81.70/49.32	MAYBE
84.19/49.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
84.19/49.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
84.19/49.96	
84.19/49.96	
84.19/49.96	H-Termination with start terms of the given HASKELL could not be shown:
84.19/49.96	
84.19/49.96	(0) HASKELL
84.19/49.96	(1) IFR [EQUIVALENT, 0 ms]
84.19/49.96	(2) HASKELL
84.19/49.96	(3) BR [EQUIVALENT, 0 ms]
84.19/49.96	(4) HASKELL
84.19/49.96	(5) COR [EQUIVALENT, 0 ms]
84.19/49.96	(6) HASKELL
84.19/49.96	(7) LetRed [EQUIVALENT, 0 ms]
84.19/49.96	(8) HASKELL
84.19/49.96	(9) NumRed [SOUND, 0 ms]
84.19/49.96	(10) HASKELL
84.19/49.96	(11) Narrow [SOUND, 0 ms]
84.19/49.96	(12) AND
84.19/49.96	    (13) QDP
84.19/49.96	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	        (15) YES
84.19/49.96	    (16) QDP
84.19/49.96	        (17) DependencyGraphProof [EQUIVALENT, 0 ms]
84.19/49.96	        (18) QDP
84.19/49.96	        (19) QDPOrderProof [EQUIVALENT, 225 ms]
84.19/49.96	        (20) QDP
84.19/49.96	        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
84.19/49.96	        (22) AND
84.19/49.96	            (23) QDP
84.19/49.96	                (24) QDPOrderProof [EQUIVALENT, 40 ms]
84.19/49.96	                (25) QDP
84.19/49.96	                (26) MNOCProof [EQUIVALENT, 0 ms]
84.19/49.96	                (27) QDP
84.19/49.96	                (28) InductionCalculusProof [EQUIVALENT, 40 ms]
84.19/49.96	                (29) QDP
84.19/49.96	                (30) QDPPairToRuleProof [EQUIVALENT, 0 ms]
84.19/49.96	                (31) AND
84.19/49.96	                    (32) QDP
84.19/49.96	                        (33) MNOCProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (34) QDP
84.19/49.96	                        (35) InductionCalculusProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (36) QDP
84.19/49.96	                        (37) QDPPairToRuleProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (38) AND
84.19/49.96	                            (39) QDP
84.19/49.96	                                (40) MNOCProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (41) QDP
84.19/49.96	                                (42) InductionCalculusProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (43) QDP
84.19/49.96	                            (44) QDP
84.19/49.96	                                (45) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (46) YES
84.19/49.96	                    (47) QDP
84.19/49.96	                        (48) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (49) YES
84.19/49.96	            (50) QDP
84.19/49.96	                (51) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (52) QDP
84.19/49.96	                (53) UsableRulesProof [EQUIVALENT, 0 ms]
84.19/49.96	                (54) QDP
84.19/49.96	                (55) QReductionProof [EQUIVALENT, 0 ms]
84.19/49.96	                (56) QDP
84.19/49.96	                (57) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (58) QDP
84.19/49.96	                (59) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (60) QDP
84.19/49.96	                (61) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (62) QDP
84.19/49.96	                (63) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (64) QDP
84.19/49.96	                (65) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (66) QDP
84.19/49.96	                (67) UsableRulesProof [EQUIVALENT, 0 ms]
84.19/49.96	                (68) QDP
84.19/49.96	                (69) QReductionProof [EQUIVALENT, 0 ms]
84.19/49.96	                (70) QDP
84.19/49.96	                (71) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (72) QDP
84.19/49.96	                (73) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                (74) QDP
84.19/49.96	                (75) DependencyGraphProof [EQUIVALENT, 0 ms]
84.19/49.96	                (76) AND
84.19/49.96	                    (77) QDP
84.19/49.96	                        (78) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (79) QDP
84.19/49.96	                        (80) TransformationProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (81) QDP
84.19/49.96	                        (82) DependencyGraphProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (83) AND
84.19/49.96	                            (84) QDP
84.19/49.96	                                (85) QDPOrderProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (86) QDP
84.19/49.96	                                (87) DependencyGraphProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (88) AND
84.19/49.96	                                    (89) QDP
84.19/49.96	                                        (90) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	                                        (91) YES
84.19/49.96	                                    (92) QDP
84.19/49.96	                                        (93) MNOCProof [EQUIVALENT, 0 ms]
84.19/49.96	                                        (94) QDP
84.19/49.96	                                        (95) InductionCalculusProof [EQUIVALENT, 0 ms]
84.19/49.96	                                        (96) QDP
84.19/49.96	                                        (97) QDPPairToRuleProof [EQUIVALENT, 0 ms]
84.19/49.96	                                        (98) AND
84.19/49.96	                                            (99) QDP
84.19/49.96	                                                (100) MNOCProof [EQUIVALENT, 0 ms]
84.19/49.96	                                                (101) QDP
84.19/49.96	                                                (102) InductionCalculusProof [EQUIVALENT, 0 ms]
84.19/49.96	                                                (103) QDP
84.19/49.96	                                            (104) QDP
84.19/49.96	                                                (105) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	                                                (106) YES
84.19/49.96	                            (107) QDP
84.19/49.96	                                (108) UsableRulesProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (109) QDP
84.19/49.96	                                (110) QReductionProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (111) QDP
84.19/49.96	                                (112) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	                                (113) YES
84.19/49.96	                    (114) QDP
84.19/49.96	                        (115) UsableRulesProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (116) QDP
84.19/49.96	                        (117) QReductionProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (118) QDP
84.19/49.96	                        (119) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	                        (120) YES
84.19/49.96	    (121) QDP
84.19/49.96	        (122) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	        (123) YES
84.19/49.96	    (124) QDP
84.19/49.96	        (125) DependencyGraphProof [EQUIVALENT, 0 ms]
84.19/49.96	        (126) QDP
84.19/49.96	        (127) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	        (128) YES
84.19/49.96	    (129) QDP
84.19/49.96	        (130) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	        (131) YES
84.19/49.96	    (132) QDP
84.19/49.96	        (133) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	        (134) YES
84.19/49.96	    (135) QDP
84.19/49.96	        (136) QDPSizeChangeProof [EQUIVALENT, 0 ms]
84.19/49.96	        (137) YES
84.19/49.96	(138) Narrow [COMPLETE, 0 ms]
84.19/49.96	(139) TRUE
84.19/49.96	
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(0)
84.19/49.96	Obligation:
84.19/49.96	mainModule Main 
84.19/49.96	module Main where {
84.19/49.96	import qualified Prelude;
84.19/49.96	}
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(1) IFR (EQUIVALENT)
84.19/49.96	If Reductions:
84.19/49.96	The following If expression
84.19/49.96	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
84.19/49.96	is transformed to
84.19/49.96	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
84.19/49.96	primDivNatS0 x y False = Zero;
84.19/49.96	"
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(2)
84.19/49.96	Obligation:
84.19/49.96	mainModule Main 
84.19/49.96	module Main where {
84.19/49.96	import qualified Prelude;
84.19/49.96	}
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(3) BR (EQUIVALENT)
84.19/49.96	Replaced joker patterns by fresh variables and removed binding patterns.
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(4)
84.19/49.96	Obligation:
84.19/49.96	mainModule Main 
84.19/49.96	module Main where {
84.19/49.96	import qualified Prelude;
84.19/49.96	}
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(5) COR (EQUIVALENT)
84.19/49.96	Cond Reductions:
84.19/49.96	The following Function with conditions
84.19/49.96	"undefined |Falseundefined;
84.19/49.96	"
84.19/49.96	is transformed to
84.19/49.96	"undefined  = undefined1;
84.19/49.96	"
84.19/49.96	"undefined0 True = undefined;
84.19/49.96	"
84.19/49.96	"undefined1  = undefined0 False;
84.19/49.96	"
84.19/49.96	The following Function with conditions
84.19/49.96	"g x n|even ng (x * x) (n `quot` 2)|otherwisef x (n - 1) (x * y);
84.19/49.96	"
84.19/49.96	is transformed to
84.19/49.96	"g x n = g2 x n;
84.19/49.96	"
84.19/49.96	"g0 x n True = f x (n - 1) (x * y);
84.19/49.96	"
84.19/49.96	"g1 x n True = g (x * x) (n `quot` 2);
84.19/49.96	g1 x n False = g0 x n otherwise;
84.19/49.96	"
84.19/49.96	"g2 x n = g1 x n (even n);
84.19/49.96	"
84.19/49.96	The following Function with conditions
84.19/49.96	"f wz 0 y = y;
84.19/49.96	f x n y = g x n where {
84.19/49.96	g x n|even ng (x * x) (n `quot` 2)|otherwisef x (n - 1) (x * y);
84.19/49.96	} 
84.19/49.96	;
84.19/49.96	"
84.19/49.96	is transformed to
84.19/49.96	"f wz yu y = f4 wz yu y;
84.19/49.96	f x n y = f0 x n y;
84.19/49.96	"
84.19/49.96	"f0 x n y = g x n where {
84.19/49.96	g x n = g2 x n;
84.19/49.96	;
84.19/49.96	g0 x n True = f x (n - 1) (x * y);
84.19/49.96	;
84.19/49.96	g1 x n True = g (x * x) (n `quot` 2);
84.19/49.96	g1 x n False = g0 x n otherwise;
84.19/49.96	;
84.19/49.96	g2 x n = g1 x n (even n);
84.19/49.96	} 
84.19/49.96	;
84.19/49.96	"
84.19/49.96	"f3 True wz yu y = y;
84.19/49.96	f3 yv yw yx yy = f0 yw yx yy;
84.19/49.96	"
84.19/49.96	"f4 wz yu y = f3 (yu == 0) wz yu y;
84.19/49.96	f4 yz zu zv = f0 yz zu zv;
84.19/49.96	"
84.19/49.96	The following Function with conditions
84.19/49.96	"^ x 0 = 1;
84.19/49.96	^ x n|n > 0f x (n - 1) x where {
84.19/49.96	f wz 0 y = y;
84.19/49.96	f x n y = g x n where {
84.19/49.96	g x n|even ng (x * x) (n `quot` 2)|otherwisef x (n - 1) (x * y);
84.19/49.96	} 
84.19/49.96	;
84.19/49.96	} 
84.19/49.96	;
84.19/49.96	^ xu xv = error [];
84.19/49.96	"
84.19/49.96	is transformed to
84.19/49.96	"^ x zy = pr4 x zy;
84.19/49.96	^ x n = pr2 x n;
84.19/49.96	^ xu xv = pr0 xu xv;
84.19/49.96	"
84.19/49.96	"pr0 xu xv = error [];
84.19/49.96	"
84.19/49.96	"pr2 x n = pr1 x n (n > 0) where {
84.19/49.96	f wz yu y = f4 wz yu y;
84.19/49.96	f x n y = f0 x n y;
84.19/49.96	;
84.19/49.96	f0 x n y = g x n where {
84.19/49.96	g x n = g2 x n;
84.19/49.96	;
84.19/49.96	g0 x n True = f x (n - 1) (x * y);
84.19/49.96	;
84.19/49.96	g1 x n True = g (x * x) (n `quot` 2);
84.19/49.96	g1 x n False = g0 x n otherwise;
84.19/49.96	;
84.19/49.96	g2 x n = g1 x n (even n);
84.19/49.96	} 
84.19/49.96	;
84.19/49.96	;
84.19/49.96	f3 True wz yu y = y;
84.19/49.96	f3 yv yw yx yy = f0 yw yx yy;
84.19/49.96	;
84.19/49.96	f4 wz yu y = f3 (yu == 0) wz yu y;
84.19/49.96	f4 yz zu zv = f0 yz zu zv;
84.19/49.96	;
84.19/49.96	pr1 x n True = f x (n - 1) x;
84.19/49.96	pr1 x n False = pr0 x n;
84.19/49.96	} 
84.19/49.96	;
84.19/49.96	pr2 zw zx = pr0 zw zx;
84.19/49.96	"
84.19/49.96	"pr3 True x zy = 1;
84.19/49.96	pr3 zz vuu vuv = pr2 vuu vuv;
84.19/49.96	"
84.19/49.96	"pr4 x zy = pr3 (zy == 0) x zy;
84.19/49.96	pr4 vuw vux = pr2 vuw vux;
84.19/49.96	"
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(6)
84.19/49.96	Obligation:
84.19/49.96	mainModule Main 
84.19/49.96	module Main where {
84.19/49.96	import qualified Prelude;
84.19/49.96	}
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(7) LetRed (EQUIVALENT)
84.19/49.96	Let/Where Reductions:
84.19/49.96	The bindings of the following Let/Where expression
84.19/49.96	"pr1 x n (n > 0) where {
84.19/49.96	f wz yu y = f4 wz yu y;
84.19/49.96	f x n y = f0 x n y;
84.19/49.96	;
84.19/49.96	f0 x n y = g x n where {
84.19/49.96	g x n = g2 x n;
84.19/49.96	;
84.19/49.96	g0 x n True = f x (n - 1) (x * y);
84.19/49.96	;
84.19/49.96	g1 x n True = g (x * x) (n `quot` 2);
84.19/49.96	g1 x n False = g0 x n otherwise;
84.19/49.96	;
84.19/49.96	g2 x n = g1 x n (even n);
84.19/49.96	} 
84.19/49.96	;
84.19/49.96	;
84.19/49.96	f3 True wz yu y = y;
84.19/49.96	f3 yv yw yx yy = f0 yw yx yy;
84.19/49.96	;
84.19/49.96	f4 wz yu y = f3 (yu == 0) wz yu y;
84.19/49.96	f4 yz zu zv = f0 yz zu zv;
84.19/49.96	;
84.19/49.96	pr1 x n True = f x (n - 1) x;
84.19/49.96	pr1 x n False = pr0 x n;
84.19/49.96	} 
84.19/49.96	"
84.19/49.96	are unpacked to the following functions on top level
84.19/49.96	"pr2F wz yu y = pr2F4 wz yu y;
84.19/49.96	pr2F x n y = pr2F0 x n y;
84.19/49.96	"
84.19/49.96	"pr2F3 True wz yu y = y;
84.19/49.96	pr2F3 yv yw yx yy = pr2F0 yw yx yy;
84.19/49.96	"
84.19/49.96	"pr2Pr1 x n True = pr2F x (n - 1) x;
84.19/49.96	pr2Pr1 x n False = pr0 x n;
84.19/49.96	"
84.19/49.96	"pr2F4 wz yu y = pr2F3 (yu == 0) wz yu y;
84.19/49.96	pr2F4 yz zu zv = pr2F0 yz zu zv;
84.19/49.96	"
84.19/49.96	"pr2F0 x n y = pr2F0G y x n;
84.19/49.96	"
84.19/49.96	The bindings of the following Let/Where expression
84.19/49.96	"g x n where {
84.19/49.96	g x n = g2 x n;
84.19/49.96	;
84.19/49.96	g0 x n True = f x (n - 1) (x * y);
84.19/49.96	;
84.19/49.96	g1 x n True = g (x * x) (n `quot` 2);
84.19/49.96	g1 x n False = g0 x n otherwise;
84.19/49.96	;
84.19/49.96	g2 x n = g1 x n (even n);
84.19/49.96	} 
84.19/49.96	"
84.19/49.96	are unpacked to the following functions on top level
84.19/49.96	"pr2F0G vuy x n = pr2F0G2 vuy x n;
84.19/49.96	"
84.19/49.96	"pr2F0G0 vuy x n True = pr2F x (n - 1) (x * vuy);
84.19/49.96	"
84.19/49.96	"pr2F0G1 vuy x n True = pr2F0G vuy (x * x) (n `quot` 2);
84.19/49.96	pr2F0G1 vuy x n False = pr2F0G0 vuy x n otherwise;
84.19/49.96	"
84.19/49.96	"pr2F0G2 vuy x n = pr2F0G1 vuy x n (even n);
84.19/49.96	"
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(8)
84.19/49.96	Obligation:
84.19/49.96	mainModule Main 
84.19/49.96	module Main where {
84.19/49.96	import qualified Prelude;
84.19/49.96	}
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(9) NumRed (SOUND)
84.19/49.96	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(10)
84.19/49.96	Obligation:
84.19/49.96	mainModule Main 
84.19/49.96	module Main where {
84.19/49.96	import qualified Prelude;
84.19/49.96	}
84.19/49.96	
84.19/49.96	----------------------------------------
84.19/49.96	
84.19/49.96	(11) Narrow (SOUND)
84.19/49.96	Haskell To QDPs
84.19/49.96	
84.19/49.96	digraph dp_graph {
84.19/49.96	node [outthreshold=100, inthreshold=100];1[label="(^)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
84.19/49.96	3[label="(^) vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
84.19/49.96	4[label="(^) vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
84.19/49.96	5[label="pr4 vuz3 vuz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
84.19/49.96	6[label="pr3 (vuz4 == fromInt (Pos Zero)) vuz3 vuz4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
84.19/49.96	7[label="pr3 (primEqInt vuz4 (fromInt (Pos Zero))) vuz3 vuz4",fontsize=16,color="burlywood",shape="box"];4738[label="vuz4/Pos vuz40",fontsize=10,color="white",style="solid",shape="box"];7 -> 4738[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4738 -> 8[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4739[label="vuz4/Neg vuz40",fontsize=10,color="white",style="solid",shape="box"];7 -> 4739[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4739 -> 9[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	8[label="pr3 (primEqInt (Pos vuz40) (fromInt (Pos Zero))) vuz3 (Pos vuz40)",fontsize=16,color="burlywood",shape="box"];4740[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];8 -> 4740[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4740 -> 10[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4741[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 4741[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4741 -> 11[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	9[label="pr3 (primEqInt (Neg vuz40) (fromInt (Pos Zero))) vuz3 (Neg vuz40)",fontsize=16,color="burlywood",shape="box"];4742[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 4742[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4742 -> 12[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4743[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 4743[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4743 -> 13[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	10[label="pr3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
84.19/49.96	11[label="pr3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
84.19/49.96	12[label="pr3 (primEqInt (Neg (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
84.19/49.96	13[label="pr3 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
84.19/49.96	14[label="pr3 (primEqInt (Pos (Succ vuz400)) (Pos Zero)) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
84.19/49.96	15[label="pr3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
84.19/49.96	16[label="pr3 (primEqInt (Neg (Succ vuz400)) (Pos Zero)) vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
84.19/49.96	17[label="pr3 (primEqInt (Neg Zero) (Pos Zero)) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
84.19/49.96	18[label="pr3 False vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
84.19/49.96	19[label="pr3 True vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
84.19/49.96	20[label="pr3 False vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
84.19/49.96	21[label="pr3 True vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
84.19/49.96	22[label="pr2 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
84.19/49.96	23[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];23 -> 27[label="",style="solid", color="black", weight=3];
84.19/49.96	24[label="pr2 vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
84.19/49.96	25 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	25[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];26[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (Pos (Succ vuz400) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];26 -> 29[label="",style="solid", color="black", weight=3];
84.19/49.96	27[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];28[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (Neg (Succ vuz400) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
84.19/49.96	29[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (compare (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
84.19/49.96	30[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (compare (Neg (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
84.19/49.96	31[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
84.19/49.96	32[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (primCmpInt (Neg (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
84.19/49.96	33[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
84.19/49.96	34[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (primCmpInt (Neg (Succ vuz400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];34 -> 36[label="",style="solid", color="black", weight=3];
84.19/49.96	35[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpNat (Succ vuz400) Zero == GT)",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
84.19/49.96	36[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (LT == GT)",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3];
84.19/49.96	37[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (GT == GT)",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
84.19/49.96	38[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) False",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
84.19/49.96	39[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) True",fontsize=16,color="black",shape="box"];39 -> 41[label="",style="solid", color="black", weight=3];
84.19/49.96	40[label="pr0 vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];40 -> 42[label="",style="solid", color="black", weight=3];
84.19/49.96	41 -> 43[label="",style="dashed", color="red", weight=0];
84.19/49.96	41[label="pr2F vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="magenta"];41 -> 44[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	42[label="error []",fontsize=16,color="black",shape="box"];42 -> 45[label="",style="solid", color="black", weight=3];
84.19/49.96	44 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	44[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];43[label="pr2F vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="triangle"];43 -> 46[label="",style="solid", color="black", weight=3];
84.19/49.96	45[label="error []",fontsize=16,color="red",shape="box"];46[label="pr2F4 vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="box"];46 -> 47[label="",style="solid", color="black", weight=3];
84.19/49.96	47[label="pr2F3 (Pos (Succ vuz400) - vuz5 == fromInt (Pos Zero)) vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="box"];47 -> 48[label="",style="solid", color="black", weight=3];
84.19/49.96	48[label="pr2F3 (primEqInt (Pos (Succ vuz400) - vuz5) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="box"];48 -> 49[label="",style="solid", color="black", weight=3];
84.19/49.96	49[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) vuz5) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) vuz5) vuz3",fontsize=16,color="burlywood",shape="box"];4744[label="vuz5/Pos vuz50",fontsize=10,color="white",style="solid",shape="box"];49 -> 4744[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4744 -> 50[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4745[label="vuz5/Neg vuz50",fontsize=10,color="white",style="solid",shape="box"];49 -> 4745[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4745 -> 51[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	50[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (Pos vuz50)) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (Pos vuz50)) vuz3",fontsize=16,color="black",shape="box"];50 -> 52[label="",style="solid", color="black", weight=3];
84.19/49.96	51[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (Neg vuz50)) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (Neg vuz50)) vuz3",fontsize=16,color="black",shape="box"];51 -> 53[label="",style="solid", color="black", weight=3];
84.19/49.96	52[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) vuz50) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) vuz50) vuz3",fontsize=16,color="burlywood",shape="box"];4746[label="vuz50/Succ vuz500",fontsize=10,color="white",style="solid",shape="box"];52 -> 4746[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4746 -> 54[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4747[label="vuz50/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 4747[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4747 -> 55[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	53[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz400) vuz50)) (fromInt (Pos Zero))) vuz3 (Pos (primPlusNat (Succ vuz400) vuz50)) vuz3",fontsize=16,color="burlywood",shape="box"];4748[label="vuz50/Succ vuz500",fontsize=10,color="white",style="solid",shape="box"];53 -> 4748[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4748 -> 56[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4749[label="vuz50/Zero",fontsize=10,color="white",style="solid",shape="box"];53 -> 4749[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4749 -> 57[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	54[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) (Succ vuz500)) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) (Succ vuz500)) vuz3",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
84.19/49.96	55[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) Zero) vuz3",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
84.19/49.96	56[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz400) (Succ vuz500))) (fromInt (Pos Zero))) vuz3 (Pos (primPlusNat (Succ vuz400) (Succ vuz500))) vuz3",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
84.19/49.96	57[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz400) Zero)) (fromInt (Pos Zero))) vuz3 (Pos (primPlusNat (Succ vuz400) Zero)) vuz3",fontsize=16,color="black",shape="box"];57 -> 61[label="",style="solid", color="black", weight=3];
84.19/49.96	58[label="pr2F3 (primEqInt (primMinusNat vuz400 vuz500) (fromInt (Pos Zero))) vuz3 (primMinusNat vuz400 vuz500) vuz3",fontsize=16,color="burlywood",shape="triangle"];4750[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];58 -> 4750[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4750 -> 62[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4751[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 4751[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4751 -> 63[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	59[label="pr2F3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="triangle"];59 -> 64[label="",style="solid", color="black", weight=3];
84.19/49.96	60 -> 59[label="",style="dashed", color="red", weight=0];
84.19/49.96	60[label="pr2F3 (primEqInt (Pos (Succ (Succ (primPlusNat vuz400 vuz500)))) (fromInt (Pos Zero))) vuz3 (Pos (Succ (Succ (primPlusNat vuz400 vuz500)))) vuz3",fontsize=16,color="magenta"];60 -> 65[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	61 -> 59[label="",style="dashed", color="red", weight=0];
84.19/49.96	61[label="pr2F3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="magenta"];62[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) vuz500) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) vuz500) vuz3",fontsize=16,color="burlywood",shape="box"];4752[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];62 -> 4752[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4752 -> 66[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4753[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];62 -> 4753[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4753 -> 67[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	63[label="pr2F3 (primEqInt (primMinusNat Zero vuz500) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero vuz500) vuz3",fontsize=16,color="burlywood",shape="box"];4754[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];63 -> 4754[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4754 -> 68[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4755[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];63 -> 4755[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4755 -> 69[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	64[label="pr2F3 (primEqInt (Pos (Succ vuz400)) (Pos Zero)) vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="box"];64 -> 70[label="",style="solid", color="black", weight=3];
84.19/49.96	65[label="Succ (primPlusNat vuz400 vuz500)",fontsize=16,color="green",shape="box"];65 -> 71[label="",style="dashed", color="green", weight=3];
84.19/49.96	66[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) (Succ vuz5000)) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];66 -> 72[label="",style="solid", color="black", weight=3];
84.19/49.96	67[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) Zero) vuz3",fontsize=16,color="black",shape="box"];67 -> 73[label="",style="solid", color="black", weight=3];
84.19/49.96	68[label="pr2F3 (primEqInt (primMinusNat Zero (Succ vuz5000)) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];68 -> 74[label="",style="solid", color="black", weight=3];
84.19/49.96	69[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero Zero) vuz3",fontsize=16,color="black",shape="box"];69 -> 75[label="",style="solid", color="black", weight=3];
84.19/49.96	70[label="pr2F3 False vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="box"];70 -> 76[label="",style="solid", color="black", weight=3];
84.19/49.96	71[label="primPlusNat vuz400 vuz500",fontsize=16,color="burlywood",shape="triangle"];4756[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];71 -> 4756[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4756 -> 77[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4757[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];71 -> 4757[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4757 -> 78[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	72 -> 58[label="",style="dashed", color="red", weight=0];
84.19/49.96	72[label="pr2F3 (primEqInt (primMinusNat vuz4000 vuz5000) (fromInt (Pos Zero))) vuz3 (primMinusNat vuz4000 vuz5000) vuz3",fontsize=16,color="magenta"];72 -> 79[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	72 -> 80[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	73 -> 59[label="",style="dashed", color="red", weight=0];
84.19/49.96	73[label="pr2F3 (primEqInt (Pos (Succ vuz4000)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="magenta"];73 -> 81[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	74[label="pr2F3 (primEqInt (Neg (Succ vuz5000)) (fromInt (Pos Zero))) vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];74 -> 82[label="",style="solid", color="black", weight=3];
84.19/49.96	75[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];75 -> 83[label="",style="solid", color="black", weight=3];
84.19/49.96	76[label="pr2F0 vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="box"];76 -> 84[label="",style="solid", color="black", weight=3];
84.19/49.96	77[label="primPlusNat (Succ vuz4000) vuz500",fontsize=16,color="burlywood",shape="box"];4758[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];77 -> 4758[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4758 -> 85[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4759[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];77 -> 4759[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4759 -> 86[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	78[label="primPlusNat Zero vuz500",fontsize=16,color="burlywood",shape="box"];4760[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];78 -> 4760[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4760 -> 87[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4761[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];78 -> 4761[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4761 -> 88[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	79[label="vuz4000",fontsize=16,color="green",shape="box"];80[label="vuz5000",fontsize=16,color="green",shape="box"];81[label="vuz4000",fontsize=16,color="green",shape="box"];82[label="pr2F3 (primEqInt (Neg (Succ vuz5000)) (Pos Zero)) vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];82 -> 89[label="",style="solid", color="black", weight=3];
84.19/49.96	83[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];83 -> 90[label="",style="solid", color="black", weight=3];
84.19/49.96	84[label="pr2F0G vuz3 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];84 -> 91[label="",style="solid", color="black", weight=3];
84.19/49.96	85[label="primPlusNat (Succ vuz4000) (Succ vuz5000)",fontsize=16,color="black",shape="box"];85 -> 92[label="",style="solid", color="black", weight=3];
84.19/49.96	86[label="primPlusNat (Succ vuz4000) Zero",fontsize=16,color="black",shape="box"];86 -> 93[label="",style="solid", color="black", weight=3];
84.19/49.96	87[label="primPlusNat Zero (Succ vuz5000)",fontsize=16,color="black",shape="box"];87 -> 94[label="",style="solid", color="black", weight=3];
84.19/49.96	88[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];88 -> 95[label="",style="solid", color="black", weight=3];
84.19/49.96	89[label="pr2F3 False vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];89 -> 96[label="",style="solid", color="black", weight=3];
84.19/49.96	90[label="pr2F3 True vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];90 -> 97[label="",style="solid", color="black", weight=3];
84.19/49.96	91[label="pr2F0G2 vuz3 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];91 -> 98[label="",style="solid", color="black", weight=3];
84.19/49.96	92[label="Succ (Succ (primPlusNat vuz4000 vuz5000))",fontsize=16,color="green",shape="box"];92 -> 99[label="",style="dashed", color="green", weight=3];
84.19/49.96	93[label="Succ vuz4000",fontsize=16,color="green",shape="box"];94[label="Succ vuz5000",fontsize=16,color="green",shape="box"];95[label="Zero",fontsize=16,color="green",shape="box"];96[label="pr2F0 vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];96 -> 100[label="",style="solid", color="black", weight=3];
84.19/49.96	97[label="vuz3",fontsize=16,color="green",shape="box"];98[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz400)) (even (Pos (Succ vuz400)))",fontsize=16,color="black",shape="box"];98 -> 101[label="",style="solid", color="black", weight=3];
84.19/49.96	99 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	99[label="primPlusNat vuz4000 vuz5000",fontsize=16,color="magenta"];99 -> 102[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	99 -> 103[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	100[label="pr2F0G vuz3 vuz3 (Neg (Succ vuz5000))",fontsize=16,color="black",shape="box"];100 -> 104[label="",style="solid", color="black", weight=3];
84.19/49.96	101[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz400)) (primEvenInt (Pos (Succ vuz400)))",fontsize=16,color="black",shape="box"];101 -> 105[label="",style="solid", color="black", weight=3];
84.19/49.96	102[label="vuz4000",fontsize=16,color="green",shape="box"];103[label="vuz5000",fontsize=16,color="green",shape="box"];104[label="pr2F0G2 vuz3 vuz3 (Neg (Succ vuz5000))",fontsize=16,color="black",shape="box"];104 -> 106[label="",style="solid", color="black", weight=3];
84.19/49.96	105 -> 256[label="",style="dashed", color="red", weight=0];
84.19/49.96	105[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz400)) (primEvenNat (Succ vuz400))",fontsize=16,color="magenta"];105 -> 257[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	105 -> 258[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	105 -> 259[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	106[label="pr2F0G1 vuz3 vuz3 (Neg (Succ vuz5000)) (even (Neg (Succ vuz5000)))",fontsize=16,color="black",shape="box"];106 -> 109[label="",style="solid", color="black", weight=3];
84.19/49.96	257[label="vuz3",fontsize=16,color="green",shape="box"];258[label="vuz400",fontsize=16,color="green",shape="box"];259[label="Succ vuz400",fontsize=16,color="green",shape="box"];256[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat vuz22)",fontsize=16,color="burlywood",shape="triangle"];4762[label="vuz22/Succ vuz220",fontsize=10,color="white",style="solid",shape="box"];256 -> 4762[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4762 -> 275[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4763[label="vuz22/Zero",fontsize=10,color="white",style="solid",shape="box"];256 -> 4763[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4763 -> 276[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	109[label="pr2F0G1 vuz3 vuz3 (Neg (Succ vuz5000)) (primEvenInt (Neg (Succ vuz5000)))",fontsize=16,color="black",shape="box"];109 -> 112[label="",style="solid", color="black", weight=3];
84.19/49.96	275[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat (Succ vuz220))",fontsize=16,color="burlywood",shape="box"];4764[label="vuz220/Succ vuz2200",fontsize=10,color="white",style="solid",shape="box"];275 -> 4764[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4764 -> 279[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4765[label="vuz220/Zero",fontsize=10,color="white",style="solid",shape="box"];275 -> 4765[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4765 -> 280[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	276[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];276 -> 281[label="",style="solid", color="black", weight=3];
84.19/49.96	112 -> 199[label="",style="dashed", color="red", weight=0];
84.19/49.96	112[label="pr2F0G1 vuz3 vuz3 (Neg (Succ vuz5000)) (primEvenNat (Succ vuz5000))",fontsize=16,color="magenta"];112 -> 200[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	112 -> 201[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	112 -> 202[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	279[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat (Succ (Succ vuz2200)))",fontsize=16,color="black",shape="box"];279 -> 284[label="",style="solid", color="black", weight=3];
84.19/49.96	280[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];280 -> 285[label="",style="solid", color="black", weight=3];
84.19/49.96	281[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) True",fontsize=16,color="black",shape="box"];281 -> 286[label="",style="solid", color="black", weight=3];
84.19/49.96	200[label="vuz3",fontsize=16,color="green",shape="box"];201[label="vuz5000",fontsize=16,color="green",shape="box"];202[label="Succ vuz5000",fontsize=16,color="green",shape="box"];199[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat vuz14)",fontsize=16,color="burlywood",shape="triangle"];4766[label="vuz14/Succ vuz140",fontsize=10,color="white",style="solid",shape="box"];199 -> 4766[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4766 -> 212[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4767[label="vuz14/Zero",fontsize=10,color="white",style="solid",shape="box"];199 -> 4767[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4767 -> 213[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	284 -> 256[label="",style="dashed", color="red", weight=0];
84.19/49.96	284[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat vuz2200)",fontsize=16,color="magenta"];284 -> 289[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	285[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) False",fontsize=16,color="black",shape="box"];285 -> 290[label="",style="solid", color="black", weight=3];
84.19/49.96	286[label="pr2F0G vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];286 -> 291[label="",style="solid", color="black", weight=3];
84.19/49.96	212[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat (Succ vuz140))",fontsize=16,color="burlywood",shape="box"];4768[label="vuz140/Succ vuz1400",fontsize=10,color="white",style="solid",shape="box"];212 -> 4768[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4768 -> 216[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4769[label="vuz140/Zero",fontsize=10,color="white",style="solid",shape="box"];212 -> 4769[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4769 -> 217[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	213[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];213 -> 218[label="",style="solid", color="black", weight=3];
84.19/49.96	289[label="vuz2200",fontsize=16,color="green",shape="box"];290[label="pr2F0G0 vuz20 vuz20 (Pos (Succ vuz21)) otherwise",fontsize=16,color="black",shape="box"];290 -> 294[label="",style="solid", color="black", weight=3];
84.19/49.96	291[label="pr2F0G2 vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];291 -> 295[label="",style="solid", color="black", weight=3];
84.19/49.96	216[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat (Succ (Succ vuz1400)))",fontsize=16,color="black",shape="box"];216 -> 227[label="",style="solid", color="black", weight=3];
84.19/49.96	217[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];217 -> 228[label="",style="solid", color="black", weight=3];
84.19/49.96	218[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) True",fontsize=16,color="black",shape="box"];218 -> 229[label="",style="solid", color="black", weight=3];
84.19/49.96	294[label="pr2F0G0 vuz20 vuz20 (Pos (Succ vuz21)) True",fontsize=16,color="black",shape="box"];294 -> 298[label="",style="solid", color="black", weight=3];
84.19/49.96	295[label="pr2F0G1 vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];295 -> 299[label="",style="solid", color="black", weight=3];
84.19/49.96	227 -> 199[label="",style="dashed", color="red", weight=0];
84.19/49.96	227[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat vuz1400)",fontsize=16,color="magenta"];227 -> 237[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	228[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) False",fontsize=16,color="black",shape="box"];228 -> 238[label="",style="solid", color="black", weight=3];
84.19/49.96	229[label="pr2F0G vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];229 -> 239[label="",style="solid", color="black", weight=3];
84.19/49.96	298 -> 302[label="",style="dashed", color="red", weight=0];
84.19/49.96	298[label="pr2F vuz20 (Pos (Succ vuz21) - fromInt (Pos (Succ Zero))) (vuz20 * vuz20)",fontsize=16,color="magenta"];298 -> 303[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	299[label="pr2F0G1 vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];299 -> 304[label="",style="solid", color="black", weight=3];
84.19/49.96	237[label="vuz1400",fontsize=16,color="green",shape="box"];238[label="pr2F0G0 vuz12 vuz12 (Neg (Succ vuz13)) otherwise",fontsize=16,color="black",shape="box"];238 -> 253[label="",style="solid", color="black", weight=3];
84.19/49.96	239[label="pr2F0G2 vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];239 -> 254[label="",style="solid", color="black", weight=3];
84.19/49.96	303 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	303[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];302[label="pr2F vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="black",shape="triangle"];302 -> 305[label="",style="solid", color="black", weight=3];
84.19/49.96	304[label="pr2F0G1 vuz20 (vuz20 * vuz20) (primQuotInt (Pos (Succ vuz21)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz21)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];304 -> 309[label="",style="solid", color="black", weight=3];
84.19/49.96	253[label="pr2F0G0 vuz12 vuz12 (Neg (Succ vuz13)) True",fontsize=16,color="black",shape="box"];253 -> 277[label="",style="solid", color="black", weight=3];
84.19/49.96	254[label="pr2F0G1 vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];254 -> 278[label="",style="solid", color="black", weight=3];
84.19/49.96	305[label="pr2F4 vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="black",shape="box"];305 -> 310[label="",style="solid", color="black", weight=3];
84.19/49.96	309[label="pr2F0G1 vuz20 (vuz20 * vuz20) (primQuotInt (Pos (Succ vuz21)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz21)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];309 -> 315[label="",style="solid", color="black", weight=3];
84.19/49.96	277 -> 282[label="",style="dashed", color="red", weight=0];
84.19/49.96	277[label="pr2F vuz12 (Neg (Succ vuz13) - fromInt (Pos (Succ Zero))) (vuz12 * vuz12)",fontsize=16,color="magenta"];277 -> 283[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	278[label="pr2F0G1 vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];278 -> 287[label="",style="solid", color="black", weight=3];
84.19/49.96	310[label="pr2F3 (Pos (Succ vuz21) - vuz24 == fromInt (Pos Zero)) vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="black",shape="box"];310 -> 316[label="",style="solid", color="black", weight=3];
84.19/49.96	315 -> 1605[label="",style="dashed", color="red", weight=0];
84.19/49.96	315[label="pr2F0G1 vuz20 (vuz20 * vuz20) (Pos (primDivNatS (Succ vuz21) (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS (Succ vuz21) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];315 -> 1606[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	315 -> 1607[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	315 -> 1608[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	315 -> 1609[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	283 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	283[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];282[label="pr2F vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="black",shape="triangle"];282 -> 288[label="",style="solid", color="black", weight=3];
84.19/49.96	287[label="pr2F0G1 vuz12 (vuz12 * vuz12) (primQuotInt (Neg (Succ vuz13)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg (Succ vuz13)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];287 -> 292[label="",style="solid", color="black", weight=3];
84.19/49.96	316 -> 3789[label="",style="dashed", color="red", weight=0];
84.19/49.96	316[label="pr2F3 (primEqInt (Pos (Succ vuz21) - vuz24) (fromInt (Pos Zero))) vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="magenta"];316 -> 3790[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	316 -> 3791[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	316 -> 3792[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	316 -> 3793[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1606[label="vuz20",fontsize=16,color="green",shape="box"];1607 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1607[label="primDivNatS (Succ vuz21) (Succ (Succ Zero))",fontsize=16,color="magenta"];1607 -> 1624[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1608[label="vuz20",fontsize=16,color="green",shape="box"];1609 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1609[label="primDivNatS (Succ vuz21) (Succ (Succ Zero))",fontsize=16,color="magenta"];1609 -> 1625[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1605[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenInt (Pos vuz106))",fontsize=16,color="black",shape="triangle"];1605 -> 1626[label="",style="solid", color="black", weight=3];
84.19/49.96	288[label="pr2F4 vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="black",shape="box"];288 -> 293[label="",style="solid", color="black", weight=3];
84.19/49.96	292[label="pr2F0G1 vuz12 (vuz12 * vuz12) (primQuotInt (Neg (Succ vuz13)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg (Succ vuz13)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];292 -> 296[label="",style="solid", color="black", weight=3];
84.19/49.96	3790[label="vuz20",fontsize=16,color="green",shape="box"];3791[label="vuz21",fontsize=16,color="green",shape="box"];3792[label="vuz20",fontsize=16,color="green",shape="box"];3793[label="vuz24",fontsize=16,color="green",shape="box"];3789[label="pr2F3 (primEqInt (Pos (Succ vuz202) - vuz203) (fromInt (Pos Zero))) vuz204 (Pos (Succ vuz202) - vuz203) (vuz204 * vuz205)",fontsize=16,color="black",shape="triangle"];3789 -> 3814[label="",style="solid", color="black", weight=3];
84.19/49.96	1624[label="Succ vuz21",fontsize=16,color="green",shape="box"];1222[label="primDivNatS vuz55 (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];4770[label="vuz55/Succ vuz550",fontsize=10,color="white",style="solid",shape="box"];1222 -> 4770[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4770 -> 1237[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4771[label="vuz55/Zero",fontsize=10,color="white",style="solid",shape="box"];1222 -> 4771[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4771 -> 1238[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1625[label="Succ vuz21",fontsize=16,color="green",shape="box"];1626[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat vuz106)",fontsize=16,color="burlywood",shape="triangle"];4772[label="vuz106/Succ vuz1060",fontsize=10,color="white",style="solid",shape="box"];1626 -> 4772[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4772 -> 1659[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4773[label="vuz106/Zero",fontsize=10,color="white",style="solid",shape="box"];1626 -> 4773[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4773 -> 1660[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	293[label="pr2F3 (Neg (Succ vuz13) - vuz23 == fromInt (Pos Zero)) vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="black",shape="box"];293 -> 297[label="",style="solid", color="black", weight=3];
84.19/49.96	296 -> 1755[label="",style="dashed", color="red", weight=0];
84.19/49.96	296[label="pr2F0G1 vuz12 (vuz12 * vuz12) (Neg (primDivNatS (Succ vuz13) (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS (Succ vuz13) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];296 -> 1756[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	296 -> 1757[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	296 -> 1758[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	296 -> 1759[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	3814[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz202)) vuz203) (fromInt (Pos Zero))) vuz204 (primMinusInt (Pos (Succ vuz202)) vuz203) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4774[label="vuz203/Pos vuz2030",fontsize=10,color="white",style="solid",shape="box"];3814 -> 4774[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4774 -> 3843[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4775[label="vuz203/Neg vuz2030",fontsize=10,color="white",style="solid",shape="box"];3814 -> 4775[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4775 -> 3844[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1237[label="primDivNatS (Succ vuz550) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1237 -> 1285[label="",style="solid", color="black", weight=3];
84.19/49.96	1238[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1238 -> 1286[label="",style="solid", color="black", weight=3];
84.19/49.96	1659[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat (Succ vuz1060))",fontsize=16,color="burlywood",shape="box"];4776[label="vuz1060/Succ vuz10600",fontsize=10,color="white",style="solid",shape="box"];1659 -> 4776[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4776 -> 1713[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4777[label="vuz1060/Zero",fontsize=10,color="white",style="solid",shape="box"];1659 -> 4777[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4777 -> 1714[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1660[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];1660 -> 1715[label="",style="solid", color="black", weight=3];
84.19/49.96	297 -> 4256[label="",style="dashed", color="red", weight=0];
84.19/49.96	297[label="pr2F3 (primEqInt (Neg (Succ vuz13) - vuz23) (fromInt (Pos Zero))) vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="magenta"];297 -> 4257[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	297 -> 4258[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	297 -> 4259[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	297 -> 4260[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1756 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1756[label="primDivNatS (Succ vuz13) (Succ (Succ Zero))",fontsize=16,color="magenta"];1756 -> 1770[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1757 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1757[label="primDivNatS (Succ vuz13) (Succ (Succ Zero))",fontsize=16,color="magenta"];1757 -> 1771[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1758[label="vuz12",fontsize=16,color="green",shape="box"];1759[label="vuz12",fontsize=16,color="green",shape="box"];1755[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenInt (Neg vuz114))",fontsize=16,color="black",shape="triangle"];1755 -> 1772[label="",style="solid", color="black", weight=3];
84.19/49.96	3843[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz202)) (Pos vuz2030)) (fromInt (Pos Zero))) vuz204 (primMinusInt (Pos (Succ vuz202)) (Pos vuz2030)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];3843 -> 3919[label="",style="solid", color="black", weight=3];
84.19/49.96	3844[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz202)) (Neg vuz2030)) (fromInt (Pos Zero))) vuz204 (primMinusInt (Pos (Succ vuz202)) (Neg vuz2030)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];3844 -> 3920[label="",style="solid", color="black", weight=3];
84.19/49.96	1285 -> 562[label="",style="dashed", color="red", weight=0];
84.19/49.96	1285[label="primDivNatS0 vuz550 (Succ Zero) (primGEqNatS vuz550 (Succ Zero))",fontsize=16,color="magenta"];1285 -> 1313[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1286[label="Zero",fontsize=16,color="green",shape="box"];1713[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat (Succ (Succ vuz10600)))",fontsize=16,color="black",shape="box"];1713 -> 1773[label="",style="solid", color="black", weight=3];
84.19/49.96	1714[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];1714 -> 1774[label="",style="solid", color="black", weight=3];
84.19/49.96	1715[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) True",fontsize=16,color="black",shape="box"];1715 -> 1775[label="",style="solid", color="black", weight=3];
84.19/49.96	4257[label="vuz13",fontsize=16,color="green",shape="box"];4258[label="vuz12",fontsize=16,color="green",shape="box"];4259[label="vuz12",fontsize=16,color="green",shape="box"];4260[label="vuz23",fontsize=16,color="green",shape="box"];4256[label="pr2F3 (primEqInt (Neg (Succ vuz214) - vuz215) (fromInt (Pos Zero))) vuz216 (Neg (Succ vuz214) - vuz215) (vuz216 * vuz217)",fontsize=16,color="black",shape="triangle"];4256 -> 4281[label="",style="solid", color="black", weight=3];
84.19/49.96	1770[label="Succ vuz13",fontsize=16,color="green",shape="box"];1771[label="Succ vuz13",fontsize=16,color="green",shape="box"];1772[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat vuz114)",fontsize=16,color="burlywood",shape="triangle"];4778[label="vuz114/Succ vuz1140",fontsize=10,color="white",style="solid",shape="box"];1772 -> 4778[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4778 -> 1793[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4779[label="vuz114/Zero",fontsize=10,color="white",style="solid",shape="box"];1772 -> 4779[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4779 -> 1794[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	3919[label="pr2F3 (primEqInt (primMinusNat (Succ vuz202) vuz2030) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz202) vuz2030) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4780[label="vuz2030/Succ vuz20300",fontsize=10,color="white",style="solid",shape="box"];3919 -> 4780[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4780 -> 4005[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4781[label="vuz2030/Zero",fontsize=10,color="white",style="solid",shape="box"];3919 -> 4781[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4781 -> 4006[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	3920 -> 4007[label="",style="dashed", color="red", weight=0];
84.19/49.96	3920[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz202) vuz2030)) (fromInt (Pos Zero))) vuz204 (Pos (primPlusNat (Succ vuz202) vuz2030)) (vuz204 * vuz205)",fontsize=16,color="magenta"];3920 -> 4008[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	3920 -> 4009[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1313[label="vuz550",fontsize=16,color="green",shape="box"];562[label="primDivNatS0 vuz1300 (Succ Zero) (primGEqNatS vuz1300 (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];4782[label="vuz1300/Succ vuz13000",fontsize=10,color="white",style="solid",shape="box"];562 -> 4782[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4782 -> 570[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4783[label="vuz1300/Zero",fontsize=10,color="white",style="solid",shape="box"];562 -> 4783[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4783 -> 571[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1773 -> 1626[label="",style="dashed", color="red", weight=0];
84.19/49.96	1773[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat vuz10600)",fontsize=16,color="magenta"];1773 -> 1795[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1774[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) False",fontsize=16,color="black",shape="box"];1774 -> 1796[label="",style="solid", color="black", weight=3];
84.19/49.96	1775[label="pr2F0G vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1775 -> 1797[label="",style="solid", color="black", weight=3];
84.19/49.96	4281[label="pr2F3 (primEqInt (primMinusInt (Neg (Succ vuz214)) vuz215) (fromInt (Pos Zero))) vuz216 (primMinusInt (Neg (Succ vuz214)) vuz215) (vuz216 * vuz217)",fontsize=16,color="burlywood",shape="box"];4784[label="vuz215/Pos vuz2150",fontsize=10,color="white",style="solid",shape="box"];4281 -> 4784[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4784 -> 4288[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4785[label="vuz215/Neg vuz2150",fontsize=10,color="white",style="solid",shape="box"];4281 -> 4785[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4785 -> 4289[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1793[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat (Succ vuz1140))",fontsize=16,color="burlywood",shape="box"];4786[label="vuz1140/Succ vuz11400",fontsize=10,color="white",style="solid",shape="box"];1793 -> 4786[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4786 -> 1807[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4787[label="vuz1140/Zero",fontsize=10,color="white",style="solid",shape="box"];1793 -> 4787[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4787 -> 1808[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1794[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];1794 -> 1809[label="",style="solid", color="black", weight=3];
84.19/49.96	4005[label="pr2F3 (primEqInt (primMinusNat (Succ vuz202) (Succ vuz20300)) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz202) (Succ vuz20300)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4005 -> 4086[label="",style="solid", color="black", weight=3];
84.19/49.96	4006[label="pr2F3 (primEqInt (primMinusNat (Succ vuz202) Zero) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz202) Zero) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4006 -> 4087[label="",style="solid", color="black", weight=3];
84.19/49.96	4008 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4008[label="primPlusNat (Succ vuz202) vuz2030",fontsize=16,color="magenta"];4008 -> 4088[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4008 -> 4089[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4009 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4009[label="primPlusNat (Succ vuz202) vuz2030",fontsize=16,color="magenta"];4009 -> 4090[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4009 -> 4091[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4007[label="pr2F3 (primEqInt (Pos vuz212) (fromInt (Pos Zero))) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="triangle"];4788[label="vuz212/Succ vuz2120",fontsize=10,color="white",style="solid",shape="box"];4007 -> 4788[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4788 -> 4092[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4789[label="vuz212/Zero",fontsize=10,color="white",style="solid",shape="box"];4007 -> 4789[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4789 -> 4093[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	570[label="primDivNatS0 (Succ vuz13000) (Succ Zero) (primGEqNatS (Succ vuz13000) (Succ Zero))",fontsize=16,color="black",shape="box"];570 -> 584[label="",style="solid", color="black", weight=3];
84.19/49.96	571[label="primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero))",fontsize=16,color="black",shape="box"];571 -> 585[label="",style="solid", color="black", weight=3];
84.19/49.96	1795[label="vuz10600",fontsize=16,color="green",shape="box"];1796[label="pr2F0G0 vuz102 (vuz103 * vuz103) (Pos vuz105) otherwise",fontsize=16,color="black",shape="box"];1796 -> 1810[label="",style="solid", color="black", weight=3];
84.19/49.96	1797[label="pr2F0G2 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1797 -> 1811[label="",style="solid", color="black", weight=3];
84.19/49.96	4288[label="pr2F3 (primEqInt (primMinusInt (Neg (Succ vuz214)) (Pos vuz2150)) (fromInt (Pos Zero))) vuz216 (primMinusInt (Neg (Succ vuz214)) (Pos vuz2150)) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4288 -> 4296[label="",style="solid", color="black", weight=3];
84.19/49.96	4289[label="pr2F3 (primEqInt (primMinusInt (Neg (Succ vuz214)) (Neg vuz2150)) (fromInt (Pos Zero))) vuz216 (primMinusInt (Neg (Succ vuz214)) (Neg vuz2150)) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4289 -> 4297[label="",style="solid", color="black", weight=3];
84.19/49.96	1807[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat (Succ (Succ vuz11400)))",fontsize=16,color="black",shape="box"];1807 -> 1817[label="",style="solid", color="black", weight=3];
84.19/49.96	1808[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];1808 -> 1818[label="",style="solid", color="black", weight=3];
84.19/49.96	1809[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) True",fontsize=16,color="black",shape="box"];1809 -> 1819[label="",style="solid", color="black", weight=3];
84.19/49.96	4086[label="pr2F3 (primEqInt (primMinusNat vuz202 vuz20300) (fromInt (Pos Zero))) vuz204 (primMinusNat vuz202 vuz20300) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="triangle"];4790[label="vuz202/Succ vuz2020",fontsize=10,color="white",style="solid",shape="box"];4086 -> 4790[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4790 -> 4165[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4791[label="vuz202/Zero",fontsize=10,color="white",style="solid",shape="box"];4086 -> 4791[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4791 -> 4166[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4087 -> 4007[label="",style="dashed", color="red", weight=0];
84.19/49.96	4087[label="pr2F3 (primEqInt (Pos (Succ vuz202)) (fromInt (Pos Zero))) vuz204 (Pos (Succ vuz202)) (vuz204 * vuz205)",fontsize=16,color="magenta"];4087 -> 4167[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4087 -> 4168[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4088[label="Succ vuz202",fontsize=16,color="green",shape="box"];4089[label="vuz2030",fontsize=16,color="green",shape="box"];4090[label="Succ vuz202",fontsize=16,color="green",shape="box"];4091[label="vuz2030",fontsize=16,color="green",shape="box"];4092[label="pr2F3 (primEqInt (Pos (Succ vuz2120)) (fromInt (Pos Zero))) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4092 -> 4169[label="",style="solid", color="black", weight=3];
84.19/49.96	4093[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4093 -> 4170[label="",style="solid", color="black", weight=3];
