="gcd1 (primEqInt (Pos vuv40) (fromInt (Pos Zero))) (Neg Zero) (Pos vuv40)",fontsize=16,color="burlywood",shape="box"];1523[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];34 -> 1523[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1523 -> 42[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1524[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 1524[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1524 -> 43[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	35[label="gcd1 (primEqInt (Neg vuv40) (fromInt (Pos Zero))) (Neg Zero) (Neg vuv40)",fontsize=16,color="burlywood",shape="box"];1525[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];35 -> 1525[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1525 -> 44[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1526[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 1526[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1526 -> 45[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	36[label="gcd0Gcd'1 (abs vuv4 == fromInt (Pos Zero)) (abs (Pos (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];36 -> 46[label="",style="solid", color="black", weight=3];
48.24/28.46	37[label="gcd1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];37 -> 47[label="",style="solid", color="black", weight=3];
48.24/28.46	38[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];38 -> 48[label="",style="solid", color="black", weight=3];
48.24/28.46	39[label="gcd1 (primEqInt (Neg (Succ vuv400)) (fromInt (Pos Zero))) (Pos Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];39 -> 49[label="",style="solid", color="black", weight=3];
48.24/28.46	40[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];40 -> 50[label="",style="solid", color="black", weight=3];
48.24/28.46	41[label="gcd0Gcd'1 (abs vuv4 == fromInt (Pos Zero)) (abs (Neg (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];41 -> 51[label="",style="solid", color="black", weight=3];
48.24/28.46	42[label="gcd1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];42 -> 52[label="",style="solid", color="black", weight=3];
48.24/28.46	43[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];43 -> 53[label="",style="solid", color="black", weight=3];
48.24/28.46	44[label="gcd1 (primEqInt (Neg (Succ vuv400)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];44 -> 54[label="",style="solid", color="black", weight=3];
48.24/28.46	45[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];45 -> 55[label="",style="solid", color="black", weight=3];
48.24/28.46	46[label="gcd0Gcd'1 (primEqInt (abs vuv4) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];46 -> 56[label="",style="solid", color="black", weight=3];
48.24/28.46	47[label="gcd1 (primEqInt (Pos (Succ vuv400)) (Pos Zero)) (Pos Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];47 -> 57[label="",style="solid", color="black", weight=3];
48.24/28.46	48[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];48 -> 58[label="",style="solid", color="black", weight=3];
48.24/28.46	49[label="gcd1 (primEqInt (Neg (Succ vuv400)) (Pos Zero)) (Pos Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];49 -> 59[label="",style="solid", color="black", weight=3];
48.24/28.46	50[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];50 -> 60[label="",style="solid", color="black", weight=3];
48.24/28.46	51[label="gcd0Gcd'1 (primEqInt (abs vuv4) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (abs vuv4)",fontsize=16,color="black",shape="box"];51 -> 61[label="",style="solid", color="black", weight=3];
48.24/28.46	52[label="gcd1 (primEqInt (Pos (Succ vuv400)) (Pos Zero)) (Neg Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];52 -> 62[label="",style="solid", color="black", weight=3];
48.24/28.46	53[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];53 -> 63[label="",style="solid", color="black", weight=3];
48.24/28.46	54[label="gcd1 (primEqInt (Neg (Succ vuv400)) (Pos Zero)) (Neg Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];54 -> 64[label="",style="solid", color="black", weight=3];
48.24/28.46	55[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];55 -> 65[label="",style="solid", color="black", weight=3];
48.24/28.46	56[label="gcd0Gcd'1 (primEqInt (absReal vuv4) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal vuv4)",fontsize=16,color="black",shape="box"];56 -> 66[label="",style="solid", color="black", weight=3];
48.24/28.46	57[label="gcd1 False (Pos Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];57 -> 67[label="",style="solid", color="black", weight=3];
48.24/28.46	58[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];58 -> 68[label="",style="solid", color="black", weight=3];
48.24/28.46	59[label="gcd1 False (Pos Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];59 -> 69[label="",style="solid", color="black", weight=3];
48.24/28.46	60[label="gcd1 True (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];60 -> 70[label="",style="solid", color="black", weight=3];
48.24/28.46	61[label="gcd0Gcd'1 (primEqInt (absReal vuv4) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal vuv4)",fontsize=16,color="black",shape="box"];61 -> 71[label="",style="solid", color="black", weight=3];
48.24/28.46	62[label="gcd1 False (Neg Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];62 -> 72[label="",style="solid", color="black", weight=3];
48.24/28.46	63[label="gcd1 True (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];63 -> 73[label="",style="solid", color="black", weight=3];
48.24/28.46	64[label="gcd1 False (Neg Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];64 -> 74[label="",style="solid", color="black", weight=3];
48.24/28.46	65[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];65 -> 75[label="",style="solid", color="black", weight=3];
48.24/28.46	66[label="gcd0Gcd'1 (primEqInt (absReal2 vuv4) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal2 vuv4)",fontsize=16,color="black",shape="box"];66 -> 76[label="",style="solid", color="black", weight=3];
48.24/28.46	67[label="gcd0 (Pos Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];67 -> 77[label="",style="solid", color="black", weight=3];
48.24/28.46	68[label="error []",fontsize=16,color="black",shape="triangle"];68 -> 78[label="",style="solid", color="black", weight=3];
48.24/28.46	69[label="gcd0 (Pos Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];69 -> 79[label="",style="solid", color="black", weight=3];
48.24/28.46	70 -> 68[label="",style="dashed", color="red", weight=0];
48.24/28.46	70[label="error []",fontsize=16,color="magenta"];71[label="gcd0Gcd'1 (primEqInt (absReal2 vuv4) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal2 vuv4)",fontsize=16,color="black",shape="box"];71 -> 80[label="",style="solid", color="black", weight=3];
48.24/28.46	72[label="gcd0 (Neg Zero) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];72 -> 81[label="",style="solid", color="black", weight=3];
48.24/28.46	73 -> 68[label="",style="dashed", color="red", weight=0];
48.24/28.46	73[label="error []",fontsize=16,color="magenta"];74[label="gcd0 (Neg Zero) (Neg (Succ vuv400))",fontsize=16,color="black",shape="box"];74 -> 82[label="",style="solid", color="black", weight=3];
48.24/28.46	75 -> 68[label="",style="dashed", color="red", weight=0];
48.24/28.46	75[label="error []",fontsize=16,color="magenta"];76[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (vuv4 >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 vuv4 (vuv4 >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];76 -> 83[label="",style="solid", color="black", weight=3];
48.24/28.46	77[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];77 -> 84[label="",style="solid", color="black", weight=3];
48.24/28.46	78[label="error []",fontsize=16,color="red",shape="box"];79[label="gcd0Gcd' (abs (Pos Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];79 -> 85[label="",style="solid", color="black", weight=3];
48.24/28.46	80[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (vuv4 >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 vuv4 (vuv4 >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];80 -> 86[label="",style="solid", color="black", weight=3];
48.24/28.46	81[label="gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];81 -> 87[label="",style="solid", color="black", weight=3];
48.24/28.46	82[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];82 -> 88[label="",style="solid", color="black", weight=3];
48.24/28.46	83[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (compare vuv4 (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 vuv4 (compare vuv4 (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];83 -> 89[label="",style="solid", color="black", weight=3];
48.24/28.46	84[label="gcd0Gcd'2 (abs (Pos Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];84 -> 90[label="",style="solid", color="black", weight=3];
48.24/28.46	85[label="gcd0Gcd'2 (abs (Pos Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];85 -> 91[label="",style="solid", color="black", weight=3];
48.24/28.46	86[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (compare vuv4 (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 vuv4 (compare vuv4 (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];86 -> 92[label="",style="solid", color="black", weight=3];
48.24/28.46	87[label="gcd0Gcd'2 (abs (Neg Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];87 -> 93[label="",style="solid", color="black", weight=3];
48.24/28.46	88[label="gcd0Gcd'2 (abs (Neg Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];88 -> 94[label="",style="solid", color="black", weight=3];
48.24/28.46	89[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (not (compare vuv4 (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 vuv4 (not (compare vuv4 (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];89 -> 95[label="",style="solid", color="black", weight=3];
48.24/28.46	90[label="gcd0Gcd'1 (abs (Pos (Succ vuv400)) == fromInt (Pos Zero)) (abs (Pos Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];90 -> 96[label="",style="solid", color="black", weight=3];
48.24/28.46	91[label="gcd0Gcd'1 (abs (Neg (Succ vuv400)) == fromInt (Pos Zero)) (abs (Pos Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];91 -> 97[label="",style="solid", color="black", weight=3];
48.24/28.46	92[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (not (compare vuv4 (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 vuv4 (not (compare vuv4 (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];92 -> 98[label="",style="solid", color="black", weight=3];
48.24/28.46	93[label="gcd0Gcd'1 (abs (Pos (Succ vuv400)) == fromInt (Pos Zero)) (abs (Neg Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
48.24/28.46	94[label="gcd0Gcd'1 (abs (Neg (Succ vuv400)) == fromInt (Pos Zero)) (abs (Neg Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
48.24/28.46	95[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (not (primCmpInt vuv4 (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 vuv4 (not (primCmpInt vuv4 (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];1527[label="vuv4/Pos vuv40",fontsize=10,color="white",style="solid",shape="box"];95 -> 1527[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1527 -> 101[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1528[label="vuv4/Neg vuv40",fontsize=10,color="white",style="solid",shape="box"];95 -> 1528[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1528 -> 102[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	96[label="gcd0Gcd'1 (primEqInt (abs (Pos (Succ vuv400))) (fromInt (Pos Zero))) (abs (Pos Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];96 -> 103[label="",style="solid", color="black", weight=3];
48.24/28.46	97[label="gcd0Gcd'1 (primEqInt (abs (Neg (Succ vuv400))) (fromInt (Pos Zero))) (abs (Pos Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];97 -> 104[label="",style="solid", color="black", weight=3];
48.24/28.46	98[label="gcd0Gcd'1 (primEqInt (absReal1 vuv4 (not (primCmpInt vuv4 (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 vuv4 (not (primCmpInt vuv4 (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];1529[label="vuv4/Pos vuv40",fontsize=10,color="white",style="solid",shape="box"];98 -> 1529[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1529 -> 105[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1530[label="vuv4/Neg vuv40",fontsize=10,color="white",style="solid",shape="box"];98 -> 1530[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1530 -> 106[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	99[label="gcd0Gcd'1 (primEqInt (abs (Pos (Succ vuv400))) (fromInt (Pos Zero))) (abs (Neg Zero)) (abs (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];99 -> 107[label="",style="solid", color="black", weight=3];
48.24/28.46	100[label="gcd0Gcd'1 (primEqInt (abs (Neg (Succ vuv400))) (fromInt (Pos Zero))) (abs (Neg Zero)) (abs (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];100 -> 108[label="",style="solid", color="black", weight=3];
48.24/28.46	101[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuv40) (not (primCmpInt (Pos vuv40) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 (Pos vuv40) (not (primCmpInt (Pos vuv40) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];1531[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];101 -> 1531[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1531 -> 109[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1532[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];101 -> 1532[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1532 -> 110[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	102[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuv40) (not (primCmpInt (Neg vuv40) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 (Neg vuv40) (not (primCmpInt (Neg vuv40) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];1533[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];102 -> 1533[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1533 -> 111[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1534[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];102 -> 1534[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1534 -> 112[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	103[label="gcd0Gcd'1 (primEqInt (absReal (Pos (Succ vuv400))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];103 -> 113[label="",style="solid", color="black", weight=3];
48.24/28.46	104[label="gcd0Gcd'1 (primEqInt (absReal (Neg (Succ vuv400))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];104 -> 114[label="",style="solid", color="black", weight=3];
48.24/28.46	105[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuv40) (not (primCmpInt (Pos vuv40) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 (Pos vuv40) (not (primCmpInt (Pos vuv40) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];1535[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];105 -> 1535[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1535 -> 115[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1536[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];105 -> 1536[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1536 -> 116[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	106[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuv40) (not (primCmpInt (Neg vuv40) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 (Neg vuv40) (not (primCmpInt (Neg vuv40) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];1537[label="vuv40/Succ vuv400",fontsize=10,color="white",style="solid",shape="box"];106 -> 1537[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1537 -> 117[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1538[label="vuv40/Zero",fontsize=10,color="white",style="solid",shape="box"];106 -> 1538[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1538 -> 118[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	107[label="gcd0Gcd'1 (primEqInt (absReal (Pos (Succ vuv400))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];107 -> 119[label="",style="solid", color="black", weight=3];
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48.24/28.46	123[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];123 -> 135[label="",style="solid", color="black", weight=3];
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48.24/28.46	134[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not (EQ == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 (Pos Zero) (not (EQ == LT)))",fontsize=16,color="black",shape="box"];134 -> 146[label="",style="solid", color="black", weight=3];
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48.24/28.46	138[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuv400)) (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];138 -> 150[label="",style="solid", color="black", weight=3];
48.24/28.46	139[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (primCmpNat (Succ vuv400) Zero == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 (Pos (Succ vuv400)) (not (primCmpNat (Succ vuv400) Zero == LT)))",fontsize=16,color="black",shape="box"];139 -> 151[label="",style="solid", color="black", weight=3];
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48.24/28.46	144[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuv400)) (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];144 -> 156[label="",style="solid", color="black", weight=3];
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48.24/28.46	146[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not False)) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 (Pos Zero) (not False))",fontsize=16,color="black",shape="box"];146 -> 158[label="",style="solid", color="black", weight=3];
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48.24/28.46	150[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuv400)) (not (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];150 -> 162[label="",style="solid", color="black", weight=3];
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48.24/28.46	156[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuv400)) (not (compare (Neg (Succ vuv400)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];156 -> 168[label="",style="solid", color="black", weight=3];
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48.24/28.46	159[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) False) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 (Neg (Succ vuv400)) False)",fontsize=16,color="black",shape="box"];159 -> 171[label="",style="solid", color="black", weight=3];
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48.24/28.46	161[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (primCmpInt (Pos (Succ vuv400)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuv400)) (not (primCmpInt (Pos (Succ vuv400)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];161 -> 173[label="",style="solid", color="black", weight=3];
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48.24/28.46	163[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not False)) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 (Pos (Succ vuv400)) (not False))",fontsize=16,color="black",shape="box"];163 -> 175[label="",style="solid", color="black", weight=3];
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48.24/28.46	168[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];168 -> 180[label="",style="solid", color="black", weight=3];
48.24/28.46	169[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal1 (Pos (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];169 -> 181[label="",style="solid", color="black", weight=3];
48.24/28.46	170[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (Pos Zero)",fontsize=16,color="black",shape="box"];170 -> 182[label="",style="solid", color="black", weight=3];
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48.24/28.46	172[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (Neg Zero)",fontsize=16,color="black",shape="box"];172 -> 184[label="",style="solid", color="black", weight=3];
48.24/28.46	173[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (primCmpInt (Pos (Succ vuv400)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuv400)) (not (primCmpInt (Pos (Succ vuv400)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];173 -> 185[label="",style="solid", color="black", weight=3];
48.24/28.46	174[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];174 -> 186[label="",style="solid", color="black", weight=3];
48.24/28.46	175[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal1 (Pos (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];175 -> 187[label="",style="solid", color="black", weight=3];