84.19/49.96	584[label="primDivNatS0 (Succ vuz13000) (Succ Zero) (primGEqNatS vuz13000 Zero)",fontsize=16,color="burlywood",shape="box"];4792[label="vuz13000/Succ vuz130000",fontsize=10,color="white",style="solid",shape="box"];584 -> 4792[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4792 -> 606[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4793[label="vuz13000/Zero",fontsize=10,color="white",style="solid",shape="box"];584 -> 4793[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4793 -> 607[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	585[label="primDivNatS0 Zero (Succ Zero) False",fontsize=16,color="black",shape="box"];585 -> 608[label="",style="solid", color="black", weight=3];
84.19/49.96	1810[label="pr2F0G0 vuz102 (vuz103 * vuz103) (Pos vuz105) True",fontsize=16,color="black",shape="box"];1810 -> 1820[label="",style="solid", color="black", weight=3];
84.19/49.96	1811[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1811 -> 1821[label="",style="solid", color="black", weight=3];
84.19/49.96	4296 -> 4311[label="",style="dashed", color="red", weight=0];
84.19/49.96	4296[label="pr2F3 (primEqInt (Neg (primPlusNat (Succ vuz214) vuz2150)) (fromInt (Pos Zero))) vuz216 (Neg (primPlusNat (Succ vuz214) vuz2150)) (vuz216 * vuz217)",fontsize=16,color="magenta"];4296 -> 4312[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4296 -> 4313[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4297 -> 4086[label="",style="dashed", color="red", weight=0];
84.19/49.96	4297[label="pr2F3 (primEqInt (primMinusNat vuz2150 (Succ vuz214)) (fromInt (Pos Zero))) vuz216 (primMinusNat vuz2150 (Succ vuz214)) (vuz216 * vuz217)",fontsize=16,color="magenta"];4297 -> 4330[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4297 -> 4331[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4297 -> 4332[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4297 -> 4333[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1817 -> 1772[label="",style="dashed", color="red", weight=0];
84.19/49.96	1817[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat vuz11400)",fontsize=16,color="magenta"];1817 -> 1829[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1818[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) False",fontsize=16,color="black",shape="box"];1818 -> 1830[label="",style="solid", color="black", weight=3];
84.19/49.96	1819[label="pr2F0G vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1819 -> 1831[label="",style="solid", color="black", weight=3];
84.19/49.96	4165[label="pr2F3 (primEqInt (primMinusNat (Succ vuz2020) vuz20300) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz2020) vuz20300) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4794[label="vuz20300/Succ vuz203000",fontsize=10,color="white",style="solid",shape="box"];4165 -> 4794[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4794 -> 4282[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4795[label="vuz20300/Zero",fontsize=10,color="white",style="solid",shape="box"];4165 -> 4795[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4795 -> 4283[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4166[label="pr2F3 (primEqInt (primMinusNat Zero vuz20300) (fromInt (Pos Zero))) vuz204 (primMinusNat Zero vuz20300) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4796[label="vuz20300/Succ vuz203000",fontsize=10,color="white",style="solid",shape="box"];4166 -> 4796[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4796 -> 4284[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4797[label="vuz20300/Zero",fontsize=10,color="white",style="solid",shape="box"];4166 -> 4797[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4797 -> 4285[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4167[label="Succ vuz202",fontsize=16,color="green",shape="box"];4168[label="Succ vuz202",fontsize=16,color="green",shape="box"];4169[label="pr2F3 (primEqInt (Pos (Succ vuz2120)) (Pos Zero)) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4169 -> 4286[label="",style="solid", color="black", weight=3];
84.19/49.96	4170[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4170 -> 4287[label="",style="solid", color="black", weight=3];
84.19/49.96	606[label="primDivNatS0 (Succ (Succ vuz130000)) (Succ Zero) (primGEqNatS (Succ vuz130000) Zero)",fontsize=16,color="black",shape="box"];606 -> 619[label="",style="solid", color="black", weight=3];
84.19/49.96	607[label="primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];607 -> 620[label="",style="solid", color="black", weight=3];
84.19/49.96	608[label="Zero",fontsize=16,color="green",shape="box"];1820 -> 1832[label="",style="dashed", color="red", weight=0];
84.19/49.96	1820[label="pr2F (vuz103 * vuz103) (Pos vuz105 - fromInt (Pos (Succ Zero))) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1820 -> 1833[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1821[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1821 -> 1834[label="",style="solid", color="black", weight=3];
84.19/49.96	4312 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4312[label="primPlusNat (Succ vuz214) vuz2150",fontsize=16,color="magenta"];4312 -> 4334[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4312 -> 4335[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4313 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4313[label="primPlusNat (Succ vuz214) vuz2150",fontsize=16,color="magenta"];4313 -> 4336[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4313 -> 4337[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4311[label="pr2F3 (primEqInt (Neg vuz219) (fromInt (Pos Zero))) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="burlywood",shape="triangle"];4798[label="vuz219/Succ vuz2190",fontsize=10,color="white",style="solid",shape="box"];4311 -> 4798[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4798 -> 4338[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4799[label="vuz219/Zero",fontsize=10,color="white",style="solid",shape="box"];4311 -> 4799[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4799 -> 4339[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4330[label="vuz216",fontsize=16,color="green",shape="box"];4331[label="vuz2150",fontsize=16,color="green",shape="box"];4332[label="vuz217",fontsize=16,color="green",shape="box"];4333[label="Succ vuz214",fontsize=16,color="green",shape="box"];1829[label="vuz11400",fontsize=16,color="green",shape="box"];1830[label="pr2F0G0 vuz110 (vuz111 * vuz111) (Neg vuz113) otherwise",fontsize=16,color="black",shape="box"];1830 -> 1835[label="",style="solid", color="black", weight=3];
84.19/49.96	1831[label="pr2F0G2 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1831 -> 1836[label="",style="solid", color="black", weight=3];
84.19/49.96	4282[label="pr2F3 (primEqInt (primMinusNat (Succ vuz2020) (Succ vuz203000)) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz2020) (Succ vuz203000)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4282 -> 4290[label="",style="solid", color="black", weight=3];
84.19/49.96	4283[label="pr2F3 (primEqInt (primMinusNat (Succ vuz2020) Zero) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz2020) Zero) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4283 -> 4291[label="",style="solid", color="black", weight=3];
84.19/49.96	4284[label="pr2F3 (primEqInt (primMinusNat Zero (Succ vuz203000)) (fromInt (Pos Zero))) vuz204 (primMinusNat Zero (Succ vuz203000)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4284 -> 4292[label="",style="solid", color="black", weight=3];
84.19/49.96	4285[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz204 (primMinusNat Zero Zero) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4285 -> 4293[label="",style="solid", color="black", weight=3];
84.19/49.96	4286[label="pr2F3 False vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4286 -> 4294[label="",style="solid", color="black", weight=3];
84.19/49.96	4287[label="pr2F3 True vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4287 -> 4295[label="",style="solid", color="black", weight=3];
84.19/49.96	619[label="primDivNatS0 (Succ (Succ vuz130000)) (Succ Zero) True",fontsize=16,color="black",shape="box"];619 -> 645[label="",style="solid", color="black", weight=3];
84.19/49.96	620[label="primDivNatS0 (Succ Zero) (Succ Zero) True",fontsize=16,color="black",shape="box"];620 -> 646[label="",style="solid", color="black", weight=3];
84.19/49.96	1833 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	1833[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];1832[label="pr2F (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="triangle"];1832 -> 1837[label="",style="solid", color="black", weight=3];
84.19/49.96	1834[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (primQuotInt (Pos vuz105) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos vuz105) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1834 -> 1846[label="",style="solid", color="black", weight=3];
84.19/49.96	4334[label="Succ vuz214",fontsize=16,color="green",shape="box"];4335[label="vuz2150",fontsize=16,color="green",shape="box"];4336[label="Succ vuz214",fontsize=16,color="green",shape="box"];4337[label="vuz2150",fontsize=16,color="green",shape="box"];4338[label="pr2F3 (primEqInt (Neg (Succ vuz2190)) (fromInt (Pos Zero))) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4338 -> 4365[label="",style="solid", color="black", weight=3];
84.19/49.96	4339[label="pr2F3 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4339 -> 4366[label="",style="solid", color="black", weight=3];
84.19/49.96	1835[label="pr2F0G0 vuz110 (vuz111 * vuz111) (Neg vuz113) True",fontsize=16,color="black",shape="box"];1835 -> 1847[label="",style="solid", color="black", weight=3];
84.19/49.96	1836[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1836 -> 1848[label="",style="solid", color="black", weight=3];
84.19/49.96	4290 -> 4086[label="",style="dashed", color="red", weight=0];
84.19/49.96	4290[label="pr2F3 (primEqInt (primMinusNat vuz2020 vuz203000) (fromInt (Pos Zero))) vuz204 (primMinusNat vuz2020 vuz203000) (vuz204 * vuz205)",fontsize=16,color="magenta"];4290 -> 4298[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4290 -> 4299[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4291 -> 4007[label="",style="dashed", color="red", weight=0];
84.19/49.96	4291[label="pr2F3 (primEqInt (Pos (Succ vuz2020)) (fromInt (Pos Zero))) vuz204 (Pos (Succ vuz2020)) (vuz204 * vuz205)",fontsize=16,color="magenta"];4291 -> 4300[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4291 -> 4301[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4292 -> 4311[label="",style="dashed", color="red", weight=0];
84.19/49.96	4292[label="pr2F3 (primEqInt (Neg (Succ vuz203000)) (fromInt (Pos Zero))) vuz204 (Neg (Succ vuz203000)) (vuz204 * vuz205)",fontsize=16,color="magenta"];4292 -> 4314[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4292 -> 4315[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4292 -> 4316[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4292 -> 4317[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4293 -> 4007[label="",style="dashed", color="red", weight=0];
84.19/49.96	4293[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz204 (Pos Zero) (vuz204 * vuz205)",fontsize=16,color="magenta"];4293 -> 4303[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4293 -> 4304[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4294[label="pr2F0 vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4294 -> 4305[label="",style="solid", color="black", weight=3];
84.19/49.96	4295[label="vuz204 * vuz205",fontsize=16,color="blue",shape="box"];4800[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4800[label="",style="solid", color="blue", weight=9];
84.19/49.96	4800 -> 4306[label="",style="solid", color="blue", weight=3];
84.19/49.96	4801[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4801[label="",style="solid", color="blue", weight=9];
84.19/49.96	4801 -> 4307[label="",style="solid", color="blue", weight=3];
84.19/49.96	4802[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4802[label="",style="solid", color="blue", weight=9];
84.19/49.96	4802 -> 4308[label="",style="solid", color="blue", weight=3];
84.19/49.96	4803[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4803[label="",style="solid", color="blue", weight=9];
84.19/49.96	4803 -> 4309[label="",style="solid", color="blue", weight=3];
84.19/49.96	4804[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4804[label="",style="solid", color="blue", weight=9];
84.19/49.96	4804 -> 4310[label="",style="solid", color="blue", weight=3];
84.19/49.96	645[label="Succ (primDivNatS (primMinusNatS (Succ (Succ vuz130000)) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];645 -> 673[label="",style="dashed", color="green", weight=3];
84.19/49.96	646[label="Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];646 -> 674[label="",style="dashed", color="green", weight=3];
84.19/49.96	1837[label="pr2F4 (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1837 -> 1849[label="",style="solid", color="black", weight=3];
84.19/49.96	1846[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (primQuotInt (Pos vuz105) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos vuz105) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1846 -> 1859[label="",style="solid", color="black", weight=3];
84.19/49.96	4365[label="pr2F3 (primEqInt (Neg (Succ vuz2190)) (Pos Zero)) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4365 -> 4378[label="",style="solid", color="black", weight=3];
84.19/49.96	4366[label="pr2F3 (primEqInt (Neg Zero) (Pos Zero)) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4366 -> 4379[label="",style="solid", color="black", weight=3];
84.19/49.96	1847 -> 1860[label="",style="dashed", color="red", weight=0];
84.19/49.96	1847[label="pr2F (vuz111 * vuz111) (Neg vuz113 - fromInt (Pos (Succ Zero))) (vuz111 * vuz111 * vuz110)",fontsize=16,color="magenta"];1847 -> 1861[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1848[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1848 -> 1862[label="",style="solid", color="black", weight=3];
84.19/49.96	4298[label="vuz2020",fontsize=16,color="green",shape="box"];4299[label="vuz203000",fontsize=16,color="green",shape="box"];4300[label="Succ vuz2020",fontsize=16,color="green",shape="box"];4301[label="Succ vuz2020",fontsize=16,color="green",shape="box"];4314[label="vuz204",fontsize=16,color="green",shape="box"];4315[label="Succ vuz203000",fontsize=16,color="green",shape="box"];4316[label="Succ vuz203000",fontsize=16,color="green",shape="box"];4317[label="vuz205",fontsize=16,color="green",shape="box"];4303[label="Zero",fontsize=16,color="green",shape="box"];4304[label="Zero",fontsize=16,color="green",shape="box"];4305[label="pr2F0G (vuz204 * vuz205) vuz204 (Pos vuz211)",fontsize=16,color="black",shape="box"];4305 -> 4340[label="",style="solid", color="black", weight=3];
84.19/49.96	4306 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.96	4306[label="vuz204 * vuz205",fontsize=16,color="magenta"];4306 -> 4341[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4306 -> 4342[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4307 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.96	4307[label="vuz204 * vuz205",fontsize=16,color="magenta"];4307 -> 4343[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4307 -> 4344[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4308 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.96	4308[label="vuz204 * vuz205",fontsize=16,color="magenta"];4308 -> 4345[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4308 -> 4346[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4309 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.96	4309[label="vuz204 * vuz205",fontsize=16,color="magenta"];4309 -> 4347[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4309 -> 4348[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4310 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.96	4310[label="vuz204 * vuz205",fontsize=16,color="magenta"];4310 -> 4349[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4310 -> 4350[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	673 -> 508[label="",style="dashed", color="red", weight=0];
84.19/49.96	673[label="primDivNatS (primMinusNatS (Succ (Succ vuz130000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];673 -> 739[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	674 -> 510[label="",style="dashed", color="red", weight=0];
84.19/49.96	674[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1849[label="pr2F3 (Pos vuz105 - vuz115 == fromInt (Pos Zero)) (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1849 -> 1863[label="",style="solid", color="black", weight=3];
84.19/49.96	1859 -> 1605[label="",style="dashed", color="red", weight=0];
84.19/49.96	1859[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos (primDivNatS vuz105 (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS vuz105 (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1859 -> 1864[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1859 -> 1865[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1859 -> 1866[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4378[label="pr2F3 False vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4378 -> 4381[label="",style="solid", color="black", weight=3];
84.19/49.96	4379[label="pr2F3 True vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4379 -> 4382[label="",style="solid", color="black", weight=3];
84.19/49.96	1861 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	1861[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];1860[label="pr2F (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="triangle"];1860 -> 1867[label="",style="solid", color="black", weight=3];
84.19/49.96	1862[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (primQuotInt (Neg vuz113) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg vuz113) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1862 -> 1874[label="",style="solid", color="black", weight=3];
84.19/49.96	4340[label="pr2F0G2 (vuz204 * vuz205) vuz204 (Pos vuz211)",fontsize=16,color="black",shape="box"];4340 -> 4367[label="",style="solid", color="black", weight=3];
84.19/49.96	4341[label="vuz204",fontsize=16,color="green",shape="box"];4342[label="vuz205",fontsize=16,color="green",shape="box"];1024[label="vuz69 * vuz20",fontsize=16,color="black",shape="triangle"];1024 -> 1029[label="",style="solid", color="black", weight=3];
84.19/49.96	4343[label="vuz204",fontsize=16,color="green",shape="box"];4344[label="vuz205",fontsize=16,color="green",shape="box"];1041[label="vuz70 * vuz20",fontsize=16,color="black",shape="triangle"];1041 -> 1046[label="",style="solid", color="black", weight=3];
84.19/49.96	4345[label="vuz205",fontsize=16,color="green",shape="box"];4346[label="vuz204",fontsize=16,color="green",shape="box"];1051[label="vuz71 * vuz20",fontsize=16,color="black",shape="triangle"];1051 -> 1056[label="",style="solid", color="black", weight=3];
84.19/49.96	4347[label="vuz205",fontsize=16,color="green",shape="box"];4348[label="vuz204",fontsize=16,color="green",shape="box"];1059[label="vuz72 * vuz20",fontsize=16,color="black",shape="triangle"];1059 -> 1064[label="",style="solid", color="black", weight=3];
84.19/49.96	4349[label="vuz204",fontsize=16,color="green",shape="box"];4350[label="vuz205",fontsize=16,color="green",shape="box"];1069[label="vuz73 * vuz20",fontsize=16,color="black",shape="triangle"];1069 -> 1074[label="",style="solid", color="black", weight=3];
84.19/49.96	739[label="vuz130000",fontsize=16,color="green",shape="box"];508[label="primDivNatS (primMinusNatS (Succ (Succ vuz1300)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];508 -> 538[label="",style="solid", color="black", weight=3];
84.19/49.96	510[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];510 -> 541[label="",style="solid", color="black", weight=3];
84.19/49.96	1863[label="pr2F3 (primEqInt (Pos vuz105 - vuz115) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1863 -> 1875[label="",style="solid", color="black", weight=3];
84.19/49.96	1864[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4805[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4805[label="",style="solid", color="blue", weight=9];
84.19/49.96	4805 -> 1876[label="",style="solid", color="blue", weight=3];
84.19/49.96	4806[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4806[label="",style="solid", color="blue", weight=9];
84.19/49.96	4806 -> 1877[label="",style="solid", color="blue", weight=3];
84.19/49.96	4807[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4807[label="",style="solid", color="blue", weight=9];
84.19/49.96	4807 -> 1878[label="",style="solid", color="blue", weight=3];
84.19/49.96	4808[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4808[label="",style="solid", color="blue", weight=9];
84.19/49.96	4808 -> 1879[label="",style="solid", color="blue", weight=3];
84.19/49.96	4809[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4809[label="",style="solid", color="blue", weight=9];
84.19/49.96	4809 -> 1880[label="",style="solid", color="blue", weight=3];
84.19/49.96	1865 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1865[label="primDivNatS vuz105 (Succ (Succ Zero))",fontsize=16,color="magenta"];1865 -> 1881[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1866 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1866[label="primDivNatS vuz105 (Succ (Succ Zero))",fontsize=16,color="magenta"];1866 -> 1882[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4381[label="pr2F0 vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4381 -> 4384[label="",style="solid", color="black", weight=3];
84.19/49.96	4382[label="vuz216 * vuz217",fontsize=16,color="blue",shape="box"];4810[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4810[label="",style="solid", color="blue", weight=9];
84.19/49.96	4810 -> 4385[label="",style="solid", color="blue", weight=3];
84.19/49.96	4811[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4811[label="",style="solid", color="blue", weight=9];
84.19/49.96	4811 -> 4386[label="",style="solid", color="blue", weight=3];
84.19/49.96	4812[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4812[label="",style="solid", color="blue", weight=9];
84.19/49.96	4812 -> 4387[label="",style="solid", color="blue", weight=3];
84.19/49.96	4813[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4813[label="",style="solid", color="blue", weight=9];
84.19/49.96	4813 -> 4388[label="",style="solid", color="blue", weight=3];
84.19/49.96	4814[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4814[label="",style="solid", color="blue", weight=9];
84.19/49.96	4814 -> 4389[label="",style="solid", color="blue", weight=3];
84.19/49.96	1867[label="pr2F4 (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1867 -> 1883[label="",style="solid", color="black", weight=3];
84.19/49.96	1874[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (primQuotInt (Neg vuz113) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg vuz113) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1874 -> 1896[label="",style="solid", color="black", weight=3];
84.19/49.96	4367[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos vuz211) (even (Pos vuz211))",fontsize=16,color="black",shape="box"];4367 -> 4380[label="",style="solid", color="black", weight=3];
84.19/49.96	1029[label="error []",fontsize=16,color="red",shape="box"];1046[label="error []",fontsize=16,color="red",shape="box"];1056[label="primMulInt vuz71 vuz20",fontsize=16,color="burlywood",shape="box"];4815[label="vuz71/Pos vuz710",fontsize=10,color="white",style="solid",shape="box"];1056 -> 4815[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4815 -> 1065[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4816[label="vuz71/Neg vuz710",fontsize=10,color="white",style="solid",shape="box"];1056 -> 4816[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4816 -> 1066[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1064[label="error []",fontsize=16,color="red",shape="box"];1074[label="error []",fontsize=16,color="red",shape="box"];538[label="primDivNatS (primMinusNatS (Succ vuz1300) Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];538 -> 554[label="",style="solid", color="black", weight=3];
84.19/49.96	541[label="primDivNatS (primMinusNatS Zero Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];541 -> 557[label="",style="solid", color="black", weight=3];
84.19/49.96	1875[label="pr2F3 (primEqInt (primMinusInt (Pos vuz105) vuz115) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusInt (Pos vuz105) vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="box"];4817[label="vuz115/Pos vuz1150",fontsize=10,color="white",style="solid",shape="box"];1875 -> 4817[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4817 -> 1897[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4818[label="vuz115/Neg vuz1150",fontsize=10,color="white",style="solid",shape="box"];1875 -> 4818[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4818 -> 1898[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1876 -> 397[label="",style="dashed", color="red", weight=0];
84.19/49.96	1876[label="vuz103 * vuz103",fontsize=16,color="magenta"];1876 -> 1899[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1877 -> 398[label="",style="dashed", color="red", weight=0];
84.19/49.96	1877[label="vuz103 * vuz103",fontsize=16,color="magenta"];1877 -> 1900[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1878 -> 399[label="",style="dashed", color="red", weight=0];
84.19/49.96	1878[label="vuz103 * vuz103",fontsize=16,color="magenta"];1878 -> 1901[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1879 -> 400[label="",style="dashed", color="red", weight=0];
84.19/49.96	1879[label="vuz103 * vuz103",fontsize=16,color="magenta"];1879 -> 1902[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1880 -> 401[label="",style="dashed", color="red", weight=0];
84.19/49.96	1880[label="vuz103 * vuz103",fontsize=16,color="magenta"];1880 -> 1903[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1881[label="vuz105",fontsize=16,color="green",shape="box"];1882[label="vuz105",fontsize=16,color="green",shape="box"];4384[label="pr2F0G (vuz216 * vuz217) vuz216 (Neg vuz218)",fontsize=16,color="black",shape="box"];4384 -> 4392[label="",style="solid", color="black", weight=3];
84.19/49.96	4385 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.96	4385[label="vuz216 * vuz217",fontsize=16,color="magenta"];4385 -> 4393[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4385 -> 4394[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4386 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.96	4386[label="vuz216 * vuz217",fontsize=16,color="magenta"];4386 -> 4395[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4386 -> 4396[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4387 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.96	4387[label="vuz216 * vuz217",fontsize=16,color="magenta"];4387 -> 4397[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4387 -> 4398[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4388 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.96	4388[label="vuz216 * vuz217",fontsize=16,color="magenta"];4388 -> 4399[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4388 -> 4400[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4389 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.96	4389[label="vuz216 * vuz217",fontsize=16,color="magenta"];4389 -> 4401[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4389 -> 4402[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1883[label="pr2F3 (Neg vuz113 - vuz116 == fromInt (Pos Zero)) (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1883 -> 1904[label="",style="solid", color="black", weight=3];
84.19/49.96	1896 -> 1755[label="",style="dashed", color="red", weight=0];
84.19/49.96	1896[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg (primDivNatS vuz113 (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS vuz113 (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1896 -> 1917[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1896 -> 1918[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1896 -> 1919[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4380[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos vuz211) (primEvenInt (Pos vuz211))",fontsize=16,color="black",shape="box"];4380 -> 4383[label="",style="solid", color="black", weight=3];
84.19/49.96	1065[label="primMulInt (Pos vuz710) vuz20",fontsize=16,color="burlywood",shape="box"];4819[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];1065 -> 4819[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4819 -> 1075[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4820[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];1065 -> 4820[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4820 -> 1076[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1066[label="primMulInt (Neg vuz710) vuz20",fontsize=16,color="burlywood",shape="box"];4821[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];1066 -> 4821[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4821 -> 1077[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4822[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];1066 -> 4822[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4822 -> 1078[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	554[label="primDivNatS (Succ vuz1300) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];554 -> 562[label="",style="solid", color="black", weight=3];
84.19/49.96	557[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];557 -> 566[label="",style="solid", color="black", weight=3];
84.19/49.96	1897[label="pr2F3 (primEqInt (primMinusInt (Pos vuz105) (Pos vuz1150)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusInt (Pos vuz105) (Pos vuz1150)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1897 -> 1920[label="",style="solid", color="black", weight=3];
84.19/49.96	1898[label="pr2F3 (primEqInt (primMinusInt (Pos vuz105) (Neg vuz1150)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusInt (Pos vuz105) (Neg vuz1150)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1898 -> 1921[label="",style="solid", color="black", weight=3];
84.19/49.96	1899[label="vuz103",fontsize=16,color="green",shape="box"];397 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.96	397[label="vuz12 * vuz12",fontsize=16,color="magenta"];397 -> 1026[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	397 -> 1027[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1900[label="vuz103",fontsize=16,color="green",shape="box"];398 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.96	398[label="vuz12 * vuz12",fontsize=16,color="magenta"];398 -> 1043[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	398 -> 1044[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1901[label="vuz103",fontsize=16,color="green",shape="box"];399 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.96	399[label="vuz12 * vuz12",fontsize=16,color="magenta"];399 -> 1053[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	399 -> 1054[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1902[label="vuz103",fontsize=16,color="green",shape="box"];400 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.96	400[label="vuz12 * vuz12",fontsize=16,color="magenta"];400 -> 1061[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	400 -> 1062[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1903[label="vuz103",fontsize=16,color="green",shape="box"];401 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.96	401[label="vuz12 * vuz12",fontsize=16,color="magenta"];401 -> 1071[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	401 -> 1072[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4392[label="pr2F0G2 (vuz216 * vuz217) vuz216 (Neg vuz218)",fontsize=16,color="black",shape="box"];4392 -> 4406[label="",style="solid", color="black", weight=3];
84.19/49.96	4393[label="vuz216",fontsize=16,color="green",shape="box"];4394[label="vuz217",fontsize=16,color="green",shape="box"];4395[label="vuz216",fontsize=16,color="green",shape="box"];4396[label="vuz217",fontsize=16,color="green",shape="box"];4397[label="vuz217",fontsize=16,color="green",shape="box"];4398[label="vuz216",fontsize=16,color="green",shape="box"];4399[label="vuz217",fontsize=16,color="green",shape="box"];4400[label="vuz216",fontsize=16,color="green",shape="box"];4401[label="vuz216",fontsize=16,color="green",shape="box"];4402[label="vuz217",fontsize=16,color="green",shape="box"];1904[label="pr2F3 (primEqInt (Neg vuz113 - vuz116) (fromInt (Pos Zero))) (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1904 -> 1922[label="",style="solid", color="black", weight=3];
84.19/49.96	1917 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1917[label="primDivNatS vuz113 (Succ (Succ Zero))",fontsize=16,color="magenta"];1917 -> 1930[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1918 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	1918[label="primDivNatS vuz113 (Succ (Succ Zero))",fontsize=16,color="magenta"];1918 -> 1931[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1919[label="vuz111 * vuz111",fontsize=16,color="blue",shape="box"];4823[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4823[label="",style="solid", color="blue", weight=9];
84.19/49.96	4823 -> 1932[label="",style="solid", color="blue", weight=3];
84.19/49.96	4824[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4824[label="",style="solid", color="blue", weight=9];
84.19/49.96	4824 -> 1933[label="",style="solid", color="blue", weight=3];
84.19/49.96	4825[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4825[label="",style="solid", color="blue", weight=9];
84.19/49.96	4825 -> 1934[label="",style="solid", color="blue", weight=3];
84.19/49.96	4826[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4826[label="",style="solid", color="blue", weight=9];
84.19/49.96	4826 -> 1935[label="",style="solid", color="blue", weight=3];
84.19/49.96	4827[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4827[label="",style="solid", color="blue", weight=9];
84.19/49.96	4827 -> 1936[label="",style="solid", color="blue", weight=3];
84.19/49.96	4383[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos vuz211) (primEvenNat vuz211)",fontsize=16,color="burlywood",shape="box"];4828[label="vuz211/Succ vuz2110",fontsize=10,color="white",style="solid",shape="box"];4383 -> 4828[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4828 -> 4390[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4829[label="vuz211/Zero",fontsize=10,color="white",style="solid",shape="box"];4383 -> 4829[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4829 -> 4391[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1075[label="primMulInt (Pos vuz710) (Pos vuz200)",fontsize=16,color="black",shape="box"];1075 -> 1081[label="",style="solid", color="black", weight=3];
84.19/49.96	1076[label="primMulInt (Pos vuz710) (Neg vuz200)",fontsize=16,color="black",shape="box"];1076 -> 1082[label="",style="solid", color="black", weight=3];
84.19/49.96	1077[label="primMulInt (Neg vuz710) (Pos vuz200)",fontsize=16,color="black",shape="box"];1077 -> 1083[label="",style="solid", color="black", weight=3];
84.19/49.96	1078[label="primMulInt (Neg vuz710) (Neg vuz200)",fontsize=16,color="black",shape="box"];1078 -> 1084[label="",style="solid", color="black", weight=3];
84.19/49.96	566[label="Zero",fontsize=16,color="green",shape="box"];1920[label="pr2F3 (primEqInt (primMinusNat vuz105 vuz1150) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat vuz105 vuz1150) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="triangle"];4830[label="vuz105/Succ vuz1050",fontsize=10,color="white",style="solid",shape="box"];1920 -> 4830[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4830 -> 1937[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4831[label="vuz105/Zero",fontsize=10,color="white",style="solid",shape="box"];1920 -> 4831[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4831 -> 1938[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1921 -> 4007[label="",style="dashed", color="red", weight=0];
84.19/49.96	1921[label="pr2F3 (primEqInt (Pos (primPlusNat vuz105 vuz1150)) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos (primPlusNat vuz105 vuz1150)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1921 -> 4022[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1921 -> 4023[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1921 -> 4024[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1921 -> 4025[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1026[label="vuz12",fontsize=16,color="green",shape="box"];1027[label="vuz12",fontsize=16,color="green",shape="box"];1043[label="vuz12",fontsize=16,color="green",shape="box"];1044[label="vuz12",fontsize=16,color="green",shape="box"];1053[label="vuz12",fontsize=16,color="green",shape="box"];1054[label="vuz12",fontsize=16,color="green",shape="box"];1061[label="vuz12",fontsize=16,color="green",shape="box"];1062[label="vuz12",fontsize=16,color="green",shape="box"];1071[label="vuz12",fontsize=16,color="green",shape="box"];1072[label="vuz12",fontsize=16,color="green",shape="box"];4406[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg vuz218) (even (Neg vuz218))",fontsize=16,color="black",shape="box"];4406 -> 4410[label="",style="solid", color="black", weight=3];
84.19/49.96	1922[label="pr2F3 (primEqInt (primMinusInt (Neg vuz113) vuz116) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusInt (Neg vuz113) vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="burlywood",shape="box"];4832[label="vuz116/Pos vuz1160",fontsize=10,color="white",style="solid",shape="box"];1922 -> 4832[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4832 -> 1942[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4833[label="vuz116/Neg vuz1160",fontsize=10,color="white",style="solid",shape="box"];1922 -> 4833[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4833 -> 1943[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1930[label="vuz113",fontsize=16,color="green",shape="box"];1931[label="vuz113",fontsize=16,color="green",shape="box"];1932 -> 397[label="",style="dashed", color="red", weight=0];
84.19/49.96	1932[label="vuz111 * vuz111",fontsize=16,color="magenta"];1932 -> 1944[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1933 -> 398[label="",style="dashed", color="red", weight=0];
84.19/49.96	1933[label="vuz111 * vuz111",fontsize=16,color="magenta"];1933 -> 1945[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1934 -> 399[label="",style="dashed", color="red", weight=0];
84.19/49.96	1934[label="vuz111 * vuz111",fontsize=16,color="magenta"];1934 -> 1946[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1935 -> 400[label="",style="dashed", color="red", weight=0];
84.19/49.96	1935[label="vuz111 * vuz111",fontsize=16,color="magenta"];1935 -> 1947[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1936 -> 401[label="",style="dashed", color="red", weight=0];
84.19/49.96	1936[label="vuz111 * vuz111",fontsize=16,color="magenta"];1936 -> 1948[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4390[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ vuz2110)) (primEvenNat (Succ vuz2110))",fontsize=16,color="burlywood",shape="box"];4834[label="vuz2110/Succ vuz21100",fontsize=10,color="white",style="solid",shape="box"];4390 -> 4834[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4834 -> 4403[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4835[label="vuz2110/Zero",fontsize=10,color="white",style="solid",shape="box"];4390 -> 4835[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4835 -> 4404[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4391[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos Zero) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4391 -> 4405[label="",style="solid", color="black", weight=3];
84.19/49.96	1081[label="Pos (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1081 -> 1107[label="",style="dashed", color="green", weight=3];
84.19/49.96	1082[label="Neg (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1082 -> 1108[label="",style="dashed", color="green", weight=3];
84.19/49.96	1083[label="Neg (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1083 -> 1109[label="",style="dashed", color="green", weight=3];
84.19/49.96	1084[label="Pos (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1084 -> 1110[label="",style="dashed", color="green", weight=3];
84.19/49.96	1937[label="pr2F3 (primEqInt (primMinusNat (Succ vuz1050) vuz1150) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat (Succ vuz1050) vuz1150) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="box"];4836[label="vuz1150/Succ vuz11500",fontsize=10,color="white",style="solid",shape="box"];1937 -> 4836[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4836 -> 1949[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4837[label="vuz1150/Zero",fontsize=10,color="white",style="solid",shape="box"];1937 -> 4837[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4837 -> 1950[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1938[label="pr2F3 (primEqInt (primMinusNat Zero vuz1150) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat Zero vuz1150) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="box"];4838[label="vuz1150/Succ vuz11500",fontsize=10,color="white",style="solid",shape="box"];1938 -> 4838[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4838 -> 1951[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4839[label="vuz1150/Zero",fontsize=10,color="white",style="solid",shape="box"];1938 -> 4839[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4839 -> 1952[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4022[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4840[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4840[label="",style="solid", color="blue", weight=9];
84.19/49.96	4840 -> 4094[label="",style="solid", color="blue", weight=3];
84.19/49.96	4841[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4841[label="",style="solid", color="blue", weight=9];
84.19/49.96	4841 -> 4095[label="",style="solid", color="blue", weight=3];
84.19/49.96	4842[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4842[label="",style="solid", color="blue", weight=9];
84.19/49.96	4842 -> 4096[label="",style="solid", color="blue", weight=3];
84.19/49.96	4843[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4843[label="",style="solid", color="blue", weight=9];
84.19/49.96	4843 -> 4097[label="",style="solid", color="blue", weight=3];
84.19/49.96	4844[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4844[label="",style="solid", color="blue", weight=9];
84.19/49.96	4844 -> 4098[label="",style="solid", color="blue", weight=3];
84.19/49.96	4023[label="vuz102",fontsize=16,color="green",shape="box"];4024 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4024[label="primPlusNat vuz105 vuz1150",fontsize=16,color="magenta"];4024 -> 4099[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4024 -> 4100[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4025 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4025[label="primPlusNat vuz105 vuz1150",fontsize=16,color="magenta"];4025 -> 4101[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4025 -> 4102[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4410[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg vuz218) (primEvenInt (Neg vuz218))",fontsize=16,color="black",shape="box"];4410 -> 4415[label="",style="solid", color="black", weight=3];
84.19/49.96	1942[label="pr2F3 (primEqInt (primMinusInt (Neg vuz113) (Pos vuz1160)) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusInt (Neg vuz113) (Pos vuz1160)) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1942 -> 1969[label="",style="solid", color="black", weight=3];
84.19/49.96	1943[label="pr2F3 (primEqInt (primMinusInt (Neg vuz113) (Neg vuz1160)) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusInt (Neg vuz113) (Neg vuz1160)) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1943 -> 1970[label="",style="solid", color="black", weight=3];
84.19/49.96	1944[label="vuz111",fontsize=16,color="green",shape="box"];1945[label="vuz111",fontsize=16,color="green",shape="box"];1946[label="vuz111",fontsize=16,color="green",shape="box"];1947[label="vuz111",fontsize=16,color="green",shape="box"];1948[label="vuz111",fontsize=16,color="green",shape="box"];4403[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ (Succ vuz21100))) (primEvenNat (Succ (Succ vuz21100)))",fontsize=16,color="black",shape="box"];4403 -> 4407[label="",style="solid", color="black", weight=3];
84.19/49.96	4404[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4404 -> 4408[label="",style="solid", color="black", weight=3];
84.19/49.96	4405[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos Zero) True",fontsize=16,color="black",shape="box"];4405 -> 4409[label="",style="solid", color="black", weight=3];
84.19/49.96	1107[label="primMulNat vuz710 vuz200",fontsize=16,color="burlywood",shape="triangle"];4845[label="vuz710/Succ vuz7100",fontsize=10,color="white",style="solid",shape="box"];1107 -> 4845[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4845 -> 1173[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4846[label="vuz710/Zero",fontsize=10,color="white",style="solid",shape="box"];1107 -> 4846[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4846 -> 1174[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1108 -> 1107[label="",style="dashed", color="red", weight=0];
84.19/49.96	1108[label="primMulNat vuz710 vuz200",fontsize=16,color="magenta"];1108 -> 1175[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1109 -> 1107[label="",style="dashed", color="red", weight=0];
84.19/49.96	1109[label="primMulNat vuz710 vuz200",fontsize=16,color="magenta"];1109 -> 1176[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1110 -> 1107[label="",style="dashed", color="red", weight=0];
84.19/49.96	1110[label="primMulNat vuz710 vuz200",fontsize=16,color="magenta"];1110 -> 1177[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1110 -> 1178[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1949[label="pr2F3 (primEqInt (primMinusNat (Succ vuz1050) (Succ vuz11500)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat (Succ vuz1050) (Succ vuz11500)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1949 -> 1971[label="",style="solid", color="black", weight=3];
84.19/49.96	1950[label="pr2F3 (primEqInt (primMinusNat (Succ vuz1050) Zero) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat (Succ vuz1050) Zero) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1950 -> 1972[label="",style="solid", color="black", weight=3];
84.19/49.96	1951[label="pr2F3 (primEqInt (primMinusNat Zero (Succ vuz11500)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat Zero (Succ vuz11500)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1951 -> 1973[label="",style="solid", color="black", weight=3];
84.19/49.96	1952[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat Zero Zero) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1952 -> 1974[label="",style="solid", color="black", weight=3];
84.19/49.96	4094 -> 397[label="",style="dashed", color="red", weight=0];
84.19/49.96	4094[label="vuz103 * vuz103",fontsize=16,color="magenta"];4094 -> 4171[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4095 -> 398[label="",style="dashed", color="red", weight=0];
84.19/49.96	4095[label="vuz103 * vuz103",fontsize=16,color="magenta"];4095 -> 4172[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4096 -> 399[label="",style="dashed", color="red", weight=0];
84.19/49.96	4096[label="vuz103 * vuz103",fontsize=16,color="magenta"];4096 -> 4173[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4097 -> 400[label="",style="dashed", color="red", weight=0];
84.19/49.96	4097[label="vuz103 * vuz103",fontsize=16,color="magenta"];4097 -> 4174[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4098 -> 401[label="",style="dashed", color="red", weight=0];
84.19/49.96	4098[label="vuz103 * vuz103",fontsize=16,color="magenta"];4098 -> 4175[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4099[label="vuz105",fontsize=16,color="green",shape="box"];4100[label="vuz1150",fontsize=16,color="green",shape="box"];4101[label="vuz105",fontsize=16,color="green",shape="box"];4102[label="vuz1150",fontsize=16,color="green",shape="box"];4415[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg vuz218) (primEvenNat vuz218)",fontsize=16,color="burlywood",shape="box"];4847[label="vuz218/Succ vuz2180",fontsize=10,color="white",style="solid",shape="box"];4415 -> 4847[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4847 -> 4421[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4848[label="vuz218/Zero",fontsize=10,color="white",style="solid",shape="box"];4415 -> 4848[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4848 -> 4422[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1969 -> 4311[label="",style="dashed", color="red", weight=0];
84.19/49.96	1969[label="pr2F3 (primEqInt (Neg (primPlusNat vuz113 vuz1160)) (fromInt (Pos Zero))) (vuz111 * vuz111) (Neg (primPlusNat vuz113 vuz1160)) (vuz111 * vuz111 * vuz110)",fontsize=16,color="magenta"];1969 -> 4318[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1969 -> 4319[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1969 -> 4320[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1969 -> 4321[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1970 -> 1920[label="",style="dashed", color="red", weight=0];
84.19/49.96	1970[label="pr2F3 (primEqInt (primMinusNat vuz1160 vuz113) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusNat vuz1160 vuz113) (vuz111 * vuz111 * vuz110)",fontsize=16,color="magenta"];1970 -> 2001[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1970 -> 2002[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1970 -> 2003[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1970 -> 2004[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4407 -> 4464[label="",style="dashed", color="red", weight=0];
84.19/49.96	4407[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ (Succ vuz21100))) (primEvenNat vuz21100)",fontsize=16,color="magenta"];4407 -> 4465[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4407 -> 4466[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4407 -> 4467[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4407 -> 4468[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4408[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) False",fontsize=16,color="black",shape="box"];4408 -> 4413[label="",style="solid", color="black", weight=3];
84.19/49.96	4409[label="pr2F0G (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4409 -> 4414[label="",style="solid", color="black", weight=3];
84.19/49.96	1173[label="primMulNat (Succ vuz7100) vuz200",fontsize=16,color="burlywood",shape="box"];4849[label="vuz200/Succ vuz2000",fontsize=10,color="white",style="solid",shape="box"];1173 -> 4849[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4849 -> 1228[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4850[label="vuz200/Zero",fontsize=10,color="white",style="solid",shape="box"];1173 -> 4850[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4850 -> 1229[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1174[label="primMulNat Zero vuz200",fontsize=16,color="burlywood",shape="box"];4851[label="vuz200/Succ vuz2000",fontsize=10,color="white",style="solid",shape="box"];1174 -> 4851[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4851 -> 1230[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4852[label="vuz200/Zero",fontsize=10,color="white",style="solid",shape="box"];1174 -> 4852[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4852 -> 1231[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	1175[label="vuz200",fontsize=16,color="green",shape="box"];1176[label="vuz710",fontsize=16,color="green",shape="box"];1177[label="vuz200",fontsize=16,color="green",shape="box"];1178[label="vuz710",fontsize=16,color="green",shape="box"];1971 -> 1920[label="",style="dashed", color="red", weight=0];
84.19/49.96	1971[label="pr2F3 (primEqInt (primMinusNat vuz1050 vuz11500) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat vuz1050 vuz11500) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1971 -> 2005[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1971 -> 2006[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1972 -> 4007[label="",style="dashed", color="red", weight=0];
84.19/49.96	1972[label="pr2F3 (primEqInt (Pos (Succ vuz1050)) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos (Succ vuz1050)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1972 -> 4030[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1972 -> 4031[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1972 -> 4032[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1972 -> 4033[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1973 -> 4311[label="",style="dashed", color="red", weight=0];
84.19/49.96	1973[label="pr2F3 (primEqInt (Neg (Succ vuz11500)) (fromInt (Pos Zero))) (vuz103 * vuz103) (Neg (Succ vuz11500)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1973 -> 4322[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1973 -> 4323[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1973 -> 4324[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1973 -> 4325[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1974 -> 4007[label="",style="dashed", color="red", weight=0];
84.19/49.96	1974[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos Zero) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1974 -> 4034[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1974 -> 4035[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1974 -> 4036[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1974 -> 4037[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4171[label="vuz103",fontsize=16,color="green",shape="box"];4172[label="vuz103",fontsize=16,color="green",shape="box"];4173[label="vuz103",fontsize=16,color="green",shape="box"];4174[label="vuz103",fontsize=16,color="green",shape="box"];4175[label="vuz103",fontsize=16,color="green",shape="box"];4421[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ vuz2180)) (primEvenNat (Succ vuz2180))",fontsize=16,color="burlywood",shape="box"];4853[label="vuz2180/Succ vuz21800",fontsize=10,color="white",style="solid",shape="box"];4421 -> 4853[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4853 -> 4428[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4854[label="vuz2180/Zero",fontsize=10,color="white",style="solid",shape="box"];4421 -> 4854[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4854 -> 4429[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4422[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg Zero) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4422 -> 4430[label="",style="solid", color="black", weight=3];
84.19/49.96	4318[label="vuz111 * vuz111",fontsize=16,color="blue",shape="box"];4855[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4855[label="",style="solid", color="blue", weight=9];
84.19/49.96	4855 -> 4351[label="",style="solid", color="blue", weight=3];
84.19/49.96	4856[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4856[label="",style="solid", color="blue", weight=9];
84.19/49.96	4856 -> 4352[label="",style="solid", color="blue", weight=3];
84.19/49.96	4857[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4857[label="",style="solid", color="blue", weight=9];
84.19/49.96	4857 -> 4353[label="",style="solid", color="blue", weight=3];
84.19/49.96	4858[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4858[label="",style="solid", color="blue", weight=9];
84.19/49.96	4858 -> 4354[label="",style="solid", color="blue", weight=3];
84.19/49.96	4859[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4859[label="",style="solid", color="blue", weight=9];
84.19/49.96	4859 -> 4355[label="",style="solid", color="blue", weight=3];
84.19/49.96	4319 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4319[label="primPlusNat vuz113 vuz1160",fontsize=16,color="magenta"];4319 -> 4356[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4319 -> 4357[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4320 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	4320[label="primPlusNat vuz113 vuz1160",fontsize=16,color="magenta"];4320 -> 4358[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4320 -> 4359[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4321[label="vuz110",fontsize=16,color="green",shape="box"];2001[label="vuz111",fontsize=16,color="green",shape="box"];2002[label="vuz1160",fontsize=16,color="green",shape="box"];2003[label="vuz110",fontsize=16,color="green",shape="box"];2004[label="vuz113",fontsize=16,color="green",shape="box"];4465[label="vuz204",fontsize=16,color="green",shape="box"];4466[label="vuz205",fontsize=16,color="green",shape="box"];4467[label="Succ vuz21100",fontsize=16,color="green",shape="box"];4468[label="vuz21100",fontsize=16,color="green",shape="box"];4464[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat vuz225)",fontsize=16,color="burlywood",shape="triangle"];4860[label="vuz225/Succ vuz2250",fontsize=10,color="white",style="solid",shape="box"];4464 -> 4860[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4860 -> 4477[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4861[label="vuz225/Zero",fontsize=10,color="white",style="solid",shape="box"];4464 -> 4861[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4861 -> 4478[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4413[label="pr2F0G0 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) otherwise",fontsize=16,color="black",shape="box"];4413 -> 4419[label="",style="solid", color="black", weight=3];
84.19/49.96	4414[label="pr2F0G2 (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4414 -> 4420[label="",style="solid", color="black", weight=3];
84.19/49.96	1228[label="primMulNat (Succ vuz7100) (Succ vuz2000)",fontsize=16,color="black",shape="box"];1228 -> 1263[label="",style="solid", color="black", weight=3];
84.19/49.96	1229[label="primMulNat (Succ vuz7100) Zero",fontsize=16,color="black",shape="box"];1229 -> 1264[label="",style="solid", color="black", weight=3];
84.19/49.96	1230[label="primMulNat Zero (Succ vuz2000)",fontsize=16,color="black",shape="box"];1230 -> 1265[label="",style="solid", color="black", weight=3];
84.19/49.96	1231[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1231 -> 1266[label="",style="solid", color="black", weight=3];
84.19/49.96	2005[label="vuz1050",fontsize=16,color="green",shape="box"];2006[label="vuz11500",fontsize=16,color="green",shape="box"];4030[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4862[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4862[label="",style="solid", color="blue", weight=9];
84.19/49.96	4862 -> 4103[label="",style="solid", color="blue", weight=3];
84.19/49.96	4863[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4863[label="",style="solid", color="blue", weight=9];
84.19/49.96	4863 -> 4104[label="",style="solid", color="blue", weight=3];
84.19/49.96	4864[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4864[label="",style="solid", color="blue", weight=9];
84.19/49.96	4864 -> 4105[label="",style="solid", color="blue", weight=3];
84.19/49.96	4865[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4865[label="",style="solid", color="blue", weight=9];
84.19/49.96	4865 -> 4106[label="",style="solid", color="blue", weight=3];
84.19/49.96	4866[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4866[label="",style="solid", color="blue", weight=9];
84.19/49.96	4866 -> 4107[label="",style="solid", color="blue", weight=3];
84.19/49.96	4031[label="vuz102",fontsize=16,color="green",shape="box"];4032[label="Succ vuz1050",fontsize=16,color="green",shape="box"];4033[label="Succ vuz1050",fontsize=16,color="green",shape="box"];4322[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4867[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4867[label="",style="solid", color="blue", weight=9];
84.19/49.96	4867 -> 4360[label="",style="solid", color="blue", weight=3];
84.19/49.96	4868[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4868[label="",style="solid", color="blue", weight=9];
84.19/49.96	4868 -> 4361[label="",style="solid", color="blue", weight=3];
84.19/49.96	4869[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4869[label="",style="solid", color="blue", weight=9];
84.19/49.96	4869 -> 4362[label="",style="solid", color="blue", weight=3];
84.19/49.96	4870[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4870[label="",style="solid", color="blue", weight=9];
84.19/49.96	4870 -> 4363[label="",style="solid", color="blue", weight=3];
84.19/49.96	4871[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4871[label="",style="solid", color="blue", weight=9];
84.19/49.96	4871 -> 4364[label="",style="solid", color="blue", weight=3];
84.19/49.96	4323[label="Succ vuz11500",fontsize=16,color="green",shape="box"];4324[label="Succ vuz11500",fontsize=16,color="green",shape="box"];4325[label="vuz102",fontsize=16,color="green",shape="box"];4034[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4872[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4872[label="",style="solid", color="blue", weight=9];
84.19/49.96	4872 -> 4108[label="",style="solid", color="blue", weight=3];
84.19/49.96	4873[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4873[label="",style="solid", color="blue", weight=9];
84.19/49.96	4873 -> 4109[label="",style="solid", color="blue", weight=3];
84.19/49.96	4874[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4874[label="",style="solid", color="blue", weight=9];
84.19/49.96	4874 -> 4110[label="",style="solid", color="blue", weight=3];
84.19/49.96	4875[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4875[label="",style="solid", color="blue", weight=9];
84.19/49.96	4875 -> 4111[label="",style="solid", color="blue", weight=3];
84.19/49.96	4876[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4876[label="",style="solid", color="blue", weight=9];
84.19/49.96	4876 -> 4112[label="",style="solid", color="blue", weight=3];
84.19/49.96	4035[label="vuz102",fontsize=16,color="green",shape="box"];4036[label="Zero",fontsize=16,color="green",shape="box"];4037[label="Zero",fontsize=16,color="green",shape="box"];4428[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ (Succ vuz21800))) (primEvenNat (Succ (Succ vuz21800)))",fontsize=16,color="black",shape="box"];4428 -> 4437[label="",style="solid", color="black", weight=3];
84.19/49.96	4429[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4429 -> 4438[label="",style="solid", color="black", weight=3];
84.19/49.96	4430[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg Zero) True",fontsize=16,color="black",shape="box"];4430 -> 4439[label="",style="solid", color="black", weight=3];
84.19/49.96	4351 -> 397[label="",style="dashed", color="red", weight=0];
84.19/49.96	4351[label="vuz111 * vuz111",fontsize=16,color="magenta"];4351 -> 4368[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4352 -> 398[label="",style="dashed", color="red", weight=0];
84.19/49.96	4352[label="vuz111 * vuz111",fontsize=16,color="magenta"];4352 -> 4369[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4353 -> 399[label="",style="dashed", color="red", weight=0];
84.19/49.96	4353[label="vuz111 * vuz111",fontsize=16,color="magenta"];4353 -> 4370[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4354 -> 400[label="",style="dashed", color="red", weight=0];
84.19/49.96	4354[label="vuz111 * vuz111",fontsize=16,color="magenta"];4354 -> 4371[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4355 -> 401[label="",style="dashed", color="red", weight=0];
84.19/49.96	4355[label="vuz111 * vuz111",fontsize=16,color="magenta"];4355 -> 4372[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4356[label="vuz113",fontsize=16,color="green",shape="box"];4357[label="vuz1160",fontsize=16,color="green",shape="box"];4358[label="vuz113",fontsize=16,color="green",shape="box"];4359[label="vuz1160",fontsize=16,color="green",shape="box"];4477[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat (Succ vuz2250))",fontsize=16,color="burlywood",shape="box"];4877[label="vuz2250/Succ vuz22500",fontsize=10,color="white",style="solid",shape="box"];4477 -> 4877[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4877 -> 4489[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4878[label="vuz2250/Zero",fontsize=10,color="white",style="solid",shape="box"];4477 -> 4878[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4878 -> 4490[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4478[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4478 -> 4491[label="",style="solid", color="black", weight=3];
84.19/49.96	4419[label="pr2F0G0 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) True",fontsize=16,color="black",shape="box"];4419 -> 4426[label="",style="solid", color="black", weight=3];
84.19/49.96	4420[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4420 -> 4427[label="",style="solid", color="black", weight=3];
84.19/49.96	1263 -> 71[label="",style="dashed", color="red", weight=0];
84.19/49.96	1263[label="primPlusNat (primMulNat vuz7100 (Succ vuz2000)) (Succ vuz2000)",fontsize=16,color="magenta"];1263 -> 1273[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1263 -> 1274[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1264[label="Zero",fontsize=16,color="green",shape="box"];1265[label="Zero",fontsize=16,color="green",shape="box"];1266[label="Zero",fontsize=16,color="green",shape="box"];4103 -> 397[label="",style="dashed", color="red", weight=0];
84.19/49.96	4103[label="vuz103 * vuz103",fontsize=16,color="magenta"];4103 -> 4176[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4104 -> 398[label="",style="dashed", color="red", weight=0];
84.19/49.96	4104[label="vuz103 * vuz103",fontsize=16,color="magenta"];4104 -> 4177[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4105 -> 399[label="",style="dashed", color="red", weight=0];
84.19/49.96	4105[label="vuz103 * vuz103",fontsize=16,color="magenta"];4105 -> 4178[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4106 -> 400[label="",style="dashed", color="red", weight=0];
84.19/49.96	4106[label="vuz103 * vuz103",fontsize=16,color="magenta"];4106 -> 4179[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4107 -> 401[label="",style="dashed", color="red", weight=0];
84.19/49.96	4107[label="vuz103 * vuz103",fontsize=16,color="magenta"];4107 -> 4180[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4360 -> 397[label="",style="dashed", color="red", weight=0];
84.19/49.96	4360[label="vuz103 * vuz103",fontsize=16,color="magenta"];4360 -> 4373[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4361 -> 398[label="",style="dashed", color="red", weight=0];
84.19/49.96	4361[label="vuz103 * vuz103",fontsize=16,color="magenta"];4361 -> 4374[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4362 -> 399[label="",style="dashed", color="red", weight=0];
84.19/49.96	4362[label="vuz103 * vuz103",fontsize=16,color="magenta"];4362 -> 4375[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4363 -> 400[label="",style="dashed", color="red", weight=0];
84.19/49.96	4363[label="vuz103 * vuz103",fontsize=16,color="magenta"];4363 -> 4376[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4364 -> 401[label="",style="dashed", color="red", weight=0];
84.19/49.96	4364[label="vuz103 * vuz103",fontsize=16,color="magenta"];4364 -> 4377[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4108 -> 397[label="",style="dashed", color="red", weight=0];
84.19/49.96	4108[label="vuz103 * vuz103",fontsize=16,color="magenta"];4108 -> 4181[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4109 -> 398[label="",style="dashed", color="red", weight=0];
84.19/49.96	4109[label="vuz103 * vuz103",fontsize=16,color="magenta"];4109 -> 4182[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4110 -> 399[label="",style="dashed", color="red", weight=0];
84.19/49.96	4110[label="vuz103 * vuz103",fontsize=16,color="magenta"];4110 -> 4183[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4111 -> 400[label="",style="dashed", color="red", weight=0];
84.19/49.96	4111[label="vuz103 * vuz103",fontsize=16,color="magenta"];4111 -> 4184[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4112 -> 401[label="",style="dashed", color="red", weight=0];
84.19/49.96	4112[label="vuz103 * vuz103",fontsize=16,color="magenta"];4112 -> 4185[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4437 -> 4546[label="",style="dashed", color="red", weight=0];
84.19/49.96	4437[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ (Succ vuz21800))) (primEvenNat vuz21800)",fontsize=16,color="magenta"];4437 -> 4547[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4437 -> 4548[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4437 -> 4549[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4437 -> 4550[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4438[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) False",fontsize=16,color="black",shape="box"];4438 -> 4449[label="",style="solid", color="black", weight=3];
84.19/49.96	4439[label="pr2F0G (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4439 -> 4450[label="",style="solid", color="black", weight=3];
84.19/49.96	4368[label="vuz111",fontsize=16,color="green",shape="box"];4369[label="vuz111",fontsize=16,color="green",shape="box"];4370[label="vuz111",fontsize=16,color="green",shape="box"];4371[label="vuz111",fontsize=16,color="green",shape="box"];4372[label="vuz111",fontsize=16,color="green",shape="box"];4489[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat (Succ (Succ vuz22500)))",fontsize=16,color="black",shape="box"];4489 -> 4498[label="",style="solid", color="black", weight=3];
84.19/49.96	4490[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4490 -> 4499[label="",style="solid", color="black", weight=3];
84.19/49.96	4491[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) True",fontsize=16,color="black",shape="box"];4491 -> 4500[label="",style="solid", color="black", weight=3];
84.19/49.96	4426 -> 4581[label="",style="dashed", color="red", weight=0];
84.19/49.96	4426[label="pr2F vuz204 (Pos (Succ Zero) - fromInt (Pos (Succ Zero))) (vuz204 * (vuz204 * vuz205))",fontsize=16,color="magenta"];4426 -> 4582[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4426 -> 4583[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4426 -> 4584[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4426 -> 4585[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4427[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4427 -> 4440[label="",style="solid", color="black", weight=3];
84.19/49.96	1273 -> 1107[label="",style="dashed", color="red", weight=0];
84.19/49.96	1273[label="primMulNat vuz7100 (Succ vuz2000)",fontsize=16,color="magenta"];1273 -> 1305[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1273 -> 1306[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	1274[label="Succ vuz2000",fontsize=16,color="green",shape="box"];4176[label="vuz103",fontsize=16,color="green",shape="box"];4177[label="vuz103",fontsize=16,color="green",shape="box"];4178[label="vuz103",fontsize=16,color="green",shape="box"];4179[label="vuz103",fontsize=16,color="green",shape="box"];4180[label="vuz103",fontsize=16,color="green",shape="box"];4373[label="vuz103",fontsize=16,color="green",shape="box"];4374[label="vuz103",fontsize=16,color="green",shape="box"];4375[label="vuz103",fontsize=16,color="green",shape="box"];4376[label="vuz103",fontsize=16,color="green",shape="box"];4377[label="vuz103",fontsize=16,color="green",shape="box"];4181[label="vuz103",fontsize=16,color="green",shape="box"];4182[label="vuz103",fontsize=16,color="green",shape="box"];4183[label="vuz103",fontsize=16,color="green",shape="box"];4184[label="vuz103",fontsize=16,color="green",shape="box"];4185[label="vuz103",fontsize=16,color="green",shape="box"];4547[label="vuz217",fontsize=16,color="green",shape="box"];4548[label="vuz21800",fontsize=16,color="green",shape="box"];4549[label="vuz216",fontsize=16,color="green",shape="box"];4550[label="Succ vuz21800",fontsize=16,color="green",shape="box"];4546[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat vuz231)",fontsize=16,color="burlywood",shape="triangle"];4879[label="vuz231/Succ vuz2310",fontsize=10,color="white",style="solid",shape="box"];4546 -> 4879[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4879 -> 4559[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4880[label="vuz231/Zero",fontsize=10,color="white",style="solid",shape="box"];4546 -> 4880[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4880 -> 4560[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4449[label="pr2F0G0 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) otherwise",fontsize=16,color="black",shape="box"];4449 -> 4461[label="",style="solid", color="black", weight=3];
84.19/49.96	4450[label="pr2F0G2 (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4450 -> 4462[label="",style="solid", color="black", weight=3];
84.19/49.96	4498 -> 4464[label="",style="dashed", color="red", weight=0];
84.19/49.96	4498[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat vuz22500)",fontsize=16,color="magenta"];4498 -> 4518[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4499[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) False",fontsize=16,color="black",shape="box"];4499 -> 4519[label="",style="solid", color="black", weight=3];
84.19/49.96	4500[label="pr2F0G (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4500 -> 4520[label="",style="solid", color="black", weight=3];
84.19/49.96	4582[label="vuz204",fontsize=16,color="green",shape="box"];4583[label="vuz205",fontsize=16,color="green",shape="box"];4584[label="Zero",fontsize=16,color="green",shape="box"];4585 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	4585[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4581[label="pr2F vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="black",shape="triangle"];4581 -> 4591[label="",style="solid", color="black", weight=3];
84.19/49.96	4440[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4440 -> 4451[label="",style="solid", color="black", weight=3];
84.19/49.96	1305[label="Succ vuz2000",fontsize=16,color="green",shape="box"];1306[label="vuz7100",fontsize=16,color="green",shape="box"];4559[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat (Succ vuz2310))",fontsize=16,color="burlywood",shape="box"];4881[label="vuz2310/Succ vuz23100",fontsize=10,color="white",style="solid",shape="box"];4559 -> 4881[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4881 -> 4578[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4882[label="vuz2310/Zero",fontsize=10,color="white",style="solid",shape="box"];4559 -> 4882[label="",style="solid", color="burlywood", weight=9];
84.19/49.96	4882 -> 4579[label="",style="solid", color="burlywood", weight=3];
84.19/49.96	4560[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4560 -> 4580[label="",style="solid", color="black", weight=3];
84.19/49.96	4461[label="pr2F0G0 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) True",fontsize=16,color="black",shape="box"];4461 -> 4482[label="",style="solid", color="black", weight=3];
84.19/49.96	4462[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4462 -> 4483[label="",style="solid", color="black", weight=3];
84.19/49.96	4518[label="vuz22500",fontsize=16,color="green",shape="box"];4519[label="pr2F0G0 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) otherwise",fontsize=16,color="black",shape="box"];4519 -> 4543[label="",style="solid", color="black", weight=3];
84.19/49.96	4520[label="pr2F0G2 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4520 -> 4544[label="",style="solid", color="black", weight=3];
84.19/49.96	4591[label="pr2F4 vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="black",shape="box"];4591 -> 4606[label="",style="solid", color="black", weight=3];
84.19/49.96	4451[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4451 -> 4463[label="",style="solid", color="black", weight=3];
84.19/49.96	4578[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat (Succ (Succ vuz23100)))",fontsize=16,color="black",shape="box"];4578 -> 4592[label="",style="solid", color="black", weight=3];
84.19/49.96	4579[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4579 -> 4593[label="",style="solid", color="black", weight=3];
84.19/49.96	4580[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) True",fontsize=16,color="black",shape="box"];4580 -> 4594[label="",style="solid", color="black", weight=3];
84.19/49.96	4482 -> 4655[label="",style="dashed", color="red", weight=0];
84.19/49.96	4482[label="pr2F vuz216 (Neg (Succ Zero) - fromInt (Pos (Succ Zero))) (vuz216 * (vuz216 * vuz217))",fontsize=16,color="magenta"];4482 -> 4656[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4482 -> 4657[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4482 -> 4658[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4482 -> 4659[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4483[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4483 -> 4501[label="",style="solid", color="black", weight=3];
84.19/49.96	4543[label="pr2F0G0 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) True",fontsize=16,color="black",shape="box"];4543 -> 4561[label="",style="solid", color="black", weight=3];
84.19/49.96	4544[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4544 -> 4562[label="",style="solid", color="black", weight=3];
84.19/49.96	4606[label="pr2F3 (Pos (Succ vuz224) - vuz232 == fromInt (Pos Zero)) vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="black",shape="box"];4606 -> 4626[label="",style="solid", color="black", weight=3];
84.19/49.96	4463 -> 1605[label="",style="dashed", color="red", weight=0];
84.19/49.96	4463[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (Pos (primDivNatS Zero (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS Zero (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4463 -> 4485[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4463 -> 4486[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4463 -> 4487[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4463 -> 4488[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4592 -> 4546[label="",style="dashed", color="red", weight=0];
84.19/49.96	4592[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat vuz23100)",fontsize=16,color="magenta"];4592 -> 4607[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4593[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) False",fontsize=16,color="black",shape="box"];4593 -> 4608[label="",style="solid", color="black", weight=3];
84.19/49.96	4594[label="pr2F0G (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4594 -> 4609[label="",style="solid", color="black", weight=3];
84.19/49.96	4656[label="vuz217",fontsize=16,color="green",shape="box"];4657[label="vuz216",fontsize=16,color="green",shape="box"];4658 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.96	4658[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4659[label="Zero",fontsize=16,color="green",shape="box"];4655[label="pr2F vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="black",shape="triangle"];4655 -> 4665[label="",style="solid", color="black", weight=3];
84.19/49.96	4501[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (primQuotInt (Neg Zero) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg Zero) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4501 -> 4521[label="",style="solid", color="black", weight=3];
84.19/49.96	4561 -> 4581[label="",style="dashed", color="red", weight=0];
84.19/49.96	4561[label="pr2F vuz222 (Pos (Succ vuz224) - fromInt (Pos (Succ Zero))) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="magenta"];4561 -> 4590[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4562[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4562 -> 4595[label="",style="solid", color="black", weight=3];
84.19/49.96	4626 -> 3789[label="",style="dashed", color="red", weight=0];
84.19/49.96	4626[label="pr2F3 (primEqInt (Pos (Succ vuz224) - vuz232) (fromInt (Pos Zero))) vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="magenta"];4626 -> 4640[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4626 -> 4641[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4626 -> 4642[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4626 -> 4643[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4485[label="vuz204",fontsize=16,color="green",shape="box"];4486 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.96	4486[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4486 -> 4511[label="",style="dashed", color="magenta", weight=3];
84.19/49.96	4487[label="vuz204 * vuz205",fontsize=16,color="blue",shape="box"];4883[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4883[label="",style="solid", color="blue", weight=9];
84.19/49.96	4883 -> 4512[label="",style="solid", color="blue", weight=3];
84.19/49.96	4884[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4884[label="",style="solid", color="blue", weight=9];
84.19/49.97	4884 -> 4513[label="",style="solid", color="blue", weight=3];
84.19/49.97	4885[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4885[label="",style="solid", color="blue", weight=9];
84.19/49.97	4885 -> 4514[label="",style="solid", color="blue", weight=3];
84.19/49.97	4886[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4886[label="",style="solid", color="blue", weight=9];
84.19/49.97	4886 -> 4515[label="",style="solid", color="blue", weight=3];
84.19/49.97	4887[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4887[label="",style="solid", color="blue", weight=9];
84.19/49.97	4887 -> 4516[label="",style="solid", color="blue", weight=3];
84.19/49.97	4488 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.97	4488[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4488 -> 4517[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4607[label="vuz23100",fontsize=16,color="green",shape="box"];4608[label="pr2F0G0 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) otherwise",fontsize=16,color="black",shape="box"];4608 -> 4627[label="",style="solid", color="black", weight=3];
84.19/49.97	4609[label="pr2F0G2 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4609 -> 4628[label="",style="solid", color="black", weight=3];
84.19/49.97	4665[label="pr2F4 vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="black",shape="box"];4665 -> 4684[label="",style="solid", color="black", weight=3];
84.19/49.97	4521[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (primQuotInt (Neg Zero) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg Zero) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4521 -> 4545[label="",style="solid", color="black", weight=3];
84.19/49.97	4590 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.97	4590[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4595[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (primQuotInt (Pos (Succ vuz224)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz224)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4595 -> 4610[label="",style="solid", color="black", weight=3];
84.19/49.97	4640[label="vuz222",fontsize=16,color="green",shape="box"];4641[label="vuz224",fontsize=16,color="green",shape="box"];4642[label="vuz222 * vuz223",fontsize=16,color="blue",shape="box"];4888[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4888[label="",style="solid", color="blue", weight=9];
84.19/49.97	4888 -> 4650[label="",style="solid", color="blue", weight=3];
84.19/49.97	4889[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4889[label="",style="solid", color="blue", weight=9];
84.19/49.97	4889 -> 4651[label="",style="solid", color="blue", weight=3];
84.19/49.97	4890[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4890[label="",style="solid", color="blue", weight=9];
84.19/49.97	4890 -> 4652[label="",style="solid", color="blue", weight=3];
84.19/49.97	4891[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4891[label="",style="solid", color="blue", weight=9];
84.19/49.97	4891 -> 4653[label="",style="solid", color="blue", weight=3];
84.19/49.97	4892[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4892[label="",style="solid", color="blue", weight=9];
84.19/49.97	4892 -> 4654[label="",style="solid", color="blue", weight=3];
84.19/49.97	4643[label="vuz232",fontsize=16,color="green",shape="box"];4511[label="Zero",fontsize=16,color="green",shape="box"];4512 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.97	4512[label="vuz204 * vuz205",fontsize=16,color="magenta"];4512 -> 4533[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4512 -> 4534[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4513 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.97	4513[label="vuz204 * vuz205",fontsize=16,color="magenta"];4513 -> 4535[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4513 -> 4536[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4514 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.97	4514[label="vuz204 * vuz205",fontsize=16,color="magenta"];4514 -> 4537[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4514 -> 4538[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4515 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.97	4515[label="vuz204 * vuz205",fontsize=16,color="magenta"];4515 -> 4539[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4515 -> 4540[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4516 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.97	4516[label="vuz204 * vuz205",fontsize=16,color="magenta"];4516 -> 4541[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4516 -> 4542[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4517[label="Zero",fontsize=16,color="green",shape="box"];4627[label="pr2F0G0 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) True",fontsize=16,color="black",shape="box"];4627 -> 4644[label="",style="solid", color="black", weight=3];
84.19/49.97	4628[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4628 -> 4645[label="",style="solid", color="black", weight=3];
84.19/49.97	4684[label="pr2F3 (Neg (Succ vuz230) - vuz233 == fromInt (Pos Zero)) vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="black",shape="box"];4684 -> 4696[label="",style="solid", color="black", weight=3];
84.19/49.97	4545 -> 1755[label="",style="dashed", color="red", weight=0];
84.19/49.97	4545[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (Neg (primDivNatS Zero (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS Zero (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4545 -> 4564[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4545 -> 4565[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4545 -> 4566[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4545 -> 4567[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4610[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (primQuotInt (Pos (Succ vuz224)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz224)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4610 -> 4629[label="",style="solid", color="black", weight=3];
84.19/49.97	4650 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.97	4650[label="vuz222 * vuz223",fontsize=16,color="magenta"];4650 -> 4666[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4650 -> 4667[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4651 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.97	4651[label="vuz222 * vuz223",fontsize=16,color="magenta"];4651 -> 4668[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4651 -> 4669[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4652 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.97	4652[label="vuz222 * vuz223",fontsize=16,color="magenta"];4652 -> 4670[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4652 -> 4671[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4653 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.97	4653[label="vuz222 * vuz223",fontsize=16,color="magenta"];4653 -> 4672[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4653 -> 4673[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4654 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.97	4654[label="vuz222 * vuz223",fontsize=16,color="magenta"];4654 -> 4674[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4654 -> 4675[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4533[label="vuz204",fontsize=16,color="green",shape="box"];4534[label="vuz205",fontsize=16,color="green",shape="box"];4535[label="vuz204",fontsize=16,color="green",shape="box"];4536[label="vuz205",fontsize=16,color="green",shape="box"];4537[label="vuz205",fontsize=16,color="green",shape="box"];4538[label="vuz204",fontsize=16,color="green",shape="box"];4539[label="vuz205",fontsize=16,color="green",shape="box"];4540[label="vuz204",fontsize=16,color="green",shape="box"];4541[label="vuz204",fontsize=16,color="green",shape="box"];4542[label="vuz205",fontsize=16,color="green",shape="box"];4644 -> 4655[label="",style="dashed", color="red", weight=0];
84.19/49.97	4644[label="pr2F vuz228 (Neg (Succ vuz230) - fromInt (Pos (Succ Zero))) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="magenta"];4644 -> 4664[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4645[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4645 -> 4676[label="",style="solid", color="black", weight=3];
84.19/49.97	4696 -> 4256[label="",style="dashed", color="red", weight=0];
84.19/49.97	4696[label="pr2F3 (primEqInt (Neg (Succ vuz230) - vuz233) (fromInt (Pos Zero))) vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="magenta"];4696 -> 4698[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4696 -> 4699[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4696 -> 4700[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4696 -> 4701[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4564 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.97	4564[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4564 -> 4599[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4565 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.97	4565[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4565 -> 4600[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4566[label="vuz216 * vuz217",fontsize=16,color="blue",shape="box"];4893[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4893[label="",style="solid", color="blue", weight=9];
84.19/49.97	4893 -> 4601[label="",style="solid", color="blue", weight=3];
84.19/49.97	4894[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4894[label="",style="solid", color="blue", weight=9];
84.19/49.97	4894 -> 4602[label="",style="solid", color="blue", weight=3];
84.19/49.97	4895[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4895[label="",style="solid", color="blue", weight=9];
84.19/49.97	4895 -> 4603[label="",style="solid", color="blue", weight=3];
84.19/49.97	4896[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4896[label="",style="solid", color="blue", weight=9];
84.19/49.97	4896 -> 4604[label="",style="solid", color="blue", weight=3];
84.19/49.97	4897[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4897[label="",style="solid", color="blue", weight=9];
84.19/49.97	4897 -> 4605[label="",style="solid", color="blue", weight=3];
84.19/49.97	4567[label="vuz216",fontsize=16,color="green",shape="box"];4629 -> 1605[label="",style="dashed", color="red", weight=0];
84.19/49.97	4629[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (primDivNatS (Succ vuz224) (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS (Succ vuz224) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4629 -> 4646[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4629 -> 4647[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4629 -> 4648[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4629 -> 4649[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4666[label="vuz222",fontsize=16,color="green",shape="box"];4667[label="vuz223",fontsize=16,color="green",shape="box"];4668[label="vuz222",fontsize=16,color="green",shape="box"];4669[label="vuz223",fontsize=16,color="green",shape="box"];4670[label="vuz223",fontsize=16,color="green",shape="box"];4671[label="vuz222",fontsize=16,color="green",shape="box"];4672[label="vuz223",fontsize=16,color="green",shape="box"];4673[label="vuz222",fontsize=16,color="green",shape="box"];4674[label="vuz222",fontsize=16,color="green",shape="box"];4675[label="vuz223",fontsize=16,color="green",shape="box"];4664 -> 23[label="",style="dashed", color="red", weight=0];
84.19/49.97	4664[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4676[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (primQuotInt (Neg (Succ vuz230)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg (Succ vuz230)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4676 -> 4685[label="",style="solid", color="black", weight=3];
84.19/49.97	4698[label="vuz230",fontsize=16,color="green",shape="box"];4699[label="vuz228",fontsize=16,color="green",shape="box"];4700[label="vuz228 * vuz229",fontsize=16,color="blue",shape="box"];4898[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4898[label="",style="solid", color="blue", weight=9];
84.19/49.97	4898 -> 4706[label="",style="solid", color="blue", weight=3];
84.19/49.97	4899[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4899[label="",style="solid", color="blue", weight=9];
84.19/49.97	4899 -> 4707[label="",style="solid", color="blue", weight=3];
84.19/49.97	4900[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4900[label="",style="solid", color="blue", weight=9];
84.19/49.97	4900 -> 4708[label="",style="solid", color="blue", weight=3];
84.19/49.97	4901[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4901[label="",style="solid", color="blue", weight=9];
84.19/49.97	4901 -> 4709[label="",style="solid", color="blue", weight=3];
84.19/49.97	4902[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4902[label="",style="solid", color="blue", weight=9];
84.19/49.97	4902 -> 4710[label="",style="solid", color="blue", weight=3];
84.19/49.97	4701[label="vuz233",fontsize=16,color="green",shape="box"];4599[label="Zero",fontsize=16,color="green",shape="box"];4600[label="Zero",fontsize=16,color="green",shape="box"];4601 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.97	4601[label="vuz216 * vuz217",fontsize=16,color="magenta"];4601 -> 4616[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4601 -> 4617[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4602 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.97	4602[label="vuz216 * vuz217",fontsize=16,color="magenta"];4602 -> 4618[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4602 -> 4619[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4603 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.97	4603[label="vuz216 * vuz217",fontsize=16,color="magenta"];4603 -> 4620[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4603 -> 4621[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4604 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.97	4604[label="vuz216 * vuz217",fontsize=16,color="magenta"];4604 -> 4622[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4604 -> 4623[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4605 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.97	4605[label="vuz216 * vuz217",fontsize=16,color="magenta"];4605 -> 4624[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4605 -> 4625[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4646[label="vuz222",fontsize=16,color="green",shape="box"];4647 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.97	4647[label="primDivNatS (Succ vuz224) (Succ (Succ Zero))",fontsize=16,color="magenta"];4647 -> 4677[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4648[label="vuz222 * vuz223",fontsize=16,color="blue",shape="box"];4903[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4903[label="",style="solid", color="blue", weight=9];
84.19/49.97	4903 -> 4678[label="",style="solid", color="blue", weight=3];
84.19/49.97	4904[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4904[label="",style="solid", color="blue", weight=9];
84.19/49.97	4904 -> 4679[label="",style="solid", color="blue", weight=3];
84.19/49.97	4905[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4905[label="",style="solid", color="blue", weight=9];
84.19/49.97	4905 -> 4680[label="",style="solid", color="blue", weight=3];
84.19/49.97	4906[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4906[label="",style="solid", color="blue", weight=9];
84.19/49.97	4906 -> 4681[label="",style="solid", color="blue", weight=3];
84.19/49.97	4907[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4907[label="",style="solid", color="blue", weight=9];
84.19/49.97	4907 -> 4682[label="",style="solid", color="blue", weight=3];
84.19/49.97	4649 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.97	4649[label="primDivNatS (Succ vuz224) (Succ (Succ Zero))",fontsize=16,color="magenta"];4649 -> 4683[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4685[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (primQuotInt (Neg (Succ vuz230)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg (Succ vuz230)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4685 -> 4697[label="",style="solid", color="black", weight=3];
84.19/49.97	4706 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.97	4706[label="vuz228 * vuz229",fontsize=16,color="magenta"];4706 -> 4718[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4706 -> 4719[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4707 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.97	4707[label="vuz228 * vuz229",fontsize=16,color="magenta"];4707 -> 4720[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4707 -> 4721[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4708 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.97	4708[label="vuz228 * vuz229",fontsize=16,color="magenta"];4708 -> 4722[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4708 -> 4723[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4709 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.97	4709[label="vuz228 * vuz229",fontsize=16,color="magenta"];4709 -> 4724[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4709 -> 4725[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4710 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.97	4710[label="vuz228 * vuz229",fontsize=16,color="magenta"];4710 -> 4726[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4710 -> 4727[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4616[label="vuz216",fontsize=16,color="green",shape="box"];4617[label="vuz217",fontsize=16,color="green",shape="box"];4618[label="vuz216",fontsize=16,color="green",shape="box"];4619[label="vuz217",fontsize=16,color="green",shape="box"];4620[label="vuz217",fontsize=16,color="green",shape="box"];4621[label="vuz216",fontsize=16,color="green",shape="box"];4622[label="vuz217",fontsize=16,color="green",shape="box"];4623[label="vuz216",fontsize=16,color="green",shape="box"];4624[label="vuz216",fontsize=16,color="green",shape="box"];4625[label="vuz217",fontsize=16,color="green",shape="box"];4677[label="Succ vuz224",fontsize=16,color="green",shape="box"];4678 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.97	4678[label="vuz222 * vuz223",fontsize=16,color="magenta"];4678 -> 4686[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4678 -> 4687[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4679 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.97	4679[label="vuz222 * vuz223",fontsize=16,color="magenta"];4679 -> 4688[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4679 -> 4689[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4680 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.97	4680[label="vuz222 * vuz223",fontsize=16,color="magenta"];4680 -> 4690[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4680 -> 4691[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4681 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.97	4681[label="vuz222 * vuz223",fontsize=16,color="magenta"];4681 -> 4692[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4681 -> 4693[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4682 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.97	4682[label="vuz222 * vuz223",fontsize=16,color="magenta"];4682 -> 4694[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4682 -> 4695[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4683[label="Succ vuz224",fontsize=16,color="green",shape="box"];4697 -> 1755[label="",style="dashed", color="red", weight=0];
84.19/49.97	4697[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (primDivNatS (Succ vuz230) (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS (Succ vuz230) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4697 -> 4702[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4697 -> 4703[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4697 -> 4704[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4697 -> 4705[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4718[label="vuz228",fontsize=16,color="green",shape="box"];4719[label="vuz229",fontsize=16,color="green",shape="box"];4720[label="vuz228",fontsize=16,color="green",shape="box"];4721[label="vuz229",fontsize=16,color="green",shape="box"];4722[label="vuz229",fontsize=16,color="green",shape="box"];4723[label="vuz228",fontsize=16,color="green",shape="box"];4724[label="vuz229",fontsize=16,color="green",shape="box"];4725[label="vuz228",fontsize=16,color="green",shape="box"];4726[label="vuz228",fontsize=16,color="green",shape="box"];4727[label="vuz229",fontsize=16,color="green",shape="box"];4686[label="vuz222",fontsize=16,color="green",shape="box"];4687[label="vuz223",fontsize=16,color="green",shape="box"];4688[label="vuz222",fontsize=16,color="green",shape="box"];4689[label="vuz223",fontsize=16,color="green",shape="box"];4690[label="vuz223",fontsize=16,color="green",shape="box"];4691[label="vuz222",fontsize=16,color="green",shape="box"];4692[label="vuz223",fontsize=16,color="green",shape="box"];4693[label="vuz222",fontsize=16,color="green",shape="box"];4694[label="vuz222",fontsize=16,color="green",shape="box"];4695[label="vuz223",fontsize=16,color="green",shape="box"];4702 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.97	4702[label="primDivNatS (Succ vuz230) (Succ (Succ Zero))",fontsize=16,color="magenta"];4702 -> 4711[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4703 -> 1222[label="",style="dashed", color="red", weight=0];
84.19/49.97	4703[label="primDivNatS (Succ vuz230) (Succ (Succ Zero))",fontsize=16,color="magenta"];4703 -> 4712[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4704[label="vuz228 * vuz229",fontsize=16,color="blue",shape="box"];4908[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4908[label="",style="solid", color="blue", weight=9];
84.19/49.97	4908 -> 4713[label="",style="solid", color="blue", weight=3];
84.19/49.97	4909[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4909[label="",style="solid", color="blue", weight=9];
84.19/49.97	4909 -> 4714[label="",style="solid", color="blue", weight=3];
84.19/49.97	4910[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4910[label="",style="solid", color="blue", weight=9];
84.19/49.97	4910 -> 4715[label="",style="solid", color="blue", weight=3];
84.19/49.97	4911[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4911[label="",style="solid", color="blue", weight=9];
84.19/49.97	4911 -> 4716[label="",style="solid", color="blue", weight=3];
84.19/49.97	4912[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4912[label="",style="solid", color="blue", weight=9];
84.19/49.97	4912 -> 4717[label="",style="solid", color="blue", weight=3];
84.19/49.97	4705[label="vuz228",fontsize=16,color="green",shape="box"];4711[label="Succ vuz230",fontsize=16,color="green",shape="box"];4712[label="Succ vuz230",fontsize=16,color="green",shape="box"];4713 -> 1024[label="",style="dashed", color="red", weight=0];
84.19/49.97	4713[label="vuz228 * vuz229",fontsize=16,color="magenta"];4713 -> 4728[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4713 -> 4729[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4714 -> 1041[label="",style="dashed", color="red", weight=0];
84.19/49.97	4714[label="vuz228 * vuz229",fontsize=16,color="magenta"];4714 -> 4730[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4714 -> 4731[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4715 -> 1051[label="",style="dashed", color="red", weight=0];
84.19/49.97	4715[label="vuz228 * vuz229",fontsize=16,color="magenta"];4715 -> 4732[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4715 -> 4733[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4716 -> 1059[label="",style="dashed", color="red", weight=0];
84.19/49.97	4716[label="vuz228 * vuz229",fontsize=16,color="magenta"];4716 -> 4734[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4716 -> 4735[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4717 -> 1069[label="",style="dashed", color="red", weight=0];
84.19/49.97	4717[label="vuz228 * vuz229",fontsize=16,color="magenta"];4717 -> 4736[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4717 -> 4737[label="",style="dashed", color="magenta", weight=3];
84.19/49.97	4728[label="vuz228",fontsize=16,color="green",shape="box"];4729[label="vuz229",fontsize=16,color="green",shape="box"];4730[label="vuz228",fontsize=16,color="green",shape="box"];4731[label="vuz229",fontsize=16,color="green",shape="box"];4732[label="vuz229",fontsize=16,color="green",shape="box"];4733[label="vuz228",fontsize=16,color="green",shape="box"];4734[label="vuz229",fontsize=16,color="green",shape="box"];4735[label="vuz228",fontsize=16,color="green",shape="box"];4736[label="vuz228",fontsize=16,color="green",shape="box"];4737[label="vuz229",fontsize=16,color="green",shape="box"];}
84.19/49.97	
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(12)
84.19/49.97	Complex Obligation (AND)
84.19/49.97	
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(13)
84.19/49.97	Obligation:
84.19/49.97	Q DP problem:
84.19/49.97	The TRS P consists of the following rules:
84.19/49.97	
84.19/49.97	   new_pr2F35(Succ(vuz4000), Succ(vuz5000), vuz3) -> new_pr2F35(vuz4000, vuz5000, vuz3)
84.19/49.97	
84.19/49.97	R is empty.
84.19/49.97	Q is empty.
84.19/49.97	We have to consider all minimal (P,Q,R)-chains.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(14) QDPSizeChangeProof (EQUIVALENT)
84.19/49.97	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. 
84.19/49.97	
84.19/49.97	From the DPs we obtained the following set of size-change graphs:
84.19/49.97	*new_pr2F35(Succ(vuz4000), Succ(vuz5000), vuz3) -> new_pr2F35(vuz4000, vuz5000, vuz3)
84.19/49.97	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
84.19/49.97	
84.19/49.97	
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(15)
84.19/49.97	YES
84.19/49.97	
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(16)
84.19/49.97	Obligation:
84.19/49.97	Q DP problem:
84.19/49.97	The TRS P consists of the following rules:
84.19/49.97	
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Zero, vuz205, h) -> new_pr2F0G10(new_sr(vuz204, vuz205, h), vuz204, new_primDivNatS1(Zero), new_primDivNatS1(Zero), h)
84.19/49.97	   new_pr2F0(vuz103, Zero, Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F31(Succ(vuz11500), new_sr4(vuz103, bb), Succ(vuz11500), vuz102, bb)
84.19/49.97	   new_pr2F32(vuz202, Neg(vuz2030), vuz204, vuz205, h) -> new_pr2F30(new_primPlusNat0(Succ(vuz202), vuz2030), vuz204, new_primPlusNat0(Succ(vuz202), vuz2030), vuz205, h)
84.19/49.97	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.19/49.97	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.19/49.97	   new_pr2F32(Zero, Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F31(Succ(vuz203000), vuz204, Succ(vuz203000), vuz205, h)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.19/49.97	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.19/49.97	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.19/49.97	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Zero), vuz205, h) -> new_pr2F(vuz204, Zero, new_fromInt, vuz205, h)
84.19/49.97	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.19/49.97	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.19/49.97	   new_pr2F2(vuz111, vuz113, Neg(vuz1160), vuz110, be) -> new_pr2F33(vuz1160, vuz113, vuz111, vuz110, be)
84.19/49.97	   new_pr2F0(vuz103, Zero, Pos(Zero), vuz102, bb) -> new_pr2F30(Zero, new_sr5(vuz103, bb), Zero, vuz102, bb)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.19/49.97	   new_pr2F3(Zero, Zero, vuz204, vuz205, h) -> new_pr2F30(Zero, vuz204, Zero, vuz205, h)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.19/49.97	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.19/49.97	   new_pr2F33(Zero, Zero, vuz103, vuz102, bb) -> new_pr2F30(Zero, new_sr5(vuz103, bb), Zero, vuz102, bb)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.19/49.97	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.19/49.97	   new_pr2F34(vuz214, Neg(vuz2150), vuz216, vuz217, bc) -> new_pr2F3(vuz2150, Succ(vuz214), vuz216, vuz217, bc)
84.19/49.97	   new_pr2F3(Zero, Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F31(Succ(vuz203000), vuz204, Succ(vuz203000), vuz205, h)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Zero, vuz217, bc) -> new_pr2F0G13(new_sr7(vuz216, vuz217, bc), vuz216, new_primDivNatS1(Zero), new_primDivNatS1(Zero), bc)
84.19/49.97	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F32(Zero, Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Zero, vuz204, Zero, vuz205, h)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.19/49.97	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.19/49.97	   new_pr2F0(vuz103, vuz105, Neg(vuz1150), vuz102, bb) -> new_pr2F30(new_primPlusNat0(vuz105, vuz1150), new_sr6(vuz103, bb), new_primPlusNat0(vuz105, vuz1150), vuz102, bb)
84.19/49.97	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.19/49.97	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Zero), vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.19/49.97	   new_pr2F33(Zero, Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F31(Succ(vuz11500), new_sr4(vuz103, bb), Succ(vuz11500), vuz102, bb)
84.19/49.97	
84.19/49.97	The TRS R consists of the following rules:
84.19/49.97	
84.19/49.97	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_primPlusNat0(Zero, Zero) -> Zero
84.19/49.97	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.19/49.97	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.19/49.97	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.19/49.97	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.19/49.97	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.19/49.97	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.19/49.97	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.19/49.97	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.19/49.97	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.19/49.97	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr13(vuz69, vuz20) -> error([])
84.19/49.97	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.19/49.97	   new_sr16(vuz73, vuz20, ce) -> error([])
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.19/49.97	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.19/49.97	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.19/49.97	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.19/49.97	   new_primMulNat0(Zero, Zero) -> Zero
84.19/49.97	   new_primDivNatS01(Zero) -> Zero
84.19/49.97	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_primDivNatS1(Zero) -> Zero
84.19/49.97	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_primDivNatS3 -> Zero
84.19/49.97	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.19/49.97	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr15(vuz72, vuz20) -> error([])
84.19/49.97	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.19/49.97	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.19/49.97	   new_sr14(vuz70, vuz20) -> error([])
84.19/49.97	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_primDivNatS2 -> new_primDivNatS3
84.19/49.97	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.19/49.97	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.19/49.97	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.19/49.97	
84.19/49.97	The set Q consists of the following terms:
84.19/49.97	
84.19/49.97	   new_sr1(x0, x1, ty_Integer)
84.19/49.97	   new_sr(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Int)
84.19/49.97	   new_sr12(Pos(x0), Neg(x1))
84.19/49.97	   new_sr12(Neg(x0), Pos(x1))
84.19/49.97	   new_sr7(x0, x1, ty_Int)
84.19/49.97	   new_sr9(x0, x1, ty_Float)
84.19/49.97	   new_sr5(x0, ty_Integer)
84.19/49.97	   new_sr10(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr4(x0, ty_Integer)
84.19/49.97	   new_sr0(x0, x1, ty_Integer)
84.19/49.97	   new_sr2(x0, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Float)
84.19/49.97	   new_sr12(Neg(x0), Neg(x1))
84.19/49.97	   new_sr(x0, x1, ty_Int)
84.19/49.97	   new_sr5(x0, ty_Int)
84.19/49.97	   new_primDivNatS1(Zero)
84.19/49.97	   new_sr6(x0, ty_Integer)
84.19/49.97	   new_sr11(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr3(x0, ty_Double)
84.19/49.97	   new_sr13(x0, x1)
84.19/49.97	   new_sr4(x0, ty_Float)
84.19/49.97	   new_sr0(x0, x1, ty_Int)
84.19/49.97	   new_primMulNat0(Zero, Zero)
84.19/49.97	   new_sr11(x0, ty_Float)
84.19/49.97	   new_sr20(x0)
84.19/49.97	   new_sr11(x0, ty_Double)
84.19/49.97	   new_sr3(x0, ty_Int)
84.19/49.97	   new_sr0(x0, x1, ty_Double)
84.19/49.97	   new_sr8(x0, x1, ty_Double)
84.19/49.97	   new_fromInt
84.19/49.97	   new_sr6(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS4(x0)
84.19/49.97	   new_sr4(x0, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Int)
84.19/49.97	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr2(x0, ty_Integer)
84.19/49.97	   new_sr21(x0, x1)
84.19/49.97	   new_primMulNat0(Zero, Succ(x0))
84.19/49.97	   new_primDivNatS2
84.19/49.97	   new_primDivNatS1(Succ(x0))
84.19/49.97	   new_sr(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr6(x0, ty_Double)
84.19/49.97	   new_sr12(Pos(x0), Pos(x1))
84.19/49.97	   new_sr8(x0, x1, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Float)
84.19/49.97	   new_sr7(x0, x1, ty_Integer)
84.19/49.97	   new_sr1(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS01(Succ(Zero))
84.19/49.97	   new_sr9(x0, x1, ty_Int)
84.19/49.97	   new_primPlusNat0(Succ(x0), Zero)
84.19/49.97	   new_sr3(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr8(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Float)
84.19/49.97	   new_sr17(x0)
84.19/49.97	   new_sr9(x0, x1, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Int)
84.19/49.97	   new_sr10(x0, ty_Double)
84.19/49.97	   new_sr5(x0, ty_Float)
84.19/49.97	   new_sr18(x0)
84.19/49.97	   new_sr4(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primPlusNat0(Zero, Succ(x0))
84.19/49.97	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primMulNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_sr16(x0, x1, x2)
84.19/49.97	   new_sr1(x0, x1, ty_Double)
84.19/49.97	   new_primDivNatS01(Succ(Succ(x0)))
84.19/49.97	   new_sr19(x0)
84.19/49.97	   new_primPlusNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_primDivNatS5(x0)
84.19/49.97	   new_sr5(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primDivNatS3
84.19/49.97	   new_sr(x0, x1, ty_Double)
84.19/49.97	   new_sr0(x0, x1, ty_Float)
84.19/49.97	   new_sr1(x0, x1, ty_Int)
84.19/49.97	   new_sr15(x0, x1)
84.19/49.97	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primDivNatS01(Zero)
84.19/49.97	   new_sr9(x0, x1, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Float)
84.19/49.97	   new_sr10(x0, ty_Integer)
84.19/49.97	   new_sr4(x0, ty_Int)
84.19/49.97	   new_sr2(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primMulNat0(Succ(x0), Zero)
84.19/49.97	   new_sr5(x0, ty_Double)
84.19/49.97	   new_primPlusNat0(Zero, Zero)
84.19/49.97	   new_sr8(x0, x1, ty_Int)
84.19/49.97	   new_sr14(x0, x1)
84.19/49.97	   new_sr3(x0, ty_Integer)
84.19/49.97	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr3(x0, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Int)
84.19/49.97	
84.19/49.97	We have to consider all minimal (P,Q,R)-chains.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(17) DependencyGraphProof (EQUIVALENT)
84.19/49.97	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 7 less nodes.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(18)
84.19/49.97	Obligation:
84.19/49.97	Q DP problem:
84.19/49.97	The TRS P consists of the following rules:
84.19/49.97	
84.19/49.97	   new_pr2F0(vuz103, Zero, Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F31(Succ(vuz11500), new_sr4(vuz103, bb), Succ(vuz11500), vuz102, bb)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.19/49.97	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.19/49.97	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Zero, vuz217, bc) -> new_pr2F0G13(new_sr7(vuz216, vuz217, bc), vuz216, new_primDivNatS1(Zero), new_primDivNatS1(Zero), bc)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F34(vuz214, Neg(vuz2150), vuz216, vuz217, bc) -> new_pr2F3(vuz2150, Succ(vuz214), vuz216, vuz217, bc)
84.19/49.97	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.19/49.97	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Zero), vuz205, h) -> new_pr2F(vuz204, Zero, new_fromInt, vuz205, h)
84.19/49.97	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.19/49.97	   new_pr2F32(vuz202, Neg(vuz2030), vuz204, vuz205, h) -> new_pr2F30(new_primPlusNat0(Succ(vuz202), vuz2030), vuz204, new_primPlusNat0(Succ(vuz202), vuz2030), vuz205, h)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Zero, vuz205, h) -> new_pr2F0G10(new_sr(vuz204, vuz205, h), vuz204, new_primDivNatS1(Zero), new_primDivNatS1(Zero), h)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.19/49.97	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.19/49.97	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.19/49.97	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.19/49.97	   new_pr2F33(Zero, Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F31(Succ(vuz11500), new_sr4(vuz103, bb), Succ(vuz11500), vuz102, bb)
84.19/49.97	   new_pr2F32(Zero, Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F31(Succ(vuz203000), vuz204, Succ(vuz203000), vuz205, h)
84.19/49.97	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.19/49.97	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.19/49.97	   new_pr2F3(Zero, Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F31(Succ(vuz203000), vuz204, Succ(vuz203000), vuz205, h)
84.19/49.97	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.19/49.97	
84.19/49.97	The TRS R consists of the following rules:
84.19/49.97	
84.19/49.97	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_primPlusNat0(Zero, Zero) -> Zero
84.19/49.97	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.19/49.97	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.19/49.97	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.19/49.97	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.19/49.97	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.19/49.97	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.19/49.97	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.19/49.97	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.19/49.97	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.19/49.97	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr13(vuz69, vuz20) -> error([])
84.19/49.97	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.19/49.97	   new_sr16(vuz73, vuz20, ce) -> error([])
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.19/49.97	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.19/49.97	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.19/49.97	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.19/49.97	   new_primMulNat0(Zero, Zero) -> Zero
84.19/49.97	   new_primDivNatS01(Zero) -> Zero
84.19/49.97	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_primDivNatS1(Zero) -> Zero
84.19/49.97	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_primDivNatS3 -> Zero
84.19/49.97	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.19/49.97	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr15(vuz72, vuz20) -> error([])
84.19/49.97	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.19/49.97	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.19/49.97	   new_sr14(vuz70, vuz20) -> error([])
84.19/49.97	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_primDivNatS2 -> new_primDivNatS3
84.19/49.97	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.19/49.97	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.19/49.97	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.19/49.97	
84.19/49.97	The set Q consists of the following terms:
84.19/49.97	
84.19/49.97	   new_sr1(x0, x1, ty_Integer)
84.19/49.97	   new_sr(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Int)
84.19/49.97	   new_sr12(Pos(x0), Neg(x1))
84.19/49.97	   new_sr12(Neg(x0), Pos(x1))
84.19/49.97	   new_sr7(x0, x1, ty_Int)
84.19/49.97	   new_sr9(x0, x1, ty_Float)
84.19/49.97	   new_sr5(x0, ty_Integer)
84.19/49.97	   new_sr10(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr4(x0, ty_Integer)
84.19/49.97	   new_sr0(x0, x1, ty_Integer)
84.19/49.97	   new_sr2(x0, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Float)
84.19/49.97	   new_sr12(Neg(x0), Neg(x1))
84.19/49.97	   new_sr(x0, x1, ty_Int)
84.19/49.97	   new_sr5(x0, ty_Int)
84.19/49.97	   new_primDivNatS1(Zero)
84.19/49.97	   new_sr6(x0, ty_Integer)
84.19/49.97	   new_sr11(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr3(x0, ty_Double)
84.19/49.97	   new_sr13(x0, x1)
84.19/49.97	   new_sr4(x0, ty_Float)
84.19/49.97	   new_sr0(x0, x1, ty_Int)
84.19/49.97	   new_primMulNat0(Zero, Zero)
84.19/49.97	   new_sr11(x0, ty_Float)
84.19/49.97	   new_sr20(x0)
84.19/49.97	   new_sr11(x0, ty_Double)
84.19/49.97	   new_sr3(x0, ty_Int)
84.19/49.97	   new_sr0(x0, x1, ty_Double)
84.19/49.97	   new_sr8(x0, x1, ty_Double)
84.19/49.97	   new_fromInt
84.19/49.97	   new_sr6(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS4(x0)
84.19/49.97	   new_sr4(x0, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Int)
84.19/49.97	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr2(x0, ty_Integer)
84.19/49.97	   new_sr21(x0, x1)
84.19/49.97	   new_primMulNat0(Zero, Succ(x0))
84.19/49.97	   new_primDivNatS2
84.19/49.97	   new_primDivNatS1(Succ(x0))
84.19/49.97	   new_sr(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr6(x0, ty_Double)
84.19/49.97	   new_sr12(Pos(x0), Pos(x1))
84.19/49.97	   new_sr8(x0, x1, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Float)
84.19/49.97	   new_sr7(x0, x1, ty_Integer)
84.19/49.97	   new_sr1(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS01(Succ(Zero))
84.19/49.97	   new_sr9(x0, x1, ty_Int)
84.19/49.97	   new_primPlusNat0(Succ(x0), Zero)
84.19/49.97	   new_sr3(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr8(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Float)
84.19/49.97	   new_sr17(x0)
84.19/49.97	   new_sr9(x0, x1, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Int)
84.19/49.97	   new_sr10(x0, ty_Double)
84.19/49.97	   new_sr5(x0, ty_Float)
84.19/49.97	   new_sr18(x0)
84.19/49.97	   new_sr4(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primPlusNat0(Zero, Succ(x0))
84.19/49.97	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primMulNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_sr16(x0, x1, x2)
84.19/49.97	   new_sr1(x0, x1, ty_Double)
84.19/49.97	   new_primDivNatS01(Succ(Succ(x0)))
84.19/49.97	   new_sr19(x0)
84.19/49.97	   new_primPlusNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_primDivNatS5(x0)
84.19/49.97	   new_sr5(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primDivNatS3
84.19/49.97	   new_sr(x0, x1, ty_Double)
84.19/49.97	   new_sr0(x0, x1, ty_Float)
84.19/49.97	   new_sr1(x0, x1, ty_Int)
84.19/49.97	   new_sr15(x0, x1)
84.19/49.97	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primDivNatS01(Zero)
84.19/49.97	   new_sr9(x0, x1, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Float)
84.19/49.97	   new_sr10(x0, ty_Integer)
84.19/49.97	   new_sr4(x0, ty_Int)
84.19/49.97	   new_sr2(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primMulNat0(Succ(x0), Zero)
84.19/49.97	   new_sr5(x0, ty_Double)
84.19/49.97	   new_primPlusNat0(Zero, Zero)
84.19/49.97	   new_sr8(x0, x1, ty_Int)
84.19/49.97	   new_sr14(x0, x1)
84.19/49.97	   new_sr3(x0, ty_Integer)
84.19/49.97	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr3(x0, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Int)
84.19/49.97	
84.19/49.97	We have to consider all minimal (P,Q,R)-chains.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(19) QDPOrderProof (EQUIVALENT)
84.19/49.97	We use the reduction pair processor [LPAR04,JAR06].