48.24/28.46	176[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (Pos Zero)",fontsize=16,color="black",shape="box"];176 -> 188[label="",style="solid", color="black", weight=3];
48.24/28.46	177[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuv400)) otherwise) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal0 (Neg (Succ vuv400)) otherwise)",fontsize=16,color="black",shape="box"];177 -> 189[label="",style="solid", color="black", weight=3];
48.24/28.46	178[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (Neg Zero)",fontsize=16,color="black",shape="box"];178 -> 190[label="",style="solid", color="black", weight=3];
48.24/28.46	179[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (primCmpInt (Pos (Succ vuv400)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Pos (Succ vuv400)) (not (primCmpInt (Pos (Succ vuv400)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];179 -> 191[label="",style="solid", color="black", weight=3];
48.24/28.46	180[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuv400)) (not (primCmpInt (Neg (Succ vuv400)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];180 -> 192[label="",style="solid", color="black", weight=3];
48.24/28.46	181[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];181 -> 193[label="",style="solid", color="black", weight=3];
48.24/28.46	182[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (abs (Pos (Succ vuv300))) (Pos Zero)",fontsize=16,color="black",shape="box"];182 -> 194[label="",style="solid", color="black", weight=3];
48.24/28.46	183[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (absReal0 (Neg (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];183 -> 195[label="",style="solid", color="black", weight=3];
48.24/28.46	184[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) (abs (Pos (Succ vuv300))) (Neg Zero)",fontsize=16,color="black",shape="box"];184 -> 196[label="",style="solid", color="black", weight=3];
48.24/28.46	185[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (primCmpNat (Succ vuv400) Zero == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuv400)) (not (primCmpNat (Succ vuv400) Zero == LT)))",fontsize=16,color="black",shape="box"];185 -> 197[label="",style="solid", color="black", weight=3];
48.24/28.46	186[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (LT == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuv400)) (not (LT == LT)))",fontsize=16,color="black",shape="box"];186 -> 198[label="",style="solid", color="black", weight=3];
48.24/28.46	187[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];187 -> 199[label="",style="solid", color="black", weight=3];
48.24/28.46	188[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (abs (Neg (Succ vuv300))) (Pos Zero)",fontsize=16,color="black",shape="box"];188 -> 200[label="",style="solid", color="black", weight=3];
48.24/28.46	189[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (absReal0 (Neg (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];189 -> 201[label="",style="solid", color="black", weight=3];
48.24/28.46	190[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) (abs (Neg (Succ vuv300))) (Neg Zero)",fontsize=16,color="black",shape="box"];190 -> 202[label="",style="solid", color="black", weight=3];
48.24/28.46	191[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (primCmpNat (Succ vuv400) Zero == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Pos (Succ vuv400)) (not (primCmpNat (Succ vuv400) Zero == LT)))",fontsize=16,color="black",shape="box"];191 -> 203[label="",style="solid", color="black", weight=3];
48.24/28.46	192[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not (LT == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuv400)) (not (LT == LT)))",fontsize=16,color="black",shape="box"];192 -> 204[label="",style="solid", color="black", weight=3];
48.24/28.46	193[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (Pos Zero)) (abs (Pos (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];193 -> 205[label="",style="solid", color="black", weight=3];
48.24/28.46	194[label="gcd0Gcd'1 True (abs (Pos (Succ vuv300))) (Pos Zero)",fontsize=16,color="black",shape="box"];194 -> 206[label="",style="solid", color="black", weight=3];
48.24/28.46	195 -> 252[label="",style="dashed", color="red", weight=0];
48.24/28.46	195[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuv400)) (fromInt (Pos Zero))) (abs (Pos (Succ vuv300))) (`negate` Neg (Succ vuv400))",fontsize=16,color="magenta"];195 -> 253[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	196[label="gcd0Gcd'1 True (abs (Pos (Succ vuv300))) (Neg Zero)",fontsize=16,color="black",shape="box"];196 -> 208[label="",style="solid", color="black", weight=3];
48.24/28.46	197[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (GT == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuv400)) (not (GT == LT)))",fontsize=16,color="black",shape="box"];197 -> 209[label="",style="solid", color="black", weight=3];
48.24/28.46	198[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not True)) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuv400)) (not True))",fontsize=16,color="black",shape="box"];198 -> 210[label="",style="solid", color="black", weight=3];
48.24/28.46	199[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (Pos Zero)) (abs (Neg (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];199 -> 211[label="",style="solid", color="black", weight=3];
48.24/28.46	200[label="gcd0Gcd'1 True (abs (Neg (Succ vuv300))) (Pos Zero)",fontsize=16,color="black",shape="box"];200 -> 212[label="",style="solid", color="black", weight=3];
48.24/28.46	201 -> 252[label="",style="dashed", color="red", weight=0];
48.24/28.46	201[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuv400)) (fromInt (Pos Zero))) (abs (Neg (Succ vuv300))) (`negate` Neg (Succ vuv400))",fontsize=16,color="magenta"];201 -> 254[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	202[label="gcd0Gcd'1 True (abs (Neg (Succ vuv300))) (Neg Zero)",fontsize=16,color="black",shape="box"];202 -> 214[label="",style="solid", color="black", weight=3];
48.24/28.46	203[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not (GT == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Pos (Succ vuv400)) (not (GT == LT)))",fontsize=16,color="black",shape="box"];203 -> 215[label="",style="solid", color="black", weight=3];
48.24/28.46	204[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) (not True)) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuv400)) (not True))",fontsize=16,color="black",shape="box"];204 -> 216[label="",style="solid", color="black", weight=3];
48.24/28.46	205[label="gcd0Gcd'1 False (abs (Pos (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];205 -> 217[label="",style="solid", color="black", weight=3];
48.24/28.46	206[label="abs (Pos (Succ vuv300))",fontsize=16,color="black",shape="triangle"];206 -> 218[label="",style="solid", color="black", weight=3];
48.24/28.46	253 -> 206[label="",style="dashed", color="red", weight=0];
48.24/28.46	253[label="abs (Pos (Succ vuv300))",fontsize=16,color="magenta"];252[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuv400)) (fromInt (Pos Zero))) vuv7 (`negate` Neg (Succ vuv400))",fontsize=16,color="black",shape="triangle"];252 -> 257[label="",style="solid", color="black", weight=3];
48.24/28.46	208 -> 206[label="",style="dashed", color="red", weight=0];
48.24/28.46	208[label="abs (Pos (Succ vuv300))",fontsize=16,color="magenta"];209[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not False)) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuv400)) (not False))",fontsize=16,color="black",shape="box"];209 -> 222[label="",style="solid", color="black", weight=3];
48.24/28.46	210[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) False) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuv400)) False)",fontsize=16,color="black",shape="box"];210 -> 223[label="",style="solid", color="black", weight=3];
48.24/28.46	211[label="gcd0Gcd'1 False (abs (Neg (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];211 -> 224[label="",style="solid", color="black", weight=3];
48.24/28.46	212[label="abs (Neg (Succ vuv300))",fontsize=16,color="black",shape="triangle"];212 -> 225[label="",style="solid", color="black", weight=3];
48.24/28.46	254 -> 212[label="",style="dashed", color="red", weight=0];
48.24/28.46	254[label="abs (Neg (Succ vuv300))",fontsize=16,color="magenta"];214 -> 212[label="",style="dashed", color="red", weight=0];
48.24/28.46	214[label="abs (Neg (Succ vuv300))",fontsize=16,color="magenta"];215[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) (not False)) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Pos (Succ vuv400)) (not False))",fontsize=16,color="black",shape="box"];215 -> 226[label="",style="solid", color="black", weight=3];
48.24/28.46	216[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuv400)) False) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuv400)) False)",fontsize=16,color="black",shape="box"];216 -> 227[label="",style="solid", color="black", weight=3];
48.24/28.46	217 -> 228[label="",style="dashed", color="red", weight=0];
48.24/28.46	217[label="gcd0Gcd'0 (abs (Pos (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="magenta"];217 -> 229[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	218[label="absReal (Pos (Succ vuv300))",fontsize=16,color="black",shape="box"];218 -> 231[label="",style="solid", color="black", weight=3];
48.24/28.46	257[label="gcd0Gcd'1 (primEqInt (primNegInt (Neg (Succ vuv400))) (fromInt (Pos Zero))) vuv7 (primNegInt (Neg (Succ vuv400)))",fontsize=16,color="black",shape="box"];257 -> 264[label="",style="solid", color="black", weight=3];
48.24/28.46	222[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];222 -> 233[label="",style="solid", color="black", weight=3];
48.24/28.46	223[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuv400)) otherwise) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal0 (Neg (Succ vuv400)) otherwise)",fontsize=16,color="black",shape="box"];223 -> 234[label="",style="solid", color="black", weight=3];
48.24/28.46	224 -> 228[label="",style="dashed", color="red", weight=0];
48.24/28.46	224[label="gcd0Gcd'0 (abs (Neg (Succ vuv300))) (Pos (Succ vuv400))",fontsize=16,color="magenta"];224 -> 230[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	225[label="absReal (Neg (Succ vuv300))",fontsize=16,color="black",shape="box"];225 -> 235[label="",style="solid", color="black", weight=3];
48.24/28.46	226[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Pos (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];226 -> 236[label="",style="solid", color="black", weight=3];
48.24/28.46	227[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuv400)) otherwise) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal0 (Neg (Succ vuv400)) otherwise)",fontsize=16,color="black",shape="box"];227 -> 237[label="",style="solid", color="black", weight=3];
48.24/28.46	229 -> 206[label="",style="dashed", color="red", weight=0];
48.24/28.46	229[label="abs (Pos (Succ vuv300))",fontsize=16,color="magenta"];228[label="gcd0Gcd'0 vuv6 (Pos (Succ vuv400))",fontsize=16,color="black",shape="triangle"];228 -> 238[label="",style="solid", color="black", weight=3];
48.24/28.46	231[label="absReal2 (Pos (Succ vuv300))",fontsize=16,color="black",shape="box"];231 -> 239[label="",style="solid", color="black", weight=3];
48.24/28.46	264 -> 232[label="",style="dashed", color="red", weight=0];
48.24/28.46	264[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) vuv7 (Pos (Succ vuv400))",fontsize=16,color="magenta"];264 -> 272[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	233 -> 232[label="",style="dashed", color="red", weight=0];
48.24/28.46	233[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) (abs (Pos Zero)) (Pos (Succ vuv400))",fontsize=16,color="magenta"];233 -> 241[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	233 -> 242[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	234[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal0 (Neg (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];234 -> 243[label="",style="solid", color="black", weight=3];
48.24/28.46	230 -> 212[label="",style="dashed", color="red", weight=0];
48.24/28.46	230[label="abs (Neg (Succ vuv300))",fontsize=16,color="magenta"];235[label="absReal2 (Neg (Succ vuv300))",fontsize=16,color="black",shape="box"];235 -> 244[label="",style="solid", color="black", weight=3];
48.24/28.46	236 -> 232[label="",style="dashed", color="red", weight=0];
48.24/28.46	236[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) (abs (Neg Zero)) (Pos (Succ vuv400))",fontsize=16,color="magenta"];236 -> 245[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	236 -> 246[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	237[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuv400)) True) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal0 (Neg (Succ vuv400)) True)",fontsize=16,color="black",shape="box"];237 -> 247[label="",style="solid", color="black", weight=3];
48.24/28.46	238[label="gcd0Gcd' (Pos (Succ vuv400)) (vuv6 `rem` Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];238 -> 248[label="",style="solid", color="black", weight=3];
48.24/28.46	239[label="absReal1 (Pos (Succ vuv300)) (Pos (Succ vuv300) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];239 -> 249[label="",style="solid", color="black", weight=3];
48.24/28.46	272[label="vuv7",fontsize=16,color="green",shape="box"];232[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (fromInt (Pos Zero))) vuv5 (Pos (Succ vuv400))",fontsize=16,color="black",shape="triangle"];232 -> 240[label="",style="solid", color="black", weight=3];
48.24/28.46	241[label="abs (Pos Zero)",fontsize=16,color="black",shape="triangle"];241 -> 251[label="",style="solid", color="black", weight=3];
48.24/28.46	242[label="vuv400",fontsize=16,color="green",shape="box"];243 -> 252[label="",style="dashed", color="red", weight=0];
48.24/28.46	243[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuv400)) (fromInt (Pos Zero))) (abs (Pos Zero)) (`negate` Neg (Succ vuv400))",fontsize=16,color="magenta"];243 -> 255[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	244[label="absReal1 (Neg (Succ vuv300)) (Neg (Succ vuv300) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];244 -> 258[label="",style="solid", color="black", weight=3];
48.24/28.46	245[label="abs (Neg Zero)",fontsize=16,color="black",shape="triangle"];245 -> 259[label="",style="solid", color="black", weight=3];
48.24/28.46	246[label="vuv400",fontsize=16,color="green",shape="box"];247 -> 252[label="",style="dashed", color="red", weight=0];
48.24/28.46	247[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuv400)) (fromInt (Pos Zero))) (abs (Neg Zero)) (`negate` Neg (Succ vuv400))",fontsize=16,color="magenta"];247 -> 256[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	248[label="gcd0Gcd'2 (Pos (Succ vuv400)) (vuv6 `rem` Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];248 -> 260[label="",style="solid", color="black", weight=3];
48.24/28.46	249[label="absReal1 (Pos (Succ vuv300)) (compare (Pos (Succ vuv300)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];249 -> 261[label="",style="solid", color="black", weight=3];
48.24/28.46	240[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv400)) (Pos Zero)) vuv5 (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];240 -> 250[label="",style="solid", color="black", weight=3];
48.24/28.46	251[label="absReal (Pos Zero)",fontsize=16,color="black",shape="box"];251 -> 262[label="",style="solid", color="black", weight=3];
48.24/28.46	255 -> 241[label="",style="dashed", color="red", weight=0];
48.24/28.46	255[label="abs (Pos Zero)",fontsize=16,color="magenta"];258[label="absReal1 (Neg (Succ vuv300)) (compare (Neg (Succ vuv300)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];258 -> 265[label="",style="solid", color="black", weight=3];
48.24/28.46	259[label="absReal (Neg Zero)",fontsize=16,color="black",shape="box"];259 -> 266[label="",style="solid", color="black", weight=3];
48.24/28.46	256 -> 245[label="",style="dashed", color="red", weight=0];
48.24/28.46	256[label="abs (Neg Zero)",fontsize=16,color="magenta"];260[label="gcd0Gcd'1 (vuv6 `rem` Pos (Succ vuv400) == fromInt (Pos Zero)) (Pos (Succ vuv400)) (vuv6 `rem` Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];260 -> 267[label="",style="solid", color="black", weight=3];
48.24/28.46	261[label="absReal1 (Pos (Succ vuv300)) (not (compare (Pos (Succ vuv300)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];261 -> 268[label="",style="solid", color="black", weight=3];
48.24/28.46	250[label="gcd0Gcd'1 False vuv5 (Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];250 -> 263[label="",style="solid", color="black", weight=3];
48.24/28.46	262[label="absReal2 (Pos Zero)",fontsize=16,color="black",shape="box"];262 -> 269[label="",style="solid", color="black", weight=3];
48.24/28.46	265[label="absReal1 (Neg (Succ vuv300)) (not (compare (Neg (Succ vuv300)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];265 -> 273[label="",style="solid", color="black", weight=3];
48.24/28.46	266[label="absReal2 (Neg Zero)",fontsize=16,color="black",shape="box"];266 -> 274[label="",style="solid", color="black", weight=3];
48.24/28.46	267[label="gcd0Gcd'1 (primEqInt (vuv6 `rem` Pos (Succ vuv400)) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (vuv6 `rem` Pos (Succ vuv400))",fontsize=16,color="black",shape="box"];267 -> 275[label="",style="solid", color="black", weight=3];
48.24/28.46	268[label="absReal1 (Pos (Succ vuv300)) (not (primCmpInt (Pos (Succ vuv300)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];268 -> 276[label="",style="solid", color="black", weight=3];
48.24/28.46	263 -> 228[label="",style="dashed", color="red", weight=0];
48.24/28.46	263[label="gcd0Gcd'0 vuv5 (Pos (Succ vuv400))",fontsize=16,color="magenta"];263 -> 270[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	263 -> 271[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	269[label="absReal1 (Pos Zero) (Pos Zero >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];269 -> 277[label="",style="solid", color="black", weight=3];
48.24/28.46	273[label="absReal1 (Neg (Succ vuv300)) (not (primCmpInt (Neg (Succ vuv300)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];273 -> 278[label="",style="solid", color="black", weight=3];
48.24/28.46	274[label="absReal1 (Neg Zero) (Neg Zero >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];274 -> 279[label="",style="solid", color="black", weight=3];
48.24/28.46	275[label="gcd0Gcd'1 (primEqInt (primRemInt vuv6 (Pos (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (primRemInt vuv6 (Pos (Succ vuv400)))",fontsize=16,color="burlywood",shape="box"];1539[label="vuv6/Pos vuv60",fontsize=10,color="white",style="solid",shape="box"];275 -> 1539[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1539 -> 280[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1540[label="vuv6/Neg vuv60",fontsize=10,color="white",style="solid",shape="box"];275 -> 1540[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1540 -> 281[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	276[label="absReal1 (Pos (Succ vuv300)) (not (primCmpInt (Pos (Succ vuv300)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];276 -> 282[label="",style="solid", color="black", weight=3];
48.24/28.46	270[label="vuv400",fontsize=16,color="green",shape="box"];271[label="vuv5",fontsize=16,color="green",shape="box"];277[label="absReal1 (Pos Zero) (compare (Pos Zero) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];277 -> 283[label="",style="solid", color="black", weight=3];
48.24/28.46	278[label="absReal1 (Neg (Succ vuv300)) (not (primCmpInt (Neg (Succ vuv300)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];278 -> 284[label="",style="solid", color="black", weight=3];
48.24/28.46	279[label="absReal1 (Neg Zero) (compare (Neg Zero) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];279 -> 285[label="",style="solid", color="black", weight=3];
48.24/28.46	280[label="gcd0Gcd'1 (primEqInt (primRemInt (Pos vuv60) (Pos (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (primRemInt (Pos vuv60) (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];280 -> 286[label="",style="solid", color="black", weight=3];
48.24/28.46	281[label="gcd0Gcd'1 (primEqInt (primRemInt (Neg vuv60) (Pos (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (primRemInt (Neg vuv60) (Pos (Succ vuv400)))",fontsize=16,color="black",shape="box"];281 -> 287[label="",style="solid", color="black", weight=3];