84.19/49.97	
84.19/49.97	
84.19/49.97	The following pairs can be oriented strictly and are deleted.
84.19/49.97	
84.19/49.97	   new_pr2F34(vuz214, Neg(vuz2150), vuz216, vuz217, bc) -> new_pr2F3(vuz2150, Succ(vuz214), vuz216, vuz217, bc)
84.19/49.97	   new_pr2F32(vuz202, Neg(vuz2030), vuz204, vuz205, h) -> new_pr2F30(new_primPlusNat0(Succ(vuz202), vuz2030), vuz204, new_primPlusNat0(Succ(vuz202), vuz2030), vuz205, h)
84.19/49.97	The remaining pairs can at least be oriented weakly.
84.19/49.97	Used ordering:  Polynomial interpretation [POLO]:
84.19/49.97	
84.19/49.97	   POL(Neg(x_1)) = 1
84.19/49.97	   POL(Pos(x_1)) = 0
84.19/49.97	   POL(Succ(x_1)) = 0
84.19/49.97	   POL(Zero) = 0
84.19/49.97	   POL([]) = 1
84.19/49.97	   POL(app(x_1, x_2)) = 1 + x_1 + x_2
84.19/49.97	   POL(error(x_1)) = 1 + x_1
84.19/49.97	   POL(new_fromInt) = 0
84.19/49.97	   POL(new_pr2F(x_1, x_2, x_3, x_4, x_5)) = x_3 + x_5
84.19/49.97	   POL(new_pr2F0(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G1(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G10(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G11(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G12(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G13(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G14(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F1(x_1, x_2, x_3, x_4, x_5)) = x_3 + x_5
84.19/49.97	   POL(new_pr2F2(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F3(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F30(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F31(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F32(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_5
84.19/49.97	   POL(new_pr2F33(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F34(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_5
84.19/49.97	   POL(new_primDivNatS01(x_1)) = 0
84.19/49.97	   POL(new_primDivNatS1(x_1)) = 0
84.19/49.97	   POL(new_primDivNatS2) = 1
84.19/49.97	   POL(new_primDivNatS3) = 1
84.19/49.97	   POL(new_primDivNatS4(x_1)) = 1 + x_1
84.19/49.97	   POL(new_primDivNatS5(x_1)) = 1 + x_1
84.19/49.97	   POL(new_primMulNat0(x_1, x_2)) = 0
84.19/49.97	   POL(new_primPlusNat0(x_1, x_2)) = 0
84.19/49.97	   POL(new_sr(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(new_sr0(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(new_sr1(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(new_sr10(x_1, x_2)) = x_1 + x_2
84.19/49.97	   POL(new_sr11(x_1, x_2)) = 1 + x_1 + x_2
84.19/49.97	   POL(new_sr12(x_1, x_2)) = 0
84.19/49.97	   POL(new_sr13(x_1, x_2)) = 1 + x_1
84.19/49.97	   POL(new_sr14(x_1, x_2)) = 1 + x_1
84.19/49.97	   POL(new_sr15(x_1, x_2)) = 1 + x_1
84.19/49.97	   POL(new_sr16(x_1, x_2, x_3)) = 1 + x_1
84.19/49.97	   POL(new_sr17(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr18(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr19(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr2(x_1, x_2)) = x_1 + x_2
84.19/49.97	   POL(new_sr20(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr21(x_1, x_2)) = 1 + x_1 + x_2
84.19/49.97	   POL(new_sr3(x_1, x_2)) = 1 + x_1 + x_2
84.19/49.97	   POL(new_sr4(x_1, x_2)) = 1 + x_1 + x_2
84.19/49.97	   POL(new_sr7(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(new_sr8(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(new_sr9(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(ty_Double) = 1
84.19/49.97	   POL(ty_Float) = 1
84.19/49.97	   POL(ty_Int) = 1
84.19/49.97	   POL(ty_Integer) = 1
84.19/49.97	   POL(ty_Ratio) = 1
84.19/49.97	
84.19/49.97	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
84.19/49.97	
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	
84.19/49.97	
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(20)
84.19/49.97	Obligation:
84.19/49.97	Q DP problem:
84.19/49.97	The TRS P consists of the following rules:
84.19/49.97	
84.19/49.97	   new_pr2F0(vuz103, Zero, Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F31(Succ(vuz11500), new_sr4(vuz103, bb), Succ(vuz11500), vuz102, bb)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.19/49.97	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.19/49.97	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Zero, vuz217, bc) -> new_pr2F0G13(new_sr7(vuz216, vuz217, bc), vuz216, new_primDivNatS1(Zero), new_primDivNatS1(Zero), bc)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.19/49.97	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Zero), vuz205, h) -> new_pr2F(vuz204, Zero, new_fromInt, vuz205, h)
84.19/49.97	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Zero, vuz205, h) -> new_pr2F0G10(new_sr(vuz204, vuz205, h), vuz204, new_primDivNatS1(Zero), new_primDivNatS1(Zero), h)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.19/49.97	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.19/49.97	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.19/49.97	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.19/49.97	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.19/49.97	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.19/49.97	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.19/49.97	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.19/49.97	   new_pr2F33(Zero, Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F31(Succ(vuz11500), new_sr4(vuz103, bb), Succ(vuz11500), vuz102, bb)
84.19/49.97	   new_pr2F32(Zero, Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F31(Succ(vuz203000), vuz204, Succ(vuz203000), vuz205, h)
84.19/49.97	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.19/49.97	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.19/49.97	   new_pr2F3(Zero, Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F31(Succ(vuz203000), vuz204, Succ(vuz203000), vuz205, h)
84.19/49.97	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.19/49.97	
84.19/49.97	The TRS R consists of the following rules:
84.19/49.97	
84.19/49.97	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_primPlusNat0(Zero, Zero) -> Zero
84.19/49.97	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.19/49.97	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.19/49.97	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.19/49.97	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.19/49.97	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.19/49.97	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.19/49.97	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.19/49.97	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.19/49.97	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.19/49.97	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr13(vuz69, vuz20) -> error([])
84.19/49.97	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.19/49.97	   new_sr16(vuz73, vuz20, ce) -> error([])
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.19/49.97	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.19/49.97	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.19/49.97	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.19/49.97	   new_primMulNat0(Zero, Zero) -> Zero
84.19/49.97	   new_primDivNatS01(Zero) -> Zero
84.19/49.97	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_primDivNatS1(Zero) -> Zero
84.19/49.97	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_primDivNatS3 -> Zero
84.19/49.97	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.19/49.97	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr15(vuz72, vuz20) -> error([])
84.19/49.97	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.19/49.97	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.19/49.97	   new_sr14(vuz70, vuz20) -> error([])
84.19/49.97	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_primDivNatS2 -> new_primDivNatS3
84.19/49.97	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.19/49.97	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.19/49.97	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.19/49.97	
84.19/49.97	The set Q consists of the following terms:
84.19/49.97	
84.19/49.97	   new_sr1(x0, x1, ty_Integer)
84.19/49.97	   new_sr(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Int)
84.19/49.97	   new_sr12(Pos(x0), Neg(x1))
84.19/49.97	   new_sr12(Neg(x0), Pos(x1))
84.19/49.97	   new_sr7(x0, x1, ty_Int)
84.19/49.97	   new_sr9(x0, x1, ty_Float)
84.19/49.97	   new_sr5(x0, ty_Integer)
84.19/49.97	   new_sr10(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr4(x0, ty_Integer)
84.19/49.97	   new_sr0(x0, x1, ty_Integer)
84.19/49.97	   new_sr2(x0, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Float)
84.19/49.97	   new_sr12(Neg(x0), Neg(x1))
84.19/49.97	   new_sr(x0, x1, ty_Int)
84.19/49.97	   new_sr5(x0, ty_Int)
84.19/49.97	   new_primDivNatS1(Zero)
84.19/49.97	   new_sr6(x0, ty_Integer)
84.19/49.97	   new_sr11(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr3(x0, ty_Double)
84.19/49.97	   new_sr13(x0, x1)
84.19/49.97	   new_sr4(x0, ty_Float)
84.19/49.97	   new_sr0(x0, x1, ty_Int)
84.19/49.97	   new_primMulNat0(Zero, Zero)
84.19/49.97	   new_sr11(x0, ty_Float)
84.19/49.97	   new_sr20(x0)
84.19/49.97	   new_sr11(x0, ty_Double)
84.19/49.97	   new_sr3(x0, ty_Int)
84.19/49.97	   new_sr0(x0, x1, ty_Double)
84.19/49.97	   new_sr8(x0, x1, ty_Double)
84.19/49.97	   new_fromInt
84.19/49.97	   new_sr6(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS4(x0)
84.19/49.97	   new_sr4(x0, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Int)
84.19/49.97	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr2(x0, ty_Integer)
84.19/49.97	   new_sr21(x0, x1)
84.19/49.97	   new_primMulNat0(Zero, Succ(x0))
84.19/49.97	   new_primDivNatS2
84.19/49.97	   new_primDivNatS1(Succ(x0))
84.19/49.97	   new_sr(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr6(x0, ty_Double)
84.19/49.97	   new_sr12(Pos(x0), Pos(x1))
84.19/49.97	   new_sr8(x0, x1, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Float)
84.19/49.97	   new_sr7(x0, x1, ty_Integer)
84.19/49.97	   new_sr1(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS01(Succ(Zero))
84.19/49.97	   new_sr9(x0, x1, ty_Int)
84.19/49.97	   new_primPlusNat0(Succ(x0), Zero)
84.19/49.97	   new_sr3(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr8(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Float)
84.19/49.97	   new_sr17(x0)
84.19/49.97	   new_sr9(x0, x1, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Int)
84.19/49.97	   new_sr10(x0, ty_Double)
84.19/49.97	   new_sr5(x0, ty_Float)
84.19/49.97	   new_sr18(x0)
84.19/49.97	   new_sr4(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primPlusNat0(Zero, Succ(x0))
84.19/49.97	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primMulNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_sr16(x0, x1, x2)
84.19/49.97	   new_sr1(x0, x1, ty_Double)
84.19/49.97	   new_primDivNatS01(Succ(Succ(x0)))
84.19/49.97	   new_sr19(x0)
84.19/49.97	   new_primPlusNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_primDivNatS5(x0)
84.19/49.97	   new_sr5(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primDivNatS3
84.19/49.97	   new_sr(x0, x1, ty_Double)
84.19/49.97	   new_sr0(x0, x1, ty_Float)
84.19/49.97	   new_sr1(x0, x1, ty_Int)
84.19/49.97	   new_sr15(x0, x1)
84.19/49.97	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primDivNatS01(Zero)
84.19/49.97	   new_sr9(x0, x1, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Float)
84.19/49.97	   new_sr10(x0, ty_Integer)
84.19/49.97	   new_sr4(x0, ty_Int)
84.19/49.97	   new_sr2(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primMulNat0(Succ(x0), Zero)
84.19/49.97	   new_sr5(x0, ty_Double)
84.19/49.97	   new_primPlusNat0(Zero, Zero)
84.19/49.97	   new_sr8(x0, x1, ty_Int)
84.19/49.97	   new_sr14(x0, x1)
84.19/49.97	   new_sr3(x0, ty_Integer)
84.19/49.97	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr3(x0, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Int)
84.19/49.97	
84.19/49.97	We have to consider all minimal (P,Q,R)-chains.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(21) DependencyGraphProof (EQUIVALENT)
84.19/49.97	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 5 less nodes.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(22)
84.19/49.97	Complex Obligation (AND)
84.19/49.97	
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(23)
84.19/49.97	Obligation:
84.19/49.97	Q DP problem:
84.19/49.97	The TRS P consists of the following rules:
84.19/49.97	
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.19/49.97	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.19/49.97	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Zero, vuz217, bc) -> new_pr2F0G13(new_sr7(vuz216, vuz217, bc), vuz216, new_primDivNatS1(Zero), new_primDivNatS1(Zero), bc)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	
84.19/49.97	The TRS R consists of the following rules:
84.19/49.97	
84.19/49.97	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_primPlusNat0(Zero, Zero) -> Zero
84.19/49.97	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.19/49.97	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.19/49.97	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.19/49.97	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.19/49.97	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.19/49.97	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.19/49.97	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.19/49.97	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.19/49.97	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.19/49.97	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr13(vuz69, vuz20) -> error([])
84.19/49.97	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.19/49.97	   new_sr16(vuz73, vuz20, ce) -> error([])
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.19/49.97	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.19/49.97	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.19/49.97	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.19/49.97	   new_primMulNat0(Zero, Zero) -> Zero
84.19/49.97	   new_primDivNatS01(Zero) -> Zero
84.19/49.97	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_primDivNatS1(Zero) -> Zero
84.19/49.97	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_primDivNatS3 -> Zero
84.19/49.97	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.19/49.97	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr15(vuz72, vuz20) -> error([])
84.19/49.97	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.19/49.97	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.19/49.97	   new_sr14(vuz70, vuz20) -> error([])
84.19/49.97	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_primDivNatS2 -> new_primDivNatS3
84.19/49.97	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.19/49.97	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.19/49.97	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.19/49.97	
84.19/49.97	The set Q consists of the following terms:
84.19/49.97	
84.19/49.97	   new_sr1(x0, x1, ty_Integer)
84.19/49.97	   new_sr(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Int)
84.19/49.97	   new_sr12(Pos(x0), Neg(x1))
84.19/49.97	   new_sr12(Neg(x0), Pos(x1))
84.19/49.97	   new_sr7(x0, x1, ty_Int)
84.19/49.97	   new_sr9(x0, x1, ty_Float)
84.19/49.97	   new_sr5(x0, ty_Integer)
84.19/49.97	   new_sr10(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr4(x0, ty_Integer)
84.19/49.97	   new_sr0(x0, x1, ty_Integer)
84.19/49.97	   new_sr2(x0, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Float)
84.19/49.97	   new_sr12(Neg(x0), Neg(x1))
84.19/49.97	   new_sr(x0, x1, ty_Int)
84.19/49.97	   new_sr5(x0, ty_Int)
84.19/49.97	   new_primDivNatS1(Zero)
84.19/49.97	   new_sr6(x0, ty_Integer)
84.19/49.97	   new_sr11(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr3(x0, ty_Double)
84.19/49.97	   new_sr13(x0, x1)
84.19/49.97	   new_sr4(x0, ty_Float)
84.19/49.97	   new_sr0(x0, x1, ty_Int)
84.19/49.97	   new_primMulNat0(Zero, Zero)
84.19/49.97	   new_sr11(x0, ty_Float)
84.19/49.97	   new_sr20(x0)
84.19/49.97	   new_sr11(x0, ty_Double)
84.19/49.97	   new_sr3(x0, ty_Int)
84.19/49.97	   new_sr0(x0, x1, ty_Double)
84.19/49.97	   new_sr8(x0, x1, ty_Double)
84.19/49.97	   new_fromInt
84.19/49.97	   new_sr6(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS4(x0)
84.19/49.97	   new_sr4(x0, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Int)
84.19/49.97	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr2(x0, ty_Integer)
84.19/49.97	   new_sr21(x0, x1)
84.19/49.97	   new_primMulNat0(Zero, Succ(x0))
84.19/49.97	   new_primDivNatS2
84.19/49.97	   new_primDivNatS1(Succ(x0))
84.19/49.97	   new_sr(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr6(x0, ty_Double)
84.19/49.97	   new_sr12(Pos(x0), Pos(x1))
84.19/49.97	   new_sr8(x0, x1, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Float)
84.19/49.97	   new_sr7(x0, x1, ty_Integer)
84.19/49.97	   new_sr1(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS01(Succ(Zero))
84.19/49.97	   new_sr9(x0, x1, ty_Int)
84.19/49.97	   new_primPlusNat0(Succ(x0), Zero)
84.19/49.97	   new_sr3(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr8(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Float)
84.19/49.97	   new_sr17(x0)
84.19/49.97	   new_sr9(x0, x1, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Int)
84.19/49.97	   new_sr10(x0, ty_Double)
84.19/49.97	   new_sr5(x0, ty_Float)
84.19/49.97	   new_sr18(x0)
84.19/49.97	   new_sr4(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primPlusNat0(Zero, Succ(x0))
84.19/49.97	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primMulNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_sr16(x0, x1, x2)
84.19/49.97	   new_sr1(x0, x1, ty_Double)
84.19/49.97	   new_primDivNatS01(Succ(Succ(x0)))
84.19/49.97	   new_sr19(x0)
84.19/49.97	   new_primPlusNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_primDivNatS5(x0)
84.19/49.97	   new_sr5(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primDivNatS3
84.19/49.97	   new_sr(x0, x1, ty_Double)
84.19/49.97	   new_sr0(x0, x1, ty_Float)
84.19/49.97	   new_sr1(x0, x1, ty_Int)
84.19/49.97	   new_sr15(x0, x1)
84.19/49.97	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primDivNatS01(Zero)
84.19/49.97	   new_sr9(x0, x1, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Float)
84.19/49.97	   new_sr10(x0, ty_Integer)
84.19/49.97	   new_sr4(x0, ty_Int)
84.19/49.97	   new_sr2(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primMulNat0(Succ(x0), Zero)
84.19/49.97	   new_sr5(x0, ty_Double)
84.19/49.97	   new_primPlusNat0(Zero, Zero)
84.19/49.97	   new_sr8(x0, x1, ty_Int)
84.19/49.97	   new_sr14(x0, x1)
84.19/49.97	   new_sr3(x0, ty_Integer)
84.19/49.97	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr3(x0, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Int)
84.19/49.97	
84.19/49.97	We have to consider all minimal (P,Q,R)-chains.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(24) QDPOrderProof (EQUIVALENT)
84.19/49.97	We use the reduction pair processor [LPAR04,JAR06].
84.19/49.97	
84.19/49.97	
84.19/49.97	The following pairs can be oriented strictly and are deleted.
84.19/49.97	
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Zero, vuz217, bc) -> new_pr2F0G13(new_sr7(vuz216, vuz217, bc), vuz216, new_primDivNatS1(Zero), new_primDivNatS1(Zero), bc)
84.19/49.97	The remaining pairs can at least be oriented weakly.
84.19/49.97	Used ordering:  Polynomial interpretation [POLO]:
84.19/49.97	
84.19/49.97	   POL(Neg(x_1)) = 0
84.19/49.97	   POL(Pos(x_1)) = x_1
84.19/49.97	   POL(Succ(x_1)) = 0
84.19/49.97	   POL(Zero) = 1
84.19/49.97	   POL([]) = 1
84.19/49.97	   POL(app(x_1, x_2)) = 1 + x_1 + x_2
84.19/49.97	   POL(error(x_1)) = 1 + x_1
84.19/49.97	   POL(new_fromInt) = 0
84.19/49.97	   POL(new_pr2F0G12(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G13(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F0G14(x_1, x_2, x_3, x_4, x_5)) = x_5
84.19/49.97	   POL(new_pr2F1(x_1, x_2, x_3, x_4, x_5)) = x_3 + x_5
84.19/49.97	   POL(new_pr2F2(x_1, x_2, x_3, x_4, x_5)) = x_3 + x_5
84.19/49.97	   POL(new_pr2F31(x_1, x_2, x_3, x_4, x_5)) = x_3 + x_5
84.19/49.97	   POL(new_pr2F34(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_5
84.19/49.97	   POL(new_primDivNatS01(x_1)) = 0
84.19/49.97	   POL(new_primDivNatS1(x_1)) = 0
84.19/49.97	   POL(new_primDivNatS2) = 1
84.19/49.97	   POL(new_primDivNatS3) = 1
84.19/49.97	   POL(new_primDivNatS4(x_1)) = 1 + x_1
84.19/49.97	   POL(new_primDivNatS5(x_1)) = 1 + x_1
84.19/49.97	   POL(new_primMulNat0(x_1, x_2)) = 0
84.19/49.97	   POL(new_primPlusNat0(x_1, x_2)) = x_2
84.19/49.97	   POL(new_sr10(x_1, x_2)) = x_1 + x_2
84.19/49.97	   POL(new_sr11(x_1, x_2)) = 1 + x_1 + x_2
84.19/49.97	   POL(new_sr12(x_1, x_2)) = 0
84.19/49.97	   POL(new_sr13(x_1, x_2)) = 1 + x_2
84.19/49.97	   POL(new_sr14(x_1, x_2)) = 1 + x_2
84.19/49.97	   POL(new_sr15(x_1, x_2)) = 1 + x_2
84.19/49.97	   POL(new_sr16(x_1, x_2, x_3)) = 1 + x_2
84.19/49.97	   POL(new_sr17(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr18(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr19(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr20(x_1)) = 1 + x_1
84.19/49.97	   POL(new_sr21(x_1, x_2)) = 1 + x_1
84.19/49.97	   POL(new_sr7(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(new_sr8(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(new_sr9(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.19/49.97	   POL(ty_Double) = 1
84.19/49.97	   POL(ty_Float) = 1
84.19/49.97	   POL(ty_Int) = 1
84.19/49.97	   POL(ty_Integer) = 1
84.19/49.97	   POL(ty_Ratio) = 1
84.19/49.97	
84.19/49.97	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
84.19/49.97	
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.19/49.97	   new_primPlusNat0(Zero, Zero) -> Zero
84.19/49.97	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.19/49.97	
84.19/49.97	
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(25)
84.19/49.97	Obligation:
84.19/49.97	Q DP problem:
84.19/49.97	The TRS P consists of the following rules:
84.19/49.97	
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.19/49.97	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.19/49.97	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	
84.19/49.97	The TRS R consists of the following rules:
84.19/49.97	
84.19/49.97	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_primPlusNat0(Zero, Zero) -> Zero
84.19/49.97	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.19/49.97	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.19/49.97	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.19/49.97	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.19/49.97	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.19/49.97	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.19/49.97	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.19/49.97	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.19/49.97	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.19/49.97	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr13(vuz69, vuz20) -> error([])
84.19/49.97	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.19/49.97	   new_sr16(vuz73, vuz20, ce) -> error([])
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.19/49.97	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.19/49.97	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.19/49.97	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.19/49.97	   new_primMulNat0(Zero, Zero) -> Zero
84.19/49.97	   new_primDivNatS01(Zero) -> Zero
84.19/49.97	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_primDivNatS1(Zero) -> Zero
84.19/49.97	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_primDivNatS3 -> Zero
84.19/49.97	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.19/49.97	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr15(vuz72, vuz20) -> error([])
84.19/49.97	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.19/49.97	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.19/49.97	   new_sr14(vuz70, vuz20) -> error([])
84.19/49.97	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_primDivNatS2 -> new_primDivNatS3
84.19/49.97	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.19/49.97	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.19/49.97	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.19/49.97	
84.19/49.97	The set Q consists of the following terms:
84.19/49.97	
84.19/49.97	   new_sr1(x0, x1, ty_Integer)
84.19/49.97	   new_sr(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Int)
84.19/49.97	   new_sr12(Pos(x0), Neg(x1))
84.19/49.97	   new_sr12(Neg(x0), Pos(x1))
84.19/49.97	   new_sr7(x0, x1, ty_Int)
84.19/49.97	   new_sr9(x0, x1, ty_Float)
84.19/49.97	   new_sr5(x0, ty_Integer)
84.19/49.97	   new_sr10(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr4(x0, ty_Integer)
84.19/49.97	   new_sr0(x0, x1, ty_Integer)
84.19/49.97	   new_sr2(x0, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Float)
84.19/49.97	   new_sr12(Neg(x0), Neg(x1))
84.19/49.97	   new_sr(x0, x1, ty_Int)
84.19/49.97	   new_sr5(x0, ty_Int)
84.19/49.97	   new_primDivNatS1(Zero)
84.19/49.97	   new_sr6(x0, ty_Integer)
84.19/49.97	   new_sr11(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr3(x0, ty_Double)
84.19/49.97	   new_sr13(x0, x1)
84.19/49.97	   new_sr4(x0, ty_Float)
84.19/49.97	   new_sr0(x0, x1, ty_Int)
84.19/49.97	   new_primMulNat0(Zero, Zero)
84.19/49.97	   new_sr11(x0, ty_Float)
84.19/49.97	   new_sr20(x0)
84.19/49.97	   new_sr11(x0, ty_Double)
84.19/49.97	   new_sr3(x0, ty_Int)
84.19/49.97	   new_sr0(x0, x1, ty_Double)
84.19/49.97	   new_sr8(x0, x1, ty_Double)
84.19/49.97	   new_fromInt
84.19/49.97	   new_sr6(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS4(x0)
84.19/49.97	   new_sr4(x0, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Int)
84.19/49.97	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr2(x0, ty_Integer)
84.19/49.97	   new_sr21(x0, x1)
84.19/49.97	   new_primMulNat0(Zero, Succ(x0))
84.19/49.97	   new_primDivNatS2
84.19/49.97	   new_primDivNatS1(Succ(x0))
84.19/49.97	   new_sr(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr6(x0, ty_Double)
84.19/49.97	   new_sr12(Pos(x0), Pos(x1))
84.19/49.97	   new_sr8(x0, x1, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Float)
84.19/49.97	   new_sr7(x0, x1, ty_Integer)
84.19/49.97	   new_sr1(x0, x1, ty_Float)
84.19/49.97	   new_primDivNatS01(Succ(Zero))
84.19/49.97	   new_sr9(x0, x1, ty_Int)
84.19/49.97	   new_primPlusNat0(Succ(x0), Zero)
84.19/49.97	   new_sr3(x0, app(ty_Ratio, x1))
84.19/49.97	   new_sr8(x0, x1, ty_Integer)
84.19/49.97	   new_sr6(x0, ty_Float)
84.19/49.97	   new_sr17(x0)
84.19/49.97	   new_sr9(x0, x1, ty_Integer)
84.19/49.97	   new_sr7(x0, x1, ty_Double)
84.19/49.97	   new_sr2(x0, ty_Int)
84.19/49.97	   new_sr10(x0, ty_Double)
84.19/49.97	   new_sr5(x0, ty_Float)
84.19/49.97	   new_sr18(x0)
84.19/49.97	   new_sr4(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primPlusNat0(Zero, Succ(x0))
84.19/49.97	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primMulNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_sr16(x0, x1, x2)
84.19/49.97	   new_sr1(x0, x1, ty_Double)
84.19/49.97	   new_primDivNatS01(Succ(Succ(x0)))
84.19/49.97	   new_sr19(x0)
84.19/49.97	   new_primPlusNat0(Succ(x0), Succ(x1))
84.19/49.97	   new_primDivNatS5(x0)
84.19/49.97	   new_sr5(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primDivNatS3
84.19/49.97	   new_sr(x0, x1, ty_Double)
84.19/49.97	   new_sr0(x0, x1, ty_Float)
84.19/49.97	   new_sr1(x0, x1, ty_Int)
84.19/49.97	   new_sr15(x0, x1)
84.19/49.97	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_primDivNatS01(Zero)
84.19/49.97	   new_sr9(x0, x1, ty_Double)
84.19/49.97	   new_sr10(x0, ty_Float)
84.19/49.97	   new_sr10(x0, ty_Integer)
84.19/49.97	   new_sr4(x0, ty_Int)
84.19/49.97	   new_sr2(x0, app(ty_Ratio, x1))
84.19/49.97	   new_primMulNat0(Succ(x0), Zero)
84.19/49.97	   new_sr5(x0, ty_Double)
84.19/49.97	   new_primPlusNat0(Zero, Zero)
84.19/49.97	   new_sr8(x0, x1, ty_Int)
84.19/49.97	   new_sr14(x0, x1)
84.19/49.97	   new_sr3(x0, ty_Integer)
84.19/49.97	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.19/49.97	   new_sr3(x0, ty_Float)
84.19/49.97	   new_sr11(x0, ty_Int)
84.19/49.97	
84.19/49.97	We have to consider all minimal (P,Q,R)-chains.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(26) MNOCProof (EQUIVALENT)
84.19/49.97	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(27)
84.19/49.97	Obligation:
84.19/49.97	Q DP problem:
84.19/49.97	The TRS P consists of the following rules:
84.19/49.97	
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.19/49.97	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.19/49.97	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.19/49.97	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.19/49.97	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.19/49.97	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.19/49.97	
84.19/49.97	The TRS R consists of the following rules:
84.19/49.97	
84.19/49.97	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_primPlusNat0(Zero, Zero) -> Zero
84.19/49.97	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.19/49.97	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.19/49.97	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.19/49.97	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.19/49.97	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.19/49.97	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.19/49.97	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.19/49.97	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.19/49.97	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.19/49.97	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.19/49.97	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.19/49.97	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr13(vuz69, vuz20) -> error([])
84.19/49.97	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.19/49.97	   new_sr16(vuz73, vuz20, ce) -> error([])
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.19/49.97	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.19/49.97	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.19/49.97	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.19/49.97	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.19/49.97	   new_primMulNat0(Zero, Zero) -> Zero
84.19/49.97	   new_primDivNatS01(Zero) -> Zero
84.19/49.97	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_primDivNatS1(Zero) -> Zero
84.19/49.97	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.19/49.97	   new_primDivNatS3 -> Zero
84.19/49.97	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.19/49.97	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.19/49.97	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr15(vuz72, vuz20) -> error([])
84.19/49.97	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.19/49.97	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_fromInt -> Pos(Succ(Zero))
84.19/49.97	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.19/49.97	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.19/49.97	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.19/49.97	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.19/49.97	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.19/49.97	   new_sr14(vuz70, vuz20) -> error([])
84.19/49.97	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.19/49.97	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.19/49.97	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.19/49.97	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.19/49.97	   new_primDivNatS2 -> new_primDivNatS3
84.19/49.97	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.19/49.97	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.19/49.97	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.19/49.97	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.19/49.97	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.19/49.97	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.19/49.97	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.19/49.97	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.19/49.97	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.19/49.97	
84.19/49.97	Q is empty.
84.19/49.97	We have to consider all (P,Q,R)-chains.
84.19/49.97	----------------------------------------
84.19/49.97	
84.19/49.97	(28) InductionCalculusProof (EQUIVALENT)
84.19/49.97	Note that final constraints are written in bold face.
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	For Pair new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd) the following chains were created:
84.19/49.97	*We consider the chain new_pr2F0G12(x0, x1, x2, Succ(Succ(x3)), x4) -> new_pr2F0G12(x0, x1, x2, x3, x4), new_pr2F0G12(x5, x6, x7, Succ(Succ(x8)), x9) -> new_pr2F0G12(x5, x6, x7, x8, x9) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F0G12(x0, x1, x2, x3, x4)=new_pr2F0G12(x5, x6, x7, Succ(Succ(x8)), x9)  ==>  new_pr2F0G12(x0, x1, x2, Succ(Succ(x3)), x4)_>=_new_pr2F0G12(x0, x1, x2, x3, x4))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F0G12(x0, x1, x2, Succ(Succ(Succ(Succ(x8)))), x4)_>=_new_pr2F0G12(x0, x1, x2, Succ(Succ(x8)), x4))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	*We consider the chain new_pr2F0G12(x10, x11, x12, Succ(Succ(x13)), x14) -> new_pr2F0G12(x10, x11, x12, x13, x14), new_pr2F0G12(x15, x16, x17, Succ(Zero), x18) -> new_pr2F1(x15, x17, new_fromInt, x16, x18) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F0G12(x10, x11, x12, x13, x14)=new_pr2F0G12(x15, x16, x17, Succ(Zero), x18)  ==>  new_pr2F0G12(x10, x11, x12, Succ(Succ(x13)), x14)_>=_new_pr2F0G12(x10, x11, x12, x13, x14))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F0G12(x10, x11, x12, Succ(Succ(Succ(Zero))), x14)_>=_new_pr2F0G12(x10, x11, x12, Succ(Zero), x14))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	*We consider the chain new_pr2F0G12(x34, x35, x36, Succ(Succ(x37)), x38) -> new_pr2F0G12(x34, x35, x36, x37, x38), new_pr2F0G12(x39, x40, x41, Zero, x42) -> new_pr2F0G13(new_sr8(x39, x40, x42), x39, new_primDivNatS1(Succ(x41)), new_primDivNatS1(Succ(x41)), x42) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F0G12(x34, x35, x36, x37, x38)=new_pr2F0G12(x39, x40, x41, Zero, x42)  ==>  new_pr2F0G12(x34, x35, x36, Succ(Succ(x37)), x38)_>=_new_pr2F0G12(x34, x35, x36, x37, x38))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F0G12(x34, x35, x36, Succ(Succ(Zero)), x38)_>=_new_pr2F0G12(x34, x35, x36, Zero, x38))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	For Pair new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd) the following chains were created:
84.19/49.97	*We consider the chain new_pr2F0G12(x91, x92, x93, Succ(Zero), x94) -> new_pr2F1(x91, x93, new_fromInt, x92, x94), new_pr2F1(x95, x96, x97, x98, x99) -> new_pr2F34(x96, x97, x95, new_sr9(x95, x98, x99), x99) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F1(x91, x93, new_fromInt, x92, x94)=new_pr2F1(x95, x96, x97, x98, x99)  ==>  new_pr2F0G12(x91, x92, x93, Succ(Zero), x94)_>=_new_pr2F1(x91, x93, new_fromInt, x92, x94))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F0G12(x91, x92, x93, Succ(Zero), x94)_>=_new_pr2F1(x91, x93, new_fromInt, x92, x94))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	For Pair new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd) the following chains were created:
84.19/49.97	*We consider the chain new_pr2F1(x159, x160, x161, x162, x163) -> new_pr2F34(x160, x161, x159, new_sr9(x159, x162, x163), x163), new_pr2F34(x164, Pos(x165), x166, x167, x168) -> new_pr2F31(new_primPlusNat0(Succ(x164), x165), x166, new_primPlusNat0(Succ(x164), x165), x167, x168) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F34(x160, x161, x159, new_sr9(x159, x162, x163), x163)=new_pr2F34(x164, Pos(x165), x166, x167, x168)  ==>  new_pr2F1(x159, x160, x161, x162, x163)_>=_new_pr2F34(x160, x161, x159, new_sr9(x159, x162, x163), x163))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F1(x159, x160, Pos(x165), x162, x163)_>=_new_pr2F34(x160, Pos(x165), x159, new_sr9(x159, x162, x163), x163))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	For Pair new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc) the following chains were created:
84.19/49.97	*We consider the chain new_pr2F34(x239, Pos(x240), x241, x242, x243) -> new_pr2F31(new_primPlusNat0(Succ(x239), x240), x241, new_primPlusNat0(Succ(x239), x240), x242, x243), new_pr2F31(Succ(x244), x245, Succ(Succ(x246)), x247, x248) -> new_pr2F0G12(x245, x247, Succ(x246), x246, x248) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F31(new_primPlusNat0(Succ(x239), x240), x241, new_primPlusNat0(Succ(x239), x240), x242, x243)=new_pr2F31(Succ(x244), x245, Succ(Succ(x246)), x247, x248)  ==>  new_pr2F34(x239, Pos(x240), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), x240), x241, new_primPlusNat0(Succ(x239), x240), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (Succ(x239)=x1016 & new_primPlusNat0(x1016, x240)=Succ(x244) & Succ(x239)=x1017 & new_primPlusNat0(x1017, x240)=Succ(Succ(x246))  ==>  new_pr2F34(x239, Pos(x240), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), x240), x241, new_primPlusNat0(Succ(x239), x240), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1016, x240)=Succ(x244) which results in the following new constraints:
84.19/49.97	
84.19/49.97	(3)    (Succ(Succ(new_primPlusNat0(x1019, x1018)))=Succ(x244) & Succ(x239)=Succ(x1019) & Succ(x239)=x1017 & new_primPlusNat0(x1017, Succ(x1018))=Succ(Succ(x246)) & (\/x1020,x1021,x1022,x1023,x1024,x1025,x1026:new_primPlusNat0(x1019, x1018)=Succ(x1020) & Succ(x1021)=x1019 & Succ(x1021)=x1022 & new_primPlusNat0(x1022, x1018)=Succ(Succ(x1023))  ==>  new_pr2F34(x1021, Pos(x1018), x1024, x1025, x1026)_>=_new_pr2F31(new_primPlusNat0(Succ(x1021), x1018), x1024, new_primPlusNat0(Succ(x1021), x1018), x1025, x1026))  ==>  new_pr2F34(x239, Pos(Succ(x1018)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1018)), x241, new_primPlusNat0(Succ(x239), Succ(x1018)), x242, x243))
84.19/49.97	
84.19/49.97	(4)    (Succ(x1027)=Succ(x244) & Succ(x239)=Succ(x1027) & Succ(x239)=x1017 & new_primPlusNat0(x1017, Zero)=Succ(Succ(x246))  ==>  new_pr2F34(x239, Pos(Zero), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Zero), x241, new_primPlusNat0(Succ(x239), Zero), x242, x243))
84.19/49.97	
84.19/49.97	(5)    (Succ(x1028)=Succ(x244) & Succ(x239)=Zero & Succ(x239)=x1017 & new_primPlusNat0(x1017, Succ(x1028))=Succ(Succ(x246))  ==>  new_pr2F34(x239, Pos(Succ(x1028)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1028)), x241, new_primPlusNat0(Succ(x239), Succ(x1028)), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(6)    (Succ(x239)=x1017 & Succ(x1018)=x1029 & new_primPlusNat0(x1017, x1029)=Succ(Succ(x246)) & (\/x1020,x1021,x1022,x1023,x1024,x1025,x1026:new_primPlusNat0(x239, x1018)=Succ(x1020) & Succ(x1021)=x239 & Succ(x1021)=x1022 & new_primPlusNat0(x1022, x1018)=Succ(Succ(x1023))  ==>  new_pr2F34(x1021, Pos(x1018), x1024, x1025, x1026)_>=_new_pr2F31(new_primPlusNat0(Succ(x1021), x1018), x1024, new_primPlusNat0(Succ(x1021), x1018), x1025, x1026))  ==>  new_pr2F34(x239, Pos(Succ(x1018)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1018)), x241, new_primPlusNat0(Succ(x239), Succ(x1018)), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(7)    (Succ(x239)=x1017 & Zero=x1047 & new_primPlusNat0(x1017, x1047)=Succ(Succ(x246))  ==>  new_pr2F34(x239, Pos(Zero), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Zero), x241, new_primPlusNat0(Succ(x239), Zero), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1017, x1029)=Succ(Succ(x246)) which results in the following new constraints:
84.19/49.97	
84.19/49.97	(8)    (Succ(Succ(new_primPlusNat0(x1031, x1030)))=Succ(Succ(x246)) & Succ(x239)=Succ(x1031) & Succ(x1018)=Succ(x1030) & (\/x1020,x1021,x1022,x1023,x1024,x1025,x1026:new_primPlusNat0(x239, x1018)=Succ(x1020) & Succ(x1021)=x239 & Succ(x1021)=x1022 & new_primPlusNat0(x1022, x1018)=Succ(Succ(x1023))  ==>  new_pr2F34(x1021, Pos(x1018), x1024, x1025, x1026)_>=_new_pr2F31(new_primPlusNat0(Succ(x1021), x1018), x1024, new_primPlusNat0(Succ(x1021), x1018), x1025, x1026)) & (\/x1032,x1033,x1034,x1035,x1036,x1037,x1038,x1039,x1040,x1041,x1042,x1043,x1044:new_primPlusNat0(x1031, x1030)=Succ(Succ(x1032)) & Succ(x1033)=x1031 & Succ(x1034)=x1030 & (\/x1035,x1036,x1037,x1038,x1039,x1040,x1041:new_primPlusNat0(x1033, x1034)=Succ(x1035) & Succ(x1036)=x1033 & Succ(x1036)=x1037 & new_primPlusNat0(x1037, x1034)=Succ(Succ(x1038))  ==>  new_pr2F34(x1036, Pos(x1034), x1039, x1040, x1041)_>=_new_pr2F31(new_primPlusNat0(Succ(x1036), x1034), x1039, new_primPlusNat0(Succ(x1036), x1034), x1040, x1041))  ==>  new_pr2F34(x1033, Pos(Succ(x1034)), x1042, x1043, x1044)_>=_new_pr2F31(new_primPlusNat0(Succ(x1033), Succ(x1034)), x1042, new_primPlusNat0(Succ(x1033), Succ(x1034)), x1043, x1044))  ==>  new_pr2F34(x239, Pos(Succ(x1018)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1018)), x241, new_primPlusNat0(Succ(x239), Succ(x1018)), x242, x243))
84.19/49.97	
84.19/49.97	(9)    (Succ(x1045)=Succ(Succ(x246)) & Succ(x239)=Succ(x1045) & Succ(x1018)=Zero & (\/x1020,x1021,x1022,x1023,x1024,x1025,x1026:new_primPlusNat0(x239, x1018)=Succ(x1020) & Succ(x1021)=x239 & Succ(x1021)=x1022 & new_primPlusNat0(x1022, x1018)=Succ(Succ(x1023))  ==>  new_pr2F34(x1021, Pos(x1018), x1024, x1025, x1026)_>=_new_pr2F31(new_primPlusNat0(Succ(x1021), x1018), x1024, new_primPlusNat0(Succ(x1021), x1018), x1025, x1026))  ==>  new_pr2F34(x239, Pos(Succ(x1018)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1018)), x241, new_primPlusNat0(Succ(x239), Succ(x1018)), x242, x243))
84.19/49.97	
84.19/49.97	(10)    (Succ(x1046)=Succ(Succ(x246)) & Succ(x239)=Zero & Succ(x1018)=Succ(x1046) & (\/x1020,x1021,x1022,x1023,x1024,x1025,x1026:new_primPlusNat0(x239, x1018)=Succ(x1020) & Succ(x1021)=x239 & Succ(x1021)=x1022 & new_primPlusNat0(x1022, x1018)=Succ(Succ(x1023))  ==>  new_pr2F34(x1021, Pos(x1018), x1024, x1025, x1026)_>=_new_pr2F31(new_primPlusNat0(Succ(x1021), x1018), x1024, new_primPlusNat0(Succ(x1021), x1018), x1025, x1026))  ==>  new_pr2F34(x239, Pos(Succ(x1018)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1018)), x241, new_primPlusNat0(Succ(x239), Succ(x1018)), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (8) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(11)    (new_pr2F34(x239, Pos(Succ(x1018)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1018)), x241, new_primPlusNat0(Succ(x239), Succ(x1018)), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1017, x1047)=Succ(Succ(x246)) which results in the following new constraints:
84.19/49.97	
84.19/49.97	(12)    (Succ(Succ(new_primPlusNat0(x1049, x1048)))=Succ(Succ(x246)) & Succ(x239)=Succ(x1049) & Zero=Succ(x1048) & (\/x1050,x1051,x1052,x1053,x1054:new_primPlusNat0(x1049, x1048)=Succ(Succ(x1050)) & Succ(x1051)=x1049 & Zero=x1048  ==>  new_pr2F34(x1051, Pos(Zero), x1052, x1053, x1054)_>=_new_pr2F31(new_primPlusNat0(Succ(x1051), Zero), x1052, new_primPlusNat0(Succ(x1051), Zero), x1053, x1054))  ==>  new_pr2F34(x239, Pos(Zero), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Zero), x241, new_primPlusNat0(Succ(x239), Zero), x242, x243))
84.19/49.97	
84.19/49.97	(13)    (Succ(x1055)=Succ(Succ(x246)) & Succ(x239)=Succ(x1055) & Zero=Zero  ==>  new_pr2F34(x239, Pos(Zero), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Zero), x241, new_primPlusNat0(Succ(x239), Zero), x242, x243))
84.19/49.97	
84.19/49.97	(14)    (Succ(x1056)=Succ(Succ(x246)) & Succ(x239)=Zero & Zero=Succ(x1056)  ==>  new_pr2F34(x239, Pos(Zero), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Zero), x241, new_primPlusNat0(Succ(x239), Zero), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(15)    (new_pr2F34(Succ(x246), Pos(Zero), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x246)), Zero), x241, new_primPlusNat0(Succ(Succ(x246)), Zero), x242, x243))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (14) using rules (I), (II).