48.24/28.46	282[label="absReal1 (Pos (Succ vuv300)) (not (primCmpNat (Succ vuv300) Zero == LT))",fontsize=16,color="black",shape="box"];282 -> 288[label="",style="solid", color="black", weight=3];
48.24/28.46	283[label="absReal1 (Pos Zero) (not (compare (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];283 -> 289[label="",style="solid", color="black", weight=3];
48.24/28.46	284[label="absReal1 (Neg (Succ vuv300)) (not (LT == LT))",fontsize=16,color="black",shape="box"];284 -> 290[label="",style="solid", color="black", weight=3];
48.24/28.46	285[label="absReal1 (Neg Zero) (not (compare (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];285 -> 291[label="",style="solid", color="black", weight=3];
48.24/28.46	286[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS vuv60 (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Pos (primModNatS vuv60 (Succ vuv400)))",fontsize=16,color="burlywood",shape="triangle"];1541[label="vuv60/Succ vuv600",fontsize=10,color="white",style="solid",shape="box"];286 -> 1541[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1541 -> 292[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1542[label="vuv60/Zero",fontsize=10,color="white",style="solid",shape="box"];286 -> 1542[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1542 -> 293[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	287[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS vuv60 (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Neg (primModNatS vuv60 (Succ vuv400)))",fontsize=16,color="burlywood",shape="triangle"];1543[label="vuv60/Succ vuv600",fontsize=10,color="white",style="solid",shape="box"];287 -> 1543[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1543 -> 294[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1544[label="vuv60/Zero",fontsize=10,color="white",style="solid",shape="box"];287 -> 1544[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1544 -> 295[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	288[label="absReal1 (Pos (Succ vuv300)) (not (GT == LT))",fontsize=16,color="black",shape="box"];288 -> 296[label="",style="solid", color="black", weight=3];
48.24/28.46	289[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];289 -> 297[label="",style="solid", color="black", weight=3];
48.24/28.46	290[label="absReal1 (Neg (Succ vuv300)) (not True)",fontsize=16,color="black",shape="box"];290 -> 298[label="",style="solid", color="black", weight=3];
48.24/28.46	291[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];291 -> 299[label="",style="solid", color="black", weight=3];
48.24/28.46	292[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuv600) (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Pos (primModNatS (Succ vuv600) (Succ vuv400)))",fontsize=16,color="black",shape="box"];292 -> 300[label="",style="solid", color="black", weight=3];
48.24/28.46	293[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS Zero (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Pos (primModNatS Zero (Succ vuv400)))",fontsize=16,color="black",shape="box"];293 -> 301[label="",style="solid", color="black", weight=3];
48.24/28.46	294[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS (Succ vuv600) (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Neg (primModNatS (Succ vuv600) (Succ vuv400)))",fontsize=16,color="black",shape="box"];294 -> 302[label="",style="solid", color="black", weight=3];
48.24/28.46	295[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS Zero (Succ vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Neg (primModNatS Zero (Succ vuv400)))",fontsize=16,color="black",shape="box"];295 -> 303[label="",style="solid", color="black", weight=3];
48.24/28.46	296[label="absReal1 (Pos (Succ vuv300)) (not False)",fontsize=16,color="black",shape="box"];296 -> 304[label="",style="solid", color="black", weight=3];
48.24/28.46	297[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];297 -> 305[label="",style="solid", color="black", weight=3];
48.24/28.46	298[label="absReal1 (Neg (Succ vuv300)) False",fontsize=16,color="black",shape="box"];298 -> 306[label="",style="solid", color="black", weight=3];
48.24/28.46	299[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];299 -> 307[label="",style="solid", color="black", weight=3];
48.24/28.46	300[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 vuv600 vuv400 (primGEqNatS vuv600 vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Pos (primModNatS0 vuv600 vuv400 (primGEqNatS vuv600 vuv400)))",fontsize=16,color="burlywood",shape="box"];1545[label="vuv600/Succ vuv6000",fontsize=10,color="white",style="solid",shape="box"];300 -> 1545[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1545 -> 308[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1546[label="vuv600/Zero",fontsize=10,color="white",style="solid",shape="box"];300 -> 1546[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1546 -> 309[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	301[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Pos Zero)",fontsize=16,color="black",shape="box"];301 -> 310[label="",style="solid", color="black", weight=3];
48.24/28.46	302[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 vuv600 vuv400 (primGEqNatS vuv600 vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Neg (primModNatS0 vuv600 vuv400 (primGEqNatS vuv600 vuv400)))",fontsize=16,color="burlywood",shape="box"];1547[label="vuv600/Succ vuv6000",fontsize=10,color="white",style="solid",shape="box"];302 -> 1547[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1547 -> 311[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1548[label="vuv600/Zero",fontsize=10,color="white",style="solid",shape="box"];302 -> 1548[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1548 -> 312[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	303[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Neg Zero)",fontsize=16,color="black",shape="box"];303 -> 313[label="",style="solid", color="black", weight=3];
48.24/28.46	304[label="absReal1 (Pos (Succ vuv300)) True",fontsize=16,color="black",shape="box"];304 -> 314[label="",style="solid", color="black", weight=3];
48.24/28.46	305[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];305 -> 315[label="",style="solid", color="black", weight=3];
48.24/28.46	306[label="absReal0 (Neg (Succ vuv300)) otherwise",fontsize=16,color="black",shape="box"];306 -> 316[label="",style="solid", color="black", weight=3];
48.24/28.46	307[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];307 -> 317[label="",style="solid", color="black", weight=3];
48.24/28.46	308[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6000) vuv400 (primGEqNatS (Succ vuv6000) vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Pos (primModNatS0 (Succ vuv6000) vuv400 (primGEqNatS (Succ vuv6000) vuv400)))",fontsize=16,color="burlywood",shape="box"];1549[label="vuv400/Succ vuv4000",fontsize=10,color="white",style="solid",shape="box"];308 -> 1549[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1549 -> 318[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1550[label="vuv400/Zero",fontsize=10,color="white",style="solid",shape="box"];308 -> 1550[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1550 -> 319[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	309[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero vuv400 (primGEqNatS Zero vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Pos (primModNatS0 Zero vuv400 (primGEqNatS Zero vuv400)))",fontsize=16,color="burlywood",shape="box"];1551[label="vuv400/Succ vuv4000",fontsize=10,color="white",style="solid",shape="box"];309 -> 1551[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1551 -> 320[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1552[label="vuv400/Zero",fontsize=10,color="white",style="solid",shape="box"];309 -> 1552[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1552 -> 321[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	310[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (Pos (Succ vuv400)) (Pos Zero)",fontsize=16,color="black",shape="box"];310 -> 322[label="",style="solid", color="black", weight=3];
48.24/28.46	311[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv6000) vuv400 (primGEqNatS (Succ vuv6000) vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Neg (primModNatS0 (Succ vuv6000) vuv400 (primGEqNatS (Succ vuv6000) vuv400)))",fontsize=16,color="burlywood",shape="box"];1553[label="vuv400/Succ vuv4000",fontsize=10,color="white",style="solid",shape="box"];311 -> 1553[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1553 -> 323[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1554[label="vuv400/Zero",fontsize=10,color="white",style="solid",shape="box"];311 -> 1554[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1554 -> 324[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	312[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero vuv400 (primGEqNatS Zero vuv400))) (fromInt (Pos Zero))) (Pos (Succ vuv400)) (Neg (primModNatS0 Zero vuv400 (primGEqNatS Zero vuv400)))",fontsize=16,color="burlywood",shape="box"];1555[label="vuv400/Succ vuv4000",fontsize=10,color="white",style="solid",shape="box"];312 -> 1555[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1555 -> 325[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1556[label="vuv400/Zero",fontsize=10,color="white",style="solid",shape="box"];312 -> 1556[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1556 -> 326[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	313[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) (Pos (Succ vuv400)) (Neg Zero)",fontsize=16,color="black",shape="box"];313 -> 327[label="",style="solid", color="black", weight=3];
48.24/28.46	314[label="Pos (Succ vuv300)",fontsize=16,color="green",shape="box"];315[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];315 -> 328[label="",style="solid", color="black", weight=3];
48.24/28.46	316[label="absReal0 (Neg (Succ vuv300)) True",fontsize=16,color="black",shape="box"];316 -> 329[label="",style="solid", color="black", weight=3];
48.24/28.46	317[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];317 -> 330[label="",style="solid", color="black", weight=3];
48.24/28.46	318[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS (Succ vuv6000) (Succ vuv4000)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Pos (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS (Succ vuv6000) (Succ vuv4000))))",fontsize=16,color="black",shape="box"];318 -> 331[label="",style="solid", color="black", weight=3];
48.24/28.46	319[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6000) Zero (primGEqNatS (Succ vuv6000) Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuv6000) Zero (primGEqNatS (Succ vuv6000) Zero)))",fontsize=16,color="black",shape="box"];319 -> 332[label="",style="solid", color="black", weight=3];
48.24/28.46	320[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuv4000) (primGEqNatS Zero (Succ vuv4000)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Pos (primModNatS0 Zero (Succ vuv4000) (primGEqNatS Zero (Succ vuv4000))))",fontsize=16,color="black",shape="box"];320 -> 333[label="",style="solid", color="black", weight=3];
48.24/28.46	321[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];321 -> 334[label="",style="solid", color="black", weight=3];
48.24/28.46	322[label="gcd0Gcd'1 True (Pos (Succ vuv400)) (Pos Zero)",fontsize=16,color="black",shape="box"];322 -> 335[label="",style="solid", color="black", weight=3];
48.24/28.46	323[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS (Succ vuv6000) (Succ vuv4000)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Neg (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS (Succ vuv6000) (Succ vuv4000))))",fontsize=16,color="black",shape="box"];323 -> 336[label="",style="solid", color="black", weight=3];
48.24/28.46	324[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv6000) Zero (primGEqNatS (Succ vuv6000) Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 (Succ vuv6000) Zero (primGEqNatS (Succ vuv6000) Zero)))",fontsize=16,color="black",shape="box"];324 -> 337[label="",style="solid", color="black", weight=3];
48.24/28.46	325[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero (Succ vuv4000) (primGEqNatS Zero (Succ vuv4000)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Neg (primModNatS0 Zero (Succ vuv4000) (primGEqNatS Zero (Succ vuv4000))))",fontsize=16,color="black",shape="box"];325 -> 338[label="",style="solid", color="black", weight=3];
48.24/28.46	326[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 Zero Zero (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];326 -> 339[label="",style="solid", color="black", weight=3];
48.24/28.46	327[label="gcd0Gcd'1 True (Pos (Succ vuv400)) (Neg Zero)",fontsize=16,color="black",shape="box"];327 -> 340[label="",style="solid", color="black", weight=3];
48.24/28.46	328[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];328 -> 341[label="",style="solid", color="black", weight=3];
48.24/28.46	329[label="`negate` Neg (Succ vuv300)",fontsize=16,color="black",shape="box"];329 -> 342[label="",style="solid", color="black", weight=3];
48.24/28.46	330[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];330 -> 343[label="",style="solid", color="black", weight=3];
48.24/28.46	331 -> 821[label="",style="dashed", color="red", weight=0];
48.24/28.46	331[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS vuv6000 vuv4000))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Pos (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS vuv6000 vuv4000)))",fontsize=16,color="magenta"];331 -> 822[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	331 -> 823[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	331 -> 824[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	331 -> 825[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	332 -> 613[label="",style="dashed", color="red", weight=0];
48.24/28.46	332[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6000) Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuv6000) Zero True))",fontsize=16,color="magenta"];332 -> 614[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	332 -> 615[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	333[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuv4000) False)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Pos (primModNatS0 Zero (Succ vuv4000) False))",fontsize=16,color="black",shape="box"];333 -> 347[label="",style="solid", color="black", weight=3];
48.24/28.46	334[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 Zero Zero True))",fontsize=16,color="black",shape="box"];334 -> 348[label="",style="solid", color="black", weight=3];
48.24/28.46	335[label="Pos (Succ vuv400)",fontsize=16,color="green",shape="box"];336 -> 865[label="",style="dashed", color="red", weight=0];
48.24/28.46	336[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS vuv6000 vuv4000))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Neg (primModNatS0 (Succ vuv6000) (Succ vuv4000) (primGEqNatS vuv6000 vuv4000)))",fontsize=16,color="magenta"];336 -> 866[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	336 -> 867[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	336 -> 868[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	336 -> 869[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	337 -> 644[label="",style="dashed", color="red", weight=0];
48.24/28.46	337[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv6000) Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 (Succ vuv6000) Zero True))",fontsize=16,color="magenta"];337 -> 645[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	337 -> 646[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	338[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero (Succ vuv4000) False)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Neg (primModNatS0 Zero (Succ vuv4000) False))",fontsize=16,color="black",shape="box"];338 -> 352[label="",style="solid", color="black", weight=3];
48.24/28.46	339[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 Zero Zero True))",fontsize=16,color="black",shape="box"];339 -> 353[label="",style="solid", color="black", weight=3];
48.24/28.46	340[label="Pos (Succ vuv400)",fontsize=16,color="green",shape="box"];341[label="Pos Zero",fontsize=16,color="green",shape="box"];342[label="primNegInt (Neg (Succ vuv300))",fontsize=16,color="black",shape="box"];342 -> 354[label="",style="solid", color="black", weight=3];
48.24/28.46	343[label="Neg Zero",fontsize=16,color="green",shape="box"];822[label="vuv6000",fontsize=16,color="green",shape="box"];823[label="vuv6000",fontsize=16,color="green",shape="box"];824[label="vuv4000",fontsize=16,color="green",shape="box"];825[label="Succ vuv4000",fontsize=16,color="green",shape="box"];821[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS vuv37 vuv38))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS vuv37 vuv38)))",fontsize=16,color="burlywood",shape="triangle"];1557[label="vuv37/Succ vuv370",fontsize=10,color="white",style="solid",shape="box"];821 -> 1557[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1557 -> 862[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1558[label="vuv37/Zero",fontsize=10,color="white",style="solid",shape="box"];821 -> 1558[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1558 -> 863[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	614[label="vuv6000",fontsize=16,color="green",shape="box"];615[label="Zero",fontsize=16,color="green",shape="box"];613[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv23) vuv24 True)) (fromInt (Pos Zero))) (Pos (Succ vuv24)) (Pos (primModNatS0 (Succ vuv23) vuv24 True))",fontsize=16,color="black",shape="triangle"];613 -> 636[label="",style="solid", color="black", weight=3];
48.24/28.46	347 -> 232[label="",style="dashed", color="red", weight=0];
48.24/28.46	347[label="gcd0Gcd'1 (primEqInt (Pos (Succ Zero)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Pos (Succ Zero))",fontsize=16,color="magenta"];347 -> 361[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	347 -> 362[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	348 -> 286[label="",style="dashed", color="red", weight=0];
48.24/28.46	348[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];348 -> 363[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	348 -> 364[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	866[label="vuv6000",fontsize=16,color="green",shape="box"];867[label="Succ vuv4000",fontsize=16,color="green",shape="box"];868[label="vuv6000",fontsize=16,color="green",shape="box"];869[label="vuv4000",fontsize=16,color="green",shape="box"];865[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS vuv42 vuv43))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS vuv42 vuv43)))",fontsize=16,color="burlywood",shape="triangle"];1559[label="vuv42/Succ vuv420",fontsize=10,color="white",style="solid",shape="box"];865 -> 1559[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1559 -> 906[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1560[label="vuv42/Zero",fontsize=10,color="white",style="solid",shape="box"];865 -> 1560[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1560 -> 907[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	645[label="vuv6000",fontsize=16,color="green",shape="box"];646[label="Zero",fontsize=16,color="green",shape="box"];644[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv26) vuv27 True)) (fromInt (Pos Zero))) (Pos (Succ vuv27)) (Neg (primModNatS0 (Succ vuv26) vuv27 True))",fontsize=16,color="black",shape="triangle"];644 -> 667[label="",style="solid", color="black", weight=3];
48.24/28.46	352 -> 687[label="",style="dashed", color="red", weight=0];
48.24/28.46	352[label="gcd0Gcd'1 (primEqInt (Neg (Succ Zero)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuv4000))) (Neg (Succ Zero))",fontsize=16,color="magenta"];352 -> 688[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	352 -> 689[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	353 -> 287[label="",style="dashed", color="red", weight=0];
48.24/28.46	353[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS (primMinusNatS Zero Zero) (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];353 -> 372[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	353 -> 373[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	354[label="Pos (Succ vuv300)",fontsize=16,color="green",shape="box"];862[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS (Succ vuv370) vuv38))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS (Succ vuv370) vuv38)))",fontsize=16,color="burlywood",shape="box"];1561[label="vuv38/Succ vuv380",fontsize=10,color="white",style="solid",shape="box"];862 -> 1561[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1561 -> 908[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1562[label="vuv38/Zero",fontsize=10,color="white",style="solid",shape="box"];862 -> 1562[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1562 -> 909[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	863[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS Zero vuv38))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS Zero vuv38)))",fontsize=16,color="burlywood",shape="box"];1563[label="vuv38/Succ vuv380",fontsize=10,color="white",style="solid",shape="box"];863 -> 1563[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1563 -> 910[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1564[label="vuv38/Zero",fontsize=10,color="white",style="solid",shape="box"];863 -> 1564[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1564 -> 911[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	636 -> 286[label="",style="dashed", color="red", weight=0];
48.24/28.46	636[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuv23) vuv24) (Succ vuv24))) (fromInt (Pos Zero))) (Pos (Succ vuv24)) (Pos (primModNatS (primMinusNatS (Succ vuv23) vuv24) (Succ vuv24)))",fontsize=16,color="magenta"];636 -> 668[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	636 -> 669[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	361[label="Pos (Succ (Succ vuv4000))",fontsize=16,color="green",shape="box"];362[label="Zero",fontsize=16,color="green",shape="box"];363[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];363 -> 379[label="",style="solid", color="black", weight=3];
48.24/28.46	364[label="Zero",fontsize=16,color="green",shape="box"];906[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS (Succ vuv420) vuv43))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS (Succ vuv420) vuv43)))",fontsize=16,color="burlywood",shape="box"];1565[label="vuv43/Succ vuv430",fontsize=10,color="white",style="solid",shape="box"];906 -> 1565[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1565 -> 913[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1566[label="vuv43/Zero",fontsize=10,color="white",style="solid",shape="box"];906 -> 1566[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1566 -> 914[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	907[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS Zero vuv43))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS Zero vuv43)))",fontsize=16,color="burlywood",shape="box"];1567[label="vuv43/Succ vuv430",fontsize=10,color="white",style="solid",shape="box"];907 -> 1567[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1567 -> 915[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1568[label="vuv43/Zero",fontsize=10,color="white",style="solid",shape="box"];907 -> 1568[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1568 -> 916[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	667 -> 287[label="",style="dashed", color="red", weight=0];
48.24/28.46	667[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS (primMinusNatS (Succ vuv26) vuv27) (Succ vuv27))) (fromInt (Pos Zero))) (Pos (Succ vuv27)) (Neg (primModNatS (primMinusNatS (Succ vuv26) vuv27) (Succ vuv27)))",fontsize=16,color="magenta"];667 -> 700[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	667 -> 701[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	688[label="Zero",fontsize=16,color="green",shape="box"];689[label="Succ vuv4000",fontsize=16,color="green",shape="box"];687[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuv29)) (fromInt (Pos Zero))) (Pos (Succ vuv30)) (Neg (Succ vuv29))",fontsize=16,color="black",shape="triangle"];687 -> 702[label="",style="solid", color="black", weight=3];
48.24/28.46	372 -> 363[label="",style="dashed", color="red", weight=0];
48.24/28.46	372[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];373[label="Zero",fontsize=16,color="green",shape="box"];908[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS (Succ vuv370) (Succ vuv380)))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS (Succ vuv370) (Succ vuv380))))",fontsize=16,color="black",shape="box"];908 -> 917[label="",style="solid", color="black", weight=3];
48.24/28.46	909[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS (Succ vuv370) Zero))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS (Succ vuv370) Zero)))",fontsize=16,color="black",shape="box"];909 -> 918[label="",style="solid", color="black", weight=3];
48.24/28.46	910[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS Zero (Succ vuv380)))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS Zero (Succ vuv380))))",fontsize=16,color="black",shape="box"];910 -> 919[label="",style="solid", color="black", weight=3];
48.24/28.46	911[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];911 -> 920[label="",style="solid", color="black", weight=3];
48.24/28.46	668[label="primMinusNatS (Succ vuv23) vuv24",fontsize=16,color="burlywood",shape="triangle"];1569[label="vuv24/Succ vuv240",fontsize=10,color="white",style="solid",shape="box"];668 -> 1569[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1569 -> 703[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1570[label="vuv24/Zero",fontsize=10,color="white",style="solid",shape="box"];668 -> 1570[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1570 -> 704[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	669[label="vuv24",fontsize=16,color="green",shape="box"];379[label="Zero",fontsize=16,color="green",shape="box"];913[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS (Succ vuv420) (Succ vuv430)))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS (Succ vuv420) (Succ vuv430))))",fontsize=16,color="black",shape="box"];913 -> 923[label="",style="solid", color="black", weight=3];
48.24/28.46	914[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS (Succ vuv420) Zero))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS (Succ vuv420) Zero)))",fontsize=16,color="black",shape="box"];914 -> 924[label="",style="solid", color="black", weight=3];
48.24/28.46	915[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS Zero (Succ vuv430)))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS Zero (Succ vuv430))))",fontsize=16,color="black",shape="box"];915 -> 925[label="",style="solid", color="black", weight=3];
48.24/28.46	916[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];916 -> 926[label="",style="solid", color="black", weight=3];
48.24/28.46	700 -> 668[label="",style="dashed", color="red", weight=0];
48.24/28.46	700[label="primMinusNatS (Succ vuv26) vuv27",fontsize=16,color="magenta"];700 -> 713[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	700 -> 714[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	701[label="vuv27",fontsize=16,color="green",shape="box"];702[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuv29)) (Pos Zero)) (Pos (Succ vuv30)) (Neg (Succ vuv29))",fontsize=16,color="black",shape="box"];702 -> 715[label="",style="solid", color="black", weight=3];
48.24/28.46	917 -> 821[label="",style="dashed", color="red", weight=0];
48.24/28.46	917[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS vuv370 vuv380))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 (primGEqNatS vuv370 vuv380)))",fontsize=16,color="magenta"];917 -> 927[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	917 -> 928[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	918 -> 613[label="",style="dashed", color="red", weight=0];
48.24/28.46	918[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 True)) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 True))",fontsize=16,color="magenta"];918 -> 929[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	918 -> 930[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	919[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 False)) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 False))",fontsize=16,color="black",shape="box"];919 -> 931[label="",style="solid", color="black", weight=3];
48.24/28.46	920 -> 613[label="",style="dashed", color="red", weight=0];
48.24/28.46	920[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv35) vuv36 True)) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (primModNatS0 (Succ vuv35) vuv36 True))",fontsize=16,color="magenta"];920 -> 932[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	920 -> 933[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	703[label="primMinusNatS (Succ vuv23) (Succ vuv240)",fontsize=16,color="black",shape="box"];703 -> 716[label="",style="solid", color="black", weight=3];
48.24/28.46	704[label="primMinusNatS (Succ vuv23) Zero",fontsize=16,color="black",shape="box"];704 -> 717[label="",style="solid", color="black", weight=3];
48.24/28.46	923 -> 865[label="",style="dashed", color="red", weight=0];
48.24/28.46	923[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS vuv420 vuv430))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 (primGEqNatS vuv420 vuv430)))",fontsize=16,color="magenta"];923 -> 938[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	923 -> 939[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	924 -> 644[label="",style="dashed", color="red", weight=0];
48.24/28.46	924[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 True)) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 True))",fontsize=16,color="magenta"];924 -> 940[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	924 -> 941[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	925[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 False)) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 False))",fontsize=16,color="black",shape="box"];925 -> 942[label="",style="solid", color="black", weight=3];
48.24/28.46	926 -> 644[label="",style="dashed", color="red", weight=0];
48.24/28.46	926[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuv40) vuv41 True)) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (primModNatS0 (Succ vuv40) vuv41 True))",fontsize=16,color="magenta"];926 -> 943[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	926 -> 944[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	713[label="vuv26",fontsize=16,color="green",shape="box"];714[label="vuv27",fontsize=16,color="green",shape="box"];715[label="gcd0Gcd'1 False (Pos (Succ vuv30)) (Neg (Succ vuv29))",fontsize=16,color="black",shape="box"];715 -> 732[label="",style="solid", color="black", weight=3];
48.24/28.46	927[label="vuv370",fontsize=16,color="green",shape="box"];928[label="vuv380",fontsize=16,color="green",shape="box"];929[label="vuv35",fontsize=16,color="green",shape="box"];930[label="vuv36",fontsize=16,color="green",shape="box"];931 -> 232[label="",style="dashed", color="red", weight=0];
48.24/28.46	931[label="gcd0Gcd'1 (primEqInt (Pos (Succ (Succ vuv35))) (fromInt (Pos Zero))) (Pos (Succ vuv36)) (Pos (Succ (Succ vuv35)))",fontsize=16,color="magenta"];931 -> 945[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	931 -> 946[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	932[label="vuv35",fontsize=16,color="green",shape="box"];933[label="vuv36",fontsize=16,color="green",shape="box"];716[label="primMinusNatS vuv23 vuv240",fontsize=16,color="burlywood",shape="triangle"];1571[label="vuv23/Succ vuv230",fontsize=10,color="white",style="solid",shape="box"];716 -> 1571[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1571 -> 733[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1572[label="vuv23/Zero",fontsize=10,color="white",style="solid",shape="box"];716 -> 1572[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1572 -> 734[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	717[label="Succ vuv23",fontsize=16,color="green",shape="box"];938[label="vuv420",fontsize=16,color="green",shape="box"];939[label="vuv430",fontsize=16,color="green",shape="box"];940[label="vuv40",fontsize=16,color="green",shape="box"];941[label="vuv41",fontsize=16,color="green",shape="box"];942 -> 687[label="",style="dashed", color="red", weight=0];
48.24/28.46	942[label="gcd0Gcd'1 (primEqInt (Neg (Succ (Succ vuv40))) (fromInt (Pos Zero))) (Pos (Succ vuv41)) (Neg (Succ (Succ vuv40)))",fontsize=16,color="magenta"];942 -> 951[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	942 -> 952[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	943[label="vuv40",fontsize=16,color="green",shape="box"];944[label="vuv41",fontsize=16,color="green",shape="box"];732[label="gcd0Gcd'0 (Pos (Succ vuv30)) (Neg (Succ vuv29))",fontsize=16,color="black",shape="box"];732 -> 747[label="",style="solid", color="black", weight=3];
48.24/28.46	945[label="Pos (Succ vuv36)",fontsize=16,color="green",shape="box"];946[label="Succ vuv35",fontsize=16,color="green",shape="box"];733[label="primMinusNatS (Succ vuv230) vuv240",fontsize=16,color="burlywood",shape="box"];1573[label="vuv240/Succ vuv2400",fontsize=10,color="white",style="solid",shape="box"];733 -> 1573[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1573 -> 748[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1574[label="vuv240/Zero",fontsize=10,color="white",style="solid",shape="box"];733 -> 1574[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1574 -> 749[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	734[label="primMinusNatS Zero vuv240",fontsize=16,color="burlywood",shape="box"];1575[label="vuv240/Succ vuv2400",fontsize=10,color="white",style="solid",shape="box"];734 -> 1575[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1575 -> 750[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1576[label="vuv240/Zero",fontsize=10,color="white",style="solid",shape="box"];734 -> 1576[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1576 -> 751[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	951[label="Succ vuv40",fontsize=16,color="green",shape="box"];952[label="vuv41",fontsize=16,color="green",shape="box"];747[label="gcd0Gcd' (Neg (Succ vuv29)) (Pos (Succ vuv30) `rem` Neg (Succ vuv29))",fontsize=16,color="black",shape="box"];747 -> 760[label="",style="solid", color="black", weight=3];
48.24/28.46	748[label="primMinusNatS (Succ vuv230) (Succ vuv2400)",fontsize=16,color="black",shape="box"];748 -> 761[label="",style="solid", color="black", weight=3];
48.24/28.46	749[label="primMinusNatS (Succ vuv230) Zero",fontsize=16,color="black",shape="box"];749 -> 762[label="",style="solid", color="black", weight=3];
48.24/28.46	750[label="primMinusNatS Zero (Succ vuv2400)",fontsize=16,color="black",shape="box"];750 -> 763[label="",style="solid", color="black", weight=3];
48.24/28.46	751[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];751 -> 764[label="",style="solid", color="black", weight=3];
48.24/28.46	760[label="gcd0Gcd'2 (Neg (Succ vuv29)) (Pos (Succ vuv30) `rem` Neg (Succ vuv29))",fontsize=16,color="black",shape="box"];760 -> 787[label="",style="solid", color="black", weight=3];
48.24/28.46	761 -> 716[label="",style="dashed", color="red", weight=0];
48.24/28.46	761[label="primMinusNatS vuv230 vuv2400",fontsize=16,color="magenta"];761 -> 788[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	761 -> 789[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	762[label="Succ vuv230",fontsize=16,color="green",shape="box"];763[label="Zero",fontsize=16,color="green",shape="box"];764[label="Zero",fontsize=16,color="green",shape="box"];787[label="gcd0Gcd'1 (Pos (Succ vuv30) `rem` Neg (Succ vuv29) == fromInt (Pos Zero)) (Neg (Succ vuv29)) (Pos (Succ vuv30) `rem` Neg (Succ vuv29))",fontsize=16,color="black",shape="box"];787 -> 805[label="",style="solid", color="black", weight=3];
48.24/28.46	788[label="vuv230",fontsize=16,color="green",shape="box"];789[label="vuv2400",fontsize=16,color="green",shape="box"];805[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuv30) `rem` Neg (Succ vuv29)) (fromInt (Pos Zero))) (Neg (Succ vuv29)) (Pos (Succ vuv30) `rem` Neg (Succ vuv29))",fontsize=16,color="black",shape="box"];805 -> 816[label="",style="solid", color="black", weight=3];
48.24/28.46	816[label="gcd0Gcd'1 (primEqInt (primRemInt (Pos (Succ vuv30)) (Neg (Succ vuv29))) (fromInt (Pos Zero))) (Neg (Succ vuv29)) (primRemInt (Pos (Succ vuv30)) (Neg (Succ vuv29)))",fontsize=16,color="black",shape="box"];816 -> 864[label="",style="solid", color="black", weight=3];
48.24/28.46	864 -> 1173[label="",style="dashed", color="red", weight=0];
48.24/28.46	864[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuv30) (Succ vuv29))) (fromInt (Pos Zero))) (Neg (Succ vuv29)) (Pos (primModNatS (Succ vuv30) (Succ vuv29)))",fontsize=16,color="magenta"];864 -> 1174[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	864 -> 1175[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	864 -> 1176[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1174[label="Succ vuv30",fontsize=16,color="green",shape="box"];1175[label="vuv29",fontsize=16,color="green",shape="box"];1176[label="Succ vuv30",fontsize=16,color="green",shape="box"];1173[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS vuv64 (Succ vuv62))) (fromInt (Pos Zero))) (Neg (Succ vuv62)) (Pos (primModNatS vuv63 (Succ vuv62)))",fontsize=16,color="burlywood",shape="triangle"];1577[label="vuv64/Succ vuv640",fontsize=10,color="white",style="solid",shape="box"];1173 -> 1577[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1577 -> 1185[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1578[label="vuv64/Zero",fontsize=10,color="white",style="solid",shape="box"];1173 -> 1578[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1578 -> 1186[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1185[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuv640) (Succ vuv62))) (fromInt (Pos Zero))) (Neg (Succ vuv62)) (Pos (primModNatS vuv63 (Succ vuv62)))",fontsize=16,color="black",shape="box"];1185 -> 1187[label="",style="solid", color="black", weight=3];
48.24/28.46	1186[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS Zero (Succ vuv62))) (fromInt (Pos Zero))) (Neg (Succ vuv62)) (Pos (primModNatS vuv63 (Succ vuv62)))",fontsize=16,color="black",shape="box"];1186 -> 1188[label="",style="solid", color="black", weight=3];
48.24/28.46	1187[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 vuv640 vuv62 (primGEqNatS vuv640 vuv62))) (fromInt (Pos Zero))) (Neg (Succ vuv62)) (Pos (primModNatS0 vuv640 vuv62 (primGEqNatS vuv640 vuv62)))",fontsize=16,color="burlywood",shape="box"];1579[label="vuv640/Succ vuv6400",fontsize=10,color="white",style="solid",shape="box"];1187 -> 1579[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1579 -> 1189[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1580[label="vuv640/Zero",fontsize=10,color="white",style="solid",shape="box"];1187 -> 1580[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1580 -> 1190[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1188[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg (Succ vuv62)) (Pos Zero)",fontsize=16,color="black",shape="box"];1188 -> 1191[label="",style="solid", color="black", weight=3];
48.24/28.46	1189[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6400) vuv62 (primGEqNatS (Succ vuv6400) vuv62))) (fromInt (Pos Zero))) (Neg (Succ vuv62)) (Pos (primModNatS0 (Succ vuv6400) vuv62 (primGEqNatS (Succ vuv6400) vuv62)))",fontsize=16,color="burlywood",shape="box"];1581[label="vuv62/Succ vuv620",fontsize=10,color="white",style="solid",shape="box"];1189 -> 1581[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1581 -> 1192[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1582[label="vuv62/Zero",fontsize=10,color="white",style="solid",shape="box"];1189 -> 1582[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1582 -> 1193[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1190[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero vuv62 (primGEqNatS Zero vuv62))) (fromInt (Pos Zero))) (Neg (Succ vuv62)) (Pos (primModNatS0 Zero vuv62 (primGEqNatS Zero vuv62)))",fontsize=16,color="burlywood",shape="box"];1583[label="vuv62/Succ vuv620",fontsize=10,color="white",style="solid",shape="box"];1190 -> 1583[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1583 -> 1194[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1584[label="vuv62/Zero",fontsize=10,color="white",style="solid",shape="box"];1190 -> 1584[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1584 -> 1195[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1191[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (Neg (Succ vuv62)) (Pos Zero)",fontsize=16,color="black",shape="box"];1191 -> 1196[label="",style="solid", color="black", weight=3];