84.19/49.97	*We consider the chain new_pr2F34(x264, Pos(x265), x266, x267, x268) -> new_pr2F31(new_primPlusNat0(Succ(x264), x265), x266, new_primPlusNat0(Succ(x264), x265), x267, x268), new_pr2F31(Succ(x269), x270, Succ(Zero), x271, x272) -> new_pr2F1(x270, Zero, new_fromInt, x271, x272) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F31(new_primPlusNat0(Succ(x264), x265), x266, new_primPlusNat0(Succ(x264), x265), x267, x268)=new_pr2F31(Succ(x269), x270, Succ(Zero), x271, x272)  ==>  new_pr2F34(x264, Pos(x265), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), x265), x266, new_primPlusNat0(Succ(x264), x265), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (Succ(x264)=x1057 & new_primPlusNat0(x1057, x265)=Succ(x269) & Succ(x264)=x1058 & new_primPlusNat0(x1058, x265)=Succ(Zero)  ==>  new_pr2F34(x264, Pos(x265), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), x265), x266, new_primPlusNat0(Succ(x264), x265), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1057, x265)=Succ(x269) which results in the following new constraints:
84.19/49.97	
84.19/49.97	(3)    (Succ(Succ(new_primPlusNat0(x1060, x1059)))=Succ(x269) & Succ(x264)=Succ(x1060) & Succ(x264)=x1058 & new_primPlusNat0(x1058, Succ(x1059))=Succ(Zero) & (\/x1061,x1062,x1063,x1064,x1065,x1066:new_primPlusNat0(x1060, x1059)=Succ(x1061) & Succ(x1062)=x1060 & Succ(x1062)=x1063 & new_primPlusNat0(x1063, x1059)=Succ(Zero)  ==>  new_pr2F34(x1062, Pos(x1059), x1064, x1065, x1066)_>=_new_pr2F31(new_primPlusNat0(Succ(x1062), x1059), x1064, new_primPlusNat0(Succ(x1062), x1059), x1065, x1066))  ==>  new_pr2F34(x264, Pos(Succ(x1059)), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Succ(x1059)), x266, new_primPlusNat0(Succ(x264), Succ(x1059)), x267, x268))
84.19/49.97	
84.19/49.97	(4)    (Succ(x1067)=Succ(x269) & Succ(x264)=Succ(x1067) & Succ(x264)=x1058 & new_primPlusNat0(x1058, Zero)=Succ(Zero)  ==>  new_pr2F34(x264, Pos(Zero), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Zero), x266, new_primPlusNat0(Succ(x264), Zero), x267, x268))
84.19/49.97	
84.19/49.97	(5)    (Succ(x1068)=Succ(x269) & Succ(x264)=Zero & Succ(x264)=x1058 & new_primPlusNat0(x1058, Succ(x1068))=Succ(Zero)  ==>  new_pr2F34(x264, Pos(Succ(x1068)), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Succ(x1068)), x266, new_primPlusNat0(Succ(x264), Succ(x1068)), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(6)    (Succ(x264)=x1058 & Succ(x1059)=x1069 & new_primPlusNat0(x1058, x1069)=Succ(Zero) & (\/x1061,x1062,x1063,x1064,x1065,x1066:new_primPlusNat0(x264, x1059)=Succ(x1061) & Succ(x1062)=x264 & Succ(x1062)=x1063 & new_primPlusNat0(x1063, x1059)=Succ(Zero)  ==>  new_pr2F34(x1062, Pos(x1059), x1064, x1065, x1066)_>=_new_pr2F31(new_primPlusNat0(Succ(x1062), x1059), x1064, new_primPlusNat0(Succ(x1062), x1059), x1065, x1066))  ==>  new_pr2F34(x264, Pos(Succ(x1059)), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Succ(x1059)), x266, new_primPlusNat0(Succ(x264), Succ(x1059)), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(7)    (Succ(x264)=x1058 & Zero=x1085 & new_primPlusNat0(x1058, x1085)=Succ(Zero)  ==>  new_pr2F34(x264, Pos(Zero), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Zero), x266, new_primPlusNat0(Succ(x264), Zero), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1058, x1069)=Succ(Zero) which results in the following new constraints:
84.19/49.97	
84.19/49.97	(8)    (Succ(Succ(new_primPlusNat0(x1071, x1070)))=Succ(Zero) & Succ(x264)=Succ(x1071) & Succ(x1059)=Succ(x1070) & (\/x1061,x1062,x1063,x1064,x1065,x1066:new_primPlusNat0(x264, x1059)=Succ(x1061) & Succ(x1062)=x264 & Succ(x1062)=x1063 & new_primPlusNat0(x1063, x1059)=Succ(Zero)  ==>  new_pr2F34(x1062, Pos(x1059), x1064, x1065, x1066)_>=_new_pr2F31(new_primPlusNat0(Succ(x1062), x1059), x1064, new_primPlusNat0(Succ(x1062), x1059), x1065, x1066)) & (\/x1072,x1073,x1074,x1075,x1076,x1077,x1078,x1079,x1080,x1081,x1082:new_primPlusNat0(x1071, x1070)=Succ(Zero) & Succ(x1072)=x1071 & Succ(x1073)=x1070 & (\/x1074,x1075,x1076,x1077,x1078,x1079:new_primPlusNat0(x1072, x1073)=Succ(x1074) & Succ(x1075)=x1072 & Succ(x1075)=x1076 & new_primPlusNat0(x1076, x1073)=Succ(Zero)  ==>  new_pr2F34(x1075, Pos(x1073), x1077, x1078, x1079)_>=_new_pr2F31(new_primPlusNat0(Succ(x1075), x1073), x1077, new_primPlusNat0(Succ(x1075), x1073), x1078, x1079))  ==>  new_pr2F34(x1072, Pos(Succ(x1073)), x1080, x1081, x1082)_>=_new_pr2F31(new_primPlusNat0(Succ(x1072), Succ(x1073)), x1080, new_primPlusNat0(Succ(x1072), Succ(x1073)), x1081, x1082))  ==>  new_pr2F34(x264, Pos(Succ(x1059)), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Succ(x1059)), x266, new_primPlusNat0(Succ(x264), Succ(x1059)), x267, x268))
84.19/49.97	
84.19/49.97	(9)    (Succ(x1083)=Succ(Zero) & Succ(x264)=Succ(x1083) & Succ(x1059)=Zero & (\/x1061,x1062,x1063,x1064,x1065,x1066:new_primPlusNat0(x264, x1059)=Succ(x1061) & Succ(x1062)=x264 & Succ(x1062)=x1063 & new_primPlusNat0(x1063, x1059)=Succ(Zero)  ==>  new_pr2F34(x1062, Pos(x1059), x1064, x1065, x1066)_>=_new_pr2F31(new_primPlusNat0(Succ(x1062), x1059), x1064, new_primPlusNat0(Succ(x1062), x1059), x1065, x1066))  ==>  new_pr2F34(x264, Pos(Succ(x1059)), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Succ(x1059)), x266, new_primPlusNat0(Succ(x264), Succ(x1059)), x267, x268))
84.19/49.97	
84.19/49.97	(10)    (Succ(x1084)=Succ(Zero) & Succ(x264)=Zero & Succ(x1059)=Succ(x1084) & (\/x1061,x1062,x1063,x1064,x1065,x1066:new_primPlusNat0(x264, x1059)=Succ(x1061) & Succ(x1062)=x264 & Succ(x1062)=x1063 & new_primPlusNat0(x1063, x1059)=Succ(Zero)  ==>  new_pr2F34(x1062, Pos(x1059), x1064, x1065, x1066)_>=_new_pr2F31(new_primPlusNat0(Succ(x1062), x1059), x1064, new_primPlusNat0(Succ(x1062), x1059), x1065, x1066))  ==>  new_pr2F34(x264, Pos(Succ(x1059)), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Succ(x1059)), x266, new_primPlusNat0(Succ(x264), Succ(x1059)), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1058, x1085)=Succ(Zero) which results in the following new constraints:
84.19/49.97	
84.19/49.97	(11)    (Succ(Succ(new_primPlusNat0(x1087, x1086)))=Succ(Zero) & Succ(x264)=Succ(x1087) & Zero=Succ(x1086) & (\/x1088,x1089,x1090,x1091:new_primPlusNat0(x1087, x1086)=Succ(Zero) & Succ(x1088)=x1087 & Zero=x1086  ==>  new_pr2F34(x1088, Pos(Zero), x1089, x1090, x1091)_>=_new_pr2F31(new_primPlusNat0(Succ(x1088), Zero), x1089, new_primPlusNat0(Succ(x1088), Zero), x1090, x1091))  ==>  new_pr2F34(x264, Pos(Zero), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Zero), x266, new_primPlusNat0(Succ(x264), Zero), x267, x268))
84.19/49.97	
84.19/49.97	(12)    (Succ(x1092)=Succ(Zero) & Succ(x264)=Succ(x1092) & Zero=Zero  ==>  new_pr2F34(x264, Pos(Zero), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Zero), x266, new_primPlusNat0(Succ(x264), Zero), x267, x268))
84.19/49.97	
84.19/49.97	(13)    (Succ(x1093)=Succ(Zero) & Succ(x264)=Zero & Zero=Succ(x1093)  ==>  new_pr2F34(x264, Pos(Zero), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(x264), Zero), x266, new_primPlusNat0(Succ(x264), Zero), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (11) using rules (I), (II).We simplified constraint (12) using rules (I), (II), (III) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(14)    (new_pr2F34(Zero, Pos(Zero), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), x266, new_primPlusNat0(Succ(Zero), Zero), x267, x268))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We solved constraint (13) using rules (I), (II).
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc) the following chains were created:
84.19/49.97	*We consider the chain new_pr2F31(Succ(x298), x299, Succ(Succ(x300)), x301, x302) -> new_pr2F0G12(x299, x301, Succ(x300), x300, x302), new_pr2F0G12(x303, x304, x305, Succ(Succ(x306)), x307) -> new_pr2F0G12(x303, x304, x305, x306, x307) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F0G12(x299, x301, Succ(x300), x300, x302)=new_pr2F0G12(x303, x304, x305, Succ(Succ(x306)), x307)  ==>  new_pr2F31(Succ(x298), x299, Succ(Succ(x300)), x301, x302)_>=_new_pr2F0G12(x299, x301, Succ(x300), x300, x302))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F31(Succ(x298), x299, Succ(Succ(Succ(Succ(x306)))), x301, x302)_>=_new_pr2F0G12(x299, x301, Succ(Succ(Succ(x306))), Succ(Succ(x306)), x302))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	*We consider the chain new_pr2F31(Succ(x308), x309, Succ(Succ(x310)), x311, x312) -> new_pr2F0G12(x309, x311, Succ(x310), x310, x312), new_pr2F0G12(x313, x314, x315, Succ(Zero), x316) -> new_pr2F1(x313, x315, new_fromInt, x314, x316) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F0G12(x309, x311, Succ(x310), x310, x312)=new_pr2F0G12(x313, x314, x315, Succ(Zero), x316)  ==>  new_pr2F31(Succ(x308), x309, Succ(Succ(x310)), x311, x312)_>=_new_pr2F0G12(x309, x311, Succ(x310), x310, x312))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F31(Succ(x308), x309, Succ(Succ(Succ(Zero))), x311, x312)_>=_new_pr2F0G12(x309, x311, Succ(Succ(Zero)), Succ(Zero), x312))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	*We consider the chain new_pr2F31(Succ(x332), x333, Succ(Succ(x334)), x335, x336) -> new_pr2F0G12(x333, x335, Succ(x334), x334, x336), new_pr2F0G12(x337, x338, x339, Zero, x340) -> new_pr2F0G13(new_sr8(x337, x338, x340), x337, new_primDivNatS1(Succ(x339)), new_primDivNatS1(Succ(x339)), x340) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F0G12(x333, x335, Succ(x334), x334, x336)=new_pr2F0G12(x337, x338, x339, Zero, x340)  ==>  new_pr2F31(Succ(x332), x333, Succ(Succ(x334)), x335, x336)_>=_new_pr2F0G12(x333, x335, Succ(x334), x334, x336))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (new_pr2F31(Succ(x332), x333, Succ(Succ(Zero)), x335, x336)_>=_new_pr2F0G12(x333, x335, Succ(Zero), Zero, x336))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	For Pair new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd) the following chains were created:
84.19/49.97	*We consider the chain new_pr2F0G12(x405, x406, x407, Zero, x408) -> new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(x407)), new_primDivNatS1(Succ(x407)), x408), new_pr2F0G13(x409, x410, x411, Succ(Zero), x412) -> new_pr2F2(x410, x411, new_fromInt, x409, x412) which results in the following constraint:
84.19/49.97	
84.19/49.97	(1)    (new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(x407)), new_primDivNatS1(Succ(x407)), x408)=new_pr2F0G13(x409, x410, x411, Succ(Zero), x412)  ==>  new_pr2F0G12(x405, x406, x407, Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(x407)), new_primDivNatS1(Succ(x407)), x408))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(2)    (Succ(x407)=x1094 & new_primDivNatS1(x1094)=Succ(Zero)  ==>  new_pr2F0G12(x405, x406, x407, Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(x407)), new_primDivNatS1(Succ(x407)), x408))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1094)=Succ(Zero) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(3)    (new_primDivNatS01(x1095)=Succ(Zero) & Succ(x407)=Succ(x1095)  ==>  new_pr2F0G12(x405, x406, x407, Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(x407)), new_primDivNatS1(Succ(x407)), x408))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(4)    (new_primDivNatS01(x1095)=Succ(Zero)  ==>  new_pr2F0G12(x405, x406, x1095, Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(x1095)), new_primDivNatS1(Succ(x1095)), x408))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1095)=Succ(Zero) which results in the following new constraints:
84.19/49.97	
84.19/49.97	(5)    (Succ(new_primDivNatS4(x1096))=Succ(Zero)  ==>  new_pr2F0G12(x405, x406, Succ(Succ(x1096)), Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(Succ(Succ(x1096)))), new_primDivNatS1(Succ(Succ(Succ(x1096)))), x408))
84.19/49.97	
84.19/49.97	(6)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G12(x405, x406, Succ(Zero), Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x408))
84.19/49.97	
84.19/49.97	
84.19/49.97	
84.19/49.97	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.19/49.97	
84.19/49.97	(7)    (new_pr2F0G12(x405, x406, Succ(Succ(x1096)), Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(Succ(Succ(x1096)))), new_primDivNatS1(Succ(Succ(Succ(x1096)))), x408))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(8)    (new_pr2F0G12(x405, x406, Succ(Zero), Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x408))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G12(x421, x422, x423, Zero, x424) -> new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(x423)), new_primDivNatS1(Succ(x423)), x424), new_pr2F0G13(x425, x426, x427, Succ(Succ(x428)), x429) -> new_pr2F0G14(x425, x426, x427, x428, x429) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(x423)), new_primDivNatS1(Succ(x423)), x424)=new_pr2F0G13(x425, x426, x427, Succ(Succ(x428)), x429)  ==>  new_pr2F0G12(x421, x422, x423, Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(x423)), new_primDivNatS1(Succ(x423)), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x423)=x1097 & new_primDivNatS1(x1097)=Succ(Succ(x428))  ==>  new_pr2F0G12(x421, x422, x423, Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(x423)), new_primDivNatS1(Succ(x423)), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1097)=Succ(Succ(x428)) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (new_primDivNatS01(x1098)=Succ(Succ(x428)) & Succ(x423)=Succ(x1098)  ==>  new_pr2F0G12(x421, x422, x423, Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(x423)), new_primDivNatS1(Succ(x423)), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(4)    (new_primDivNatS01(x1098)=Succ(Succ(x428))  ==>  new_pr2F0G12(x421, x422, x1098, Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(x1098)), new_primDivNatS1(Succ(x1098)), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1098)=Succ(Succ(x428)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(5)    (Succ(new_primDivNatS4(x1099))=Succ(Succ(x428))  ==>  new_pr2F0G12(x421, x422, Succ(Succ(x1099)), Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(Succ(Succ(x1099)))), new_primDivNatS1(Succ(Succ(Succ(x1099)))), x424))
84.27/49.98	
84.27/49.98	(6)    (Succ(new_primDivNatS2)=Succ(Succ(x428))  ==>  new_pr2F0G12(x421, x422, Succ(Zero), Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G12(x421, x422, Succ(Succ(x1099)), Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(Succ(Succ(x1099)))), new_primDivNatS1(Succ(Succ(Succ(x1099)))), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(8)    (new_pr2F0G12(x421, x422, Succ(Zero), Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G12(x442, x443, x444, Zero, x445) -> new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(x444)), new_primDivNatS1(Succ(x444)), x445), new_pr2F0G13(x446, x447, x448, Zero, x449) -> new_pr2F0G13(x446, new_sr10(x447, x449), new_primDivNatS1(x448), new_primDivNatS1(x448), x449) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(x444)), new_primDivNatS1(Succ(x444)), x445)=new_pr2F0G13(x446, x447, x448, Zero, x449)  ==>  new_pr2F0G12(x442, x443, x444, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(x444)), new_primDivNatS1(Succ(x444)), x445))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x444)=x1100 & new_primDivNatS1(x1100)=Zero  ==>  new_pr2F0G12(x442, x443, x444, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(x444)), new_primDivNatS1(Succ(x444)), x445))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1100)=Zero which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Zero=Zero & Succ(x444)=Zero  ==>  new_pr2F0G12(x442, x443, x444, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(x444)), new_primDivNatS1(Succ(x444)), x445))
84.27/49.98	
84.27/49.98	(4)    (new_primDivNatS01(x1101)=Zero & Succ(x444)=Succ(x1101)  ==>  new_pr2F0G12(x442, x443, x444, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(x444)), new_primDivNatS1(Succ(x444)), x445))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(5)    (new_primDivNatS01(x1101)=Zero  ==>  new_pr2F0G12(x442, x443, x1101, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(x1101)), new_primDivNatS1(Succ(x1101)), x445))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1101)=Zero which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Zero=Zero  ==>  new_pr2F0G12(x442, x443, Zero, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x445))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G12(x442, x443, Zero, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x445))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G13(x478, x479, x480, Succ(Zero), x481) -> new_pr2F2(x479, x480, new_fromInt, x478, x481), new_pr2F2(x482, x483, Pos(x484), x485, x486) -> new_pr2F31(new_primPlusNat0(x483, x484), new_sr11(x482, x486), new_primPlusNat0(x483, x484), x485, x486) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F2(x479, x480, new_fromInt, x478, x481)=new_pr2F2(x482, x483, Pos(x484), x485, x486)  ==>  new_pr2F0G13(x478, x479, x480, Succ(Zero), x481)_>=_new_pr2F2(x479, x480, new_fromInt, x478, x481))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_fromInt=Pos(x484)  ==>  new_pr2F0G13(x478, x479, x480, Succ(Zero), x481)_>=_new_pr2F2(x479, x480, new_fromInt, x478, x481))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_fromInt=Pos(x484) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (Pos(Succ(Zero))=Pos(x484)  ==>  new_pr2F0G13(x478, x479, x480, Succ(Zero), x481)_>=_new_pr2F2(x479, x480, new_fromInt, x478, x481))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(4)    (new_pr2F0G13(x478, x479, x480, Succ(Zero), x481)_>=_new_pr2F2(x479, x480, new_fromInt, x478, x481))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F2(x531, x532, Pos(x533), x534, x535) -> new_pr2F31(new_primPlusNat0(x532, x533), new_sr11(x531, x535), new_primPlusNat0(x532, x533), x534, x535), new_pr2F31(Succ(x536), x537, Succ(Succ(x538)), x539, x540) -> new_pr2F0G12(x537, x539, Succ(x538), x538, x540) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F31(new_primPlusNat0(x532, x533), new_sr11(x531, x535), new_primPlusNat0(x532, x533), x534, x535)=new_pr2F31(Succ(x536), x537, Succ(Succ(x538)), x539, x540)  ==>  new_pr2F2(x531, x532, Pos(x533), x534, x535)_>=_new_pr2F31(new_primPlusNat0(x532, x533), new_sr11(x531, x535), new_primPlusNat0(x532, x533), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primPlusNat0(x532, x533)=Succ(x536) & new_primPlusNat0(x532, x533)=Succ(Succ(x538))  ==>  new_pr2F2(x531, x532, Pos(x533), x534, x535)_>=_new_pr2F31(new_primPlusNat0(x532, x533), new_sr11(x531, x535), new_primPlusNat0(x532, x533), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x532, x533)=Succ(x536) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Succ(Succ(new_primPlusNat0(x1104, x1103)))=Succ(x536) & new_primPlusNat0(Succ(x1104), Succ(x1103))=Succ(Succ(x538)) & (\/x1105,x1106,x1107,x1108,x1109:new_primPlusNat0(x1104, x1103)=Succ(x1105) & new_primPlusNat0(x1104, x1103)=Succ(Succ(x1106))  ==>  new_pr2F2(x1107, x1104, Pos(x1103), x1108, x1109)_>=_new_pr2F31(new_primPlusNat0(x1104, x1103), new_sr11(x1107, x1109), new_primPlusNat0(x1104, x1103), x1108, x1109))  ==>  new_pr2F2(x531, Succ(x1104), Pos(Succ(x1103)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1104), Succ(x1103)), new_sr11(x531, x535), new_primPlusNat0(Succ(x1104), Succ(x1103)), x534, x535))
84.27/49.98	
84.27/49.98	(4)    (Succ(x1110)=Succ(x536) & new_primPlusNat0(Succ(x1110), Zero)=Succ(Succ(x538))  ==>  new_pr2F2(x531, Succ(x1110), Pos(Zero), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1110), Zero), new_sr11(x531, x535), new_primPlusNat0(Succ(x1110), Zero), x534, x535))
84.27/49.98	
84.27/49.98	(5)    (Succ(x1111)=Succ(x536) & new_primPlusNat0(Zero, Succ(x1111))=Succ(Succ(x538))  ==>  new_pr2F2(x531, Zero, Pos(Succ(x1111)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1111)), new_sr11(x531, x535), new_primPlusNat0(Zero, Succ(x1111)), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Succ(x1104)=x1112 & Succ(x1103)=x1113 & new_primPlusNat0(x1112, x1113)=Succ(Succ(x538)) & (\/x1105,x1106,x1107,x1108,x1109:new_primPlusNat0(x1104, x1103)=Succ(x1105) & new_primPlusNat0(x1104, x1103)=Succ(Succ(x1106))  ==>  new_pr2F2(x1107, x1104, Pos(x1103), x1108, x1109)_>=_new_pr2F31(new_primPlusNat0(x1104, x1103), new_sr11(x1107, x1109), new_primPlusNat0(x1104, x1103), x1108, x1109))  ==>  new_pr2F2(x531, Succ(x1104), Pos(Succ(x1103)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1104), Succ(x1103)), new_sr11(x531, x535), new_primPlusNat0(Succ(x1104), Succ(x1103)), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (Succ(x1110)=x1129 & Zero=x1130 & new_primPlusNat0(x1129, x1130)=Succ(Succ(x538))  ==>  new_pr2F2(x531, Succ(x1110), Pos(Zero), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1110), Zero), new_sr11(x531, x535), new_primPlusNat0(Succ(x1110), Zero), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(8)    (Zero=x1140 & Succ(x1111)=x1141 & new_primPlusNat0(x1140, x1141)=Succ(Succ(x538))  ==>  new_pr2F2(x531, Zero, Pos(Succ(x1111)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1111)), new_sr11(x531, x535), new_primPlusNat0(Zero, Succ(x1111)), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1112, x1113)=Succ(Succ(x538)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(9)    (Succ(Succ(new_primPlusNat0(x1115, x1114)))=Succ(Succ(x538)) & Succ(x1104)=Succ(x1115) & Succ(x1103)=Succ(x1114) & (\/x1105,x1106,x1107,x1108,x1109:new_primPlusNat0(x1104, x1103)=Succ(x1105) & new_primPlusNat0(x1104, x1103)=Succ(Succ(x1106))  ==>  new_pr2F2(x1107, x1104, Pos(x1103), x1108, x1109)_>=_new_pr2F31(new_primPlusNat0(x1104, x1103), new_sr11(x1107, x1109), new_primPlusNat0(x1104, x1103), x1108, x1109)) & (\/x1116,x1117,x1118,x1119,x1120,x1121,x1122,x1123,x1124,x1125,x1126:new_primPlusNat0(x1115, x1114)=Succ(Succ(x1116)) & Succ(x1117)=x1115 & Succ(x1118)=x1114 & (\/x1119,x1120,x1121,x1122,x1123:new_primPlusNat0(x1117, x1118)=Succ(x1119) & new_primPlusNat0(x1117, x1118)=Succ(Succ(x1120))  ==>  new_pr2F2(x1121, x1117, Pos(x1118), x1122, x1123)_>=_new_pr2F31(new_primPlusNat0(x1117, x1118), new_sr11(x1121, x1123), new_primPlusNat0(x1117, x1118), x1122, x1123))  ==>  new_pr2F2(x1124, Succ(x1117), Pos(Succ(x1118)), x1125, x1126)_>=_new_pr2F31(new_primPlusNat0(Succ(x1117), Succ(x1118)), new_sr11(x1124, x1126), new_primPlusNat0(Succ(x1117), Succ(x1118)), x1125, x1126))  ==>  new_pr2F2(x531, Succ(x1104), Pos(Succ(x1103)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1104), Succ(x1103)), new_sr11(x531, x535), new_primPlusNat0(Succ(x1104), Succ(x1103)), x534, x535))
84.27/49.98	
84.27/49.98	(10)    (Succ(x1127)=Succ(Succ(x538)) & Succ(x1104)=Succ(x1127) & Succ(x1103)=Zero & (\/x1105,x1106,x1107,x1108,x1109:new_primPlusNat0(x1104, x1103)=Succ(x1105) & new_primPlusNat0(x1104, x1103)=Succ(Succ(x1106))  ==>  new_pr2F2(x1107, x1104, Pos(x1103), x1108, x1109)_>=_new_pr2F31(new_primPlusNat0(x1104, x1103), new_sr11(x1107, x1109), new_primPlusNat0(x1104, x1103), x1108, x1109))  ==>  new_pr2F2(x531, Succ(x1104), Pos(Succ(x1103)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1104), Succ(x1103)), new_sr11(x531, x535), new_primPlusNat0(Succ(x1104), Succ(x1103)), x534, x535))
84.27/49.98	
84.27/49.98	(11)    (Succ(x1128)=Succ(Succ(x538)) & Succ(x1104)=Zero & Succ(x1103)=Succ(x1128) & (\/x1105,x1106,x1107,x1108,x1109:new_primPlusNat0(x1104, x1103)=Succ(x1105) & new_primPlusNat0(x1104, x1103)=Succ(Succ(x1106))  ==>  new_pr2F2(x1107, x1104, Pos(x1103), x1108, x1109)_>=_new_pr2F31(new_primPlusNat0(x1104, x1103), new_sr11(x1107, x1109), new_primPlusNat0(x1104, x1103), x1108, x1109))  ==>  new_pr2F2(x531, Succ(x1104), Pos(Succ(x1103)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1104), Succ(x1103)), new_sr11(x531, x535), new_primPlusNat0(Succ(x1104), Succ(x1103)), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(12)    (new_pr2F2(x531, Succ(x1104), Pos(Succ(x1103)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1104), Succ(x1103)), new_sr11(x531, x535), new_primPlusNat0(Succ(x1104), Succ(x1103)), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1129, x1130)=Succ(Succ(x538)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(13)    (Succ(Succ(new_primPlusNat0(x1132, x1131)))=Succ(Succ(x538)) & Succ(x1110)=Succ(x1132) & Zero=Succ(x1131) & (\/x1133,x1134,x1135,x1136,x1137:new_primPlusNat0(x1132, x1131)=Succ(Succ(x1133)) & Succ(x1134)=x1132 & Zero=x1131  ==>  new_pr2F2(x1135, Succ(x1134), Pos(Zero), x1136, x1137)_>=_new_pr2F31(new_primPlusNat0(Succ(x1134), Zero), new_sr11(x1135, x1137), new_primPlusNat0(Succ(x1134), Zero), x1136, x1137))  ==>  new_pr2F2(x531, Succ(x1110), Pos(Zero), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1110), Zero), new_sr11(x531, x535), new_primPlusNat0(Succ(x1110), Zero), x534, x535))
84.27/49.98	
84.27/49.98	(14)    (Succ(x1138)=Succ(Succ(x538)) & Succ(x1110)=Succ(x1138) & Zero=Zero  ==>  new_pr2F2(x531, Succ(x1110), Pos(Zero), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1110), Zero), new_sr11(x531, x535), new_primPlusNat0(Succ(x1110), Zero), x534, x535))
84.27/49.98	
84.27/49.98	(15)    (Succ(x1139)=Succ(Succ(x538)) & Succ(x1110)=Zero & Zero=Succ(x1139)  ==>  new_pr2F2(x531, Succ(x1110), Pos(Zero), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1110), Zero), new_sr11(x531, x535), new_primPlusNat0(Succ(x1110), Zero), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (13) using rules (I), (II).We simplified constraint (14) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(16)    (new_pr2F2(x531, Succ(Succ(x538)), Pos(Zero), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x538)), Zero), new_sr11(x531, x535), new_primPlusNat0(Succ(Succ(x538)), Zero), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (15) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1140, x1141)=Succ(Succ(x538)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(17)    (Succ(Succ(new_primPlusNat0(x1143, x1142)))=Succ(Succ(x538)) & Zero=Succ(x1143) & Succ(x1111)=Succ(x1142) & (\/x1144,x1145,x1146,x1147,x1148:new_primPlusNat0(x1143, x1142)=Succ(Succ(x1144)) & Zero=x1143 & Succ(x1145)=x1142  ==>  new_pr2F2(x1146, Zero, Pos(Succ(x1145)), x1147, x1148)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1145)), new_sr11(x1146, x1148), new_primPlusNat0(Zero, Succ(x1145)), x1147, x1148))  ==>  new_pr2F2(x531, Zero, Pos(Succ(x1111)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1111)), new_sr11(x531, x535), new_primPlusNat0(Zero, Succ(x1111)), x534, x535))
84.27/49.98	
84.27/49.98	(18)    (Succ(x1149)=Succ(Succ(x538)) & Zero=Succ(x1149) & Succ(x1111)=Zero  ==>  new_pr2F2(x531, Zero, Pos(Succ(x1111)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1111)), new_sr11(x531, x535), new_primPlusNat0(Zero, Succ(x1111)), x534, x535))
84.27/49.98	
84.27/49.98	(19)    (Succ(x1150)=Succ(Succ(x538)) & Zero=Zero & Succ(x1111)=Succ(x1150)  ==>  new_pr2F2(x531, Zero, Pos(Succ(x1111)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1111)), new_sr11(x531, x535), new_primPlusNat0(Zero, Succ(x1111)), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (17) using rules (I), (II).We solved constraint (18) using rules (I), (II).We simplified constraint (19) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(20)    (new_pr2F2(x531, Zero, Pos(Succ(Succ(x538))), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x538))), new_sr11(x531, x535), new_primPlusNat0(Zero, Succ(Succ(x538))), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F2(x556, x557, Pos(x558), x559, x560) -> new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560), new_pr2F31(Succ(x561), x562, Succ(Zero), x563, x564) -> new_pr2F1(x562, Zero, new_fromInt, x563, x564) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560)=new_pr2F31(Succ(x561), x562, Succ(Zero), x563, x564)  ==>  new_pr2F2(x556, x557, Pos(x558), x559, x560)_>=_new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primPlusNat0(x557, x558)=Succ(x561) & new_primPlusNat0(x557, x558)=Succ(Zero)  ==>  new_pr2F2(x556, x557, Pos(x558), x559, x560)_>=_new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x557, x558)=Succ(x561) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Succ(Succ(new_primPlusNat0(x1152, x1151)))=Succ(x561) & new_primPlusNat0(Succ(x1152), Succ(x1151))=Succ(Zero) & (\/x1153,x1154,x1155,x1156:new_primPlusNat0(x1152, x1151)=Succ(x1153) & new_primPlusNat0(x1152, x1151)=Succ(Zero)  ==>  new_pr2F2(x1154, x1152, Pos(x1151), x1155, x1156)_>=_new_pr2F31(new_primPlusNat0(x1152, x1151), new_sr11(x1154, x1156), new_primPlusNat0(x1152, x1151), x1155, x1156))  ==>  new_pr2F2(x556, Succ(x1152), Pos(Succ(x1151)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1152), Succ(x1151)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1152), Succ(x1151)), x559, x560))
84.27/49.98	
84.27/49.98	(4)    (Succ(x1157)=Succ(x561) & new_primPlusNat0(Succ(x1157), Zero)=Succ(Zero)  ==>  new_pr2F2(x556, Succ(x1157), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1157), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1157), Zero), x559, x560))
84.27/49.98	
84.27/49.98	(5)    (Succ(x1158)=Succ(x561) & new_primPlusNat0(Zero, Succ(x1158))=Succ(Zero)  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1158)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1158)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1158)), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Succ(x1152)=x1159 & Succ(x1151)=x1160 & new_primPlusNat0(x1159, x1160)=Succ(Zero) & (\/x1153,x1154,x1155,x1156:new_primPlusNat0(x1152, x1151)=Succ(x1153) & new_primPlusNat0(x1152, x1151)=Succ(Zero)  ==>  new_pr2F2(x1154, x1152, Pos(x1151), x1155, x1156)_>=_new_pr2F31(new_primPlusNat0(x1152, x1151), new_sr11(x1154, x1156), new_primPlusNat0(x1152, x1151), x1155, x1156))  ==>  new_pr2F2(x556, Succ(x1152), Pos(Succ(x1151)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1152), Succ(x1151)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1152), Succ(x1151)), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (Succ(x1157)=x1174 & Zero=x1175 & new_primPlusNat0(x1174, x1175)=Succ(Zero)  ==>  new_pr2F2(x556, Succ(x1157), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1157), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1157), Zero), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(8)    (Zero=x1184 & Succ(x1158)=x1185 & new_primPlusNat0(x1184, x1185)=Succ(Zero)  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1158)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1158)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1158)), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1159, x1160)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(9)    (Succ(Succ(new_primPlusNat0(x1162, x1161)))=Succ(Zero) & Succ(x1152)=Succ(x1162) & Succ(x1151)=Succ(x1161) & (\/x1153,x1154,x1155,x1156:new_primPlusNat0(x1152, x1151)=Succ(x1153) & new_primPlusNat0(x1152, x1151)=Succ(Zero)  ==>  new_pr2F2(x1154, x1152, Pos(x1151), x1155, x1156)_>=_new_pr2F31(new_primPlusNat0(x1152, x1151), new_sr11(x1154, x1156), new_primPlusNat0(x1152, x1151), x1155, x1156)) & (\/x1163,x1164,x1165,x1166,x1167,x1168,x1169,x1170,x1171:new_primPlusNat0(x1162, x1161)=Succ(Zero) & Succ(x1163)=x1162 & Succ(x1164)=x1161 & (\/x1165,x1166,x1167,x1168:new_primPlusNat0(x1163, x1164)=Succ(x1165) & new_primPlusNat0(x1163, x1164)=Succ(Zero)  ==>  new_pr2F2(x1166, x1163, Pos(x1164), x1167, x1168)_>=_new_pr2F31(new_primPlusNat0(x1163, x1164), new_sr11(x1166, x1168), new_primPlusNat0(x1163, x1164), x1167, x1168))  ==>  new_pr2F2(x1169, Succ(x1163), Pos(Succ(x1164)), x1170, x1171)_>=_new_pr2F31(new_primPlusNat0(Succ(x1163), Succ(x1164)), new_sr11(x1169, x1171), new_primPlusNat0(Succ(x1163), Succ(x1164)), x1170, x1171))  ==>  new_pr2F2(x556, Succ(x1152), Pos(Succ(x1151)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1152), Succ(x1151)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1152), Succ(x1151)), x559, x560))
84.27/49.98	
84.27/49.98	(10)    (Succ(x1172)=Succ(Zero) & Succ(x1152)=Succ(x1172) & Succ(x1151)=Zero & (\/x1153,x1154,x1155,x1156:new_primPlusNat0(x1152, x1151)=Succ(x1153) & new_primPlusNat0(x1152, x1151)=Succ(Zero)  ==>  new_pr2F2(x1154, x1152, Pos(x1151), x1155, x1156)_>=_new_pr2F31(new_primPlusNat0(x1152, x1151), new_sr11(x1154, x1156), new_primPlusNat0(x1152, x1151), x1155, x1156))  ==>  new_pr2F2(x556, Succ(x1152), Pos(Succ(x1151)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1152), Succ(x1151)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1152), Succ(x1151)), x559, x560))
84.27/49.98	
84.27/49.98	(11)    (Succ(x1173)=Succ(Zero) & Succ(x1152)=Zero & Succ(x1151)=Succ(x1173) & (\/x1153,x1154,x1155,x1156:new_primPlusNat0(x1152, x1151)=Succ(x1153) & new_primPlusNat0(x1152, x1151)=Succ(Zero)  ==>  new_pr2F2(x1154, x1152, Pos(x1151), x1155, x1156)_>=_new_pr2F31(new_primPlusNat0(x1152, x1151), new_sr11(x1154, x1156), new_primPlusNat0(x1152, x1151), x1155, x1156))  ==>  new_pr2F2(x556, Succ(x1152), Pos(Succ(x1151)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1152), Succ(x1151)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1152), Succ(x1151)), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1174, x1175)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(12)    (Succ(Succ(new_primPlusNat0(x1177, x1176)))=Succ(Zero) & Succ(x1157)=Succ(x1177) & Zero=Succ(x1176) & (\/x1178,x1179,x1180,x1181:new_primPlusNat0(x1177, x1176)=Succ(Zero) & Succ(x1178)=x1177 & Zero=x1176  ==>  new_pr2F2(x1179, Succ(x1178), Pos(Zero), x1180, x1181)_>=_new_pr2F31(new_primPlusNat0(Succ(x1178), Zero), new_sr11(x1179, x1181), new_primPlusNat0(Succ(x1178), Zero), x1180, x1181))  ==>  new_pr2F2(x556, Succ(x1157), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1157), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1157), Zero), x559, x560))
84.27/49.98	
84.27/49.98	(13)    (Succ(x1182)=Succ(Zero) & Succ(x1157)=Succ(x1182) & Zero=Zero  ==>  new_pr2F2(x556, Succ(x1157), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1157), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1157), Zero), x559, x560))
84.27/49.98	
84.27/49.98	(14)    (Succ(x1183)=Succ(Zero) & Succ(x1157)=Zero & Zero=Succ(x1183)  ==>  new_pr2F2(x556, Succ(x1157), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1157), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1157), Zero), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(15)    (new_pr2F2(x556, Succ(Zero), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(Zero), Zero), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (14) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1184, x1185)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(16)    (Succ(Succ(new_primPlusNat0(x1187, x1186)))=Succ(Zero) & Zero=Succ(x1187) & Succ(x1158)=Succ(x1186) & (\/x1188,x1189,x1190,x1191:new_primPlusNat0(x1187, x1186)=Succ(Zero) & Zero=x1187 & Succ(x1188)=x1186  ==>  new_pr2F2(x1189, Zero, Pos(Succ(x1188)), x1190, x1191)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1188)), new_sr11(x1189, x1191), new_primPlusNat0(Zero, Succ(x1188)), x1190, x1191))  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1158)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1158)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1158)), x559, x560))
84.27/49.98	
84.27/49.98	(17)    (Succ(x1192)=Succ(Zero) & Zero=Succ(x1192) & Succ(x1158)=Zero  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1158)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1158)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1158)), x559, x560))
84.27/49.98	
84.27/49.98	(18)    (Succ(x1193)=Succ(Zero) & Zero=Zero & Succ(x1158)=Succ(x1193)  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1158)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1158)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1158)), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (16) using rules (I), (II).We solved constraint (17) using rules (I), (II).We simplified constraint (18) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(19)    (new_pr2F2(x556, Zero, Pos(Succ(Zero)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Zero)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(Zero)), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F31(Succ(x598), x599, Succ(Zero), x600, x601) -> new_pr2F1(x599, Zero, new_fromInt, x600, x601), new_pr2F1(x602, x603, x604, x605, x606) -> new_pr2F34(x603, x604, x602, new_sr9(x602, x605, x606), x606) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F1(x599, Zero, new_fromInt, x600, x601)=new_pr2F1(x602, x603, x604, x605, x606)  ==>  new_pr2F31(Succ(x598), x599, Succ(Zero), x600, x601)_>=_new_pr2F1(x599, Zero, new_fromInt, x600, x601))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F31(Succ(x598), x599, Succ(Zero), x600, x601)_>=_new_pr2F1(x599, Zero, new_fromInt, x600, x601))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G13(x701, x702, x703, Succ(Succ(x704)), x705) -> new_pr2F0G14(x701, x702, x703, x704, x705), new_pr2F0G14(x706, x707, x708, Succ(Zero), x709) -> new_pr2F2(x707, x708, new_fromInt, x706, x709) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G14(x701, x702, x703, x704, x705)=new_pr2F0G14(x706, x707, x708, Succ(Zero), x709)  ==>  new_pr2F0G13(x701, x702, x703, Succ(Succ(x704)), x705)_>=_new_pr2F0G14(x701, x702, x703, x704, x705))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F0G13(x701, x702, x703, Succ(Succ(Succ(Zero))), x705)_>=_new_pr2F0G14(x701, x702, x703, Succ(Zero), x705))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G13(x710, x711, x712, Succ(Succ(x713)), x714) -> new_pr2F0G14(x710, x711, x712, x713, x714), new_pr2F0G14(x715, x716, x717, Succ(Succ(x718)), x719) -> new_pr2F0G14(x715, x716, x717, x718, x719) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G14(x710, x711, x712, x713, x714)=new_pr2F0G14(x715, x716, x717, Succ(Succ(x718)), x719)  ==>  new_pr2F0G13(x710, x711, x712, Succ(Succ(x713)), x714)_>=_new_pr2F0G14(x710, x711, x712, x713, x714))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F0G13(x710, x711, x712, Succ(Succ(Succ(Succ(x718)))), x714)_>=_new_pr2F0G14(x710, x711, x712, Succ(Succ(x718)), x714))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G13(x720, x721, x722, Succ(Succ(x723)), x724) -> new_pr2F0G14(x720, x721, x722, x723, x724), new_pr2F0G14(x725, x726, x727, Zero, x728) -> new_pr2F0G13(x725, new_sr10(x726, x728), new_primDivNatS1(x727), new_primDivNatS1(x727), x728) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G14(x720, x721, x722, x723, x724)=new_pr2F0G14(x725, x726, x727, Zero, x728)  ==>  new_pr2F0G13(x720, x721, x722, Succ(Succ(x723)), x724)_>=_new_pr2F0G14(x720, x721, x722, x723, x724))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F0G13(x720, x721, x722, Succ(Succ(Zero)), x724)_>=_new_pr2F0G14(x720, x721, x722, Zero, x724))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G14(x762, x763, x764, Succ(Zero), x765) -> new_pr2F2(x763, x764, new_fromInt, x762, x765), new_pr2F2(x766, x767, Pos(x768), x769, x770) -> new_pr2F31(new_primPlusNat0(x767, x768), new_sr11(x766, x770), new_primPlusNat0(x767, x768), x769, x770) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F2(x763, x764, new_fromInt, x762, x765)=new_pr2F2(x766, x767, Pos(x768), x769, x770)  ==>  new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_fromInt=Pos(x768)  ==>  new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_fromInt=Pos(x768) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (Pos(Succ(Zero))=Pos(x768)  ==>  new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(4)    (new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G14(x845, x846, x847, Succ(Succ(x848)), x849) -> new_pr2F0G14(x845, x846, x847, x848, x849), new_pr2F0G14(x850, x851, x852, Succ(Zero), x853) -> new_pr2F2(x851, x852, new_fromInt, x850, x853) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G14(x845, x846, x847, x848, x849)=new_pr2F0G14(x850, x851, x852, Succ(Zero), x853)  ==>  new_pr2F0G14(x845, x846, x847, Succ(Succ(x848)), x849)_>=_new_pr2F0G14(x845, x846, x847, x848, x849))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F0G14(x845, x846, x847, Succ(Succ(Succ(Zero))), x849)_>=_new_pr2F0G14(x845, x846, x847, Succ(Zero), x849))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G14(x854, x855, x856, Succ(Succ(x857)), x858) -> new_pr2F0G14(x854, x855, x856, x857, x858), new_pr2F0G14(x859, x860, x861, Succ(Succ(x862)), x863) -> new_pr2F0G14(x859, x860, x861, x862, x863) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G14(x854, x855, x856, x857, x858)=new_pr2F0G14(x859, x860, x861, Succ(Succ(x862)), x863)  ==>  new_pr2F0G14(x854, x855, x856, Succ(Succ(x857)), x858)_>=_new_pr2F0G14(x854, x855, x856, x857, x858))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F0G14(x854, x855, x856, Succ(Succ(Succ(Succ(x862)))), x858)_>=_new_pr2F0G14(x854, x855, x856, Succ(Succ(x862)), x858))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G14(x864, x865, x866, Succ(Succ(x867)), x868) -> new_pr2F0G14(x864, x865, x866, x867, x868), new_pr2F0G14(x869, x870, x871, Zero, x872) -> new_pr2F0G13(x869, new_sr10(x870, x872), new_primDivNatS1(x871), new_primDivNatS1(x871), x872) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G14(x864, x865, x866, x867, x868)=new_pr2F0G14(x869, x870, x871, Zero, x872)  ==>  new_pr2F0G14(x864, x865, x866, Succ(Succ(x867)), x868)_>=_new_pr2F0G14(x864, x865, x866, x867, x868))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F0G14(x864, x865, x866, Succ(Succ(Zero)), x868)_>=_new_pr2F0G14(x864, x865, x866, Zero, x868))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G14(x902, x903, x904, Zero, x905) -> new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(x904), new_primDivNatS1(x904), x905), new_pr2F0G13(x906, x907, x908, Succ(Zero), x909) -> new_pr2F2(x907, x908, new_fromInt, x906, x909) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(x904), new_primDivNatS1(x904), x905)=new_pr2F0G13(x906, x907, x908, Succ(Zero), x909)  ==>  new_pr2F0G14(x902, x903, x904, Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(x904), new_primDivNatS1(x904), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primDivNatS1(x904)=Succ(Zero)  ==>  new_pr2F0G14(x902, x903, x904, Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(x904), new_primDivNatS1(x904), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x904)=Succ(Zero) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (new_primDivNatS01(x1194)=Succ(Zero)  ==>  new_pr2F0G14(x902, x903, Succ(x1194), Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(Succ(x1194)), new_primDivNatS1(Succ(x1194)), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1194)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(4)    (Succ(new_primDivNatS4(x1195))=Succ(Zero)  ==>  new_pr2F0G14(x902, x903, Succ(Succ(Succ(x1195))), Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(Succ(Succ(Succ(x1195)))), new_primDivNatS1(Succ(Succ(Succ(x1195)))), x905))
84.27/49.98	
84.27/49.98	(5)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G14(x902, x903, Succ(Succ(Zero)), Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (new_pr2F0G14(x902, x903, Succ(Succ(Succ(x1195))), Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(Succ(Succ(Succ(x1195)))), new_primDivNatS1(Succ(Succ(Succ(x1195)))), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G14(x902, x903, Succ(Succ(Zero)), Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G14(x918, x919, x920, Zero, x921) -> new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(x920), new_primDivNatS1(x920), x921), new_pr2F0G13(x922, x923, x924, Succ(Succ(x925)), x926) -> new_pr2F0G14(x922, x923, x924, x925, x926) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(x920), new_primDivNatS1(x920), x921)=new_pr2F0G13(x922, x923, x924, Succ(Succ(x925)), x926)  ==>  new_pr2F0G14(x918, x919, x920, Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(x920), new_primDivNatS1(x920), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primDivNatS1(x920)=Succ(Succ(x925))  ==>  new_pr2F0G14(x918, x919, x920, Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(x920), new_primDivNatS1(x920), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x920)=Succ(Succ(x925)) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (new_primDivNatS01(x1196)=Succ(Succ(x925))  ==>  new_pr2F0G14(x918, x919, Succ(x1196), Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(Succ(x1196)), new_primDivNatS1(Succ(x1196)), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1196)=Succ(Succ(x925)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(4)    (Succ(new_primDivNatS4(x1197))=Succ(Succ(x925))  ==>  new_pr2F0G14(x918, x919, Succ(Succ(Succ(x1197))), Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(Succ(Succ(Succ(x1197)))), new_primDivNatS1(Succ(Succ(Succ(x1197)))), x921))
84.27/49.98	
84.27/49.98	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x925))  ==>  new_pr2F0G14(x918, x919, Succ(Succ(Zero)), Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (new_pr2F0G14(x918, x919, Succ(Succ(Succ(x1197))), Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(Succ(Succ(Succ(x1197)))), new_primDivNatS1(Succ(Succ(Succ(x1197)))), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G14(x918, x919, Succ(Succ(Zero)), Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G14(x939, x940, x941, Zero, x942) -> new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(x941), new_primDivNatS1(x941), x942), new_pr2F0G13(x943, x944, x945, Zero, x946) -> new_pr2F0G13(x943, new_sr10(x944, x946), new_primDivNatS1(x945), new_primDivNatS1(x945), x946) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(x941), new_primDivNatS1(x941), x942)=new_pr2F0G13(x943, x944, x945, Zero, x946)  ==>  new_pr2F0G14(x939, x940, x941, Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(x941), new_primDivNatS1(x941), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primDivNatS1(x941)=Zero  ==>  new_pr2F0G14(x939, x940, x941, Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(x941), new_primDivNatS1(x941), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x941)=Zero which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Zero=Zero  ==>  new_pr2F0G14(x939, x940, Zero, Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x942))
84.27/49.98	
84.27/49.98	(4)    (new_primDivNatS01(x1198)=Zero  ==>  new_pr2F0G14(x939, x940, Succ(x1198), Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(Succ(x1198)), new_primDivNatS1(Succ(x1198)), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(5)    (new_pr2F0G14(x939, x940, Zero, Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1198)=Zero which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Zero=Zero  ==>  new_pr2F0G14(x939, x940, Succ(Zero), Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G14(x939, x940, Succ(Zero), Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G13(x971, x972, x973, Zero, x974) -> new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(x973), new_primDivNatS1(x973), x974), new_pr2F0G13(x975, x976, x977, Succ(Zero), x978) -> new_pr2F2(x976, x977, new_fromInt, x975, x978) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(x973), new_primDivNatS1(x973), x974)=new_pr2F0G13(x975, x976, x977, Succ(Zero), x978)  ==>  new_pr2F0G13(x971, x972, x973, Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(x973), new_primDivNatS1(x973), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primDivNatS1(x973)=Succ(Zero)  ==>  new_pr2F0G13(x971, x972, x973, Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(x973), new_primDivNatS1(x973), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x973)=Succ(Zero) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (new_primDivNatS01(x1200)=Succ(Zero)  ==>  new_pr2F0G13(x971, x972, Succ(x1200), Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(Succ(x1200)), new_primDivNatS1(Succ(x1200)), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1200)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(4)    (Succ(new_primDivNatS4(x1201))=Succ(Zero)  ==>  new_pr2F0G13(x971, x972, Succ(Succ(Succ(x1201))), Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(Succ(Succ(Succ(x1201)))), new_primDivNatS1(Succ(Succ(Succ(x1201)))), x974))
84.27/49.98	
84.27/49.98	(5)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G13(x971, x972, Succ(Succ(Zero)), Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (new_pr2F0G13(x971, x972, Succ(Succ(Succ(x1201))), Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(Succ(Succ(Succ(x1201)))), new_primDivNatS1(Succ(Succ(Succ(x1201)))), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G13(x971, x972, Succ(Succ(Zero)), Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G13(x987, x988, x989, Zero, x990) -> new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(x989), new_primDivNatS1(x989), x990), new_pr2F0G13(x991, x992, x993, Succ(Succ(x994)), x995) -> new_pr2F0G14(x991, x992, x993, x994, x995) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(x989), new_primDivNatS1(x989), x990)=new_pr2F0G13(x991, x992, x993, Succ(Succ(x994)), x995)  ==>  new_pr2F0G13(x987, x988, x989, Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(x989), new_primDivNatS1(x989), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primDivNatS1(x989)=Succ(Succ(x994))  ==>  new_pr2F0G13(x987, x988, x989, Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(x989), new_primDivNatS1(x989), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x989)=Succ(Succ(x994)) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (new_primDivNatS01(x1202)=Succ(Succ(x994))  ==>  new_pr2F0G13(x987, x988, Succ(x1202), Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(Succ(x1202)), new_primDivNatS1(Succ(x1202)), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1202)=Succ(Succ(x994)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(4)    (Succ(new_primDivNatS4(x1203))=Succ(Succ(x994))  ==>  new_pr2F0G13(x987, x988, Succ(Succ(Succ(x1203))), Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(Succ(Succ(Succ(x1203)))), new_primDivNatS1(Succ(Succ(Succ(x1203)))), x990))
84.27/49.98	
84.27/49.98	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x994))  ==>  new_pr2F0G13(x987, x988, Succ(Succ(Zero)), Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (new_pr2F0G13(x987, x988, Succ(Succ(Succ(x1203))), Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(Succ(Succ(Succ(x1203)))), new_primDivNatS1(Succ(Succ(Succ(x1203)))), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G13(x987, x988, Succ(Succ(Zero)), Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G13(x1008, x1009, x1010, Zero, x1011) -> new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(x1010), new_primDivNatS1(x1010), x1011), new_pr2F0G13(x1012, x1013, x1014, Zero, x1015) -> new_pr2F0G13(x1012, new_sr10(x1013, x1015), new_primDivNatS1(x1014), new_primDivNatS1(x1014), x1015) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(x1010), new_primDivNatS1(x1010), x1011)=new_pr2F0G13(x1012, x1013, x1014, Zero, x1015)  ==>  new_pr2F0G13(x1008, x1009, x1010, Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(x1010), new_primDivNatS1(x1010), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primDivNatS1(x1010)=Zero  ==>  new_pr2F0G13(x1008, x1009, x1010, Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(x1010), new_primDivNatS1(x1010), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1010)=Zero which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Zero=Zero  ==>  new_pr2F0G13(x1008, x1009, Zero, Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1011))
84.27/49.98	
84.27/49.98	(4)    (new_primDivNatS01(x1204)=Zero  ==>  new_pr2F0G13(x1008, x1009, Succ(x1204), Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(Succ(x1204)), new_primDivNatS1(Succ(x1204)), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(5)    (new_pr2F0G13(x1008, x1009, Zero, Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1204)=Zero which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Zero=Zero  ==>  new_pr2F0G13(x1008, x1009, Succ(Zero), Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G13(x1008, x1009, Succ(Zero), Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	To summarize, we get the following constraints P__>=_ for the following pairs.