48.24/28.46	1192[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6400) (Succ vuv620) (primGEqNatS (Succ vuv6400) (Succ vuv620)))) (fromInt (Pos Zero))) (Neg (Succ (Succ vuv620))) (Pos (primModNatS0 (Succ vuv6400) (Succ vuv620) (primGEqNatS (Succ vuv6400) (Succ vuv620))))",fontsize=16,color="black",shape="box"];1192 -> 1197[label="",style="solid", color="black", weight=3];
48.24/28.46	1193[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6400) Zero (primGEqNatS (Succ vuv6400) Zero))) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 (Succ vuv6400) Zero (primGEqNatS (Succ vuv6400) Zero)))",fontsize=16,color="black",shape="box"];1193 -> 1198[label="",style="solid", color="black", weight=3];
48.24/28.46	1194[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuv620) (primGEqNatS Zero (Succ vuv620)))) (fromInt (Pos Zero))) (Neg (Succ (Succ vuv620))) (Pos (primModNatS0 Zero (Succ vuv620) (primGEqNatS Zero (Succ vuv620))))",fontsize=16,color="black",shape="box"];1194 -> 1199[label="",style="solid", color="black", weight=3];
48.24/28.46	1195[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];1195 -> 1200[label="",style="solid", color="black", weight=3];
48.24/28.46	1196[label="gcd0Gcd'1 True (Neg (Succ vuv62)) (Pos Zero)",fontsize=16,color="black",shape="box"];1196 -> 1201[label="",style="solid", color="black", weight=3];
48.24/28.46	1197 -> 1449[label="",style="dashed", color="red", weight=0];
48.24/28.46	1197[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6400) (Succ vuv620) (primGEqNatS vuv6400 vuv620))) (fromInt (Pos Zero))) (Neg (Succ (Succ vuv620))) (Pos (primModNatS0 (Succ vuv6400) (Succ vuv620) (primGEqNatS vuv6400 vuv620)))",fontsize=16,color="magenta"];1197 -> 1450[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1197 -> 1451[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1197 -> 1452[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1197 -> 1453[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1198 -> 1357[label="",style="dashed", color="red", weight=0];
48.24/28.46	1198[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv6400) Zero True)) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 (Succ vuv6400) Zero True))",fontsize=16,color="magenta"];1198 -> 1358[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1198 -> 1359[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1199[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuv620) False)) (fromInt (Pos Zero))) (Neg (Succ (Succ vuv620))) (Pos (primModNatS0 Zero (Succ vuv620) False))",fontsize=16,color="black",shape="box"];1199 -> 1205[label="",style="solid", color="black", weight=3];
48.24/28.46	1200[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 Zero Zero True))",fontsize=16,color="black",shape="box"];1200 -> 1206[label="",style="solid", color="black", weight=3];
48.24/28.46	1201[label="Neg (Succ vuv62)",fontsize=16,color="green",shape="box"];1450[label="vuv6400",fontsize=16,color="green",shape="box"];1451[label="Succ vuv620",fontsize=16,color="green",shape="box"];1452[label="vuv6400",fontsize=16,color="green",shape="box"];1453[label="vuv620",fontsize=16,color="green",shape="box"];1449[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS vuv80 vuv81))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS vuv80 vuv81)))",fontsize=16,color="burlywood",shape="triangle"];1585[label="vuv80/Succ vuv800",fontsize=10,color="white",style="solid",shape="box"];1449 -> 1585[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1585 -> 1490[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1586[label="vuv80/Zero",fontsize=10,color="white",style="solid",shape="box"];1449 -> 1586[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1586 -> 1491[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1358[label="vuv6400",fontsize=16,color="green",shape="box"];1359[label="Zero",fontsize=16,color="green",shape="box"];1357[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv72) vuv73 True)) (fromInt (Pos Zero))) (Neg (Succ vuv73)) (Pos (primModNatS0 (Succ vuv72) vuv73 True))",fontsize=16,color="black",shape="triangle"];1357 -> 1380[label="",style="solid", color="black", weight=3];
48.24/28.46	1205 -> 232[label="",style="dashed", color="red", weight=0];
48.24/28.46	1205[label="gcd0Gcd'1 (primEqInt (Pos (Succ Zero)) (fromInt (Pos Zero))) (Neg (Succ (Succ vuv620))) (Pos (Succ Zero))",fontsize=16,color="magenta"];1205 -> 1214[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1205 -> 1215[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1206 -> 1173[label="",style="dashed", color="red", weight=0];
48.24/28.46	1206[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero))) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];1206 -> 1216[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1206 -> 1217[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1206 -> 1218[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1490[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS (Succ vuv800) vuv81))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS (Succ vuv800) vuv81)))",fontsize=16,color="burlywood",shape="box"];1587[label="vuv81/Succ vuv810",fontsize=10,color="white",style="solid",shape="box"];1490 -> 1587[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1587 -> 1492[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1588[label="vuv81/Zero",fontsize=10,color="white",style="solid",shape="box"];1490 -> 1588[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1588 -> 1493[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1491[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS Zero vuv81))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS Zero vuv81)))",fontsize=16,color="burlywood",shape="box"];1589[label="vuv81/Succ vuv810",fontsize=10,color="white",style="solid",shape="box"];1491 -> 1589[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1589 -> 1494[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1590[label="vuv81/Zero",fontsize=10,color="white",style="solid",shape="box"];1491 -> 1590[label="",style="solid", color="burlywood", weight=9];
48.24/28.46	1590 -> 1495[label="",style="solid", color="burlywood", weight=3];
48.24/28.46	1380 -> 1173[label="",style="dashed", color="red", weight=0];
48.24/28.46	1380[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuv72) vuv73) (Succ vuv73))) (fromInt (Pos Zero))) (Neg (Succ vuv73)) (Pos (primModNatS (primMinusNatS (Succ vuv72) vuv73) (Succ vuv73)))",fontsize=16,color="magenta"];1380 -> 1387[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1380 -> 1388[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1380 -> 1389[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1214[label="Neg (Succ (Succ vuv620))",fontsize=16,color="green",shape="box"];1215[label="Zero",fontsize=16,color="green",shape="box"];1216 -> 716[label="",style="dashed", color="red", weight=0];
48.24/28.46	1216[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];1216 -> 1227[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1216 -> 1228[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1217[label="Zero",fontsize=16,color="green",shape="box"];1218 -> 716[label="",style="dashed", color="red", weight=0];
48.24/28.46	1218[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];1218 -> 1229[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1218 -> 1230[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1492[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS (Succ vuv800) (Succ vuv810)))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS (Succ vuv800) (Succ vuv810))))",fontsize=16,color="black",shape="box"];1492 -> 1496[label="",style="solid", color="black", weight=3];
48.24/28.46	1493[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS (Succ vuv800) Zero))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS (Succ vuv800) Zero)))",fontsize=16,color="black",shape="box"];1493 -> 1497[label="",style="solid", color="black", weight=3];
48.24/28.46	1494[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS Zero (Succ vuv810)))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS Zero (Succ vuv810))))",fontsize=16,color="black",shape="box"];1494 -> 1498[label="",style="solid", color="black", weight=3];
48.24/28.46	1495[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];1495 -> 1499[label="",style="solid", color="black", weight=3];
48.24/28.46	1387 -> 716[label="",style="dashed", color="red", weight=0];
48.24/28.46	1387[label="primMinusNatS (Succ vuv72) vuv73",fontsize=16,color="magenta"];1387 -> 1394[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1387 -> 1395[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1388[label="vuv73",fontsize=16,color="green",shape="box"];1389 -> 716[label="",style="dashed", color="red", weight=0];
48.24/28.46	1389[label="primMinusNatS (Succ vuv72) vuv73",fontsize=16,color="magenta"];1389 -> 1396[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1389 -> 1397[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1227[label="Zero",fontsize=16,color="green",shape="box"];1228[label="Zero",fontsize=16,color="green",shape="box"];1229[label="Zero",fontsize=16,color="green",shape="box"];1230[label="Zero",fontsize=16,color="green",shape="box"];1496 -> 1449[label="",style="dashed", color="red", weight=0];
48.24/28.46	1496[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS vuv800 vuv810))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 (primGEqNatS vuv800 vuv810)))",fontsize=16,color="magenta"];1496 -> 1500[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1496 -> 1501[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1497 -> 1357[label="",style="dashed", color="red", weight=0];
48.24/28.46	1497[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 True)) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 True))",fontsize=16,color="magenta"];1497 -> 1502[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1497 -> 1503[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1498[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 False)) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 False))",fontsize=16,color="black",shape="box"];1498 -> 1504[label="",style="solid", color="black", weight=3];
48.24/28.46	1499 -> 1357[label="",style="dashed", color="red", weight=0];
48.24/28.46	1499[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuv78) vuv79 True)) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (primModNatS0 (Succ vuv78) vuv79 True))",fontsize=16,color="magenta"];1499 -> 1505[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1499 -> 1506[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1394[label="Succ vuv72",fontsize=16,color="green",shape="box"];1395[label="vuv73",fontsize=16,color="green",shape="box"];1396[label="Succ vuv72",fontsize=16,color="green",shape="box"];1397[label="vuv73",fontsize=16,color="green",shape="box"];1500[label="vuv800",fontsize=16,color="green",shape="box"];1501[label="vuv810",fontsize=16,color="green",shape="box"];1502[label="vuv78",fontsize=16,color="green",shape="box"];1503[label="vuv79",fontsize=16,color="green",shape="box"];1504 -> 232[label="",style="dashed", color="red", weight=0];
48.24/28.46	1504[label="gcd0Gcd'1 (primEqInt (Pos (Succ (Succ vuv78))) (fromInt (Pos Zero))) (Neg (Succ vuv79)) (Pos (Succ (Succ vuv78)))",fontsize=16,color="magenta"];1504 -> 1507[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1504 -> 1508[label="",style="dashed", color="magenta", weight=3];
48.24/28.46	1505[label="vuv78",fontsize=16,color="green",shape="box"];1506[label="vuv79",fontsize=16,color="green",shape="box"];1507[label="Neg (Succ vuv79)",fontsize=16,color="green",shape="box"];1508[label="Succ vuv78",fontsize=16,color="green",shape="box"];}
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(12)
48.24/28.46	Complex Obligation (AND)
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(13)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Zero) -> new_gcd0Gcd'14(vuv40, vuv41)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'16(Succ(Zero), Zero) -> new_gcd0Gcd'16(new_primMinusNatS0, Zero)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'17(Succ(Zero), Zero, vuv63) -> new_gcd0Gcd'17(new_primMinusNatS2(Zero, Zero), Zero, new_primMinusNatS2(Zero, Zero))
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.46	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Zero) -> new_gcd0Gcd'14(vuv40, vuv41)
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'16(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'14(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'1(Succ(Zero), Zero) -> new_gcd0Gcd'1(new_primMinusNatS0, Zero)
48.24/28.46	   new_gcd0Gcd'12(vuv400, vuv5) -> new_gcd0Gcd'0(vuv5, vuv400)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'14(vuv26, vuv27) -> new_gcd0Gcd'16(new_primMinusNatS1(vuv26, vuv27), vuv27)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'16(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'17(Succ(Zero), Succ(vuv620), vuv63) -> new_gcd0Gcd'12(Zero, Neg(Succ(Succ(vuv620))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Zero) -> new_gcd0Gcd'16(new_primMinusNatS0, Zero)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'16(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Zero)), Zero) -> new_gcd0Gcd'1(new_primMinusNatS0, Zero)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'14(vuv6000, Zero)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	   new_primMinusNatS0 -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS0
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(14) DependencyGraphProof (EQUIVALENT)
48.24/28.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(15)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'12(vuv400, vuv5) -> new_gcd0Gcd'0(vuv5, vuv400)
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Zero) -> new_gcd0Gcd'14(vuv40, vuv41)
48.24/28.46	   new_gcd0Gcd'14(vuv26, vuv27) -> new_gcd0Gcd'16(new_primMinusNatS1(vuv26, vuv27), vuv27)
48.24/28.46	   new_gcd0Gcd'16(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'14(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'16(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'17(Succ(Zero), Succ(vuv620), vuv63) -> new_gcd0Gcd'12(Zero, Neg(Succ(Succ(vuv620))))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Zero) -> new_gcd0Gcd'14(vuv40, vuv41)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'16(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'14(vuv6000, Zero)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	   new_primMinusNatS0 -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS0
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(16) QDPOrderProof (EQUIVALENT)
48.24/28.46	We use the reduction pair processor [LPAR04,JAR06].
48.24/28.46	
48.24/28.46	
48.24/28.46	The following pairs can be oriented strictly and are deleted.
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Zero) -> new_gcd0Gcd'14(vuv40, vuv41)
48.24/28.46	   new_gcd0Gcd'16(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'14(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Zero) -> new_gcd0Gcd'14(vuv40, vuv41)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'14(vuv6000, Zero)
48.24/28.46	The remaining pairs can at least be oriented weakly.
48.24/28.46	Used ordering:  Polynomial interpretation [POLO]:
48.24/28.46	
48.24/28.46	   POL(Neg(x_1)) = x_1
48.24/28.46	   POL(Pos(x_1)) = 0
48.24/28.46	   POL(Succ(x_1)) = 1 + x_1
48.24/28.46	   POL(Zero) = 0
48.24/28.46	   POL(new_gcd0Gcd'0(x_1, x_2)) = x_1
48.24/28.46	   POL(new_gcd0Gcd'1(x_1, x_2)) = 0
48.24/28.46	   POL(new_gcd0Gcd'10(x_1, x_2, x_3, x_4)) = 0
48.24/28.46	   POL(new_gcd0Gcd'11(x_1, x_2)) = 0
48.24/28.46	   POL(new_gcd0Gcd'12(x_1, x_2)) = x_2
48.24/28.46	   POL(new_gcd0Gcd'13(x_1, x_2, x_3, x_4)) = 2 + x_1
48.24/28.46	   POL(new_gcd0Gcd'14(x_1, x_2)) = 1 + x_1
48.24/28.46	   POL(new_gcd0Gcd'15(x_1, x_2)) = 1 + x_1
48.24/28.46	   POL(new_gcd0Gcd'16(x_1, x_2)) = x_1
48.24/28.46	   POL(new_gcd0Gcd'17(x_1, x_2, x_3)) = 1 + x_2
48.24/28.46	   POL(new_gcd0Gcd'18(x_1, x_2, x_3, x_4)) = 1 + x_2
48.24/28.46	   POL(new_gcd0Gcd'19(x_1, x_2)) = 1 + x_2
48.24/28.46	   POL(new_primMinusNatS1(x_1, x_2)) = 1 + x_1
48.24/28.46	   POL(new_primMinusNatS2(x_1, x_2)) = x_1
48.24/28.46	
48.24/28.46	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.46	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(17)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'12(vuv400, vuv5) -> new_gcd0Gcd'0(vuv5, vuv400)
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'14(vuv26, vuv27) -> new_gcd0Gcd'16(new_primMinusNatS1(vuv26, vuv27), vuv27)
48.24/28.46	   new_gcd0Gcd'16(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'17(Succ(Zero), Succ(vuv620), vuv63) -> new_gcd0Gcd'12(Zero, Neg(Succ(Succ(vuv620))))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'16(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	   new_primMinusNatS0 -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS0
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(18) DependencyGraphProof (EQUIVALENT)
48.24/28.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(19)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'12(vuv400, vuv5) -> new_gcd0Gcd'0(vuv5, vuv400)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'17(Succ(Zero), Succ(vuv620), vuv63) -> new_gcd0Gcd'12(Zero, Neg(Succ(Succ(vuv620))))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	   new_primMinusNatS0 -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS0
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(20) TransformationProof (EQUIVALENT)
48.24/28.46	By instantiating [LPAR04] the rule new_gcd0Gcd'12(vuv400, vuv5) -> new_gcd0Gcd'0(vuv5, vuv400) we obtained the following new rules [LPAR04]:
48.24/28.46	
48.24/28.46	   (new_gcd0Gcd'12(Zero, Pos(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Pos(Succ(Succ(z0))), Zero),new_gcd0Gcd'12(Zero, Pos(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Pos(Succ(Succ(z0))), Zero))
48.24/28.46	   (new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0)),new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0)))
48.24/28.46	   (new_gcd0Gcd'12(Zero, Neg(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Neg(Succ(Succ(z0))), Zero),new_gcd0Gcd'12(Zero, Neg(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Neg(Succ(Succ(z0))), Zero))
48.24/28.46	   (new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0)),new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0)))
48.24/28.46	
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(21)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'17(Succ(Zero), Succ(vuv620), vuv63) -> new_gcd0Gcd'12(Zero, Neg(Succ(Succ(vuv620))))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.46	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.46	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.46	   new_gcd0Gcd'12(Zero, Pos(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Pos(Succ(Succ(z0))), Zero)
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'12(Zero, Neg(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Neg(Succ(Succ(z0))), Zero)
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	   new_primMinusNatS0 -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS0
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(22) DependencyGraphProof (EQUIVALENT)
48.24/28.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(23)
48.24/28.46	Complex Obligation (AND)
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(24)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	   new_primMinusNatS0 -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS0
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(25) UsableRulesProof (EQUIVALENT)
48.24/28.46	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.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(26)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS0
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(27) QReductionProof (EQUIVALENT)
48.24/28.46	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
48.24/28.46	
48.24/28.46	   new_primMinusNatS1(x0, Zero)
48.24/28.46	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.46	   new_primMinusNatS0
48.24/28.46	
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(28)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(29) QDPOrderProof (EQUIVALENT)
48.24/28.46	We use the reduction pair processor [LPAR04,JAR06].
48.24/28.46	
48.24/28.46	
48.24/28.46	The following pairs can be oriented strictly and are deleted.
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Zero, vuv63) -> new_gcd0Gcd'19(vuv6400, Zero)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Zero) -> new_gcd0Gcd'19(vuv78, vuv79)
48.24/28.46	The remaining pairs can at least be oriented weakly.
48.24/28.46	Used ordering:  Polynomial interpretation [POLO]:
48.24/28.46	
48.24/28.46	   POL(Neg(x_1)) = 0
48.24/28.46	   POL(Succ(x_1)) = 1 + x_1
48.24/28.46	   POL(Zero) = 0
48.24/28.46	   POL(new_gcd0Gcd'0(x_1, x_2)) = 1 + x_2
48.24/28.46	   POL(new_gcd0Gcd'12(x_1, x_2)) = 1 + x_1
48.24/28.46	   POL(new_gcd0Gcd'13(x_1, x_2, x_3, x_4)) = 1 + x_2
48.24/28.46	   POL(new_gcd0Gcd'15(x_1, x_2)) = 1 + x_2
48.24/28.46	   POL(new_gcd0Gcd'17(x_1, x_2, x_3)) = x_1
48.24/28.46	   POL(new_gcd0Gcd'18(x_1, x_2, x_3, x_4)) = 2 + x_1
48.24/28.46	   POL(new_gcd0Gcd'19(x_1, x_2)) = 1 + x_1
48.24/28.46	   POL(new_primMinusNatS2(x_1, x_2)) = x_1
48.24/28.46	
48.24/28.46	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(30)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'19(vuv72, vuv73) -> new_gcd0Gcd'17(new_primMinusNatS2(Succ(vuv72), vuv73), vuv73, new_primMinusNatS2(Succ(vuv72), vuv73))
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(31) DependencyGraphProof (EQUIVALENT)
48.24/28.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(32)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30))
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(33) TransformationProof (EQUIVALENT)
48.24/28.46	By instantiating [LPAR04] the rule new_gcd0Gcd'15(vuv29, vuv30) -> new_gcd0Gcd'17(Succ(vuv30), vuv29, Succ(vuv30)) we obtained the following new rules [LPAR04]:
48.24/28.46	
48.24/28.46	   (new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1)),new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1)))
48.24/28.46	   (new_gcd0Gcd'15(Zero, Succ(z0)) -> new_gcd0Gcd'17(Succ(Succ(z0)), Zero, Succ(Succ(z0))),new_gcd0Gcd'15(Zero, Succ(z0)) -> new_gcd0Gcd'17(Succ(Succ(z0)), Zero, Succ(Succ(z0))))
48.24/28.46	
48.24/28.46	
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(34)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'15(Zero, Succ(vuv4000))
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.46	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.46	   new_gcd0Gcd'15(Zero, Succ(z0)) -> new_gcd0Gcd'17(Succ(Succ(z0)), Zero, Succ(Succ(z0)))
48.24/28.46	
48.24/28.46	The TRS R consists of the following rules:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.46	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.46	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.46	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.46	
48.24/28.46	The set Q consists of the following terms:
48.24/28.46	
48.24/28.46	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.46	   new_primMinusNatS2(Zero, Zero)
48.24/28.46	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.46	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.46	
48.24/28.46	We have to consider all minimal (P,Q,R)-chains.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(35) DependencyGraphProof (EQUIVALENT)
48.24/28.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
48.24/28.46	----------------------------------------
48.24/28.46	
48.24/28.46	(36)
48.24/28.46	Obligation:
48.24/28.46	Q DP problem:
48.24/28.46	The TRS P consists of the following rules:
48.24/28.46	
48.24/28.46	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.46	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.46	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.46	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(37) UsableRulesProof (EQUIVALENT)
48.24/28.47	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.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(38)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(39) QReductionProof (EQUIVALENT)
48.24/28.47	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(40)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	   new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620)
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(41) TransformationProof (EQUIVALENT)
48.24/28.47	By instantiating [LPAR04] the rule new_gcd0Gcd'17(Succ(Succ(vuv6400)), Succ(vuv620), vuv63) -> new_gcd0Gcd'18(vuv6400, Succ(vuv620), vuv6400, vuv620) we obtained the following new rules [LPAR04]:
48.24/28.47	
48.24/28.47	   (new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0),new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0))
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(42)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	   new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(43) InductionCalculusProof (EQUIVALENT)
48.24/28.47	Note that final constraints are written in bold face.
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79))) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'18(x3, x4, Zero, Succ(x5)) -> new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))), new_gcd0Gcd'12(Succ(x6), Neg(Succ(x7))) -> new_gcd0Gcd'0(Neg(Succ(x7)), Succ(x6)) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4)))=new_gcd0Gcd'12(Succ(x6), Neg(Succ(x7)))  ==>  new_gcd0Gcd'18(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'18(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0)) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'12(Succ(x30), Neg(Succ(x31))) -> new_gcd0Gcd'0(Neg(Succ(x31)), Succ(x30)), new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x33)) -> new_gcd0Gcd'13(x32, Succ(x33), x32, x33) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'0(Neg(Succ(x31)), Succ(x30))=new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x33))  ==>  new_gcd0Gcd'12(Succ(x30), Neg(Succ(x31)))_>=_new_gcd0Gcd'0(Neg(Succ(x31)), Succ(x30)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'12(Succ(x30), Neg(Succ(Succ(x32))))_>=_new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x30)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Neg(Succ(Succ(x50))), Succ(x51)) -> new_gcd0Gcd'13(x50, Succ(x51), x50, x51), new_gcd0Gcd'13(x52, x53, Zero, Succ(x54)) -> new_gcd0Gcd'15(Succ(x52), x53) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x50, Succ(x51), x50, x51)=new_gcd0Gcd'13(x52, x53, Zero, Succ(x54))  ==>  new_gcd0Gcd'0(Neg(Succ(Succ(x50))), Succ(x51))_>=_new_gcd0Gcd'13(x50, Succ(x51), x50, x51))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Succ(Succ(x54)))_>=_new_gcd0Gcd'13(Zero, Succ(Succ(x54)), Zero, Succ(x54)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Neg(Succ(Succ(x59))), Succ(x60)) -> new_gcd0Gcd'13(x59, Succ(x60), x59, x60), new_gcd0Gcd'13(x61, x62, Succ(x63), Succ(x64)) -> new_gcd0Gcd'13(x61, x62, x63, x64) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x59, Succ(x60), x59, x60)=new_gcd0Gcd'13(x61, x62, Succ(x63), Succ(x64))  ==>  new_gcd0Gcd'0(Neg(Succ(Succ(x59))), Succ(x60))_>=_new_gcd0Gcd'13(x59, Succ(x60), x59, x60))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(x63)))), Succ(Succ(x64)))_>=_new_gcd0Gcd'13(Succ(x63), Succ(Succ(x64)), Succ(x63), Succ(x64)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'13(x79, x80, Zero, Succ(x81)) -> new_gcd0Gcd'15(Succ(x79), x80), new_gcd0Gcd'15(Succ(x82), x83) -> new_gcd0Gcd'17(Succ(x83), Succ(x82), Succ(x83)) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'15(Succ(x79), x80)=new_gcd0Gcd'15(Succ(x82), x83)  ==>  new_gcd0Gcd'13(x79, x80, Zero, Succ(x81))_>=_new_gcd0Gcd'15(Succ(x79), x80))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'13(x79, x80, Zero, Succ(x81))_>=_new_gcd0Gcd'15(Succ(x79), x80))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1)) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'15(Succ(x107), x108) -> new_gcd0Gcd'17(Succ(x108), Succ(x107), Succ(x108)), new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x110), Succ(Succ(x109))) -> new_gcd0Gcd'18(x109, Succ(x110), x109, x110) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'17(Succ(x108), Succ(x107), Succ(x108))=new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x110), Succ(Succ(x109)))  ==>  new_gcd0Gcd'15(Succ(x107), x108)_>=_new_gcd0Gcd'17(Succ(x108), Succ(x107), Succ(x108)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'15(Succ(x107), Succ(x109))_>=_new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x107), Succ(Succ(x109))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'18(x111, x112, Succ(x113), Succ(x114)) -> new_gcd0Gcd'18(x111, x112, x113, x114), new_gcd0Gcd'18(x115, x116, Zero, Succ(x117)) -> new_gcd0Gcd'12(Succ(x115), Neg(Succ(x116))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x111, x112, x113, x114)=new_gcd0Gcd'18(x115, x116, Zero, Succ(x117))  ==>  new_gcd0Gcd'18(x111, x112, Succ(x113), Succ(x114))_>=_new_gcd0Gcd'18(x111, x112, x113, x114))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'18(x111, x112, Succ(Zero), Succ(Succ(x117)))_>=_new_gcd0Gcd'18(x111, x112, Zero, Succ(x117)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'18(x134, x135, Succ(x136), Succ(x137)) -> new_gcd0Gcd'18(x134, x135, x136, x137), new_gcd0Gcd'18(x138, x139, Succ(x140), Succ(x141)) -> new_gcd0Gcd'18(x138, x139, x140, x141) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x134, x135, x136, x137)=new_gcd0Gcd'18(x138, x139, Succ(x140), Succ(x141))  ==>  new_gcd0Gcd'18(x134, x135, Succ(x136), Succ(x137))_>=_new_gcd0Gcd'18(x134, x135, x136, x137))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'18(x134, x135, Succ(Succ(x140)), Succ(Succ(x141)))_>=_new_gcd0Gcd'18(x134, x135, Succ(x140), Succ(x141)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'13(x162, x163, Succ(x164), Succ(x165)) -> new_gcd0Gcd'13(x162, x163, x164, x165), new_gcd0Gcd'13(x166, x167, Zero, Succ(x168)) -> new_gcd0Gcd'15(Succ(x166), x167) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x162, x163, x164, x165)=new_gcd0Gcd'13(x166, x167, Zero, Succ(x168))  ==>  new_gcd0Gcd'13(x162, x163, Succ(x164), Succ(x165))_>=_new_gcd0Gcd'13(x162, x163, x164, x165))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'13(x162, x163, Succ(Zero), Succ(Succ(x168)))_>=_new_gcd0Gcd'13(x162, x163, Zero, Succ(x168)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'13(x177, x178, Succ(x179), Succ(x180)) -> new_gcd0Gcd'13(x177, x178, x179, x180), new_gcd0Gcd'13(x181, x182, Succ(x183), Succ(x184)) -> new_gcd0Gcd'13(x181, x182, x183, x184) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x177, x178, x179, x180)=new_gcd0Gcd'13(x181, x182, Succ(x183), Succ(x184))  ==>  new_gcd0Gcd'13(x177, x178, Succ(x179), Succ(x180))_>=_new_gcd0Gcd'13(x177, x178, x179, x180))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'13(x177, x178, Succ(Succ(x183)), Succ(Succ(x184)))_>=_new_gcd0Gcd'13(x177, x178, Succ(x183), Succ(x184)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'17(Succ(Succ(x189)), Succ(x190), Succ(Succ(x189))) -> new_gcd0Gcd'18(x189, Succ(x190), x189, x190), new_gcd0Gcd'18(x191, x192, Zero, Succ(x193)) -> new_gcd0Gcd'12(Succ(x191), Neg(Succ(x192))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x189, Succ(x190), x189, x190)=new_gcd0Gcd'18(x191, x192, Zero, Succ(x193))  ==>  new_gcd0Gcd'17(Succ(Succ(x189)), Succ(x190), Succ(Succ(x189)))_>=_new_gcd0Gcd'18(x189, Succ(x190), x189, x190))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'17(Succ(Succ(Zero)), Succ(Succ(x193)), Succ(Succ(Zero)))_>=_new_gcd0Gcd'18(Zero, Succ(Succ(x193)), Zero, Succ(x193)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'17(Succ(Succ(x202)), Succ(x203), Succ(Succ(x202))) -> new_gcd0Gcd'18(x202, Succ(x203), x202, x203), new_gcd0Gcd'18(x204, x205, Succ(x206), Succ(x207)) -> new_gcd0Gcd'18(x204, x205, x206, x207) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x202, Succ(x203), x202, x203)=new_gcd0Gcd'18(x204, x205, Succ(x206), Succ(x207))  ==>  new_gcd0Gcd'17(Succ(Succ(x202)), Succ(x203), Succ(Succ(x202)))_>=_new_gcd0Gcd'18(x202, Succ(x203), x202, x203))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'17(Succ(Succ(Succ(x206))), Succ(Succ(x207)), Succ(Succ(Succ(x206))))_>=_new_gcd0Gcd'18(Succ(x206), Succ(Succ(x207)), Succ(x206), Succ(x207)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	To summarize, we get the following constraints P__>=_ for the following pairs.
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'18(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'12(Succ(x30), Neg(Succ(Succ(x32))))_>=_new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x30)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Succ(Succ(x54)))_>=_new_gcd0Gcd'13(Zero, Succ(Succ(x54)), Zero, Succ(x54)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(x63)))), Succ(Succ(x64)))_>=_new_gcd0Gcd'13(Succ(x63), Succ(Succ(x64)), Succ(x63), Succ(x64)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'13(x79, x80, Zero, Succ(x81))_>=_new_gcd0Gcd'15(Succ(x79), x80))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'15(Succ(x107), Succ(x109))_>=_new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x107), Succ(Succ(x109))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'18(x111, x112, Succ(Zero), Succ(Succ(x117)))_>=_new_gcd0Gcd'18(x111, x112, Zero, Succ(x117)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'18(x134, x135, Succ(Succ(x140)), Succ(Succ(x141)))_>=_new_gcd0Gcd'18(x134, x135, Succ(x140), Succ(x141)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'13(x162, x163, Succ(Zero), Succ(Succ(x168)))_>=_new_gcd0Gcd'13(x162, x163, Zero, Succ(x168)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'13(x177, x178, Succ(Succ(x183)), Succ(Succ(x184)))_>=_new_gcd0Gcd'13(x177, x178, Succ(x183), Succ(x184)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'17(Succ(Succ(Zero)), Succ(Succ(x193)), Succ(Succ(Zero)))_>=_new_gcd0Gcd'18(Zero, Succ(Succ(x193)), Zero, Succ(x193)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'17(Succ(Succ(Succ(x206))), Succ(Succ(x207)), Succ(Succ(Succ(x206))))_>=_new_gcd0Gcd'18(Succ(x206), Succ(Succ(x207)), Succ(x206), Succ(x207)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	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. 
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(44)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	   new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(45) NonInfProof (EQUIVALENT)
48.24/28.47	The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
48.24/28.47	
48.24/28.47	Note that final constraints are written in bold face.