84.27/49.98	
84.27/49.98	*new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x0, x1, x2, Succ(Succ(Succ(Succ(x8)))), x4)_>=_new_pr2F0G12(x0, x1, x2, Succ(Succ(x8)), x4))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x10, x11, x12, Succ(Succ(Succ(Zero))), x14)_>=_new_pr2F0G12(x10, x11, x12, Succ(Zero), x14))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x34, x35, x36, Succ(Succ(Zero)), x38)_>=_new_pr2F0G12(x34, x35, x36, Zero, x38))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x91, x92, x93, Succ(Zero), x94)_>=_new_pr2F1(x91, x93, new_fromInt, x92, x94))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.98	
84.27/49.98	*(new_pr2F1(x159, x160, Pos(x165), x162, x163)_>=_new_pr2F34(x160, Pos(x165), x159, new_sr9(x159, x162, x163), x163))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.98	
84.27/49.98	*(new_pr2F34(Succ(x246), Pos(Zero), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x246)), Zero), x241, new_primPlusNat0(Succ(Succ(x246)), Zero), x242, x243))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F34(x239, Pos(Succ(x1018)), x241, x242, x243)_>=_new_pr2F31(new_primPlusNat0(Succ(x239), Succ(x1018)), x241, new_primPlusNat0(Succ(x239), Succ(x1018)), x242, x243))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F34(Zero, Pos(Zero), x266, x267, x268)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), x266, new_primPlusNat0(Succ(Zero), Zero), x267, x268))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.98	
84.27/49.98	*(new_pr2F31(Succ(x298), x299, Succ(Succ(Succ(Succ(x306)))), x301, x302)_>=_new_pr2F0G12(x299, x301, Succ(Succ(Succ(x306))), Succ(Succ(x306)), x302))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F31(Succ(x308), x309, Succ(Succ(Succ(Zero))), x311, x312)_>=_new_pr2F0G12(x309, x311, Succ(Succ(Zero)), Succ(Zero), x312))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F31(Succ(x332), x333, Succ(Succ(Zero)), x335, x336)_>=_new_pr2F0G12(x333, x335, Succ(Zero), Zero, x336))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x405, x406, Succ(Succ(x1096)), Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(Succ(Succ(x1096)))), new_primDivNatS1(Succ(Succ(Succ(x1096)))), x408))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x405, x406, Succ(Zero), Zero, x408)_>=_new_pr2F0G13(new_sr8(x405, x406, x408), x405, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x408))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x421, x422, Succ(Succ(x1099)), Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(Succ(Succ(x1099)))), new_primDivNatS1(Succ(Succ(Succ(x1099)))), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x421, x422, Succ(Zero), Zero, x424)_>=_new_pr2F0G13(new_sr8(x421, x422, x424), x421, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x424))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G12(x442, x443, Zero, Zero, x445)_>=_new_pr2F0G13(new_sr8(x442, x443, x445), x442, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x445))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x478, x479, x480, Succ(Zero), x481)_>=_new_pr2F2(x479, x480, new_fromInt, x478, x481))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.98	
84.27/49.98	*(new_pr2F2(x531, Succ(Succ(x538)), Pos(Zero), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x538)), Zero), new_sr11(x531, x535), new_primPlusNat0(Succ(Succ(x538)), Zero), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F2(x531, Zero, Pos(Succ(Succ(x538))), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x538))), new_sr11(x531, x535), new_primPlusNat0(Zero, Succ(Succ(x538))), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F2(x531, Succ(x1104), Pos(Succ(x1103)), x534, x535)_>=_new_pr2F31(new_primPlusNat0(Succ(x1104), Succ(x1103)), new_sr11(x531, x535), new_primPlusNat0(Succ(x1104), Succ(x1103)), x534, x535))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F2(x556, Succ(Zero), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(Zero), Zero), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F2(x556, Zero, Pos(Succ(Zero)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Zero)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(Zero)), x559, x560))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.98	
84.27/49.98	*(new_pr2F31(Succ(x598), x599, Succ(Zero), x600, x601)_>=_new_pr2F1(x599, Zero, new_fromInt, x600, x601))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x701, x702, x703, Succ(Succ(Succ(Zero))), x705)_>=_new_pr2F0G14(x701, x702, x703, Succ(Zero), x705))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x710, x711, x712, Succ(Succ(Succ(Succ(x718)))), x714)_>=_new_pr2F0G14(x710, x711, x712, Succ(Succ(x718)), x714))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x720, x721, x722, Succ(Succ(Zero)), x724)_>=_new_pr2F0G14(x720, x721, x722, Zero, x724))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x845, x846, x847, Succ(Succ(Succ(Zero))), x849)_>=_new_pr2F0G14(x845, x846, x847, Succ(Zero), x849))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x854, x855, x856, Succ(Succ(Succ(Succ(x862)))), x858)_>=_new_pr2F0G14(x854, x855, x856, Succ(Succ(x862)), x858))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x864, x865, x866, Succ(Succ(Zero)), x868)_>=_new_pr2F0G14(x864, x865, x866, Zero, x868))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x902, x903, Succ(Succ(Succ(x1195))), Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(Succ(Succ(Succ(x1195)))), new_primDivNatS1(Succ(Succ(Succ(x1195)))), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x902, x903, Succ(Succ(Zero)), Zero, x905)_>=_new_pr2F0G13(x902, new_sr10(x903, x905), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x905))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x918, x919, Succ(Succ(Succ(x1197))), Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(Succ(Succ(Succ(x1197)))), new_primDivNatS1(Succ(Succ(Succ(x1197)))), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x918, x919, Succ(Succ(Zero)), Zero, x921)_>=_new_pr2F0G13(x918, new_sr10(x919, x921), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x921))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x939, x940, Zero, Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G14(x939, x940, Succ(Zero), Zero, x942)_>=_new_pr2F0G13(x939, new_sr10(x940, x942), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x942))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x971, x972, Succ(Succ(Succ(x1201))), Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(Succ(Succ(Succ(x1201)))), new_primDivNatS1(Succ(Succ(Succ(x1201)))), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x971, x972, Succ(Succ(Zero)), Zero, x974)_>=_new_pr2F0G13(x971, new_sr10(x972, x974), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x974))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x987, x988, Succ(Succ(Succ(x1203))), Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(Succ(Succ(Succ(x1203)))), new_primDivNatS1(Succ(Succ(Succ(x1203)))), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x987, x988, Succ(Succ(Zero)), Zero, x990)_>=_new_pr2F0G13(x987, new_sr10(x988, x990), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x990))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x1008, x1009, Zero, Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	*(new_pr2F0G13(x1008, x1009, Succ(Zero), Zero, x1011)_>=_new_pr2F0G13(x1008, new_sr10(x1009, x1011), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1011))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	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. 
84.27/49.98	----------------------------------------
84.27/49.98	
84.27/49.98	(29)
84.27/49.98	Obligation:
84.27/49.98	Q DP problem:
84.27/49.98	The TRS P consists of the following rules:
84.27/49.98	
84.27/49.98	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.27/49.98	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.98	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.98	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.98	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	
84.27/49.98	The TRS R consists of the following rules:
84.27/49.98	
84.27/49.98	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.98	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/49.98	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/49.98	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/49.98	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/49.98	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.98	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.98	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.98	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/49.98	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.98	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.98	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/49.98	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/49.98	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/49.98	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/49.98	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/49.98	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.98	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/49.98	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.98	   new_sr13(vuz69, vuz20) -> error([])
84.27/49.98	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/49.98	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/49.98	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/49.98	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/49.98	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/49.98	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/49.98	   new_primMulNat0(Zero, Zero) -> Zero
84.27/49.98	   new_primDivNatS01(Zero) -> Zero
84.27/49.98	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.98	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_primDivNatS1(Zero) -> Zero
84.27/49.98	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.98	   new_primDivNatS3 -> Zero
84.27/49.98	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/49.98	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.98	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.98	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.98	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr15(vuz72, vuz20) -> error([])
84.27/49.98	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.98	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_fromInt -> Pos(Succ(Zero))
84.27/49.98	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/49.98	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.98	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.98	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.98	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/49.98	   new_sr14(vuz70, vuz20) -> error([])
84.27/49.98	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.98	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.98	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.98	   new_primDivNatS2 -> new_primDivNatS3
84.27/49.98	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.98	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/49.98	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/49.98	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.98	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/49.98	
84.27/49.98	The set Q consists of the following terms:
84.27/49.98	
84.27/49.98	   new_sr1(x0, x1, ty_Integer)
84.27/49.98	   new_sr(x0, x1, ty_Integer)
84.27/49.98	   new_sr6(x0, ty_Int)
84.27/49.98	   new_sr12(Pos(x0), Neg(x1))
84.27/49.98	   new_sr12(Neg(x0), Pos(x1))
84.27/49.98	   new_sr7(x0, x1, ty_Int)
84.27/49.98	   new_sr9(x0, x1, ty_Float)
84.27/49.98	   new_sr5(x0, ty_Integer)
84.27/49.98	   new_sr10(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr4(x0, ty_Integer)
84.27/49.98	   new_sr0(x0, x1, ty_Integer)
84.27/49.98	   new_sr2(x0, ty_Double)
84.27/49.98	   new_sr2(x0, ty_Float)
84.27/49.98	   new_sr12(Neg(x0), Neg(x1))
84.27/49.98	   new_sr(x0, x1, ty_Int)
84.27/49.98	   new_sr5(x0, ty_Int)
84.27/49.98	   new_primDivNatS1(Zero)
84.27/49.98	   new_sr6(x0, ty_Integer)
84.27/49.98	   new_sr11(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr3(x0, ty_Double)
84.27/49.98	   new_sr13(x0, x1)
84.27/49.98	   new_sr4(x0, ty_Float)
84.27/49.98	   new_sr0(x0, x1, ty_Int)
84.27/49.98	   new_primMulNat0(Zero, Zero)
84.27/49.98	   new_sr11(x0, ty_Float)
84.27/49.98	   new_sr20(x0)
84.27/49.98	   new_sr11(x0, ty_Double)
84.27/49.98	   new_sr3(x0, ty_Int)
84.27/49.98	   new_sr0(x0, x1, ty_Double)
84.27/49.98	   new_sr8(x0, x1, ty_Double)
84.27/49.98	   new_fromInt
84.27/49.98	   new_sr6(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr(x0, x1, ty_Float)
84.27/49.98	   new_primDivNatS4(x0)
84.27/49.98	   new_sr4(x0, ty_Double)
84.27/49.98	   new_sr10(x0, ty_Int)
84.27/49.98	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr2(x0, ty_Integer)
84.27/49.98	   new_sr21(x0, x1)
84.27/49.98	   new_primMulNat0(Zero, Succ(x0))
84.27/49.98	   new_primDivNatS2
84.27/49.98	   new_primDivNatS1(Succ(x0))
84.27/49.98	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr6(x0, ty_Double)
84.27/49.98	   new_sr12(Pos(x0), Pos(x1))
84.27/49.98	   new_sr8(x0, x1, ty_Float)
84.27/49.98	   new_sr11(x0, ty_Integer)
84.27/49.98	   new_sr7(x0, x1, ty_Float)
84.27/49.98	   new_sr7(x0, x1, ty_Integer)
84.27/49.98	   new_sr1(x0, x1, ty_Float)
84.27/49.98	   new_primDivNatS01(Succ(Zero))
84.27/49.98	   new_sr9(x0, x1, ty_Int)
84.27/49.98	   new_primPlusNat0(Succ(x0), Zero)
84.27/49.98	   new_sr3(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr8(x0, x1, ty_Integer)
84.27/49.98	   new_sr6(x0, ty_Float)
84.27/49.98	   new_sr17(x0)
84.27/49.98	   new_sr9(x0, x1, ty_Integer)
84.27/49.98	   new_sr7(x0, x1, ty_Double)
84.27/49.98	   new_sr2(x0, ty_Int)
84.27/49.98	   new_sr10(x0, ty_Double)
84.27/49.98	   new_sr5(x0, ty_Float)
84.27/49.98	   new_sr18(x0)
84.27/49.98	   new_sr4(x0, app(ty_Ratio, x1))
84.27/49.98	   new_primPlusNat0(Zero, Succ(x0))
84.27/49.98	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/49.98	   new_sr16(x0, x1, x2)
84.27/49.98	   new_sr1(x0, x1, ty_Double)
84.27/49.98	   new_primDivNatS01(Succ(Succ(x0)))
84.27/49.98	   new_sr19(x0)
84.27/49.98	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/49.98	   new_primDivNatS5(x0)
84.27/49.98	   new_sr5(x0, app(ty_Ratio, x1))
84.27/49.98	   new_primDivNatS3
84.27/49.98	   new_sr(x0, x1, ty_Double)
84.27/49.98	   new_sr0(x0, x1, ty_Float)
84.27/49.98	   new_sr1(x0, x1, ty_Int)
84.27/49.98	   new_sr15(x0, x1)
84.27/49.98	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_primDivNatS01(Zero)
84.27/49.98	   new_sr9(x0, x1, ty_Double)
84.27/49.98	   new_sr10(x0, ty_Float)
84.27/49.98	   new_sr10(x0, ty_Integer)
84.27/49.98	   new_sr4(x0, ty_Int)
84.27/49.98	   new_sr2(x0, app(ty_Ratio, x1))
84.27/49.98	   new_primMulNat0(Succ(x0), Zero)
84.27/49.98	   new_sr5(x0, ty_Double)
84.27/49.98	   new_primPlusNat0(Zero, Zero)
84.27/49.98	   new_sr8(x0, x1, ty_Int)
84.27/49.98	   new_sr14(x0, x1)
84.27/49.98	   new_sr3(x0, ty_Integer)
84.27/49.98	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr3(x0, ty_Float)
84.27/49.98	   new_sr11(x0, ty_Int)
84.27/49.98	
84.27/49.98	We have to consider all minimal (P,Q,R)-chains.
84.27/49.98	----------------------------------------
84.27/49.98	
84.27/49.98	(30) QDPPairToRuleProof (EQUIVALENT)
84.27/49.98	The dependency pair new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd) was transformed to the following new rules:
84.27/49.98	   anew_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.98	   new_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.98	   new_new_pr2F0G12(Succ(Zero)) -> cons_new_pr2F0G12(Succ(Zero))
84.27/49.98	   new_new_pr2F0G12(Zero) -> cons_new_pr2F0G12(Zero)
84.27/49.98	
84.27/49.98	the following new pairs maintain the fan-in:
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/49.98	
84.27/49.98	the following new pairs maintain the fan-out:
84.27/49.98	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/49.98	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/49.98	
84.27/49.98	----------------------------------------
84.27/49.98	
84.27/49.98	(31)
84.27/49.98	Complex Obligation (AND)
84.27/49.98	
84.27/49.98	----------------------------------------
84.27/49.98	
84.27/49.98	(32)
84.27/49.98	Obligation:
84.27/49.98	Q DP problem:
84.27/49.98	The TRS P consists of the following rules:
84.27/49.98	
84.27/49.98	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.98	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.98	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.98	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/49.98	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/49.98	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/49.98	
84.27/49.98	The TRS R consists of the following rules:
84.27/49.98	
84.27/49.98	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.98	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/49.98	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/49.98	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/49.98	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/49.98	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.98	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.98	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.98	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/49.98	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.98	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.98	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/49.98	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/49.98	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/49.98	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/49.98	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/49.98	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.98	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/49.98	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.98	   new_sr13(vuz69, vuz20) -> error([])
84.27/49.98	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/49.98	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/49.98	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/49.98	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/49.98	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/49.98	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/49.98	   new_primMulNat0(Zero, Zero) -> Zero
84.27/49.98	   new_primDivNatS01(Zero) -> Zero
84.27/49.98	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.98	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_primDivNatS1(Zero) -> Zero
84.27/49.98	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.98	   new_primDivNatS3 -> Zero
84.27/49.98	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/49.98	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.98	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.98	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.98	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr15(vuz72, vuz20) -> error([])
84.27/49.98	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.98	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_fromInt -> Pos(Succ(Zero))
84.27/49.98	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/49.98	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.98	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.98	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.98	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/49.98	   new_sr14(vuz70, vuz20) -> error([])
84.27/49.98	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.98	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.98	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.98	   new_primDivNatS2 -> new_primDivNatS3
84.27/49.98	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.98	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/49.98	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/49.98	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.98	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/49.98	   anew_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.98	   new_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.98	   new_new_pr2F0G12(Succ(Zero)) -> cons_new_pr2F0G12(Succ(Zero))
84.27/49.98	   new_new_pr2F0G12(Zero) -> cons_new_pr2F0G12(Zero)
84.27/49.98	
84.27/49.98	The set Q consists of the following terms:
84.27/49.98	
84.27/49.98	   new_sr1(x0, x1, ty_Integer)
84.27/49.98	   new_sr(x0, x1, ty_Integer)
84.27/49.98	   new_sr6(x0, ty_Int)
84.27/49.98	   new_sr12(Pos(x0), Neg(x1))
84.27/49.98	   new_sr12(Neg(x0), Pos(x1))
84.27/49.98	   new_sr7(x0, x1, ty_Int)
84.27/49.98	   new_sr9(x0, x1, ty_Float)
84.27/49.98	   new_sr5(x0, ty_Integer)
84.27/49.98	   new_sr10(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr4(x0, ty_Integer)
84.27/49.98	   new_sr0(x0, x1, ty_Integer)
84.27/49.98	   new_sr2(x0, ty_Double)
84.27/49.98	   new_sr2(x0, ty_Float)
84.27/49.98	   new_sr12(Neg(x0), Neg(x1))
84.27/49.98	   new_sr(x0, x1, ty_Int)
84.27/49.98	   new_sr5(x0, ty_Int)
84.27/49.98	   new_primDivNatS1(Zero)
84.27/49.98	   new_sr6(x0, ty_Integer)
84.27/49.98	   new_sr11(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr3(x0, ty_Double)
84.27/49.98	   new_sr13(x0, x1)
84.27/49.98	   new_sr4(x0, ty_Float)
84.27/49.98	   new_sr0(x0, x1, ty_Int)
84.27/49.98	   new_primMulNat0(Zero, Zero)
84.27/49.98	   new_sr11(x0, ty_Float)
84.27/49.98	   new_sr20(x0)
84.27/49.98	   new_sr11(x0, ty_Double)
84.27/49.98	   new_sr3(x0, ty_Int)
84.27/49.98	   new_sr0(x0, x1, ty_Double)
84.27/49.98	   new_sr8(x0, x1, ty_Double)
84.27/49.98	   new_fromInt
84.27/49.98	   new_sr6(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr(x0, x1, ty_Float)
84.27/49.98	   new_primDivNatS4(x0)
84.27/49.98	   new_sr4(x0, ty_Double)
84.27/49.98	   new_sr10(x0, ty_Int)
84.27/49.98	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr2(x0, ty_Integer)
84.27/49.98	   new_sr21(x0, x1)
84.27/49.98	   new_primMulNat0(Zero, Succ(x0))
84.27/49.98	   new_primDivNatS2
84.27/49.98	   new_primDivNatS1(Succ(x0))
84.27/49.98	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr6(x0, ty_Double)
84.27/49.98	   new_sr12(Pos(x0), Pos(x1))
84.27/49.98	   new_sr8(x0, x1, ty_Float)
84.27/49.98	   new_sr11(x0, ty_Integer)
84.27/49.98	   new_sr7(x0, x1, ty_Float)
84.27/49.98	   new_sr7(x0, x1, ty_Integer)
84.27/49.98	   new_sr1(x0, x1, ty_Float)
84.27/49.98	   new_primDivNatS01(Succ(Zero))
84.27/49.98	   new_sr9(x0, x1, ty_Int)
84.27/49.98	   new_primPlusNat0(Succ(x0), Zero)
84.27/49.98	   new_sr3(x0, app(ty_Ratio, x1))
84.27/49.98	   new_sr8(x0, x1, ty_Integer)
84.27/49.98	   new_sr6(x0, ty_Float)
84.27/49.98	   new_sr17(x0)
84.27/49.98	   new_sr9(x0, x1, ty_Integer)
84.27/49.98	   new_sr7(x0, x1, ty_Double)
84.27/49.98	   new_sr2(x0, ty_Int)
84.27/49.98	   new_sr10(x0, ty_Double)
84.27/49.98	   new_sr5(x0, ty_Float)
84.27/49.98	   new_sr18(x0)
84.27/49.98	   new_sr4(x0, app(ty_Ratio, x1))
84.27/49.98	   new_primPlusNat0(Zero, Succ(x0))
84.27/49.98	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/49.98	   new_sr16(x0, x1, x2)
84.27/49.98	   new_sr1(x0, x1, ty_Double)
84.27/49.98	   new_primDivNatS01(Succ(Succ(x0)))
84.27/49.98	   new_sr19(x0)
84.27/49.98	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/49.98	   new_primDivNatS5(x0)
84.27/49.98	   new_sr5(x0, app(ty_Ratio, x1))
84.27/49.98	   new_primDivNatS3
84.27/49.98	   new_sr(x0, x1, ty_Double)
84.27/49.98	   new_sr0(x0, x1, ty_Float)
84.27/49.98	   new_sr1(x0, x1, ty_Int)
84.27/49.98	   new_sr15(x0, x1)
84.27/49.98	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_primDivNatS01(Zero)
84.27/49.98	   new_sr9(x0, x1, ty_Double)
84.27/49.98	   new_sr10(x0, ty_Float)
84.27/49.98	   new_sr10(x0, ty_Integer)
84.27/49.98	   new_sr4(x0, ty_Int)
84.27/49.98	   new_sr2(x0, app(ty_Ratio, x1))
84.27/49.98	   new_primMulNat0(Succ(x0), Zero)
84.27/49.98	   new_sr5(x0, ty_Double)
84.27/49.98	   new_primPlusNat0(Zero, Zero)
84.27/49.98	   new_sr8(x0, x1, ty_Int)
84.27/49.98	   new_sr14(x0, x1)
84.27/49.98	   new_sr3(x0, ty_Integer)
84.27/49.98	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/49.98	   new_sr3(x0, ty_Float)
84.27/49.98	   new_sr11(x0, ty_Int)
84.27/49.98	   new_new_pr2F0G12(Succ(Succ(x0)))
84.27/49.98	   anew_new_pr2F0G12(Succ(Succ(x0)))
84.27/49.98	   new_new_pr2F0G12(Succ(Zero))
84.27/49.98	   new_new_pr2F0G12(Zero)
84.27/49.98	
84.27/49.98	We have to consider all minimal (P,Q,R)-chains.
84.27/49.98	----------------------------------------
84.27/49.98	
84.27/49.98	(33) MNOCProof (EQUIVALENT)
84.27/49.98	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
84.27/49.98	----------------------------------------
84.27/49.98	
84.27/49.98	(34)
84.27/49.98	Obligation:
84.27/49.98	Q DP problem:
84.27/49.98	The TRS P consists of the following rules:
84.27/49.98	
84.27/49.98	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.98	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.98	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.98	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.98	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.98	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/49.98	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/49.98	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/49.98	
84.27/49.98	The TRS R consists of the following rules:
84.27/49.98	
84.27/49.98	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.98	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/49.98	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/49.98	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/49.98	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/49.98	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.98	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.98	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.98	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/49.98	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.98	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.98	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/49.98	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/49.98	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/49.98	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/49.98	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/49.98	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.98	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/49.98	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.98	   new_sr13(vuz69, vuz20) -> error([])
84.27/49.98	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/49.98	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/49.98	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/49.98	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/49.98	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/49.98	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/49.98	   new_primMulNat0(Zero, Zero) -> Zero
84.27/49.98	   new_primDivNatS01(Zero) -> Zero
84.27/49.98	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.98	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_primDivNatS1(Zero) -> Zero
84.27/49.98	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.98	   new_primDivNatS3 -> Zero
84.27/49.98	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/49.98	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.98	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.98	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.98	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr15(vuz72, vuz20) -> error([])
84.27/49.98	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.98	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_fromInt -> Pos(Succ(Zero))
84.27/49.98	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/49.98	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.98	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.98	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.98	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.98	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/49.98	   new_sr14(vuz70, vuz20) -> error([])
84.27/49.98	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.98	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.98	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.98	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.98	   new_primDivNatS2 -> new_primDivNatS3
84.27/49.98	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.98	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/49.98	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/49.98	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.98	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.98	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/49.98	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.98	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.98	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/49.98	   anew_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.98	   new_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.98	   new_new_pr2F0G12(Succ(Zero)) -> cons_new_pr2F0G12(Succ(Zero))
84.27/49.98	   new_new_pr2F0G12(Zero) -> cons_new_pr2F0G12(Zero)
84.27/49.98	
84.27/49.98	Q is empty.
84.27/49.98	We have to consider all (P,Q,R)-chains.
84.27/49.98	----------------------------------------
84.27/49.98	
84.27/49.98	(35) InductionCalculusProof (EQUIVALENT)
84.27/49.98	Note that final constraints are written in bold face.
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G12(x4, x5, x6, Succ(Zero), x7) -> new_pr2F1(x4, x6, new_fromInt, x5, x7), new_pr2F1(x8, x9, x10, x11, x12) -> new_pr2F34(x9, x10, x8, new_sr9(x8, x11, x12), x12) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F1(x4, x6, new_fromInt, x5, x7)=new_pr2F1(x8, x9, x10, x11, x12)  ==>  new_pr2F0G12(x4, x5, x6, Succ(Zero), x7)_>=_new_pr2F1(x4, x6, new_fromInt, x5, x7))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F0G12(x4, x5, x6, Succ(Zero), x7)_>=_new_pr2F1(x4, x6, new_fromInt, x5, x7))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F1(x79, x80, x81, x82, x83) -> new_pr2F34(x80, x81, x79, new_sr9(x79, x82, x83), x83), new_pr2F34(x84, Pos(x85), x86, x87, x88) -> new_pr2F31(new_primPlusNat0(Succ(x84), x85), x86, new_primPlusNat0(Succ(x84), x85), x87, x88) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F34(x80, x81, x79, new_sr9(x79, x82, x83), x83)=new_pr2F34(x84, Pos(x85), x86, x87, x88)  ==>  new_pr2F1(x79, x80, x81, x82, x83)_>=_new_pr2F34(x80, x81, x79, new_sr9(x79, x82, x83), x83))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F1(x79, x80, Pos(x85), x82, x83)_>=_new_pr2F34(x80, Pos(x85), x79, new_sr9(x79, x82, x83), x83))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F34(x169, Pos(x170), x171, x172, x173) -> new_pr2F31(new_primPlusNat0(Succ(x169), x170), x171, new_primPlusNat0(Succ(x169), x170), x172, x173), new_pr2F31(Succ(x174), x175, Succ(Succ(x176)), x177, x178) -> new_pr2F0G12(x175, x177, Succ(x176), x176, x178) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F31(new_primPlusNat0(Succ(x169), x170), x171, new_primPlusNat0(Succ(x169), x170), x172, x173)=new_pr2F31(Succ(x174), x175, Succ(Succ(x176)), x177, x178)  ==>  new_pr2F34(x169, Pos(x170), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), x170), x171, new_primPlusNat0(Succ(x169), x170), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x169)=x1278 & new_primPlusNat0(x1278, x170)=Succ(x174) & Succ(x169)=x1279 & new_primPlusNat0(x1279, x170)=Succ(Succ(x176))  ==>  new_pr2F34(x169, Pos(x170), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), x170), x171, new_primPlusNat0(Succ(x169), x170), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1278, x170)=Succ(x174) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Succ(Succ(new_primPlusNat0(x1281, x1280)))=Succ(x174) & Succ(x169)=Succ(x1281) & Succ(x169)=x1279 & new_primPlusNat0(x1279, Succ(x1280))=Succ(Succ(x176)) & (\/x1282,x1283,x1284,x1285,x1286,x1287,x1288:new_primPlusNat0(x1281, x1280)=Succ(x1282) & Succ(x1283)=x1281 & Succ(x1283)=x1284 & new_primPlusNat0(x1284, x1280)=Succ(Succ(x1285))  ==>  new_pr2F34(x1283, Pos(x1280), x1286, x1287, x1288)_>=_new_pr2F31(new_primPlusNat0(Succ(x1283), x1280), x1286, new_primPlusNat0(Succ(x1283), x1280), x1287, x1288))  ==>  new_pr2F34(x169, Pos(Succ(x1280)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1280)), x171, new_primPlusNat0(Succ(x169), Succ(x1280)), x172, x173))
84.27/49.98	
84.27/49.98	(4)    (Succ(x1289)=Succ(x174) & Succ(x169)=Succ(x1289) & Succ(x169)=x1279 & new_primPlusNat0(x1279, Zero)=Succ(Succ(x176))  ==>  new_pr2F34(x169, Pos(Zero), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Zero), x171, new_primPlusNat0(Succ(x169), Zero), x172, x173))
84.27/49.98	
84.27/49.98	(5)    (Succ(x1290)=Succ(x174) & Succ(x169)=Zero & Succ(x169)=x1279 & new_primPlusNat0(x1279, Succ(x1290))=Succ(Succ(x176))  ==>  new_pr2F34(x169, Pos(Succ(x1290)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1290)), x171, new_primPlusNat0(Succ(x169), Succ(x1290)), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Succ(x169)=x1279 & Succ(x1280)=x1291 & new_primPlusNat0(x1279, x1291)=Succ(Succ(x176)) & (\/x1282,x1283,x1284,x1285,x1286,x1287,x1288:new_primPlusNat0(x169, x1280)=Succ(x1282) & Succ(x1283)=x169 & Succ(x1283)=x1284 & new_primPlusNat0(x1284, x1280)=Succ(Succ(x1285))  ==>  new_pr2F34(x1283, Pos(x1280), x1286, x1287, x1288)_>=_new_pr2F31(new_primPlusNat0(Succ(x1283), x1280), x1286, new_primPlusNat0(Succ(x1283), x1280), x1287, x1288))  ==>  new_pr2F34(x169, Pos(Succ(x1280)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1280)), x171, new_primPlusNat0(Succ(x169), Succ(x1280)), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (Succ(x169)=x1279 & Zero=x1309 & new_primPlusNat0(x1279, x1309)=Succ(Succ(x176))  ==>  new_pr2F34(x169, Pos(Zero), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Zero), x171, new_primPlusNat0(Succ(x169), Zero), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1279, x1291)=Succ(Succ(x176)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(8)    (Succ(Succ(new_primPlusNat0(x1293, x1292)))=Succ(Succ(x176)) & Succ(x169)=Succ(x1293) & Succ(x1280)=Succ(x1292) & (\/x1282,x1283,x1284,x1285,x1286,x1287,x1288:new_primPlusNat0(x169, x1280)=Succ(x1282) & Succ(x1283)=x169 & Succ(x1283)=x1284 & new_primPlusNat0(x1284, x1280)=Succ(Succ(x1285))  ==>  new_pr2F34(x1283, Pos(x1280), x1286, x1287, x1288)_>=_new_pr2F31(new_primPlusNat0(Succ(x1283), x1280), x1286, new_primPlusNat0(Succ(x1283), x1280), x1287, x1288)) & (\/x1294,x1295,x1296,x1297,x1298,x1299,x1300,x1301,x1302,x1303,x1304,x1305,x1306:new_primPlusNat0(x1293, x1292)=Succ(Succ(x1294)) & Succ(x1295)=x1293 & Succ(x1296)=x1292 & (\/x1297,x1298,x1299,x1300,x1301,x1302,x1303:new_primPlusNat0(x1295, x1296)=Succ(x1297) & Succ(x1298)=x1295 & Succ(x1298)=x1299 & new_primPlusNat0(x1299, x1296)=Succ(Succ(x1300))  ==>  new_pr2F34(x1298, Pos(x1296), x1301, x1302, x1303)_>=_new_pr2F31(new_primPlusNat0(Succ(x1298), x1296), x1301, new_primPlusNat0(Succ(x1298), x1296), x1302, x1303))  ==>  new_pr2F34(x1295, Pos(Succ(x1296)), x1304, x1305, x1306)_>=_new_pr2F31(new_primPlusNat0(Succ(x1295), Succ(x1296)), x1304, new_primPlusNat0(Succ(x1295), Succ(x1296)), x1305, x1306))  ==>  new_pr2F34(x169, Pos(Succ(x1280)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1280)), x171, new_primPlusNat0(Succ(x169), Succ(x1280)), x172, x173))
84.27/49.98	
84.27/49.98	(9)    (Succ(x1307)=Succ(Succ(x176)) & Succ(x169)=Succ(x1307) & Succ(x1280)=Zero & (\/x1282,x1283,x1284,x1285,x1286,x1287,x1288:new_primPlusNat0(x169, x1280)=Succ(x1282) & Succ(x1283)=x169 & Succ(x1283)=x1284 & new_primPlusNat0(x1284, x1280)=Succ(Succ(x1285))  ==>  new_pr2F34(x1283, Pos(x1280), x1286, x1287, x1288)_>=_new_pr2F31(new_primPlusNat0(Succ(x1283), x1280), x1286, new_primPlusNat0(Succ(x1283), x1280), x1287, x1288))  ==>  new_pr2F34(x169, Pos(Succ(x1280)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1280)), x171, new_primPlusNat0(Succ(x169), Succ(x1280)), x172, x173))
84.27/49.98	
84.27/49.98	(10)    (Succ(x1308)=Succ(Succ(x176)) & Succ(x169)=Zero & Succ(x1280)=Succ(x1308) & (\/x1282,x1283,x1284,x1285,x1286,x1287,x1288:new_primPlusNat0(x169, x1280)=Succ(x1282) & Succ(x1283)=x169 & Succ(x1283)=x1284 & new_primPlusNat0(x1284, x1280)=Succ(Succ(x1285))  ==>  new_pr2F34(x1283, Pos(x1280), x1286, x1287, x1288)_>=_new_pr2F31(new_primPlusNat0(Succ(x1283), x1280), x1286, new_primPlusNat0(Succ(x1283), x1280), x1287, x1288))  ==>  new_pr2F34(x169, Pos(Succ(x1280)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1280)), x171, new_primPlusNat0(Succ(x169), Succ(x1280)), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (8) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(11)    (new_pr2F34(x169, Pos(Succ(x1280)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1280)), x171, new_primPlusNat0(Succ(x169), Succ(x1280)), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1279, x1309)=Succ(Succ(x176)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(12)    (Succ(Succ(new_primPlusNat0(x1311, x1310)))=Succ(Succ(x176)) & Succ(x169)=Succ(x1311) & Zero=Succ(x1310) & (\/x1312,x1313,x1314,x1315,x1316:new_primPlusNat0(x1311, x1310)=Succ(Succ(x1312)) & Succ(x1313)=x1311 & Zero=x1310  ==>  new_pr2F34(x1313, Pos(Zero), x1314, x1315, x1316)_>=_new_pr2F31(new_primPlusNat0(Succ(x1313), Zero), x1314, new_primPlusNat0(Succ(x1313), Zero), x1315, x1316))  ==>  new_pr2F34(x169, Pos(Zero), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Zero), x171, new_primPlusNat0(Succ(x169), Zero), x172, x173))
84.27/49.98	
84.27/49.98	(13)    (Succ(x1317)=Succ(Succ(x176)) & Succ(x169)=Succ(x1317) & Zero=Zero  ==>  new_pr2F34(x169, Pos(Zero), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Zero), x171, new_primPlusNat0(Succ(x169), Zero), x172, x173))
84.27/49.98	
84.27/49.98	(14)    (Succ(x1318)=Succ(Succ(x176)) & Succ(x169)=Zero & Zero=Succ(x1318)  ==>  new_pr2F34(x169, Pos(Zero), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Zero), x171, new_primPlusNat0(Succ(x169), Zero), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(15)    (new_pr2F34(Succ(x176), Pos(Zero), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x176)), Zero), x171, new_primPlusNat0(Succ(Succ(x176)), Zero), x172, x173))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (14) using rules (I), (II).
84.27/49.98	*We consider the chain new_pr2F34(x194, Pos(x195), x196, x197, x198) -> new_pr2F31(new_primPlusNat0(Succ(x194), x195), x196, new_primPlusNat0(Succ(x194), x195), x197, x198), new_pr2F31(Succ(x199), x200, Succ(Zero), x201, x202) -> new_pr2F1(x200, Zero, new_fromInt, x201, x202) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F31(new_primPlusNat0(Succ(x194), x195), x196, new_primPlusNat0(Succ(x194), x195), x197, x198)=new_pr2F31(Succ(x199), x200, Succ(Zero), x201, x202)  ==>  new_pr2F34(x194, Pos(x195), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), x195), x196, new_primPlusNat0(Succ(x194), x195), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x194)=x1319 & new_primPlusNat0(x1319, x195)=Succ(x199) & Succ(x194)=x1320 & new_primPlusNat0(x1320, x195)=Succ(Zero)  ==>  new_pr2F34(x194, Pos(x195), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), x195), x196, new_primPlusNat0(Succ(x194), x195), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1319, x195)=Succ(x199) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Succ(Succ(new_primPlusNat0(x1322, x1321)))=Succ(x199) & Succ(x194)=Succ(x1322) & Succ(x194)=x1320 & new_primPlusNat0(x1320, Succ(x1321))=Succ(Zero) & (\/x1323,x1324,x1325,x1326,x1327,x1328:new_primPlusNat0(x1322, x1321)=Succ(x1323) & Succ(x1324)=x1322 & Succ(x1324)=x1325 & new_primPlusNat0(x1325, x1321)=Succ(Zero)  ==>  new_pr2F34(x1324, Pos(x1321), x1326, x1327, x1328)_>=_new_pr2F31(new_primPlusNat0(Succ(x1324), x1321), x1326, new_primPlusNat0(Succ(x1324), x1321), x1327, x1328))  ==>  new_pr2F34(x194, Pos(Succ(x1321)), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Succ(x1321)), x196, new_primPlusNat0(Succ(x194), Succ(x1321)), x197, x198))
84.27/49.98	
84.27/49.98	(4)    (Succ(x1329)=Succ(x199) & Succ(x194)=Succ(x1329) & Succ(x194)=x1320 & new_primPlusNat0(x1320, Zero)=Succ(Zero)  ==>  new_pr2F34(x194, Pos(Zero), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Zero), x196, new_primPlusNat0(Succ(x194), Zero), x197, x198))
84.27/49.98	
84.27/49.98	(5)    (Succ(x1330)=Succ(x199) & Succ(x194)=Zero & Succ(x194)=x1320 & new_primPlusNat0(x1320, Succ(x1330))=Succ(Zero)  ==>  new_pr2F34(x194, Pos(Succ(x1330)), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Succ(x1330)), x196, new_primPlusNat0(Succ(x194), Succ(x1330)), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Succ(x194)=x1320 & Succ(x1321)=x1331 & new_primPlusNat0(x1320, x1331)=Succ(Zero) & (\/x1323,x1324,x1325,x1326,x1327,x1328:new_primPlusNat0(x194, x1321)=Succ(x1323) & Succ(x1324)=x194 & Succ(x1324)=x1325 & new_primPlusNat0(x1325, x1321)=Succ(Zero)  ==>  new_pr2F34(x1324, Pos(x1321), x1326, x1327, x1328)_>=_new_pr2F31(new_primPlusNat0(Succ(x1324), x1321), x1326, new_primPlusNat0(Succ(x1324), x1321), x1327, x1328))  ==>  new_pr2F34(x194, Pos(Succ(x1321)), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Succ(x1321)), x196, new_primPlusNat0(Succ(x194), Succ(x1321)), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (Succ(x194)=x1320 & Zero=x1347 & new_primPlusNat0(x1320, x1347)=Succ(Zero)  ==>  new_pr2F34(x194, Pos(Zero), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Zero), x196, new_primPlusNat0(Succ(x194), Zero), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1320, x1331)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(8)    (Succ(Succ(new_primPlusNat0(x1333, x1332)))=Succ(Zero) & Succ(x194)=Succ(x1333) & Succ(x1321)=Succ(x1332) & (\/x1323,x1324,x1325,x1326,x1327,x1328:new_primPlusNat0(x194, x1321)=Succ(x1323) & Succ(x1324)=x194 & Succ(x1324)=x1325 & new_primPlusNat0(x1325, x1321)=Succ(Zero)  ==>  new_pr2F34(x1324, Pos(x1321), x1326, x1327, x1328)_>=_new_pr2F31(new_primPlusNat0(Succ(x1324), x1321), x1326, new_primPlusNat0(Succ(x1324), x1321), x1327, x1328)) & (\/x1334,x1335,x1336,x1337,x1338,x1339,x1340,x1341,x1342,x1343,x1344:new_primPlusNat0(x1333, x1332)=Succ(Zero) & Succ(x1334)=x1333 & Succ(x1335)=x1332 & (\/x1336,x1337,x1338,x1339,x1340,x1341:new_primPlusNat0(x1334, x1335)=Succ(x1336) & Succ(x1337)=x1334 & Succ(x1337)=x1338 & new_primPlusNat0(x1338, x1335)=Succ(Zero)  ==>  new_pr2F34(x1337, Pos(x1335), x1339, x1340, x1341)_>=_new_pr2F31(new_primPlusNat0(Succ(x1337), x1335), x1339, new_primPlusNat0(Succ(x1337), x1335), x1340, x1341))  ==>  new_pr2F34(x1334, Pos(Succ(x1335)), x1342, x1343, x1344)_>=_new_pr2F31(new_primPlusNat0(Succ(x1334), Succ(x1335)), x1342, new_primPlusNat0(Succ(x1334), Succ(x1335)), x1343, x1344))  ==>  new_pr2F34(x194, Pos(Succ(x1321)), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Succ(x1321)), x196, new_primPlusNat0(Succ(x194), Succ(x1321)), x197, x198))
84.27/49.98	
84.27/49.98	(9)    (Succ(x1345)=Succ(Zero) & Succ(x194)=Succ(x1345) & Succ(x1321)=Zero & (\/x1323,x1324,x1325,x1326,x1327,x1328:new_primPlusNat0(x194, x1321)=Succ(x1323) & Succ(x1324)=x194 & Succ(x1324)=x1325 & new_primPlusNat0(x1325, x1321)=Succ(Zero)  ==>  new_pr2F34(x1324, Pos(x1321), x1326, x1327, x1328)_>=_new_pr2F31(new_primPlusNat0(Succ(x1324), x1321), x1326, new_primPlusNat0(Succ(x1324), x1321), x1327, x1328))  ==>  new_pr2F34(x194, Pos(Succ(x1321)), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Succ(x1321)), x196, new_primPlusNat0(Succ(x194), Succ(x1321)), x197, x198))
84.27/49.98	
84.27/49.98	(10)    (Succ(x1346)=Succ(Zero) & Succ(x194)=Zero & Succ(x1321)=Succ(x1346) & (\/x1323,x1324,x1325,x1326,x1327,x1328:new_primPlusNat0(x194, x1321)=Succ(x1323) & Succ(x1324)=x194 & Succ(x1324)=x1325 & new_primPlusNat0(x1325, x1321)=Succ(Zero)  ==>  new_pr2F34(x1324, Pos(x1321), x1326, x1327, x1328)_>=_new_pr2F31(new_primPlusNat0(Succ(x1324), x1321), x1326, new_primPlusNat0(Succ(x1324), x1321), x1327, x1328))  ==>  new_pr2F34(x194, Pos(Succ(x1321)), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Succ(x1321)), x196, new_primPlusNat0(Succ(x194), Succ(x1321)), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1320, x1347)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(11)    (Succ(Succ(new_primPlusNat0(x1349, x1348)))=Succ(Zero) & Succ(x194)=Succ(x1349) & Zero=Succ(x1348) & (\/x1350,x1351,x1352,x1353:new_primPlusNat0(x1349, x1348)=Succ(Zero) & Succ(x1350)=x1349 & Zero=x1348  ==>  new_pr2F34(x1350, Pos(Zero), x1351, x1352, x1353)_>=_new_pr2F31(new_primPlusNat0(Succ(x1350), Zero), x1351, new_primPlusNat0(Succ(x1350), Zero), x1352, x1353))  ==>  new_pr2F34(x194, Pos(Zero), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Zero), x196, new_primPlusNat0(Succ(x194), Zero), x197, x198))
84.27/49.98	
84.27/49.98	(12)    (Succ(x1354)=Succ(Zero) & Succ(x194)=Succ(x1354) & Zero=Zero  ==>  new_pr2F34(x194, Pos(Zero), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Zero), x196, new_primPlusNat0(Succ(x194), Zero), x197, x198))
84.27/49.98	
84.27/49.98	(13)    (Succ(x1355)=Succ(Zero) & Succ(x194)=Zero & Zero=Succ(x1355)  ==>  new_pr2F34(x194, Pos(Zero), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(x194), Zero), x196, new_primPlusNat0(Succ(x194), Zero), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (11) using rules (I), (II).We simplified constraint (12) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(14)    (new_pr2F34(Zero, Pos(Zero), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), x196, new_primPlusNat0(Succ(Zero), Zero), x197, x198))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (13) using rules (I), (II).