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79))) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'18(x3, x4, Zero, Succ(x5)) -> new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))), new_gcd0Gcd'12(Succ(x6), Neg(Succ(x7))) -> new_gcd0Gcd'0(Neg(Succ(x7)), Succ(x6)) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4)))=new_gcd0Gcd'12(Succ(x6), Neg(Succ(x7)))  ==>  new_gcd0Gcd'18(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'18(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0)) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'12(Succ(x30), Neg(Succ(x31))) -> new_gcd0Gcd'0(Neg(Succ(x31)), Succ(x30)), new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x33)) -> new_gcd0Gcd'13(x32, Succ(x33), x32, x33) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'0(Neg(Succ(x31)), Succ(x30))=new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x33))  ==>  new_gcd0Gcd'12(Succ(x30), Neg(Succ(x31)))_>=_new_gcd0Gcd'0(Neg(Succ(x31)), Succ(x30)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'12(Succ(x30), Neg(Succ(Succ(x32))))_>=_new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x30)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Neg(Succ(Succ(x50))), Succ(x51)) -> new_gcd0Gcd'13(x50, Succ(x51), x50, x51), new_gcd0Gcd'13(x52, x53, Zero, Succ(x54)) -> new_gcd0Gcd'15(Succ(x52), x53) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x50, Succ(x51), x50, x51)=new_gcd0Gcd'13(x52, x53, Zero, Succ(x54))  ==>  new_gcd0Gcd'0(Neg(Succ(Succ(x50))), Succ(x51))_>=_new_gcd0Gcd'13(x50, Succ(x51), x50, x51))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Succ(Succ(x54)))_>=_new_gcd0Gcd'13(Zero, Succ(Succ(x54)), Zero, Succ(x54)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Neg(Succ(Succ(x59))), Succ(x60)) -> new_gcd0Gcd'13(x59, Succ(x60), x59, x60), new_gcd0Gcd'13(x61, x62, Succ(x63), Succ(x64)) -> new_gcd0Gcd'13(x61, x62, x63, x64) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x59, Succ(x60), x59, x60)=new_gcd0Gcd'13(x61, x62, Succ(x63), Succ(x64))  ==>  new_gcd0Gcd'0(Neg(Succ(Succ(x59))), Succ(x60))_>=_new_gcd0Gcd'13(x59, Succ(x60), x59, x60))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(x63)))), Succ(Succ(x64)))_>=_new_gcd0Gcd'13(Succ(x63), Succ(Succ(x64)), Succ(x63), Succ(x64)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'13(x79, x80, Zero, Succ(x81)) -> new_gcd0Gcd'15(Succ(x79), x80), new_gcd0Gcd'15(Succ(x82), x83) -> new_gcd0Gcd'17(Succ(x83), Succ(x82), Succ(x83)) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'15(Succ(x79), x80)=new_gcd0Gcd'15(Succ(x82), x83)  ==>  new_gcd0Gcd'13(x79, x80, Zero, Succ(x81))_>=_new_gcd0Gcd'15(Succ(x79), x80))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'13(x79, x80, Zero, Succ(x81))_>=_new_gcd0Gcd'15(Succ(x79), x80))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1)) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'15(Succ(x107), x108) -> new_gcd0Gcd'17(Succ(x108), Succ(x107), Succ(x108)), new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x110), Succ(Succ(x109))) -> new_gcd0Gcd'18(x109, Succ(x110), x109, x110) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'17(Succ(x108), Succ(x107), Succ(x108))=new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x110), Succ(Succ(x109)))  ==>  new_gcd0Gcd'15(Succ(x107), x108)_>=_new_gcd0Gcd'17(Succ(x108), Succ(x107), Succ(x108)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'15(Succ(x107), Succ(x109))_>=_new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x107), Succ(Succ(x109))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'18(x111, x112, Succ(x113), Succ(x114)) -> new_gcd0Gcd'18(x111, x112, x113, x114), new_gcd0Gcd'18(x115, x116, Zero, Succ(x117)) -> new_gcd0Gcd'12(Succ(x115), Neg(Succ(x116))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x111, x112, x113, x114)=new_gcd0Gcd'18(x115, x116, Zero, Succ(x117))  ==>  new_gcd0Gcd'18(x111, x112, Succ(x113), Succ(x114))_>=_new_gcd0Gcd'18(x111, x112, x113, x114))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'18(x111, x112, Succ(Zero), Succ(Succ(x117)))_>=_new_gcd0Gcd'18(x111, x112, Zero, Succ(x117)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'18(x134, x135, Succ(x136), Succ(x137)) -> new_gcd0Gcd'18(x134, x135, x136, x137), new_gcd0Gcd'18(x138, x139, Succ(x140), Succ(x141)) -> new_gcd0Gcd'18(x138, x139, x140, x141) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x134, x135, x136, x137)=new_gcd0Gcd'18(x138, x139, Succ(x140), Succ(x141))  ==>  new_gcd0Gcd'18(x134, x135, Succ(x136), Succ(x137))_>=_new_gcd0Gcd'18(x134, x135, x136, x137))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'18(x134, x135, Succ(Succ(x140)), Succ(Succ(x141)))_>=_new_gcd0Gcd'18(x134, x135, Succ(x140), Succ(x141)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'13(x162, x163, Succ(x164), Succ(x165)) -> new_gcd0Gcd'13(x162, x163, x164, x165), new_gcd0Gcd'13(x166, x167, Zero, Succ(x168)) -> new_gcd0Gcd'15(Succ(x166), x167) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x162, x163, x164, x165)=new_gcd0Gcd'13(x166, x167, Zero, Succ(x168))  ==>  new_gcd0Gcd'13(x162, x163, Succ(x164), Succ(x165))_>=_new_gcd0Gcd'13(x162, x163, x164, x165))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'13(x162, x163, Succ(Zero), Succ(Succ(x168)))_>=_new_gcd0Gcd'13(x162, x163, Zero, Succ(x168)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'13(x177, x178, Succ(x179), Succ(x180)) -> new_gcd0Gcd'13(x177, x178, x179, x180), new_gcd0Gcd'13(x181, x182, Succ(x183), Succ(x184)) -> new_gcd0Gcd'13(x181, x182, x183, x184) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'13(x177, x178, x179, x180)=new_gcd0Gcd'13(x181, x182, Succ(x183), Succ(x184))  ==>  new_gcd0Gcd'13(x177, x178, Succ(x179), Succ(x180))_>=_new_gcd0Gcd'13(x177, x178, x179, x180))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'13(x177, x178, Succ(Succ(x183)), Succ(Succ(x184)))_>=_new_gcd0Gcd'13(x177, x178, Succ(x183), Succ(x184)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'17(Succ(Succ(x189)), Succ(x190), Succ(Succ(x189))) -> new_gcd0Gcd'18(x189, Succ(x190), x189, x190), new_gcd0Gcd'18(x191, x192, Zero, Succ(x193)) -> new_gcd0Gcd'12(Succ(x191), Neg(Succ(x192))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x189, Succ(x190), x189, x190)=new_gcd0Gcd'18(x191, x192, Zero, Succ(x193))  ==>  new_gcd0Gcd'17(Succ(Succ(x189)), Succ(x190), Succ(Succ(x189)))_>=_new_gcd0Gcd'18(x189, Succ(x190), x189, x190))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'17(Succ(Succ(Zero)), Succ(Succ(x193)), Succ(Succ(Zero)))_>=_new_gcd0Gcd'18(Zero, Succ(Succ(x193)), Zero, Succ(x193)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'17(Succ(Succ(x202)), Succ(x203), Succ(Succ(x202))) -> new_gcd0Gcd'18(x202, Succ(x203), x202, x203), new_gcd0Gcd'18(x204, x205, Succ(x206), Succ(x207)) -> new_gcd0Gcd'18(x204, x205, x206, x207) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'18(x202, Succ(x203), x202, x203)=new_gcd0Gcd'18(x204, x205, Succ(x206), Succ(x207))  ==>  new_gcd0Gcd'17(Succ(Succ(x202)), Succ(x203), Succ(Succ(x202)))_>=_new_gcd0Gcd'18(x202, Succ(x203), x202, x203))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'17(Succ(Succ(Succ(x206))), Succ(Succ(x207)), Succ(Succ(Succ(x206))))_>=_new_gcd0Gcd'18(Succ(x206), Succ(Succ(x207)), Succ(x206), Succ(x207)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	To summarize, we get the following constraints P__>=_ for the following pairs.
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'18(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'12(Succ(x3), Neg(Succ(x4))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'12(Succ(x30), Neg(Succ(Succ(x32))))_>=_new_gcd0Gcd'0(Neg(Succ(Succ(x32))), Succ(x30)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Succ(Succ(x54)))_>=_new_gcd0Gcd'13(Zero, Succ(Succ(x54)), Zero, Succ(x54)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(x63)))), Succ(Succ(x64)))_>=_new_gcd0Gcd'13(Succ(x63), Succ(Succ(x64)), Succ(x63), Succ(x64)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'13(x79, x80, Zero, Succ(x81))_>=_new_gcd0Gcd'15(Succ(x79), x80))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'15(Succ(x107), Succ(x109))_>=_new_gcd0Gcd'17(Succ(Succ(x109)), Succ(x107), Succ(Succ(x109))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'18(x111, x112, Succ(Zero), Succ(Succ(x117)))_>=_new_gcd0Gcd'18(x111, x112, Zero, Succ(x117)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'18(x134, x135, Succ(Succ(x140)), Succ(Succ(x141)))_>=_new_gcd0Gcd'18(x134, x135, Succ(x140), Succ(x141)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'13(x162, x163, Succ(Zero), Succ(Succ(x168)))_>=_new_gcd0Gcd'13(x162, x163, Zero, Succ(x168)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'13(x177, x178, Succ(Succ(x183)), Succ(Succ(x184)))_>=_new_gcd0Gcd'13(x177, x178, Succ(x183), Succ(x184)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'17(Succ(Succ(Zero)), Succ(Succ(x193)), Succ(Succ(Zero)))_>=_new_gcd0Gcd'18(Zero, Succ(Succ(x193)), Zero, Succ(x193)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'17(Succ(Succ(Succ(x206))), Succ(Succ(x207)), Succ(Succ(Succ(x206))))_>=_new_gcd0Gcd'18(Succ(x206), Succ(Succ(x207)), Succ(x206), Succ(x207)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	Using the following integer polynomial ordering the  resulting constraints can be solved 
48.24/28.47	
48.24/28.47	Polynomial interpretation [NONINF]:
48.24/28.47	
48.24/28.47	   POL(Neg(x_1)) = 0
48.24/28.47	   POL(Succ(x_1)) = 1 + x_1
48.24/28.47	   POL(Zero) = 0
48.24/28.47	   POL(c) = -1
48.24/28.47	   POL(new_gcd0Gcd'0(x_1, x_2)) = -x_1
48.24/28.47	   POL(new_gcd0Gcd'12(x_1, x_2)) = -x_2
48.24/28.47	   POL(new_gcd0Gcd'13(x_1, x_2, x_3, x_4)) = 1 + x_1 - x_2 - x_3 + x_4
48.24/28.47	   POL(new_gcd0Gcd'15(x_1, x_2)) = 1 + x_1 - x_2
48.24/28.47	   POL(new_gcd0Gcd'17(x_1, x_2, x_3)) = 1 + x_2 - x_3
48.24/28.47	   POL(new_gcd0Gcd'18(x_1, x_2, x_3, x_4)) = -x_3 + x_4
48.24/28.47	
48.24/28.47	
48.24/28.47	The following pairs  are in P_>:
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	The following pairs are in P_bound:
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Zero, Succ(vuv810)) -> new_gcd0Gcd'12(Succ(vuv78), Neg(Succ(vuv79)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	There are no usable rules
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(46)
48.24/28.47	Complex Obligation (AND)
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(47)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Neg(Succ(z1))) -> new_gcd0Gcd'0(Neg(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Neg(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'13(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	   new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(48) DependencyGraphProof (EQUIVALENT)
48.24/28.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 4 less nodes.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(49)
48.24/28.47	Complex Obligation (AND)
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(50)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(51) QDPSizeChangeProof (EQUIVALENT)
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	From the DPs we obtained the following set of size-change graphs:
48.24/28.47	*new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(52)
48.24/28.47	YES
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(53)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(54) QDPSizeChangeProof (EQUIVALENT)
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	From the DPs we obtained the following set of size-change graphs:
48.24/28.47	*new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(55)
48.24/28.47	YES
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(56)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Zero, Succ(vuv430)) -> new_gcd0Gcd'15(Succ(vuv40), vuv41)
48.24/28.47	   new_gcd0Gcd'15(Succ(z0), z1) -> new_gcd0Gcd'17(Succ(z1), Succ(z0), Succ(z1))
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	   new_gcd0Gcd'17(Succ(Succ(x0)), Succ(z0), Succ(Succ(x0))) -> new_gcd0Gcd'18(x0, Succ(z0), x0, z0)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(57) DependencyGraphProof (EQUIVALENT)
48.24/28.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 3 less nodes.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(58)
48.24/28.47	Complex Obligation (AND)
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(59)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(60) QDPSizeChangeProof (EQUIVALENT)
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	From the DPs we obtained the following set of size-change graphs:
48.24/28.47	*new_gcd0Gcd'18(vuv78, vuv79, Succ(vuv800), Succ(vuv810)) -> new_gcd0Gcd'18(vuv78, vuv79, vuv800, vuv810)
48.24/28.47	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(61)
48.24/28.47	YES
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(62)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(63) QDPSizeChangeProof (EQUIVALENT)
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	From the DPs we obtained the following set of size-change graphs:
48.24/28.47	*new_gcd0Gcd'13(vuv40, vuv41, Succ(vuv420), Succ(vuv430)) -> new_gcd0Gcd'13(vuv40, vuv41, vuv420, vuv430)
48.24/28.47	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(64)
48.24/28.47	YES
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(65)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'12(Zero, Pos(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Pos(Succ(Succ(z0))), Zero)
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	   new_primMinusNatS0 -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS0
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(66) UsableRulesProof (EQUIVALENT)
48.24/28.47	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.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(67)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'12(Zero, Pos(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Pos(Succ(Succ(z0))), Zero)
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.47	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS0
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(68) QReductionProof (EQUIVALENT)
48.24/28.47	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
48.24/28.47	
48.24/28.47	   new_primMinusNatS0
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(69)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'12(Zero, Pos(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Pos(Succ(Succ(z0))), Zero)
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.47	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(70) TransformationProof (EQUIVALENT)
48.24/28.47	By narrowing [LPAR04] the rule new_gcd0Gcd'11(vuv23, vuv24) -> new_gcd0Gcd'1(new_primMinusNatS1(vuv23, vuv24), vuv24) at position [0] we obtained the following new rules [LPAR04]:
48.24/28.47	
48.24/28.47	   (new_gcd0Gcd'11(x0, Succ(x1)) -> new_gcd0Gcd'1(new_primMinusNatS2(x0, x1), Succ(x1)),new_gcd0Gcd'11(x0, Succ(x1)) -> new_gcd0Gcd'1(new_primMinusNatS2(x0, x1), Succ(x1)))
48.24/28.47	   (new_gcd0Gcd'11(x0, Zero) -> new_gcd0Gcd'1(Succ(x0), Zero),new_gcd0Gcd'11(x0, Zero) -> new_gcd0Gcd'1(Succ(x0), Zero))
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(71)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'12(Zero, Pos(Succ(Succ(z0)))) -> new_gcd0Gcd'0(Pos(Succ(Succ(z0))), Zero)
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Zero)), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Zero), Succ(vuv4000)) -> new_gcd0Gcd'12(Zero, Pos(Succ(Succ(vuv4000))))
48.24/28.47	   new_gcd0Gcd'11(x0, Succ(x1)) -> new_gcd0Gcd'1(new_primMinusNatS2(x0, x1), Succ(x1))
48.24/28.47	   new_gcd0Gcd'11(x0, Zero) -> new_gcd0Gcd'1(Succ(x0), Zero)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.47	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(72) DependencyGraphProof (EQUIVALENT)
48.24/28.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 4 less nodes.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(73)
48.24/28.47	Complex Obligation (AND)
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(74)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'11(x0, Zero) -> new_gcd0Gcd'1(Succ(x0), Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.47	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(75) UsableRulesProof (EQUIVALENT)
48.24/28.47	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.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(76)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'11(x0, Zero) -> new_gcd0Gcd'1(Succ(x0), Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(77) QReductionProof (EQUIVALENT)
48.24/28.47	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(78)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'11(x0, Zero) -> new_gcd0Gcd'1(Succ(x0), Zero)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(79) MRRProof (EQUIVALENT)
48.24/28.47	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.