84.27/49.98	*We consider the chain new_pr2F34(x228, Pos(x229), x230, x231, x232) -> new_pr2F31(new_primPlusNat0(Succ(x228), x229), x230, new_primPlusNat0(Succ(x228), x229), x231, x232), new_pr2F31(Succ(x233), x234, Succ(Succ(x235)), x236, x237) -> H(x234, x236, Succ(x235), x237, anew_new_pr2F0G12(x235)) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F31(new_primPlusNat0(Succ(x228), x229), x230, new_primPlusNat0(Succ(x228), x229), x231, x232)=new_pr2F31(Succ(x233), x234, Succ(Succ(x235)), x236, x237)  ==>  new_pr2F34(x228, Pos(x229), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), x229), x230, new_primPlusNat0(Succ(x228), x229), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x228)=x1356 & new_primPlusNat0(x1356, x229)=Succ(x233) & Succ(x228)=x1357 & new_primPlusNat0(x1357, x229)=Succ(Succ(x235))  ==>  new_pr2F34(x228, Pos(x229), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), x229), x230, new_primPlusNat0(Succ(x228), x229), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1356, x229)=Succ(x233) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Succ(Succ(new_primPlusNat0(x1359, x1358)))=Succ(x233) & Succ(x228)=Succ(x1359) & Succ(x228)=x1357 & new_primPlusNat0(x1357, Succ(x1358))=Succ(Succ(x235)) & (\/x1360,x1361,x1362,x1363,x1364,x1365,x1366:new_primPlusNat0(x1359, x1358)=Succ(x1360) & Succ(x1361)=x1359 & Succ(x1361)=x1362 & new_primPlusNat0(x1362, x1358)=Succ(Succ(x1363))  ==>  new_pr2F34(x1361, Pos(x1358), x1364, x1365, x1366)_>=_new_pr2F31(new_primPlusNat0(Succ(x1361), x1358), x1364, new_primPlusNat0(Succ(x1361), x1358), x1365, x1366))  ==>  new_pr2F34(x228, Pos(Succ(x1358)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1358)), x230, new_primPlusNat0(Succ(x228), Succ(x1358)), x231, x232))
84.27/49.98	
84.27/49.98	(4)    (Succ(x1367)=Succ(x233) & Succ(x228)=Succ(x1367) & Succ(x228)=x1357 & new_primPlusNat0(x1357, Zero)=Succ(Succ(x235))  ==>  new_pr2F34(x228, Pos(Zero), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Zero), x230, new_primPlusNat0(Succ(x228), Zero), x231, x232))
84.27/49.98	
84.27/49.98	(5)    (Succ(x1368)=Succ(x233) & Succ(x228)=Zero & Succ(x228)=x1357 & new_primPlusNat0(x1357, Succ(x1368))=Succ(Succ(x235))  ==>  new_pr2F34(x228, Pos(Succ(x1368)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1368)), x230, new_primPlusNat0(Succ(x228), Succ(x1368)), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Succ(x228)=x1357 & Succ(x1358)=x1369 & new_primPlusNat0(x1357, x1369)=Succ(Succ(x235)) & (\/x1360,x1361,x1362,x1363,x1364,x1365,x1366:new_primPlusNat0(x228, x1358)=Succ(x1360) & Succ(x1361)=x228 & Succ(x1361)=x1362 & new_primPlusNat0(x1362, x1358)=Succ(Succ(x1363))  ==>  new_pr2F34(x1361, Pos(x1358), x1364, x1365, x1366)_>=_new_pr2F31(new_primPlusNat0(Succ(x1361), x1358), x1364, new_primPlusNat0(Succ(x1361), x1358), x1365, x1366))  ==>  new_pr2F34(x228, Pos(Succ(x1358)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1358)), x230, new_primPlusNat0(Succ(x228), Succ(x1358)), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (Succ(x228)=x1357 & Zero=x1387 & new_primPlusNat0(x1357, x1387)=Succ(Succ(x235))  ==>  new_pr2F34(x228, Pos(Zero), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Zero), x230, new_primPlusNat0(Succ(x228), Zero), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1357, x1369)=Succ(Succ(x235)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(8)    (Succ(Succ(new_primPlusNat0(x1371, x1370)))=Succ(Succ(x235)) & Succ(x228)=Succ(x1371) & Succ(x1358)=Succ(x1370) & (\/x1360,x1361,x1362,x1363,x1364,x1365,x1366:new_primPlusNat0(x228, x1358)=Succ(x1360) & Succ(x1361)=x228 & Succ(x1361)=x1362 & new_primPlusNat0(x1362, x1358)=Succ(Succ(x1363))  ==>  new_pr2F34(x1361, Pos(x1358), x1364, x1365, x1366)_>=_new_pr2F31(new_primPlusNat0(Succ(x1361), x1358), x1364, new_primPlusNat0(Succ(x1361), x1358), x1365, x1366)) & (\/x1372,x1373,x1374,x1375,x1376,x1377,x1378,x1379,x1380,x1381,x1382,x1383,x1384:new_primPlusNat0(x1371, x1370)=Succ(Succ(x1372)) & Succ(x1373)=x1371 & Succ(x1374)=x1370 & (\/x1375,x1376,x1377,x1378,x1379,x1380,x1381:new_primPlusNat0(x1373, x1374)=Succ(x1375) & Succ(x1376)=x1373 & Succ(x1376)=x1377 & new_primPlusNat0(x1377, x1374)=Succ(Succ(x1378))  ==>  new_pr2F34(x1376, Pos(x1374), x1379, x1380, x1381)_>=_new_pr2F31(new_primPlusNat0(Succ(x1376), x1374), x1379, new_primPlusNat0(Succ(x1376), x1374), x1380, x1381))  ==>  new_pr2F34(x1373, Pos(Succ(x1374)), x1382, x1383, x1384)_>=_new_pr2F31(new_primPlusNat0(Succ(x1373), Succ(x1374)), x1382, new_primPlusNat0(Succ(x1373), Succ(x1374)), x1383, x1384))  ==>  new_pr2F34(x228, Pos(Succ(x1358)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1358)), x230, new_primPlusNat0(Succ(x228), Succ(x1358)), x231, x232))
84.27/49.98	
84.27/49.98	(9)    (Succ(x1385)=Succ(Succ(x235)) & Succ(x228)=Succ(x1385) & Succ(x1358)=Zero & (\/x1360,x1361,x1362,x1363,x1364,x1365,x1366:new_primPlusNat0(x228, x1358)=Succ(x1360) & Succ(x1361)=x228 & Succ(x1361)=x1362 & new_primPlusNat0(x1362, x1358)=Succ(Succ(x1363))  ==>  new_pr2F34(x1361, Pos(x1358), x1364, x1365, x1366)_>=_new_pr2F31(new_primPlusNat0(Succ(x1361), x1358), x1364, new_primPlusNat0(Succ(x1361), x1358), x1365, x1366))  ==>  new_pr2F34(x228, Pos(Succ(x1358)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1358)), x230, new_primPlusNat0(Succ(x228), Succ(x1358)), x231, x232))
84.27/49.98	
84.27/49.98	(10)    (Succ(x1386)=Succ(Succ(x235)) & Succ(x228)=Zero & Succ(x1358)=Succ(x1386) & (\/x1360,x1361,x1362,x1363,x1364,x1365,x1366:new_primPlusNat0(x228, x1358)=Succ(x1360) & Succ(x1361)=x228 & Succ(x1361)=x1362 & new_primPlusNat0(x1362, x1358)=Succ(Succ(x1363))  ==>  new_pr2F34(x1361, Pos(x1358), x1364, x1365, x1366)_>=_new_pr2F31(new_primPlusNat0(Succ(x1361), x1358), x1364, new_primPlusNat0(Succ(x1361), x1358), x1365, x1366))  ==>  new_pr2F34(x228, Pos(Succ(x1358)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1358)), x230, new_primPlusNat0(Succ(x228), Succ(x1358)), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (8) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(11)    (new_pr2F34(x228, Pos(Succ(x1358)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1358)), x230, new_primPlusNat0(Succ(x228), Succ(x1358)), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1357, x1387)=Succ(Succ(x235)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(12)    (Succ(Succ(new_primPlusNat0(x1389, x1388)))=Succ(Succ(x235)) & Succ(x228)=Succ(x1389) & Zero=Succ(x1388) & (\/x1390,x1391,x1392,x1393,x1394:new_primPlusNat0(x1389, x1388)=Succ(Succ(x1390)) & Succ(x1391)=x1389 & Zero=x1388  ==>  new_pr2F34(x1391, Pos(Zero), x1392, x1393, x1394)_>=_new_pr2F31(new_primPlusNat0(Succ(x1391), Zero), x1392, new_primPlusNat0(Succ(x1391), Zero), x1393, x1394))  ==>  new_pr2F34(x228, Pos(Zero), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Zero), x230, new_primPlusNat0(Succ(x228), Zero), x231, x232))
84.27/49.98	
84.27/49.98	(13)    (Succ(x1395)=Succ(Succ(x235)) & Succ(x228)=Succ(x1395) & Zero=Zero  ==>  new_pr2F34(x228, Pos(Zero), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Zero), x230, new_primPlusNat0(Succ(x228), Zero), x231, x232))
84.27/49.98	
84.27/49.98	(14)    (Succ(x1396)=Succ(Succ(x235)) & Succ(x228)=Zero & Zero=Succ(x1396)  ==>  new_pr2F34(x228, Pos(Zero), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Zero), x230, new_primPlusNat0(Succ(x228), Zero), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(15)    (new_pr2F34(Succ(x235), Pos(Zero), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x235)), Zero), x230, new_primPlusNat0(Succ(Succ(x235)), Zero), x231, x232))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (14) using rules (I), (II).
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F31(Succ(x248), x249, Succ(Succ(x250)), x251, x252) -> new_pr2F0G12(x249, x251, Succ(x250), x250, x252), new_pr2F0G12(x253, x254, x255, Succ(Zero), x256) -> new_pr2F1(x253, x255, new_fromInt, x254, x256) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G12(x249, x251, Succ(x250), x250, x252)=new_pr2F0G12(x253, x254, x255, Succ(Zero), x256)  ==>  new_pr2F31(Succ(x248), x249, Succ(Succ(x250)), x251, x252)_>=_new_pr2F0G12(x249, x251, Succ(x250), x250, x252))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F31(Succ(x248), x249, Succ(Succ(Succ(Zero))), x251, x252)_>=_new_pr2F0G12(x249, x251, Succ(Succ(Zero)), Succ(Zero), x252))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F31(Succ(x272), x273, Succ(Succ(x274)), x275, x276) -> new_pr2F0G12(x273, x275, Succ(x274), x274, x276), new_pr2F0G12(x277, x278, x279, Zero, x280) -> new_pr2F0G13(new_sr8(x277, x278, x280), x277, new_primDivNatS1(Succ(x279)), new_primDivNatS1(Succ(x279)), x280) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G12(x273, x275, Succ(x274), x274, x276)=new_pr2F0G12(x277, x278, x279, Zero, x280)  ==>  new_pr2F31(Succ(x272), x273, Succ(Succ(x274)), x275, x276)_>=_new_pr2F0G12(x273, x275, Succ(x274), x274, x276))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_pr2F31(Succ(x272), x273, Succ(Succ(Zero)), x275, x276)_>=_new_pr2F0G12(x273, x275, Succ(Zero), Zero, x276))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G12(x356, x357, x358, Zero, x359) -> new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(x358)), new_primDivNatS1(Succ(x358)), x359), new_pr2F0G13(x360, x361, x362, Succ(Zero), x363) -> new_pr2F2(x361, x362, new_fromInt, x360, x363) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(x358)), new_primDivNatS1(Succ(x358)), x359)=new_pr2F0G13(x360, x361, x362, Succ(Zero), x363)  ==>  new_pr2F0G12(x356, x357, x358, Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(x358)), new_primDivNatS1(Succ(x358)), x359))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x358)=x1397 & new_primDivNatS1(x1397)=Succ(Zero)  ==>  new_pr2F0G12(x356, x357, x358, Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(x358)), new_primDivNatS1(Succ(x358)), x359))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1397)=Succ(Zero) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (new_primDivNatS01(x1398)=Succ(Zero) & Succ(x358)=Succ(x1398)  ==>  new_pr2F0G12(x356, x357, x358, Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(x358)), new_primDivNatS1(Succ(x358)), x359))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(4)    (new_primDivNatS01(x1398)=Succ(Zero)  ==>  new_pr2F0G12(x356, x357, x1398, Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(x1398)), new_primDivNatS1(Succ(x1398)), x359))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1398)=Succ(Zero) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(5)    (Succ(new_primDivNatS4(x1399))=Succ(Zero)  ==>  new_pr2F0G12(x356, x357, Succ(Succ(x1399)), Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(Succ(Succ(x1399)))), new_primDivNatS1(Succ(Succ(Succ(x1399)))), x359))
84.27/49.98	
84.27/49.98	(6)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G12(x356, x357, Succ(Zero), Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x359))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G12(x356, x357, Succ(Succ(x1399)), Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(Succ(Succ(x1399)))), new_primDivNatS1(Succ(Succ(Succ(x1399)))), x359))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(8)    (new_pr2F0G12(x356, x357, Succ(Zero), Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x359))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G12(x372, x373, x374, Zero, x375) -> new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(x374)), new_primDivNatS1(Succ(x374)), x375), new_pr2F0G13(x376, x377, x378, Succ(Succ(x379)), x380) -> new_pr2F0G14(x376, x377, x378, x379, x380) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(x374)), new_primDivNatS1(Succ(x374)), x375)=new_pr2F0G13(x376, x377, x378, Succ(Succ(x379)), x380)  ==>  new_pr2F0G12(x372, x373, x374, Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(x374)), new_primDivNatS1(Succ(x374)), x375))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x374)=x1400 & new_primDivNatS1(x1400)=Succ(Succ(x379))  ==>  new_pr2F0G12(x372, x373, x374, Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(x374)), new_primDivNatS1(Succ(x374)), x375))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1400)=Succ(Succ(x379)) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (new_primDivNatS01(x1401)=Succ(Succ(x379)) & Succ(x374)=Succ(x1401)  ==>  new_pr2F0G12(x372, x373, x374, Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(x374)), new_primDivNatS1(Succ(x374)), x375))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(4)    (new_primDivNatS01(x1401)=Succ(Succ(x379))  ==>  new_pr2F0G12(x372, x373, x1401, Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(x1401)), new_primDivNatS1(Succ(x1401)), x375))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1401)=Succ(Succ(x379)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(5)    (Succ(new_primDivNatS4(x1402))=Succ(Succ(x379))  ==>  new_pr2F0G12(x372, x373, Succ(Succ(x1402)), Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(Succ(Succ(x1402)))), new_primDivNatS1(Succ(Succ(Succ(x1402)))), x375))
84.27/49.98	
84.27/49.98	(6)    (Succ(new_primDivNatS2)=Succ(Succ(x379))  ==>  new_pr2F0G12(x372, x373, Succ(Zero), Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x375))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G12(x372, x373, Succ(Succ(x1402)), Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(Succ(Succ(x1402)))), new_primDivNatS1(Succ(Succ(Succ(x1402)))), x375))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(8)    (new_pr2F0G12(x372, x373, Succ(Zero), Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x375))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	*We consider the chain new_pr2F0G12(x393, x394, x395, Zero, x396) -> new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(x395)), new_primDivNatS1(Succ(x395)), x396), new_pr2F0G13(x397, x398, x399, Zero, x400) -> new_pr2F0G13(x397, new_sr10(x398, x400), new_primDivNatS1(x399), new_primDivNatS1(x399), x400) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(x395)), new_primDivNatS1(Succ(x395)), x396)=new_pr2F0G13(x397, x398, x399, Zero, x400)  ==>  new_pr2F0G12(x393, x394, x395, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(x395)), new_primDivNatS1(Succ(x395)), x396))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (Succ(x395)=x1403 & new_primDivNatS1(x1403)=Zero  ==>  new_pr2F0G12(x393, x394, x395, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(x395)), new_primDivNatS1(Succ(x395)), x396))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1403)=Zero which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Zero=Zero & Succ(x395)=Zero  ==>  new_pr2F0G12(x393, x394, x395, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(x395)), new_primDivNatS1(Succ(x395)), x396))
84.27/49.98	
84.27/49.98	(4)    (new_primDivNatS01(x1404)=Zero & Succ(x395)=Succ(x1404)  ==>  new_pr2F0G12(x393, x394, x395, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(x395)), new_primDivNatS1(Succ(x395)), x396))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(5)    (new_primDivNatS01(x1404)=Zero  ==>  new_pr2F0G12(x393, x394, x1404, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(x1404)), new_primDivNatS1(Succ(x1404)), x396))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1404)=Zero which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Zero=Zero  ==>  new_pr2F0G12(x393, x394, Zero, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x396))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (new_pr2F0G12(x393, x394, Zero, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x396))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F0G13(x437, x438, x439, Succ(Zero), x440) -> new_pr2F2(x438, x439, new_fromInt, x437, x440), new_pr2F2(x441, x442, Pos(x443), x444, x445) -> new_pr2F31(new_primPlusNat0(x442, x443), new_sr11(x441, x445), new_primPlusNat0(x442, x443), x444, x445) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F2(x438, x439, new_fromInt, x437, x440)=new_pr2F2(x441, x442, Pos(x443), x444, x445)  ==>  new_pr2F0G13(x437, x438, x439, Succ(Zero), x440)_>=_new_pr2F2(x438, x439, new_fromInt, x437, x440))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_fromInt=Pos(x443)  ==>  new_pr2F0G13(x437, x438, x439, Succ(Zero), x440)_>=_new_pr2F2(x438, x439, new_fromInt, x437, x440))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_fromInt=Pos(x443) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(3)    (Pos(Succ(Zero))=Pos(x443)  ==>  new_pr2F0G13(x437, x438, x439, Succ(Zero), x440)_>=_new_pr2F2(x438, x439, new_fromInt, x437, x440))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(4)    (new_pr2F0G13(x437, x438, x439, Succ(Zero), x440)_>=_new_pr2F2(x438, x439, new_fromInt, x437, x440))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	For Pair new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be) the following chains were created:
84.27/49.98	*We consider the chain new_pr2F2(x497, x498, Pos(x499), x500, x501) -> new_pr2F31(new_primPlusNat0(x498, x499), new_sr11(x497, x501), new_primPlusNat0(x498, x499), x500, x501), new_pr2F31(Succ(x502), x503, Succ(Succ(x504)), x505, x506) -> new_pr2F0G12(x503, x505, Succ(x504), x504, x506) which results in the following constraint:
84.27/49.98	
84.27/49.98	(1)    (new_pr2F31(new_primPlusNat0(x498, x499), new_sr11(x497, x501), new_primPlusNat0(x498, x499), x500, x501)=new_pr2F31(Succ(x502), x503, Succ(Succ(x504)), x505, x506)  ==>  new_pr2F2(x497, x498, Pos(x499), x500, x501)_>=_new_pr2F31(new_primPlusNat0(x498, x499), new_sr11(x497, x501), new_primPlusNat0(x498, x499), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(2)    (new_primPlusNat0(x498, x499)=Succ(x502) & new_primPlusNat0(x498, x499)=Succ(Succ(x504))  ==>  new_pr2F2(x497, x498, Pos(x499), x500, x501)_>=_new_pr2F31(new_primPlusNat0(x498, x499), new_sr11(x497, x501), new_primPlusNat0(x498, x499), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x498, x499)=Succ(x502) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(3)    (Succ(Succ(new_primPlusNat0(x1407, x1406)))=Succ(x502) & new_primPlusNat0(Succ(x1407), Succ(x1406))=Succ(Succ(x504)) & (\/x1408,x1409,x1410,x1411,x1412:new_primPlusNat0(x1407, x1406)=Succ(x1408) & new_primPlusNat0(x1407, x1406)=Succ(Succ(x1409))  ==>  new_pr2F2(x1410, x1407, Pos(x1406), x1411, x1412)_>=_new_pr2F31(new_primPlusNat0(x1407, x1406), new_sr11(x1410, x1412), new_primPlusNat0(x1407, x1406), x1411, x1412))  ==>  new_pr2F2(x497, Succ(x1407), Pos(Succ(x1406)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1407), Succ(x1406)), new_sr11(x497, x501), new_primPlusNat0(Succ(x1407), Succ(x1406)), x500, x501))
84.27/49.98	
84.27/49.98	(4)    (Succ(x1413)=Succ(x502) & new_primPlusNat0(Succ(x1413), Zero)=Succ(Succ(x504))  ==>  new_pr2F2(x497, Succ(x1413), Pos(Zero), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1413), Zero), new_sr11(x497, x501), new_primPlusNat0(Succ(x1413), Zero), x500, x501))
84.27/49.98	
84.27/49.98	(5)    (Succ(x1414)=Succ(x502) & new_primPlusNat0(Zero, Succ(x1414))=Succ(Succ(x504))  ==>  new_pr2F2(x497, Zero, Pos(Succ(x1414)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1414)), new_sr11(x497, x501), new_primPlusNat0(Zero, Succ(x1414)), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(6)    (Succ(x1407)=x1415 & Succ(x1406)=x1416 & new_primPlusNat0(x1415, x1416)=Succ(Succ(x504)) & (\/x1408,x1409,x1410,x1411,x1412:new_primPlusNat0(x1407, x1406)=Succ(x1408) & new_primPlusNat0(x1407, x1406)=Succ(Succ(x1409))  ==>  new_pr2F2(x1410, x1407, Pos(x1406), x1411, x1412)_>=_new_pr2F31(new_primPlusNat0(x1407, x1406), new_sr11(x1410, x1412), new_primPlusNat0(x1407, x1406), x1411, x1412))  ==>  new_pr2F2(x497, Succ(x1407), Pos(Succ(x1406)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1407), Succ(x1406)), new_sr11(x497, x501), new_primPlusNat0(Succ(x1407), Succ(x1406)), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(7)    (Succ(x1413)=x1432 & Zero=x1433 & new_primPlusNat0(x1432, x1433)=Succ(Succ(x504))  ==>  new_pr2F2(x497, Succ(x1413), Pos(Zero), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1413), Zero), new_sr11(x497, x501), new_primPlusNat0(Succ(x1413), Zero), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(8)    (Zero=x1443 & Succ(x1414)=x1444 & new_primPlusNat0(x1443, x1444)=Succ(Succ(x504))  ==>  new_pr2F2(x497, Zero, Pos(Succ(x1414)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1414)), new_sr11(x497, x501), new_primPlusNat0(Zero, Succ(x1414)), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1415, x1416)=Succ(Succ(x504)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(9)    (Succ(Succ(new_primPlusNat0(x1418, x1417)))=Succ(Succ(x504)) & Succ(x1407)=Succ(x1418) & Succ(x1406)=Succ(x1417) & (\/x1408,x1409,x1410,x1411,x1412:new_primPlusNat0(x1407, x1406)=Succ(x1408) & new_primPlusNat0(x1407, x1406)=Succ(Succ(x1409))  ==>  new_pr2F2(x1410, x1407, Pos(x1406), x1411, x1412)_>=_new_pr2F31(new_primPlusNat0(x1407, x1406), new_sr11(x1410, x1412), new_primPlusNat0(x1407, x1406), x1411, x1412)) & (\/x1419,x1420,x1421,x1422,x1423,x1424,x1425,x1426,x1427,x1428,x1429:new_primPlusNat0(x1418, x1417)=Succ(Succ(x1419)) & Succ(x1420)=x1418 & Succ(x1421)=x1417 & (\/x1422,x1423,x1424,x1425,x1426:new_primPlusNat0(x1420, x1421)=Succ(x1422) & new_primPlusNat0(x1420, x1421)=Succ(Succ(x1423))  ==>  new_pr2F2(x1424, x1420, Pos(x1421), x1425, x1426)_>=_new_pr2F31(new_primPlusNat0(x1420, x1421), new_sr11(x1424, x1426), new_primPlusNat0(x1420, x1421), x1425, x1426))  ==>  new_pr2F2(x1427, Succ(x1420), Pos(Succ(x1421)), x1428, x1429)_>=_new_pr2F31(new_primPlusNat0(Succ(x1420), Succ(x1421)), new_sr11(x1427, x1429), new_primPlusNat0(Succ(x1420), Succ(x1421)), x1428, x1429))  ==>  new_pr2F2(x497, Succ(x1407), Pos(Succ(x1406)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1407), Succ(x1406)), new_sr11(x497, x501), new_primPlusNat0(Succ(x1407), Succ(x1406)), x500, x501))
84.27/49.98	
84.27/49.98	(10)    (Succ(x1430)=Succ(Succ(x504)) & Succ(x1407)=Succ(x1430) & Succ(x1406)=Zero & (\/x1408,x1409,x1410,x1411,x1412:new_primPlusNat0(x1407, x1406)=Succ(x1408) & new_primPlusNat0(x1407, x1406)=Succ(Succ(x1409))  ==>  new_pr2F2(x1410, x1407, Pos(x1406), x1411, x1412)_>=_new_pr2F31(new_primPlusNat0(x1407, x1406), new_sr11(x1410, x1412), new_primPlusNat0(x1407, x1406), x1411, x1412))  ==>  new_pr2F2(x497, Succ(x1407), Pos(Succ(x1406)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1407), Succ(x1406)), new_sr11(x497, x501), new_primPlusNat0(Succ(x1407), Succ(x1406)), x500, x501))
84.27/49.98	
84.27/49.98	(11)    (Succ(x1431)=Succ(Succ(x504)) & Succ(x1407)=Zero & Succ(x1406)=Succ(x1431) & (\/x1408,x1409,x1410,x1411,x1412:new_primPlusNat0(x1407, x1406)=Succ(x1408) & new_primPlusNat0(x1407, x1406)=Succ(Succ(x1409))  ==>  new_pr2F2(x1410, x1407, Pos(x1406), x1411, x1412)_>=_new_pr2F31(new_primPlusNat0(x1407, x1406), new_sr11(x1410, x1412), new_primPlusNat0(x1407, x1406), x1411, x1412))  ==>  new_pr2F2(x497, Succ(x1407), Pos(Succ(x1406)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1407), Succ(x1406)), new_sr11(x497, x501), new_primPlusNat0(Succ(x1407), Succ(x1406)), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(12)    (new_pr2F2(x497, Succ(x1407), Pos(Succ(x1406)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1407), Succ(x1406)), new_sr11(x497, x501), new_primPlusNat0(Succ(x1407), Succ(x1406)), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1432, x1433)=Succ(Succ(x504)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(13)    (Succ(Succ(new_primPlusNat0(x1435, x1434)))=Succ(Succ(x504)) & Succ(x1413)=Succ(x1435) & Zero=Succ(x1434) & (\/x1436,x1437,x1438,x1439,x1440:new_primPlusNat0(x1435, x1434)=Succ(Succ(x1436)) & Succ(x1437)=x1435 & Zero=x1434  ==>  new_pr2F2(x1438, Succ(x1437), Pos(Zero), x1439, x1440)_>=_new_pr2F31(new_primPlusNat0(Succ(x1437), Zero), new_sr11(x1438, x1440), new_primPlusNat0(Succ(x1437), Zero), x1439, x1440))  ==>  new_pr2F2(x497, Succ(x1413), Pos(Zero), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1413), Zero), new_sr11(x497, x501), new_primPlusNat0(Succ(x1413), Zero), x500, x501))
84.27/49.98	
84.27/49.98	(14)    (Succ(x1441)=Succ(Succ(x504)) & Succ(x1413)=Succ(x1441) & Zero=Zero  ==>  new_pr2F2(x497, Succ(x1413), Pos(Zero), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1413), Zero), new_sr11(x497, x501), new_primPlusNat0(Succ(x1413), Zero), x500, x501))
84.27/49.98	
84.27/49.98	(15)    (Succ(x1442)=Succ(Succ(x504)) & Succ(x1413)=Zero & Zero=Succ(x1442)  ==>  new_pr2F2(x497, Succ(x1413), Pos(Zero), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1413), Zero), new_sr11(x497, x501), new_primPlusNat0(Succ(x1413), Zero), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (13) using rules (I), (II).We simplified constraint (14) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.98	
84.27/49.98	(16)    (new_pr2F2(x497, Succ(Succ(x504)), Pos(Zero), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x504)), Zero), new_sr11(x497, x501), new_primPlusNat0(Succ(Succ(x504)), Zero), x500, x501))
84.27/49.98	
84.27/49.98	
84.27/49.98	
84.27/49.98	We solved constraint (15) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1443, x1444)=Succ(Succ(x504)) which results in the following new constraints:
84.27/49.98	
84.27/49.98	(17)    (Succ(Succ(new_primPlusNat0(x1446, x1445)))=Succ(Succ(x504)) & Zero=Succ(x1446) & Succ(x1414)=Succ(x1445) & (\/x1447,x1448,x1449,x1450,x1451:new_primPlusNat0(x1446, x1445)=Succ(Succ(x1447)) & Zero=x1446 & Succ(x1448)=x1445  ==>  new_pr2F2(x1449, Zero, Pos(Succ(x1448)), x1450, x1451)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1448)), new_sr11(x1449, x1451), new_primPlusNat0(Zero, Succ(x1448)), x1450, x1451))  ==>  new_pr2F2(x497, Zero, Pos(Succ(x1414)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1414)), new_sr11(x497, x501), new_primPlusNat0(Zero, Succ(x1414)), x500, x501))
84.27/49.99	
84.27/49.99	(18)    (Succ(x1452)=Succ(Succ(x504)) & Zero=Succ(x1452) & Succ(x1414)=Zero  ==>  new_pr2F2(x497, Zero, Pos(Succ(x1414)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1414)), new_sr11(x497, x501), new_primPlusNat0(Zero, Succ(x1414)), x500, x501))
84.27/49.99	
84.27/49.99	(19)    (Succ(x1453)=Succ(Succ(x504)) & Zero=Zero & Succ(x1414)=Succ(x1453)  ==>  new_pr2F2(x497, Zero, Pos(Succ(x1414)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1414)), new_sr11(x497, x501), new_primPlusNat0(Zero, Succ(x1414)), x500, x501))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (17) using rules (I), (II).We solved constraint (18) using rules (I), (II).We simplified constraint (19) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(20)    (new_pr2F2(x497, Zero, Pos(Succ(Succ(x504))), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x504))), new_sr11(x497, x501), new_primPlusNat0(Zero, Succ(Succ(x504))), x500, x501))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F2(x522, x523, Pos(x524), x525, x526) -> new_pr2F31(new_primPlusNat0(x523, x524), new_sr11(x522, x526), new_primPlusNat0(x523, x524), x525, x526), new_pr2F31(Succ(x527), x528, Succ(Zero), x529, x530) -> new_pr2F1(x528, Zero, new_fromInt, x529, x530) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F31(new_primPlusNat0(x523, x524), new_sr11(x522, x526), new_primPlusNat0(x523, x524), x525, x526)=new_pr2F31(Succ(x527), x528, Succ(Zero), x529, x530)  ==>  new_pr2F2(x522, x523, Pos(x524), x525, x526)_>=_new_pr2F31(new_primPlusNat0(x523, x524), new_sr11(x522, x526), new_primPlusNat0(x523, x524), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primPlusNat0(x523, x524)=Succ(x527) & new_primPlusNat0(x523, x524)=Succ(Zero)  ==>  new_pr2F2(x522, x523, Pos(x524), x525, x526)_>=_new_pr2F31(new_primPlusNat0(x523, x524), new_sr11(x522, x526), new_primPlusNat0(x523, x524), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x523, x524)=Succ(x527) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Succ(Succ(new_primPlusNat0(x1455, x1454)))=Succ(x527) & new_primPlusNat0(Succ(x1455), Succ(x1454))=Succ(Zero) & (\/x1456,x1457,x1458,x1459:new_primPlusNat0(x1455, x1454)=Succ(x1456) & new_primPlusNat0(x1455, x1454)=Succ(Zero)  ==>  new_pr2F2(x1457, x1455, Pos(x1454), x1458, x1459)_>=_new_pr2F31(new_primPlusNat0(x1455, x1454), new_sr11(x1457, x1459), new_primPlusNat0(x1455, x1454), x1458, x1459))  ==>  new_pr2F2(x522, Succ(x1455), Pos(Succ(x1454)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1455), Succ(x1454)), new_sr11(x522, x526), new_primPlusNat0(Succ(x1455), Succ(x1454)), x525, x526))
84.27/49.99	
84.27/49.99	(4)    (Succ(x1460)=Succ(x527) & new_primPlusNat0(Succ(x1460), Zero)=Succ(Zero)  ==>  new_pr2F2(x522, Succ(x1460), Pos(Zero), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1460), Zero), new_sr11(x522, x526), new_primPlusNat0(Succ(x1460), Zero), x525, x526))
84.27/49.99	
84.27/49.99	(5)    (Succ(x1461)=Succ(x527) & new_primPlusNat0(Zero, Succ(x1461))=Succ(Zero)  ==>  new_pr2F2(x522, Zero, Pos(Succ(x1461)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1461)), new_sr11(x522, x526), new_primPlusNat0(Zero, Succ(x1461)), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Succ(x1455)=x1462 & Succ(x1454)=x1463 & new_primPlusNat0(x1462, x1463)=Succ(Zero) & (\/x1456,x1457,x1458,x1459:new_primPlusNat0(x1455, x1454)=Succ(x1456) & new_primPlusNat0(x1455, x1454)=Succ(Zero)  ==>  new_pr2F2(x1457, x1455, Pos(x1454), x1458, x1459)_>=_new_pr2F31(new_primPlusNat0(x1455, x1454), new_sr11(x1457, x1459), new_primPlusNat0(x1455, x1454), x1458, x1459))  ==>  new_pr2F2(x522, Succ(x1455), Pos(Succ(x1454)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1455), Succ(x1454)), new_sr11(x522, x526), new_primPlusNat0(Succ(x1455), Succ(x1454)), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (Succ(x1460)=x1477 & Zero=x1478 & new_primPlusNat0(x1477, x1478)=Succ(Zero)  ==>  new_pr2F2(x522, Succ(x1460), Pos(Zero), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1460), Zero), new_sr11(x522, x526), new_primPlusNat0(Succ(x1460), Zero), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(8)    (Zero=x1487 & Succ(x1461)=x1488 & new_primPlusNat0(x1487, x1488)=Succ(Zero)  ==>  new_pr2F2(x522, Zero, Pos(Succ(x1461)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1461)), new_sr11(x522, x526), new_primPlusNat0(Zero, Succ(x1461)), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1462, x1463)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(9)    (Succ(Succ(new_primPlusNat0(x1465, x1464)))=Succ(Zero) & Succ(x1455)=Succ(x1465) & Succ(x1454)=Succ(x1464) & (\/x1456,x1457,x1458,x1459:new_primPlusNat0(x1455, x1454)=Succ(x1456) & new_primPlusNat0(x1455, x1454)=Succ(Zero)  ==>  new_pr2F2(x1457, x1455, Pos(x1454), x1458, x1459)_>=_new_pr2F31(new_primPlusNat0(x1455, x1454), new_sr11(x1457, x1459), new_primPlusNat0(x1455, x1454), x1458, x1459)) & (\/x1466,x1467,x1468,x1469,x1470,x1471,x1472,x1473,x1474:new_primPlusNat0(x1465, x1464)=Succ(Zero) & Succ(x1466)=x1465 & Succ(x1467)=x1464 & (\/x1468,x1469,x1470,x1471:new_primPlusNat0(x1466, x1467)=Succ(x1468) & new_primPlusNat0(x1466, x1467)=Succ(Zero)  ==>  new_pr2F2(x1469, x1466, Pos(x1467), x1470, x1471)_>=_new_pr2F31(new_primPlusNat0(x1466, x1467), new_sr11(x1469, x1471), new_primPlusNat0(x1466, x1467), x1470, x1471))  ==>  new_pr2F2(x1472, Succ(x1466), Pos(Succ(x1467)), x1473, x1474)_>=_new_pr2F31(new_primPlusNat0(Succ(x1466), Succ(x1467)), new_sr11(x1472, x1474), new_primPlusNat0(Succ(x1466), Succ(x1467)), x1473, x1474))  ==>  new_pr2F2(x522, Succ(x1455), Pos(Succ(x1454)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1455), Succ(x1454)), new_sr11(x522, x526), new_primPlusNat0(Succ(x1455), Succ(x1454)), x525, x526))
84.27/49.99	
84.27/49.99	(10)    (Succ(x1475)=Succ(Zero) & Succ(x1455)=Succ(x1475) & Succ(x1454)=Zero & (\/x1456,x1457,x1458,x1459:new_primPlusNat0(x1455, x1454)=Succ(x1456) & new_primPlusNat0(x1455, x1454)=Succ(Zero)  ==>  new_pr2F2(x1457, x1455, Pos(x1454), x1458, x1459)_>=_new_pr2F31(new_primPlusNat0(x1455, x1454), new_sr11(x1457, x1459), new_primPlusNat0(x1455, x1454), x1458, x1459))  ==>  new_pr2F2(x522, Succ(x1455), Pos(Succ(x1454)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1455), Succ(x1454)), new_sr11(x522, x526), new_primPlusNat0(Succ(x1455), Succ(x1454)), x525, x526))
84.27/49.99	
84.27/49.99	(11)    (Succ(x1476)=Succ(Zero) & Succ(x1455)=Zero & Succ(x1454)=Succ(x1476) & (\/x1456,x1457,x1458,x1459:new_primPlusNat0(x1455, x1454)=Succ(x1456) & new_primPlusNat0(x1455, x1454)=Succ(Zero)  ==>  new_pr2F2(x1457, x1455, Pos(x1454), x1458, x1459)_>=_new_pr2F31(new_primPlusNat0(x1455, x1454), new_sr11(x1457, x1459), new_primPlusNat0(x1455, x1454), x1458, x1459))  ==>  new_pr2F2(x522, Succ(x1455), Pos(Succ(x1454)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1455), Succ(x1454)), new_sr11(x522, x526), new_primPlusNat0(Succ(x1455), Succ(x1454)), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1477, x1478)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(12)    (Succ(Succ(new_primPlusNat0(x1480, x1479)))=Succ(Zero) & Succ(x1460)=Succ(x1480) & Zero=Succ(x1479) & (\/x1481,x1482,x1483,x1484:new_primPlusNat0(x1480, x1479)=Succ(Zero) & Succ(x1481)=x1480 & Zero=x1479  ==>  new_pr2F2(x1482, Succ(x1481), Pos(Zero), x1483, x1484)_>=_new_pr2F31(new_primPlusNat0(Succ(x1481), Zero), new_sr11(x1482, x1484), new_primPlusNat0(Succ(x1481), Zero), x1483, x1484))  ==>  new_pr2F2(x522, Succ(x1460), Pos(Zero), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1460), Zero), new_sr11(x522, x526), new_primPlusNat0(Succ(x1460), Zero), x525, x526))
84.27/49.99	
84.27/49.99	(13)    (Succ(x1485)=Succ(Zero) & Succ(x1460)=Succ(x1485) & Zero=Zero  ==>  new_pr2F2(x522, Succ(x1460), Pos(Zero), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1460), Zero), new_sr11(x522, x526), new_primPlusNat0(Succ(x1460), Zero), x525, x526))
84.27/49.99	
84.27/49.99	(14)    (Succ(x1486)=Succ(Zero) & Succ(x1460)=Zero & Zero=Succ(x1486)  ==>  new_pr2F2(x522, Succ(x1460), Pos(Zero), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(x1460), Zero), new_sr11(x522, x526), new_primPlusNat0(Succ(x1460), Zero), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(15)    (new_pr2F2(x522, Succ(Zero), Pos(Zero), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), new_sr11(x522, x526), new_primPlusNat0(Succ(Zero), Zero), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (14) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1487, x1488)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(16)    (Succ(Succ(new_primPlusNat0(x1490, x1489)))=Succ(Zero) & Zero=Succ(x1490) & Succ(x1461)=Succ(x1489) & (\/x1491,x1492,x1493,x1494:new_primPlusNat0(x1490, x1489)=Succ(Zero) & Zero=x1490 & Succ(x1491)=x1489  ==>  new_pr2F2(x1492, Zero, Pos(Succ(x1491)), x1493, x1494)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1491)), new_sr11(x1492, x1494), new_primPlusNat0(Zero, Succ(x1491)), x1493, x1494))  ==>  new_pr2F2(x522, Zero, Pos(Succ(x1461)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1461)), new_sr11(x522, x526), new_primPlusNat0(Zero, Succ(x1461)), x525, x526))
84.27/49.99	
84.27/49.99	(17)    (Succ(x1495)=Succ(Zero) & Zero=Succ(x1495) & Succ(x1461)=Zero  ==>  new_pr2F2(x522, Zero, Pos(Succ(x1461)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1461)), new_sr11(x522, x526), new_primPlusNat0(Zero, Succ(x1461)), x525, x526))
84.27/49.99	
84.27/49.99	(18)    (Succ(x1496)=Succ(Zero) & Zero=Zero & Succ(x1461)=Succ(x1496)  ==>  new_pr2F2(x522, Zero, Pos(Succ(x1461)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1461)), new_sr11(x522, x526), new_primPlusNat0(Zero, Succ(x1461)), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (16) using rules (I), (II).We solved constraint (17) using rules (I), (II).We simplified constraint (18) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(19)    (new_pr2F2(x522, Zero, Pos(Succ(Zero)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Zero)), new_sr11(x522, x526), new_primPlusNat0(Zero, Succ(Zero)), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F2(x556, x557, Pos(x558), x559, x560) -> new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560), new_pr2F31(Succ(x561), x562, Succ(Succ(x563)), x564, x565) -> H(x562, x564, Succ(x563), x565, anew_new_pr2F0G12(x563)) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560)=new_pr2F31(Succ(x561), x562, Succ(Succ(x563)), x564, x565)  ==>  new_pr2F2(x556, x557, Pos(x558), x559, x560)_>=_new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primPlusNat0(x557, x558)=Succ(x561) & new_primPlusNat0(x557, x558)=Succ(Succ(x563))  ==>  new_pr2F2(x556, x557, Pos(x558), x559, x560)_>=_new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x557, x558)=Succ(x561) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Succ(Succ(new_primPlusNat0(x1498, x1497)))=Succ(x561) & new_primPlusNat0(Succ(x1498), Succ(x1497))=Succ(Succ(x563)) & (\/x1499,x1500,x1501,x1502,x1503:new_primPlusNat0(x1498, x1497)=Succ(x1499) & new_primPlusNat0(x1498, x1497)=Succ(Succ(x1500))  ==>  new_pr2F2(x1501, x1498, Pos(x1497), x1502, x1503)_>=_new_pr2F31(new_primPlusNat0(x1498, x1497), new_sr11(x1501, x1503), new_primPlusNat0(x1498, x1497), x1502, x1503))  ==>  new_pr2F2(x556, Succ(x1498), Pos(Succ(x1497)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1498), Succ(x1497)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1498), Succ(x1497)), x559, x560))
84.27/49.99	
84.27/49.99	(4)    (Succ(x1504)=Succ(x561) & new_primPlusNat0(Succ(x1504), Zero)=Succ(Succ(x563))  ==>  new_pr2F2(x556, Succ(x1504), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1504), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1504), Zero), x559, x560))
84.27/49.99	
84.27/49.99	(5)    (Succ(x1505)=Succ(x561) & new_primPlusNat0(Zero, Succ(x1505))=Succ(Succ(x563))  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1505)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1505)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1505)), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Succ(x1498)=x1506 & Succ(x1497)=x1507 & new_primPlusNat0(x1506, x1507)=Succ(Succ(x563)) & (\/x1499,x1500,x1501,x1502,x1503:new_primPlusNat0(x1498, x1497)=Succ(x1499) & new_primPlusNat0(x1498, x1497)=Succ(Succ(x1500))  ==>  new_pr2F2(x1501, x1498, Pos(x1497), x1502, x1503)_>=_new_pr2F31(new_primPlusNat0(x1498, x1497), new_sr11(x1501, x1503), new_primPlusNat0(x1498, x1497), x1502, x1503))  ==>  new_pr2F2(x556, Succ(x1498), Pos(Succ(x1497)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1498), Succ(x1497)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1498), Succ(x1497)), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (Succ(x1504)=x1523 & Zero=x1524 & new_primPlusNat0(x1523, x1524)=Succ(Succ(x563))  ==>  new_pr2F2(x556, Succ(x1504), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1504), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1504), Zero), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(8)    (Zero=x1534 & Succ(x1505)=x1535 & new_primPlusNat0(x1534, x1535)=Succ(Succ(x563))  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1505)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1505)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1505)), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1506, x1507)=Succ(Succ(x563)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(9)    (Succ(Succ(new_primPlusNat0(x1509, x1508)))=Succ(Succ(x563)) & Succ(x1498)=Succ(x1509) & Succ(x1497)=Succ(x1508) & (\/x1499,x1500,x1501,x1502,x1503:new_primPlusNat0(x1498, x1497)=Succ(x1499) & new_primPlusNat0(x1498, x1497)=Succ(Succ(x1500))  ==>  new_pr2F2(x1501, x1498, Pos(x1497), x1502, x1503)_>=_new_pr2F31(new_primPlusNat0(x1498, x1497), new_sr11(x1501, x1503), new_primPlusNat0(x1498, x1497), x1502, x1503)) & (\/x1510,x1511,x1512,x1513,x1514,x1515,x1516,x1517,x1518,x1519,x1520:new_primPlusNat0(x1509, x1508)=Succ(Succ(x1510)) & Succ(x1511)=x1509 & Succ(x1512)=x1508 & (\/x1513,x1514,x1515,x1516,x1517:new_primPlusNat0(x1511, x1512)=Succ(x1513) & new_primPlusNat0(x1511, x1512)=Succ(Succ(x1514))  ==>  new_pr2F2(x1515, x1511, Pos(x1512), x1516, x1517)_>=_new_pr2F31(new_primPlusNat0(x1511, x1512), new_sr11(x1515, x1517), new_primPlusNat0(x1511, x1512), x1516, x1517))  ==>  new_pr2F2(x1518, Succ(x1511), Pos(Succ(x1512)), x1519, x1520)_>=_new_pr2F31(new_primPlusNat0(Succ(x1511), Succ(x1512)), new_sr11(x1518, x1520), new_primPlusNat0(Succ(x1511), Succ(x1512)), x1519, x1520))  ==>  new_pr2F2(x556, Succ(x1498), Pos(Succ(x1497)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1498), Succ(x1497)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1498), Succ(x1497)), x559, x560))
84.27/49.99	
84.27/49.99	(10)    (Succ(x1521)=Succ(Succ(x563)) & Succ(x1498)=Succ(x1521) & Succ(x1497)=Zero & (\/x1499,x1500,x1501,x1502,x1503:new_primPlusNat0(x1498, x1497)=Succ(x1499) & new_primPlusNat0(x1498, x1497)=Succ(Succ(x1500))  ==>  new_pr2F2(x1501, x1498, Pos(x1497), x1502, x1503)_>=_new_pr2F31(new_primPlusNat0(x1498, x1497), new_sr11(x1501, x1503), new_primPlusNat0(x1498, x1497), x1502, x1503))  ==>  new_pr2F2(x556, Succ(x1498), Pos(Succ(x1497)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1498), Succ(x1497)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1498), Succ(x1497)), x559, x560))
84.27/49.99	
84.27/49.99	(11)    (Succ(x1522)=Succ(Succ(x563)) & Succ(x1498)=Zero & Succ(x1497)=Succ(x1522) & (\/x1499,x1500,x1501,x1502,x1503:new_primPlusNat0(x1498, x1497)=Succ(x1499) & new_primPlusNat0(x1498, x1497)=Succ(Succ(x1500))  ==>  new_pr2F2(x1501, x1498, Pos(x1497), x1502, x1503)_>=_new_pr2F31(new_primPlusNat0(x1498, x1497), new_sr11(x1501, x1503), new_primPlusNat0(x1498, x1497), x1502, x1503))  ==>  new_pr2F2(x556, Succ(x1498), Pos(Succ(x1497)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1498), Succ(x1497)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1498), Succ(x1497)), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(12)    (new_pr2F2(x556, Succ(x1498), Pos(Succ(x1497)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1498), Succ(x1497)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1498), Succ(x1497)), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1523, x1524)=Succ(Succ(x563)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(13)    (Succ(Succ(new_primPlusNat0(x1526, x1525)))=Succ(Succ(x563)) & Succ(x1504)=Succ(x1526) & Zero=Succ(x1525) & (\/x1527,x1528,x1529,x1530,x1531:new_primPlusNat0(x1526, x1525)=Succ(Succ(x1527)) & Succ(x1528)=x1526 & Zero=x1525  ==>  new_pr2F2(x1529, Succ(x1528), Pos(Zero), x1530, x1531)_>=_new_pr2F31(new_primPlusNat0(Succ(x1528), Zero), new_sr11(x1529, x1531), new_primPlusNat0(Succ(x1528), Zero), x1530, x1531))  ==>  new_pr2F2(x556, Succ(x1504), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1504), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1504), Zero), x559, x560))
84.27/49.99	
84.27/49.99	(14)    (Succ(x1532)=Succ(Succ(x563)) & Succ(x1504)=Succ(x1532) & Zero=Zero  ==>  new_pr2F2(x556, Succ(x1504), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1504), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1504), Zero), x559, x560))
84.27/49.99	
84.27/49.99	(15)    (Succ(x1533)=Succ(Succ(x563)) & Succ(x1504)=Zero & Zero=Succ(x1533)  ==>  new_pr2F2(x556, Succ(x1504), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1504), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1504), Zero), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (13) using rules (I), (II).We simplified constraint (14) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(16)    (new_pr2F2(x556, Succ(Succ(x563)), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x563)), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(Succ(x563)), Zero), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (15) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1534, x1535)=Succ(Succ(x563)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(17)    (Succ(Succ(new_primPlusNat0(x1537, x1536)))=Succ(Succ(x563)) & Zero=Succ(x1537) & Succ(x1505)=Succ(x1536) & (\/x1538,x1539,x1540,x1541,x1542:new_primPlusNat0(x1537, x1536)=Succ(Succ(x1538)) & Zero=x1537 & Succ(x1539)=x1536  ==>  new_pr2F2(x1540, Zero, Pos(Succ(x1539)), x1541, x1542)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1539)), new_sr11(x1540, x1542), new_primPlusNat0(Zero, Succ(x1539)), x1541, x1542))  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1505)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1505)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1505)), x559, x560))
84.27/49.99	
84.27/49.99	(18)    (Succ(x1543)=Succ(Succ(x563)) & Zero=Succ(x1543) & Succ(x1505)=Zero  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1505)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1505)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1505)), x559, x560))
84.27/49.99	