48.24/28.47	
48.24/28.47	Strictly oriented dependency pairs:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Zero) -> new_gcd0Gcd'11(vuv6000, Zero)
48.24/28.47	
48.24/28.47	
48.24/28.47	Used ordering: Polynomial interpretation [POLO]:
48.24/28.47	
48.24/28.47	   POL(Succ(x_1)) = 1 + x_1
48.24/28.47	   POL(Zero) = 1
48.24/28.47	   POL(new_gcd0Gcd'1(x_1, x_2)) = 1 + 2*x_1 + x_2
48.24/28.47	   POL(new_gcd0Gcd'11(x_1, x_2)) = 2 + 2*x_1 + 2*x_2
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(80)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'11(x0, Zero) -> new_gcd0Gcd'1(Succ(x0), Zero)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(81) DependencyGraphProof (EQUIVALENT)
48.24/28.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(82)
48.24/28.47	TRUE
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(83)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'11(x0, Succ(x1)) -> new_gcd0Gcd'1(new_primMinusNatS2(x0, x1), Succ(x1))
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(vuv23, Succ(vuv240)) -> new_primMinusNatS2(vuv23, vuv240)
48.24/28.47	   new_primMinusNatS1(vuv23, Zero) -> Succ(vuv23)
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(84) UsableRulesProof (EQUIVALENT)
48.24/28.47	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.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(85)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'11(x0, Succ(x1)) -> new_gcd0Gcd'1(new_primMinusNatS2(x0, x1), Succ(x1))
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(86) QReductionProof (EQUIVALENT)
48.24/28.47	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
48.24/28.47	
48.24/28.47	   new_primMinusNatS1(x0, Zero)
48.24/28.47	   new_primMinusNatS1(x0, Succ(x1))
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(87)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'11(x0, Succ(x1)) -> new_gcd0Gcd'1(new_primMinusNatS2(x0, x1), Succ(x1))
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(88) QDPOrderProof (EQUIVALENT)
48.24/28.47	We use the reduction pair processor [LPAR04,JAR06].
48.24/28.47	
48.24/28.47	
48.24/28.47	The following pairs can be oriented strictly and are deleted.
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'11(x0, Succ(x1)) -> new_gcd0Gcd'1(new_primMinusNatS2(x0, x1), Succ(x1))
48.24/28.47	The remaining pairs can at least be oriented weakly.
48.24/28.47	Used ordering:  Polynomial interpretation [POLO]:
48.24/28.47	
48.24/28.47	   POL(Pos(x_1)) = x_1
48.24/28.47	   POL(Succ(x_1)) = 1 + x_1
48.24/28.47	   POL(Zero) = 0
48.24/28.47	   POL(new_gcd0Gcd'0(x_1, x_2)) = x_1 + x_2
48.24/28.47	   POL(new_gcd0Gcd'1(x_1, x_2)) = x_1 + x_2
48.24/28.47	   POL(new_gcd0Gcd'10(x_1, x_2, x_3, x_4)) = 2 + x_1 + x_2
48.24/28.47	   POL(new_gcd0Gcd'11(x_1, x_2)) = 2 + x_1 + x_2
48.24/28.47	   POL(new_gcd0Gcd'12(x_1, x_2)) = x_1 + x_2
48.24/28.47	   POL(new_primMinusNatS2(x_1, x_2)) = x_1
48.24/28.47	
48.24/28.47	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(89)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	   new_gcd0Gcd'1(Succ(Succ(vuv6000)), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Zero) -> new_gcd0Gcd'11(vuv35, vuv36)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(90) DependencyGraphProof (EQUIVALENT)
48.24/28.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(91)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(92) InductionCalculusProof (EQUIVALENT)
48.24/28.47	Note that final constraints are written in bold face.
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'10(x0, x1, Succ(x2), Succ(x3)) -> new_gcd0Gcd'10(x0, x1, x2, x3), new_gcd0Gcd'10(x4, x5, Succ(x6), Succ(x7)) -> new_gcd0Gcd'10(x4, x5, x6, x7) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x0, x1, x2, x3)=new_gcd0Gcd'10(x4, x5, Succ(x6), Succ(x7))  ==>  new_gcd0Gcd'10(x0, x1, Succ(x2), Succ(x3))_>=_new_gcd0Gcd'10(x0, x1, x2, x3))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'10(x0, x1, Succ(Succ(x6)), Succ(Succ(x7)))_>=_new_gcd0Gcd'10(x0, x1, Succ(x6), Succ(x7)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'10(x8, x9, Succ(x10), Succ(x11)) -> new_gcd0Gcd'10(x8, x9, x10, x11), new_gcd0Gcd'10(x12, x13, Zero, Succ(x14)) -> new_gcd0Gcd'12(Succ(x12), Pos(Succ(x13))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x8, x9, x10, x11)=new_gcd0Gcd'10(x12, x13, Zero, Succ(x14))  ==>  new_gcd0Gcd'10(x8, x9, Succ(x10), Succ(x11))_>=_new_gcd0Gcd'10(x8, x9, x10, x11))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'10(x8, x9, Succ(Zero), Succ(Succ(x14)))_>=_new_gcd0Gcd'10(x8, x9, Zero, Succ(x14)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36))) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'10(x29, x30, Zero, Succ(x31)) -> new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))), new_gcd0Gcd'12(Succ(x32), Pos(Succ(x33))) -> new_gcd0Gcd'0(Pos(Succ(x33)), Succ(x32)) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30)))=new_gcd0Gcd'12(Succ(x32), Pos(Succ(x33)))  ==>  new_gcd0Gcd'10(x29, x30, Zero, Succ(x31))_>=_new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'10(x29, x30, Zero, Succ(x31))_>=_new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0)) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'12(Succ(x43), Pos(Succ(x44))) -> new_gcd0Gcd'0(Pos(Succ(x44)), Succ(x43)), new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x46)) -> new_gcd0Gcd'10(x45, Succ(x46), x45, x46) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'0(Pos(Succ(x44)), Succ(x43))=new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x46))  ==>  new_gcd0Gcd'12(Succ(x43), Pos(Succ(x44)))_>=_new_gcd0Gcd'0(Pos(Succ(x44)), Succ(x43)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'12(Succ(x43), Pos(Succ(Succ(x45))))_>=_new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x43)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Pos(Succ(Succ(x47))), Succ(x48)) -> new_gcd0Gcd'10(x47, Succ(x48), x47, x48), new_gcd0Gcd'10(x49, x50, Succ(x51), Succ(x52)) -> new_gcd0Gcd'10(x49, x50, x51, x52) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x47, Succ(x48), x47, x48)=new_gcd0Gcd'10(x49, x50, Succ(x51), Succ(x52))  ==>  new_gcd0Gcd'0(Pos(Succ(Succ(x47))), Succ(x48))_>=_new_gcd0Gcd'10(x47, Succ(x48), x47, x48))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(x51)))), Succ(Succ(x52)))_>=_new_gcd0Gcd'10(Succ(x51), Succ(Succ(x52)), Succ(x51), Succ(x52)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Pos(Succ(Succ(x53))), Succ(x54)) -> new_gcd0Gcd'10(x53, Succ(x54), x53, x54), new_gcd0Gcd'10(x55, x56, Zero, Succ(x57)) -> new_gcd0Gcd'12(Succ(x55), Pos(Succ(x56))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x53, Succ(x54), x53, x54)=new_gcd0Gcd'10(x55, x56, Zero, Succ(x57))  ==>  new_gcd0Gcd'0(Pos(Succ(Succ(x53))), Succ(x54))_>=_new_gcd0Gcd'10(x53, Succ(x54), x53, x54))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Succ(Succ(x57)))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x57)), Zero, Succ(x57)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	To summarize, we get the following constraints P__>=_ for the following pairs.
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'10(x0, x1, Succ(Succ(x6)), Succ(Succ(x7)))_>=_new_gcd0Gcd'10(x0, x1, Succ(x6), Succ(x7)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'10(x8, x9, Succ(Zero), Succ(Succ(x14)))_>=_new_gcd0Gcd'10(x8, x9, Zero, Succ(x14)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'10(x29, x30, Zero, Succ(x31))_>=_new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'12(Succ(x43), Pos(Succ(Succ(x45))))_>=_new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x43)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(x51)))), Succ(Succ(x52)))_>=_new_gcd0Gcd'10(Succ(x51), Succ(Succ(x52)), Succ(x51), Succ(x52)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Succ(Succ(x57)))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x57)), Zero, Succ(x57)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	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. 
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(93)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(94) NonInfProof (EQUIVALENT)
48.24/28.47	The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
48.24/28.47	
48.24/28.47	Note that final constraints are written in bold face.
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'10(x0, x1, Succ(x2), Succ(x3)) -> new_gcd0Gcd'10(x0, x1, x2, x3), new_gcd0Gcd'10(x4, x5, Succ(x6), Succ(x7)) -> new_gcd0Gcd'10(x4, x5, x6, x7) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x0, x1, x2, x3)=new_gcd0Gcd'10(x4, x5, Succ(x6), Succ(x7))  ==>  new_gcd0Gcd'10(x0, x1, Succ(x2), Succ(x3))_>=_new_gcd0Gcd'10(x0, x1, x2, x3))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'10(x0, x1, Succ(Succ(x6)), Succ(Succ(x7)))_>=_new_gcd0Gcd'10(x0, x1, Succ(x6), Succ(x7)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'10(x8, x9, Succ(x10), Succ(x11)) -> new_gcd0Gcd'10(x8, x9, x10, x11), new_gcd0Gcd'10(x12, x13, Zero, Succ(x14)) -> new_gcd0Gcd'12(Succ(x12), Pos(Succ(x13))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x8, x9, x10, x11)=new_gcd0Gcd'10(x12, x13, Zero, Succ(x14))  ==>  new_gcd0Gcd'10(x8, x9, Succ(x10), Succ(x11))_>=_new_gcd0Gcd'10(x8, x9, x10, x11))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'10(x8, x9, Succ(Zero), Succ(Succ(x14)))_>=_new_gcd0Gcd'10(x8, x9, Zero, Succ(x14)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36))) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'10(x29, x30, Zero, Succ(x31)) -> new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))), new_gcd0Gcd'12(Succ(x32), Pos(Succ(x33))) -> new_gcd0Gcd'0(Pos(Succ(x33)), Succ(x32)) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30)))=new_gcd0Gcd'12(Succ(x32), Pos(Succ(x33)))  ==>  new_gcd0Gcd'10(x29, x30, Zero, Succ(x31))_>=_new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'10(x29, x30, Zero, Succ(x31))_>=_new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0)) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'12(Succ(x43), Pos(Succ(x44))) -> new_gcd0Gcd'0(Pos(Succ(x44)), Succ(x43)), new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x46)) -> new_gcd0Gcd'10(x45, Succ(x46), x45, x46) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'0(Pos(Succ(x44)), Succ(x43))=new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x46))  ==>  new_gcd0Gcd'12(Succ(x43), Pos(Succ(x44)))_>=_new_gcd0Gcd'0(Pos(Succ(x44)), Succ(x43)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'12(Succ(x43), Pos(Succ(Succ(x45))))_>=_new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x43)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	For Pair new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000) the following chains were created:
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Pos(Succ(Succ(x47))), Succ(x48)) -> new_gcd0Gcd'10(x47, Succ(x48), x47, x48), new_gcd0Gcd'10(x49, x50, Succ(x51), Succ(x52)) -> new_gcd0Gcd'10(x49, x50, x51, x52) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x47, Succ(x48), x47, x48)=new_gcd0Gcd'10(x49, x50, Succ(x51), Succ(x52))  ==>  new_gcd0Gcd'0(Pos(Succ(Succ(x47))), Succ(x48))_>=_new_gcd0Gcd'10(x47, Succ(x48), x47, x48))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(x51)))), Succ(Succ(x52)))_>=_new_gcd0Gcd'10(Succ(x51), Succ(Succ(x52)), Succ(x51), Succ(x52)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*We consider the chain new_gcd0Gcd'0(Pos(Succ(Succ(x53))), Succ(x54)) -> new_gcd0Gcd'10(x53, Succ(x54), x53, x54), new_gcd0Gcd'10(x55, x56, Zero, Succ(x57)) -> new_gcd0Gcd'12(Succ(x55), Pos(Succ(x56))) which results in the following constraint:
48.24/28.47	
48.24/28.47	(1)    (new_gcd0Gcd'10(x53, Succ(x54), x53, x54)=new_gcd0Gcd'10(x55, x56, Zero, Succ(x57))  ==>  new_gcd0Gcd'0(Pos(Succ(Succ(x53))), Succ(x54))_>=_new_gcd0Gcd'10(x53, Succ(x54), x53, x54))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
48.24/28.47	
48.24/28.47	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Succ(Succ(x57)))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x57)), Zero, Succ(x57)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	To summarize, we get the following constraints P__>=_ for the following pairs.
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'10(x0, x1, Succ(Succ(x6)), Succ(Succ(x7)))_>=_new_gcd0Gcd'10(x0, x1, Succ(x6), Succ(x7)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'10(x8, x9, Succ(Zero), Succ(Succ(x14)))_>=_new_gcd0Gcd'10(x8, x9, Zero, Succ(x14)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'10(x29, x30, Zero, Succ(x31))_>=_new_gcd0Gcd'12(Succ(x29), Pos(Succ(x30))))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'12(Succ(x43), Pos(Succ(Succ(x45))))_>=_new_gcd0Gcd'0(Pos(Succ(Succ(x45))), Succ(x43)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	*new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(x51)))), Succ(Succ(x52)))_>=_new_gcd0Gcd'10(Succ(x51), Succ(Succ(x52)), Succ(x51), Succ(x52)))
48.24/28.47	
48.24/28.47	
48.24/28.47	*(new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Succ(Succ(x57)))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x57)), Zero, Succ(x57)))
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	Using the following integer polynomial ordering the  resulting constraints can be solved 
48.24/28.47	
48.24/28.47	Polynomial interpretation [NONINF]:
48.24/28.47	
48.24/28.47	   POL(Pos(x_1)) = 1
48.24/28.47	   POL(Succ(x_1)) = 1 + x_1
48.24/28.47	   POL(Zero) = 0
48.24/28.47	   POL(c) = -1
48.24/28.47	   POL(new_gcd0Gcd'0(x_1, x_2)) = 1 + x_2
48.24/28.47	   POL(new_gcd0Gcd'10(x_1, x_2, x_3, x_4)) = 1 + x_1 - x_3 + x_4
48.24/28.47	   POL(new_gcd0Gcd'12(x_1, x_2)) = x_1 + x_2
48.24/28.47	
48.24/28.47	
48.24/28.47	The following pairs  are in P_>:
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	The following pairs are in P_bound:
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	   new_gcd0Gcd'0(Pos(Succ(Succ(vuv6000))), Succ(vuv4000)) -> new_gcd0Gcd'10(vuv6000, Succ(vuv4000), vuv6000, vuv4000)
48.24/28.47	There are no usable rules
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(95)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Zero, Succ(vuv380)) -> new_gcd0Gcd'12(Succ(vuv35), Pos(Succ(vuv36)))
48.24/28.47	   new_gcd0Gcd'12(Succ(z0), Pos(Succ(z1))) -> new_gcd0Gcd'0(Pos(Succ(z1)), Succ(z0))
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(96) DependencyGraphProof (EQUIVALENT)
48.24/28.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(97)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	
48.24/28.47	The TRS R consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Zero) -> Succ(vuv230)
48.24/28.47	   new_primMinusNatS2(Zero, Zero) -> Zero
48.24/28.47	   new_primMinusNatS2(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS2(vuv230, vuv2400)
48.24/28.47	   new_primMinusNatS2(Zero, Succ(vuv2400)) -> Zero
48.24/28.47	
48.24/28.47	The set Q consists of the following terms:
48.24/28.47	
48.24/28.47	   new_primMinusNatS2(Succ(x0), Zero)
48.24/28.47	   new_primMinusNatS2(Zero, Zero)
48.24/28.47	   new_primMinusNatS2(Succ(x0), Succ(x1))
48.24/28.47	   new_primMinusNatS2(Zero, Succ(x0))
48.24/28.47	
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(98) QDPSizeChangeProof (EQUIVALENT)
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	From the DPs we obtained the following set of size-change graphs:
48.24/28.47	*new_gcd0Gcd'10(vuv35, vuv36, Succ(vuv370), Succ(vuv380)) -> new_gcd0Gcd'10(vuv35, vuv36, vuv370, vuv380)
48.24/28.47	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(99)
48.24/28.47	YES
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(100)
48.24/28.47	Obligation:
48.24/28.47	Q DP problem:
48.24/28.47	The TRS P consists of the following rules:
48.24/28.47	
48.24/28.47	   new_primMinusNatS(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS(vuv230, vuv2400)
48.24/28.47	
48.24/28.47	R is empty.
48.24/28.47	Q is empty.
48.24/28.47	We have to consider all minimal (P,Q,R)-chains.
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(101) QDPSizeChangeProof (EQUIVALENT)
48.24/28.47	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. 
48.24/28.47	
48.24/28.47	From the DPs we obtained the following set of size-change graphs:
48.24/28.47	*new_primMinusNatS(Succ(vuv230), Succ(vuv2400)) -> new_primMinusNatS(vuv230, vuv2400)
48.24/28.47	The graph contains the following edges 1 > 1, 2 > 2
48.24/28.47	
48.24/28.47	
48.24/28.47	----------------------------------------
48.24/28.47	
48.24/28.47	(102)
48.24/28.47	YES
48.46/28.51	EOF