84.27/49.99	(19)    (Succ(x1544)=Succ(Succ(x563)) & Zero=Zero & Succ(x1505)=Succ(x1544)  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1505)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1505)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1505)), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (17) using rules (I), (II).We solved constraint (18) using rules (I), (II).We simplified constraint (19) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(20)    (new_pr2F2(x556, Zero, Pos(Succ(Succ(x563))), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x563))), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(Succ(x563))), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F31(Succ(x580), x581, Succ(Zero), x582, x583) -> new_pr2F1(x581, Zero, new_fromInt, x582, x583), new_pr2F1(x584, x585, x586, x587, x588) -> new_pr2F34(x585, x586, x584, new_sr9(x584, x587, x588), x588) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F1(x581, Zero, new_fromInt, x582, x583)=new_pr2F1(x584, x585, x586, x587, x588)  ==>  new_pr2F31(Succ(x580), x581, Succ(Zero), x582, x583)_>=_new_pr2F1(x581, Zero, new_fromInt, x582, x583))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F31(Succ(x580), x581, Succ(Zero), x582, x583)_>=_new_pr2F1(x581, Zero, new_fromInt, x582, x583))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G13(x690, x691, x692, Succ(Succ(x693)), x694) -> new_pr2F0G14(x690, x691, x692, x693, x694), new_pr2F0G14(x695, x696, x697, Succ(Zero), x698) -> new_pr2F2(x696, x697, new_fromInt, x695, x698) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G14(x690, x691, x692, x693, x694)=new_pr2F0G14(x695, x696, x697, Succ(Zero), x698)  ==>  new_pr2F0G13(x690, x691, x692, Succ(Succ(x693)), x694)_>=_new_pr2F0G14(x690, x691, x692, x693, x694))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F0G13(x690, x691, x692, Succ(Succ(Succ(Zero))), x694)_>=_new_pr2F0G14(x690, x691, x692, Succ(Zero), x694))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G13(x699, x700, x701, Succ(Succ(x702)), x703) -> new_pr2F0G14(x699, x700, x701, x702, x703), new_pr2F0G14(x704, x705, x706, Succ(Succ(x707)), x708) -> new_pr2F0G14(x704, x705, x706, x707, x708) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G14(x699, x700, x701, x702, x703)=new_pr2F0G14(x704, x705, x706, Succ(Succ(x707)), x708)  ==>  new_pr2F0G13(x699, x700, x701, Succ(Succ(x702)), x703)_>=_new_pr2F0G14(x699, x700, x701, x702, x703))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F0G13(x699, x700, x701, Succ(Succ(Succ(Succ(x707)))), x703)_>=_new_pr2F0G14(x699, x700, x701, Succ(Succ(x707)), x703))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G13(x709, x710, x711, Succ(Succ(x712)), x713) -> new_pr2F0G14(x709, x710, x711, x712, x713), new_pr2F0G14(x714, x715, x716, Zero, x717) -> new_pr2F0G13(x714, new_sr10(x715, x717), new_primDivNatS1(x716), new_primDivNatS1(x716), x717) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G14(x709, x710, x711, x712, x713)=new_pr2F0G14(x714, x715, x716, Zero, x717)  ==>  new_pr2F0G13(x709, x710, x711, Succ(Succ(x712)), x713)_>=_new_pr2F0G14(x709, x710, x711, x712, x713))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F0G13(x709, x710, x711, Succ(Succ(Zero)), x713)_>=_new_pr2F0G14(x709, x710, x711, Zero, x713))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G14(x762, x763, x764, Succ(Zero), x765) -> new_pr2F2(x763, x764, new_fromInt, x762, x765), new_pr2F2(x766, x767, Pos(x768), x769, x770) -> new_pr2F31(new_primPlusNat0(x767, x768), new_sr11(x766, x770), new_primPlusNat0(x767, x768), x769, x770) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F2(x763, x764, new_fromInt, x762, x765)=new_pr2F2(x766, x767, Pos(x768), x769, x770)  ==>  new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_fromInt=Pos(x768)  ==>  new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_fromInt=Pos(x768) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (Pos(Succ(Zero))=Pos(x768)  ==>  new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(4)    (new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G14(x852, x853, x854, Succ(Succ(x855)), x856) -> new_pr2F0G14(x852, x853, x854, x855, x856), new_pr2F0G14(x857, x858, x859, Succ(Zero), x860) -> new_pr2F2(x858, x859, new_fromInt, x857, x860) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G14(x852, x853, x854, x855, x856)=new_pr2F0G14(x857, x858, x859, Succ(Zero), x860)  ==>  new_pr2F0G14(x852, x853, x854, Succ(Succ(x855)), x856)_>=_new_pr2F0G14(x852, x853, x854, x855, x856))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F0G14(x852, x853, x854, Succ(Succ(Succ(Zero))), x856)_>=_new_pr2F0G14(x852, x853, x854, Succ(Zero), x856))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G14(x861, x862, x863, Succ(Succ(x864)), x865) -> new_pr2F0G14(x861, x862, x863, x864, x865), new_pr2F0G14(x866, x867, x868, Succ(Succ(x869)), x870) -> new_pr2F0G14(x866, x867, x868, x869, x870) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G14(x861, x862, x863, x864, x865)=new_pr2F0G14(x866, x867, x868, Succ(Succ(x869)), x870)  ==>  new_pr2F0G14(x861, x862, x863, Succ(Succ(x864)), x865)_>=_new_pr2F0G14(x861, x862, x863, x864, x865))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F0G14(x861, x862, x863, Succ(Succ(Succ(Succ(x869)))), x865)_>=_new_pr2F0G14(x861, x862, x863, Succ(Succ(x869)), x865))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G14(x871, x872, x873, Succ(Succ(x874)), x875) -> new_pr2F0G14(x871, x872, x873, x874, x875), new_pr2F0G14(x876, x877, x878, Zero, x879) -> new_pr2F0G13(x876, new_sr10(x877, x879), new_primDivNatS1(x878), new_primDivNatS1(x878), x879) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G14(x871, x872, x873, x874, x875)=new_pr2F0G14(x876, x877, x878, Zero, x879)  ==>  new_pr2F0G14(x871, x872, x873, Succ(Succ(x874)), x875)_>=_new_pr2F0G14(x871, x872, x873, x874, x875))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F0G14(x871, x872, x873, Succ(Succ(Zero)), x875)_>=_new_pr2F0G14(x871, x872, x873, Zero, x875))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G14(x920, x921, x922, Zero, x923) -> new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(x922), new_primDivNatS1(x922), x923), new_pr2F0G13(x924, x925, x926, Succ(Zero), x927) -> new_pr2F2(x925, x926, new_fromInt, x924, x927) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(x922), new_primDivNatS1(x922), x923)=new_pr2F0G13(x924, x925, x926, Succ(Zero), x927)  ==>  new_pr2F0G14(x920, x921, x922, Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(x922), new_primDivNatS1(x922), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primDivNatS1(x922)=Succ(Zero)  ==>  new_pr2F0G14(x920, x921, x922, Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(x922), new_primDivNatS1(x922), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x922)=Succ(Zero) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_primDivNatS01(x1545)=Succ(Zero)  ==>  new_pr2F0G14(x920, x921, Succ(x1545), Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(Succ(x1545)), new_primDivNatS1(Succ(x1545)), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1545)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(4)    (Succ(new_primDivNatS4(x1546))=Succ(Zero)  ==>  new_pr2F0G14(x920, x921, Succ(Succ(Succ(x1546))), Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(Succ(Succ(Succ(x1546)))), new_primDivNatS1(Succ(Succ(Succ(x1546)))), x923))
84.27/49.99	
84.27/49.99	(5)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G14(x920, x921, Succ(Succ(Zero)), Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (new_pr2F0G14(x920, x921, Succ(Succ(Succ(x1546))), Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(Succ(Succ(Succ(x1546)))), new_primDivNatS1(Succ(Succ(Succ(x1546)))), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G14(x920, x921, Succ(Succ(Zero)), Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G14(x936, x937, x938, Zero, x939) -> new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(x938), new_primDivNatS1(x938), x939), new_pr2F0G13(x940, x941, x942, Succ(Succ(x943)), x944) -> new_pr2F0G14(x940, x941, x942, x943, x944) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(x938), new_primDivNatS1(x938), x939)=new_pr2F0G13(x940, x941, x942, Succ(Succ(x943)), x944)  ==>  new_pr2F0G14(x936, x937, x938, Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(x938), new_primDivNatS1(x938), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primDivNatS1(x938)=Succ(Succ(x943))  ==>  new_pr2F0G14(x936, x937, x938, Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(x938), new_primDivNatS1(x938), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x938)=Succ(Succ(x943)) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_primDivNatS01(x1547)=Succ(Succ(x943))  ==>  new_pr2F0G14(x936, x937, Succ(x1547), Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(Succ(x1547)), new_primDivNatS1(Succ(x1547)), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1547)=Succ(Succ(x943)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(4)    (Succ(new_primDivNatS4(x1548))=Succ(Succ(x943))  ==>  new_pr2F0G14(x936, x937, Succ(Succ(Succ(x1548))), Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(Succ(Succ(Succ(x1548)))), new_primDivNatS1(Succ(Succ(Succ(x1548)))), x939))
84.27/49.99	
84.27/49.99	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x943))  ==>  new_pr2F0G14(x936, x937, Succ(Succ(Zero)), Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (new_pr2F0G14(x936, x937, Succ(Succ(Succ(x1548))), Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(Succ(Succ(Succ(x1548)))), new_primDivNatS1(Succ(Succ(Succ(x1548)))), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G14(x936, x937, Succ(Succ(Zero)), Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G14(x957, x958, x959, Zero, x960) -> new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(x959), new_primDivNatS1(x959), x960), new_pr2F0G13(x961, x962, x963, Zero, x964) -> new_pr2F0G13(x961, new_sr10(x962, x964), new_primDivNatS1(x963), new_primDivNatS1(x963), x964) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(x959), new_primDivNatS1(x959), x960)=new_pr2F0G13(x961, x962, x963, Zero, x964)  ==>  new_pr2F0G14(x957, x958, x959, Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(x959), new_primDivNatS1(x959), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primDivNatS1(x959)=Zero  ==>  new_pr2F0G14(x957, x958, x959, Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(x959), new_primDivNatS1(x959), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x959)=Zero which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Zero=Zero  ==>  new_pr2F0G14(x957, x958, Zero, Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x960))
84.27/49.99	
84.27/49.99	(4)    (new_primDivNatS01(x1549)=Zero  ==>  new_pr2F0G14(x957, x958, Succ(x1549), Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(Succ(x1549)), new_primDivNatS1(Succ(x1549)), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(5)    (new_pr2F0G14(x957, x958, Zero, Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1549)=Zero which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Zero=Zero  ==>  new_pr2F0G14(x957, x958, Succ(Zero), Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G14(x957, x958, Succ(Zero), Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G13(x997, x998, x999, Zero, x1000) -> new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(x999), new_primDivNatS1(x999), x1000), new_pr2F0G13(x1001, x1002, x1003, Succ(Zero), x1004) -> new_pr2F2(x1002, x1003, new_fromInt, x1001, x1004) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(x999), new_primDivNatS1(x999), x1000)=new_pr2F0G13(x1001, x1002, x1003, Succ(Zero), x1004)  ==>  new_pr2F0G13(x997, x998, x999, Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(x999), new_primDivNatS1(x999), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primDivNatS1(x999)=Succ(Zero)  ==>  new_pr2F0G13(x997, x998, x999, Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(x999), new_primDivNatS1(x999), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x999)=Succ(Zero) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_primDivNatS01(x1551)=Succ(Zero)  ==>  new_pr2F0G13(x997, x998, Succ(x1551), Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(Succ(x1551)), new_primDivNatS1(Succ(x1551)), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1551)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(4)    (Succ(new_primDivNatS4(x1552))=Succ(Zero)  ==>  new_pr2F0G13(x997, x998, Succ(Succ(Succ(x1552))), Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(Succ(Succ(Succ(x1552)))), new_primDivNatS1(Succ(Succ(Succ(x1552)))), x1000))
84.27/49.99	
84.27/49.99	(5)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G13(x997, x998, Succ(Succ(Zero)), Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (new_pr2F0G13(x997, x998, Succ(Succ(Succ(x1552))), Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(Succ(Succ(Succ(x1552)))), new_primDivNatS1(Succ(Succ(Succ(x1552)))), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G13(x997, x998, Succ(Succ(Zero)), Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G13(x1013, x1014, x1015, Zero, x1016) -> new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(x1015), new_primDivNatS1(x1015), x1016), new_pr2F0G13(x1017, x1018, x1019, Succ(Succ(x1020)), x1021) -> new_pr2F0G14(x1017, x1018, x1019, x1020, x1021) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(x1015), new_primDivNatS1(x1015), x1016)=new_pr2F0G13(x1017, x1018, x1019, Succ(Succ(x1020)), x1021)  ==>  new_pr2F0G13(x1013, x1014, x1015, Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(x1015), new_primDivNatS1(x1015), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primDivNatS1(x1015)=Succ(Succ(x1020))  ==>  new_pr2F0G13(x1013, x1014, x1015, Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(x1015), new_primDivNatS1(x1015), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1015)=Succ(Succ(x1020)) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_primDivNatS01(x1553)=Succ(Succ(x1020))  ==>  new_pr2F0G13(x1013, x1014, Succ(x1553), Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(Succ(x1553)), new_primDivNatS1(Succ(x1553)), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1553)=Succ(Succ(x1020)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(4)    (Succ(new_primDivNatS4(x1554))=Succ(Succ(x1020))  ==>  new_pr2F0G13(x1013, x1014, Succ(Succ(Succ(x1554))), Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(Succ(Succ(Succ(x1554)))), new_primDivNatS1(Succ(Succ(Succ(x1554)))), x1016))
84.27/49.99	
84.27/49.99	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x1020))  ==>  new_pr2F0G13(x1013, x1014, Succ(Succ(Zero)), Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (new_pr2F0G13(x1013, x1014, Succ(Succ(Succ(x1554))), Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(Succ(Succ(Succ(x1554)))), new_primDivNatS1(Succ(Succ(Succ(x1554)))), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G13(x1013, x1014, Succ(Succ(Zero)), Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G13(x1034, x1035, x1036, Zero, x1037) -> new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(x1036), new_primDivNatS1(x1036), x1037), new_pr2F0G13(x1038, x1039, x1040, Zero, x1041) -> new_pr2F0G13(x1038, new_sr10(x1039, x1041), new_primDivNatS1(x1040), new_primDivNatS1(x1040), x1041) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(x1036), new_primDivNatS1(x1036), x1037)=new_pr2F0G13(x1038, x1039, x1040, Zero, x1041)  ==>  new_pr2F0G13(x1034, x1035, x1036, Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(x1036), new_primDivNatS1(x1036), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_primDivNatS1(x1036)=Zero  ==>  new_pr2F0G13(x1034, x1035, x1036, Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(x1036), new_primDivNatS1(x1036), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1036)=Zero which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Zero=Zero  ==>  new_pr2F0G13(x1034, x1035, Zero, Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1037))
84.27/49.99	
84.27/49.99	(4)    (new_primDivNatS01(x1555)=Zero  ==>  new_pr2F0G13(x1034, x1035, Succ(x1555), Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(Succ(x1555)), new_primDivNatS1(Succ(x1555)), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(5)    (new_pr2F0G13(x1034, x1035, Zero, Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1555)=Zero which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Zero=Zero  ==>  new_pr2F0G13(x1034, x1035, Succ(Zero), Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G13(x1034, x1035, Succ(Zero), Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800)) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F31(Succ(x1124), x1125, Succ(Succ(x1126)), x1127, x1128) -> H(x1125, x1127, Succ(x1126), x1128, anew_new_pr2F0G12(x1126)), H(x1129, x1130, x1131, x1132, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(x1129, x1130, x1131, Succ(Zero), x1132) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (H(x1125, x1127, Succ(x1126), x1128, anew_new_pr2F0G12(x1126))=H(x1129, x1130, x1131, x1132, cons_new_pr2F0G12(Succ(Zero)))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(x1126)), x1127, x1128)_>=_H(x1125, x1127, Succ(x1126), x1128, anew_new_pr2F0G12(x1126)))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (anew_new_pr2F0G12(x1126)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(x1126)), x1127, x1128)_>=_H(x1125, x1127, Succ(x1126), x1128, anew_new_pr2F0G12(x1126)))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on anew_new_pr2F0G12(x1126)=cons_new_pr2F0G12(Succ(Zero)) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_new_pr2F0G12(x1557)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(x1557)))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(x1557))), x1128, anew_new_pr2F0G12(Succ(Succ(x1557)))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_new_pr2F0G12(x1557)=cons_new_pr2F0G12(Succ(Zero)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(4)    (new_new_pr2F0G12(x1558)=cons_new_pr2F0G12(Succ(Zero)) & (\/x1559,x1560,x1561,x1562:new_new_pr2F0G12(x1558)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1559), x1560, Succ(Succ(Succ(Succ(x1558)))), x1561, x1562)_>=_H(x1560, x1561, Succ(Succ(Succ(x1558))), x1562, anew_new_pr2F0G12(Succ(Succ(x1558)))))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(Succ(Succ(x1558)))))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(Succ(Succ(x1558))))), x1128, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1558)))))))
84.27/49.99	
84.27/49.99	(5)    (cons_new_pr2F0G12(Succ(Zero))=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(Succ(Zero))))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(Succ(Zero)))), x1128, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/49.99	
84.27/49.99	(6)    (cons_new_pr2F0G12(Zero)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(Zero)))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(Zero))), x1128, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rule (VI) where we applied the induction hypothesis (\/x1559,x1560,x1561,x1562:new_new_pr2F0G12(x1558)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1559), x1560, Succ(Succ(Succ(Succ(x1558)))), x1561, x1562)_>=_H(x1560, x1561, Succ(Succ(Succ(x1558))), x1562, anew_new_pr2F0G12(Succ(Succ(x1558))))) with sigma = [x1559 / x1124, x1560 / x1125, x1561 / x1127, x1562 / x1128] which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(x1558)))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(x1558))), x1128, anew_new_pr2F0G12(Succ(Succ(x1558))))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(Succ(Succ(x1558)))))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(Succ(Succ(x1558))))), x1128, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1558)))))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(8)    (new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(Succ(Zero))))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(Succ(Zero)))), x1128, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (6) using rules (I), (II).
84.27/49.99	*We consider the chain new_pr2F31(Succ(x1133), x1134, Succ(Succ(x1135)), x1136, x1137) -> H(x1134, x1136, Succ(x1135), x1137, anew_new_pr2F0G12(x1135)), H(x1138, x1139, x1140, x1141, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(x1138, x1139, x1140, Zero, x1141) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (H(x1134, x1136, Succ(x1135), x1137, anew_new_pr2F0G12(x1135))=H(x1138, x1139, x1140, x1141, cons_new_pr2F0G12(Zero))  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(x1135)), x1136, x1137)_>=_H(x1134, x1136, Succ(x1135), x1137, anew_new_pr2F0G12(x1135)))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (anew_new_pr2F0G12(x1135)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(x1135)), x1136, x1137)_>=_H(x1134, x1136, Succ(x1135), x1137, anew_new_pr2F0G12(x1135)))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on anew_new_pr2F0G12(x1135)=cons_new_pr2F0G12(Zero) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_new_pr2F0G12(x1563)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(x1563)))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(x1563))), x1137, anew_new_pr2F0G12(Succ(Succ(x1563)))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_new_pr2F0G12(x1563)=cons_new_pr2F0G12(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(4)    (new_new_pr2F0G12(x1564)=cons_new_pr2F0G12(Zero) & (\/x1565,x1566,x1567,x1568:new_new_pr2F0G12(x1564)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1565), x1566, Succ(Succ(Succ(Succ(x1564)))), x1567, x1568)_>=_H(x1566, x1567, Succ(Succ(Succ(x1564))), x1568, anew_new_pr2F0G12(Succ(Succ(x1564)))))  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(Succ(Succ(x1564)))))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(Succ(Succ(x1564))))), x1137, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1564)))))))
84.27/49.99	
84.27/49.99	(5)    (cons_new_pr2F0G12(Succ(Zero))=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(Succ(Zero))))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(Succ(Zero)))), x1137, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/49.99	
84.27/49.99	(6)    (cons_new_pr2F0G12(Zero)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(Zero)))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(Zero))), x1137, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rule (VI) where we applied the induction hypothesis (\/x1565,x1566,x1567,x1568:new_new_pr2F0G12(x1564)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1565), x1566, Succ(Succ(Succ(Succ(x1564)))), x1567, x1568)_>=_H(x1566, x1567, Succ(Succ(Succ(x1564))), x1568, anew_new_pr2F0G12(Succ(Succ(x1564))))) with sigma = [x1565 / x1133, x1566 / x1134, x1567 / x1136, x1568 / x1137] which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(x1564)))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(x1564))), x1137, anew_new_pr2F0G12(Succ(Succ(x1564))))  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(Succ(Succ(x1564)))))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(Succ(Succ(x1564))))), x1137, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1564)))))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(8)    (new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(Zero)))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(Zero))), x1137, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) the following chains were created:
84.27/49.99	*We consider the chain H(x1142, x1143, x1144, x1145, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(x1142, x1143, x1144, Succ(Zero), x1145), new_pr2F0G12(x1146, x1147, x1148, Succ(Zero), x1149) -> new_pr2F1(x1146, x1148, new_fromInt, x1147, x1149) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G12(x1142, x1143, x1144, Succ(Zero), x1145)=new_pr2F0G12(x1146, x1147, x1148, Succ(Zero), x1149)  ==>  H(x1142, x1143, x1144, x1145, cons_new_pr2F0G12(Succ(Zero)))_>=_new_pr2F0G12(x1142, x1143, x1144, Succ(Zero), x1145))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (H(x1142, x1143, x1144, x1145, cons_new_pr2F0G12(Succ(Zero)))_>=_new_pr2F0G12(x1142, x1143, x1144, Succ(Zero), x1145))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) the following chains were created:
84.27/49.99	*We consider the chain H(x1226, x1227, x1228, x1229, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(x1226, x1227, x1228, Zero, x1229), new_pr2F0G12(x1230, x1231, x1232, Zero, x1233) -> new_pr2F0G13(new_sr8(x1230, x1231, x1233), x1230, new_primDivNatS1(Succ(x1232)), new_primDivNatS1(Succ(x1232)), x1233) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G12(x1226, x1227, x1228, Zero, x1229)=new_pr2F0G12(x1230, x1231, x1232, Zero, x1233)  ==>  H(x1226, x1227, x1228, x1229, cons_new_pr2F0G12(Zero))_>=_new_pr2F0G12(x1226, x1227, x1228, Zero, x1229))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (H(x1226, x1227, x1228, x1229, cons_new_pr2F0G12(Zero))_>=_new_pr2F0G12(x1226, x1227, x1228, Zero, x1229))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	To summarize, we get the following constraints P__>=_ for the following pairs.
84.27/49.99	
84.27/49.99	*new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.99	
84.27/49.99	*(new_pr2F0G12(x4, x5, x6, Succ(Zero), x7)_>=_new_pr2F1(x4, x6, new_fromInt, x5, x7))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.99	
84.27/49.99	*(new_pr2F1(x79, x80, Pos(x85), x82, x83)_>=_new_pr2F34(x80, Pos(x85), x79, new_sr9(x79, x82, x83), x83))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.99	
84.27/49.99	*(new_pr2F34(Succ(x176), Pos(Zero), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x176)), Zero), x171, new_primPlusNat0(Succ(Succ(x176)), Zero), x172, x173))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F34(x169, Pos(Succ(x1280)), x171, x172, x173)_>=_new_pr2F31(new_primPlusNat0(Succ(x169), Succ(x1280)), x171, new_primPlusNat0(Succ(x169), Succ(x1280)), x172, x173))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F34(Zero, Pos(Zero), x196, x197, x198)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), x196, new_primPlusNat0(Succ(Zero), Zero), x197, x198))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F34(Succ(x235), Pos(Zero), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x235)), Zero), x230, new_primPlusNat0(Succ(Succ(x235)), Zero), x231, x232))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F34(x228, Pos(Succ(x1358)), x230, x231, x232)_>=_new_pr2F31(new_primPlusNat0(Succ(x228), Succ(x1358)), x230, new_primPlusNat0(Succ(x228), Succ(x1358)), x231, x232))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.99	
84.27/49.99	*(new_pr2F31(Succ(x248), x249, Succ(Succ(Succ(Zero))), x251, x252)_>=_new_pr2F0G12(x249, x251, Succ(Succ(Zero)), Succ(Zero), x252))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F31(Succ(x272), x273, Succ(Succ(Zero)), x275, x276)_>=_new_pr2F0G12(x273, x275, Succ(Zero), Zero, x276))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.99	
84.27/49.99	*(new_pr2F0G12(x356, x357, Succ(Succ(x1399)), Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(Succ(Succ(x1399)))), new_primDivNatS1(Succ(Succ(Succ(x1399)))), x359))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G12(x356, x357, Succ(Zero), Zero, x359)_>=_new_pr2F0G13(new_sr8(x356, x357, x359), x356, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x359))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G12(x372, x373, Succ(Succ(x1402)), Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(Succ(Succ(x1402)))), new_primDivNatS1(Succ(Succ(Succ(x1402)))), x375))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G12(x372, x373, Succ(Zero), Zero, x375)_>=_new_pr2F0G13(new_sr8(x372, x373, x375), x372, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x375))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G12(x393, x394, Zero, Zero, x396)_>=_new_pr2F0G13(new_sr8(x393, x394, x396), x393, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x396))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x437, x438, x439, Succ(Zero), x440)_>=_new_pr2F2(x438, x439, new_fromInt, x437, x440))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.99	
84.27/49.99	*(new_pr2F2(x497, Succ(Succ(x504)), Pos(Zero), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x504)), Zero), new_sr11(x497, x501), new_primPlusNat0(Succ(Succ(x504)), Zero), x500, x501))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F2(x497, Zero, Pos(Succ(Succ(x504))), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x504))), new_sr11(x497, x501), new_primPlusNat0(Zero, Succ(Succ(x504))), x500, x501))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F2(x497, Succ(x1407), Pos(Succ(x1406)), x500, x501)_>=_new_pr2F31(new_primPlusNat0(Succ(x1407), Succ(x1406)), new_sr11(x497, x501), new_primPlusNat0(Succ(x1407), Succ(x1406)), x500, x501))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F2(x522, Succ(Zero), Pos(Zero), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), new_sr11(x522, x526), new_primPlusNat0(Succ(Zero), Zero), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F2(x522, Zero, Pos(Succ(Zero)), x525, x526)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Zero)), new_sr11(x522, x526), new_primPlusNat0(Zero, Succ(Zero)), x525, x526))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F2(x556, Succ(Succ(x563)), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x563)), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(Succ(x563)), Zero), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F2(x556, Zero, Pos(Succ(Succ(x563))), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x563))), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(Succ(x563))), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F2(x556, Succ(x1498), Pos(Succ(x1497)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1498), Succ(x1497)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1498), Succ(x1497)), x559, x560))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.99	
84.27/49.99	*(new_pr2F31(Succ(x580), x581, Succ(Zero), x582, x583)_>=_new_pr2F1(x581, Zero, new_fromInt, x582, x583))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x690, x691, x692, Succ(Succ(Succ(Zero))), x694)_>=_new_pr2F0G14(x690, x691, x692, Succ(Zero), x694))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x699, x700, x701, Succ(Succ(Succ(Succ(x707)))), x703)_>=_new_pr2F0G14(x699, x700, x701, Succ(Succ(x707)), x703))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x709, x710, x711, Succ(Succ(Zero)), x713)_>=_new_pr2F0G14(x709, x710, x711, Zero, x713))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x762, x763, x764, Succ(Zero), x765)_>=_new_pr2F2(x763, x764, new_fromInt, x762, x765))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x852, x853, x854, Succ(Succ(Succ(Zero))), x856)_>=_new_pr2F0G14(x852, x853, x854, Succ(Zero), x856))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x861, x862, x863, Succ(Succ(Succ(Succ(x869)))), x865)_>=_new_pr2F0G14(x861, x862, x863, Succ(Succ(x869)), x865))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x871, x872, x873, Succ(Succ(Zero)), x875)_>=_new_pr2F0G14(x871, x872, x873, Zero, x875))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x920, x921, Succ(Succ(Succ(x1546))), Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(Succ(Succ(Succ(x1546)))), new_primDivNatS1(Succ(Succ(Succ(x1546)))), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x920, x921, Succ(Succ(Zero)), Zero, x923)_>=_new_pr2F0G13(x920, new_sr10(x921, x923), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x923))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x936, x937, Succ(Succ(Succ(x1548))), Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(Succ(Succ(Succ(x1548)))), new_primDivNatS1(Succ(Succ(Succ(x1548)))), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x936, x937, Succ(Succ(Zero)), Zero, x939)_>=_new_pr2F0G13(x936, new_sr10(x937, x939), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x939))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x957, x958, Zero, Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G14(x957, x958, Succ(Zero), Zero, x960)_>=_new_pr2F0G13(x957, new_sr10(x958, x960), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x960))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x997, x998, Succ(Succ(Succ(x1552))), Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(Succ(Succ(Succ(x1552)))), new_primDivNatS1(Succ(Succ(Succ(x1552)))), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x997, x998, Succ(Succ(Zero)), Zero, x1000)_>=_new_pr2F0G13(x997, new_sr10(x998, x1000), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1000))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x1013, x1014, Succ(Succ(Succ(x1554))), Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(Succ(Succ(Succ(x1554)))), new_primDivNatS1(Succ(Succ(Succ(x1554)))), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x1013, x1014, Succ(Succ(Zero)), Zero, x1016)_>=_new_pr2F0G13(x1013, new_sr10(x1014, x1016), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1016))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x1034, x1035, Zero, Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F0G13(x1034, x1035, Succ(Zero), Zero, x1037)_>=_new_pr2F0G13(x1034, new_sr10(x1035, x1037), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1037))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/49.99	
84.27/49.99	*(new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(x1558)))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(x1558))), x1128, anew_new_pr2F0G12(Succ(Succ(x1558))))  ==>  new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(Succ(Succ(x1558)))))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(Succ(Succ(x1558))))), x1128, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1558)))))))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F31(Succ(x1124), x1125, Succ(Succ(Succ(Succ(Succ(Zero))))), x1127, x1128)_>=_H(x1125, x1127, Succ(Succ(Succ(Succ(Zero)))), x1128, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(x1564)))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(x1564))), x1137, anew_new_pr2F0G12(Succ(Succ(x1564))))  ==>  new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(Succ(Succ(x1564)))))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(Succ(Succ(x1564))))), x1137, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1564)))))))
84.27/49.99	
84.27/49.99	
84.27/49.99	*(new_pr2F31(Succ(x1133), x1134, Succ(Succ(Succ(Succ(Zero)))), x1136, x1137)_>=_H(x1134, x1136, Succ(Succ(Succ(Zero))), x1137, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/49.99	
84.27/49.99	*(H(x1142, x1143, x1144, x1145, cons_new_pr2F0G12(Succ(Zero)))_>=_new_pr2F0G12(x1142, x1143, x1144, Succ(Zero), x1145))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/49.99	
84.27/49.99	*(H(x1226, x1227, x1228, x1229, cons_new_pr2F0G12(Zero))_>=_new_pr2F0G12(x1226, x1227, x1228, Zero, x1229))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	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. 
84.27/49.99	----------------------------------------
84.27/49.99	
84.27/49.99	(36)
84.27/49.99	Obligation:
84.27/49.99	Q DP problem:
84.27/49.99	The TRS P consists of the following rules:
84.27/49.99	
84.27/49.99	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.99	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.99	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.99	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.99	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.99	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/49.99	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/49.99	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/49.99	
84.27/49.99	The TRS R consists of the following rules:
84.27/49.99	
84.27/49.99	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.99	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/49.99	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/49.99	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/49.99	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/49.99	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.99	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.99	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.99	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/49.99	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.99	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.99	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/49.99	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/49.99	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/49.99	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/49.99	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/49.99	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.99	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/49.99	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.99	   new_sr13(vuz69, vuz20) -> error([])
84.27/49.99	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/49.99	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/49.99	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/49.99	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/49.99	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/49.99	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/49.99	   new_primMulNat0(Zero, Zero) -> Zero
84.27/49.99	   new_primDivNatS01(Zero) -> Zero
84.27/49.99	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.99	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_primDivNatS1(Zero) -> Zero
84.27/49.99	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.99	   new_primDivNatS3 -> Zero
84.27/49.99	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/49.99	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.99	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.99	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.99	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr15(vuz72, vuz20) -> error([])
84.27/49.99	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.99	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_fromInt -> Pos(Succ(Zero))
84.27/49.99	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/49.99	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.99	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.99	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.99	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/49.99	   new_sr14(vuz70, vuz20) -> error([])
84.27/49.99	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.99	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.99	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.99	   new_primDivNatS2 -> new_primDivNatS3
84.27/49.99	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.99	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/49.99	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/49.99	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.99	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/49.99	   anew_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.99	   new_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.99	   new_new_pr2F0G12(Succ(Zero)) -> cons_new_pr2F0G12(Succ(Zero))
84.27/49.99	   new_new_pr2F0G12(Zero) -> cons_new_pr2F0G12(Zero)
84.27/49.99	
84.27/49.99	The set Q consists of the following terms:
84.27/49.99	
84.27/49.99	   new_sr1(x0, x1, ty_Integer)
84.27/49.99	   new_sr(x0, x1, ty_Integer)
84.27/49.99	   new_sr6(x0, ty_Int)
84.27/49.99	   new_sr12(Pos(x0), Neg(x1))
84.27/49.99	   new_sr12(Neg(x0), Pos(x1))
84.27/49.99	   new_sr7(x0, x1, ty_Int)
84.27/49.99	   new_sr9(x0, x1, ty_Float)
84.27/49.99	   new_sr5(x0, ty_Integer)
84.27/49.99	   new_sr10(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr4(x0, ty_Integer)
84.27/49.99	   new_sr0(x0, x1, ty_Integer)
84.27/49.99	   new_sr2(x0, ty_Double)
84.27/49.99	   new_sr2(x0, ty_Float)
84.27/49.99	   new_sr12(Neg(x0), Neg(x1))
84.27/49.99	   new_sr(x0, x1, ty_Int)
84.27/49.99	   new_sr5(x0, ty_Int)
84.27/49.99	   new_primDivNatS1(Zero)
84.27/49.99	   new_sr6(x0, ty_Integer)
84.27/49.99	   new_sr11(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr3(x0, ty_Double)
84.27/49.99	   new_sr13(x0, x1)
84.27/49.99	   new_sr4(x0, ty_Float)
84.27/49.99	   new_sr0(x0, x1, ty_Int)
84.27/49.99	   new_primMulNat0(Zero, Zero)
84.27/49.99	   new_sr11(x0, ty_Float)
84.27/49.99	   new_sr20(x0)
84.27/49.99	   new_sr11(x0, ty_Double)
84.27/49.99	   new_sr3(x0, ty_Int)
84.27/49.99	   new_sr0(x0, x1, ty_Double)
84.27/49.99	   new_sr8(x0, x1, ty_Double)
84.27/49.99	   new_fromInt
84.27/49.99	   new_sr6(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr(x0, x1, ty_Float)
84.27/49.99	   new_primDivNatS4(x0)
84.27/49.99	   new_sr4(x0, ty_Double)
84.27/49.99	   new_sr10(x0, ty_Int)
84.27/49.99	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr2(x0, ty_Integer)
84.27/49.99	   new_sr21(x0, x1)
84.27/49.99	   new_primMulNat0(Zero, Succ(x0))
84.27/49.99	   new_primDivNatS2
84.27/49.99	   new_primDivNatS1(Succ(x0))
84.27/49.99	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr6(x0, ty_Double)
84.27/49.99	   new_sr12(Pos(x0), Pos(x1))
84.27/49.99	   new_sr8(x0, x1, ty_Float)
84.27/49.99	   new_sr11(x0, ty_Integer)
84.27/49.99	   new_sr7(x0, x1, ty_Float)
84.27/49.99	   new_sr7(x0, x1, ty_Integer)
84.27/49.99	   new_sr1(x0, x1, ty_Float)
84.27/49.99	   new_primDivNatS01(Succ(Zero))
84.27/49.99	   new_sr9(x0, x1, ty_Int)
84.27/49.99	   new_primPlusNat0(Succ(x0), Zero)
84.27/49.99	   new_sr3(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr8(x0, x1, ty_Integer)
84.27/49.99	   new_sr6(x0, ty_Float)
84.27/49.99	   new_sr17(x0)
84.27/49.99	   new_sr9(x0, x1, ty_Integer)
84.27/49.99	   new_sr7(x0, x1, ty_Double)
84.27/49.99	   new_sr2(x0, ty_Int)
84.27/49.99	   new_sr10(x0, ty_Double)
84.27/49.99	   new_sr5(x0, ty_Float)
84.27/49.99	   new_sr18(x0)
84.27/49.99	   new_sr4(x0, app(ty_Ratio, x1))
84.27/49.99	   new_primPlusNat0(Zero, Succ(x0))
84.27/49.99	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/49.99	   new_sr16(x0, x1, x2)
84.27/49.99	   new_sr1(x0, x1, ty_Double)
84.27/49.99	   new_primDivNatS01(Succ(Succ(x0)))
84.27/49.99	   new_sr19(x0)
84.27/49.99	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/49.99	   new_primDivNatS5(x0)
84.27/49.99	   new_sr5(x0, app(ty_Ratio, x1))
84.27/49.99	   new_primDivNatS3
84.27/49.99	   new_sr(x0, x1, ty_Double)
84.27/49.99	   new_sr0(x0, x1, ty_Float)
84.27/49.99	   new_sr1(x0, x1, ty_Int)
84.27/49.99	   new_sr15(x0, x1)
84.27/49.99	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_primDivNatS01(Zero)
84.27/49.99	   new_sr9(x0, x1, ty_Double)
84.27/49.99	   new_sr10(x0, ty_Float)
84.27/49.99	   new_sr10(x0, ty_Integer)
84.27/49.99	   new_sr4(x0, ty_Int)
84.27/49.99	   new_sr2(x0, app(ty_Ratio, x1))
84.27/49.99	   new_primMulNat0(Succ(x0), Zero)
84.27/49.99	   new_sr5(x0, ty_Double)
84.27/49.99	   new_primPlusNat0(Zero, Zero)
84.27/49.99	   new_sr8(x0, x1, ty_Int)
84.27/49.99	   new_sr14(x0, x1)
84.27/49.99	   new_sr3(x0, ty_Integer)
84.27/49.99	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr3(x0, ty_Float)
84.27/49.99	   new_sr11(x0, ty_Int)
84.27/49.99	   new_new_pr2F0G12(Succ(Succ(x0)))
84.27/49.99	   anew_new_pr2F0G12(Succ(Succ(x0)))
84.27/49.99	   new_new_pr2F0G12(Succ(Zero))
84.27/49.99	   new_new_pr2F0G12(Zero)
84.27/49.99	
84.27/49.99	We have to consider all minimal (P,Q,R)-chains.
84.27/49.99	----------------------------------------
84.27/49.99	
84.27/49.99	(37) QDPPairToRuleProof (EQUIVALENT)
84.27/49.99	The dependency pair new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be) was transformed to the following new rules:
84.27/49.99	   anew_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/49.99	   new_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/49.99	   new_new_pr2F0G14(Succ(Zero)) -> cons_new_pr2F0G14(Succ(Zero))
84.27/49.99	   new_new_pr2F0G14(Zero) -> cons_new_pr2F0G14(Zero)
84.27/49.99	
84.27/49.99	the following new pairs maintain the fan-in:
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> H'(vuz110, vuz111, vuz113, be, anew_new_pr2F0G14(vuz11400))
84.27/49.99	
84.27/49.99	the following new pairs maintain the fan-out:
84.27/49.99	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be)
84.27/49.99	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be)
84.27/49.99	
84.27/49.99	----------------------------------------
84.27/49.99	
84.27/49.99	(38)
84.27/49.99	Complex Obligation (AND)
84.27/49.99	
84.27/49.99	----------------------------------------
84.27/49.99	
84.27/49.99	(39)
84.27/49.99	Obligation:
84.27/49.99	Q DP problem:
84.27/49.99	The TRS P consists of the following rules:
84.27/49.99	
84.27/49.99	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.99	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.99	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.99	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.99	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/49.99	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/49.99	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> H'(vuz110, vuz111, vuz113, be, anew_new_pr2F0G14(vuz11400))
84.27/49.99	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be)
84.27/49.99	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be)
84.27/49.99	
84.27/49.99	The TRS R consists of the following rules:
84.27/49.99	
84.27/49.99	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.99	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/49.99	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/49.99	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/49.99	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/49.99	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.99	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.99	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.99	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/49.99	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.99	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.99	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/49.99	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/49.99	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/49.99	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/49.99	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/49.99	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.99	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/49.99	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.99	   new_sr13(vuz69, vuz20) -> error([])
84.27/49.99	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/49.99	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/49.99	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/49.99	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/49.99	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/49.99	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/49.99	   new_primMulNat0(Zero, Zero) -> Zero
84.27/49.99	   new_primDivNatS01(Zero) -> Zero
84.27/49.99	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.99	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_primDivNatS1(Zero) -> Zero
84.27/49.99	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.99	   new_primDivNatS3 -> Zero
84.27/49.99	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/49.99	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.99	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.99	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.99	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr15(vuz72, vuz20) -> error([])
84.27/49.99	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.99	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_fromInt -> Pos(Succ(Zero))
84.27/49.99	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/49.99	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.99	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.99	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.99	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/49.99	   new_sr14(vuz70, vuz20) -> error([])
84.27/49.99	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.99	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.99	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.99	   new_primDivNatS2 -> new_primDivNatS3
84.27/49.99	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.99	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/49.99	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/49.99	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.99	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/49.99	   anew_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.99	   new_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.99	   new_new_pr2F0G12(Succ(Zero)) -> cons_new_pr2F0G12(Succ(Zero))
84.27/49.99	   new_new_pr2F0G12(Zero) -> cons_new_pr2F0G12(Zero)
84.27/49.99	   anew_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/49.99	   new_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/49.99	   new_new_pr2F0G14(Succ(Zero)) -> cons_new_pr2F0G14(Succ(Zero))
84.27/49.99	   new_new_pr2F0G14(Zero) -> cons_new_pr2F0G14(Zero)
84.27/49.99	
84.27/49.99	The set Q consists of the following terms:
84.27/49.99	
84.27/49.99	   new_sr1(x0, x1, ty_Integer)
84.27/49.99	   new_sr(x0, x1, ty_Integer)
84.27/49.99	   new_sr6(x0, ty_Int)
84.27/49.99	   new_sr12(Pos(x0), Neg(x1))
84.27/49.99	   new_sr12(Neg(x0), Pos(x1))
84.27/49.99	   new_sr7(x0, x1, ty_Int)
84.27/49.99	   new_sr9(x0, x1, ty_Float)
84.27/49.99	   new_sr5(x0, ty_Integer)
84.27/49.99	   new_sr10(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr4(x0, ty_Integer)
84.27/49.99	   new_sr0(x0, x1, ty_Integer)
84.27/49.99	   new_sr2(x0, ty_Double)
84.27/49.99	   new_sr2(x0, ty_Float)
84.27/49.99	   new_sr12(Neg(x0), Neg(x1))
84.27/49.99	   new_sr(x0, x1, ty_Int)
84.27/49.99	   new_sr5(x0, ty_Int)
84.27/49.99	   new_primDivNatS1(Zero)
84.27/49.99	   new_sr6(x0, ty_Integer)
84.27/49.99	   new_sr11(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr3(x0, ty_Double)
84.27/49.99	   new_sr13(x0, x1)
84.27/49.99	   new_sr4(x0, ty_Float)
84.27/49.99	   new_sr0(x0, x1, ty_Int)
84.27/49.99	   new_primMulNat0(Zero, Zero)
84.27/49.99	   new_sr11(x0, ty_Float)
84.27/49.99	   new_sr20(x0)
84.27/49.99	   new_sr11(x0, ty_Double)
84.27/49.99	   new_sr3(x0, ty_Int)
84.27/49.99	   new_sr0(x0, x1, ty_Double)
84.27/49.99	   new_sr8(x0, x1, ty_Double)
84.27/49.99	   new_fromInt
84.27/49.99	   new_sr6(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr(x0, x1, ty_Float)
84.27/49.99	   new_primDivNatS4(x0)
84.27/49.99	   new_sr4(x0, ty_Double)
84.27/49.99	   new_sr10(x0, ty_Int)
84.27/49.99	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr2(x0, ty_Integer)
84.27/49.99	   new_sr21(x0, x1)
84.27/49.99	   new_primMulNat0(Zero, Succ(x0))
84.27/49.99	   new_primDivNatS2
84.27/49.99	   new_primDivNatS1(Succ(x0))
84.27/49.99	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr6(x0, ty_Double)
84.27/49.99	   new_sr12(Pos(x0), Pos(x1))
84.27/49.99	   new_sr8(x0, x1, ty_Float)
84.27/49.99	   new_sr11(x0, ty_Integer)
84.27/49.99	   new_sr7(x0, x1, ty_Float)
84.27/49.99	   new_sr7(x0, x1, ty_Integer)
84.27/49.99	   new_sr1(x0, x1, ty_Float)
84.27/49.99	   new_primDivNatS01(Succ(Zero))
84.27/49.99	   new_sr9(x0, x1, ty_Int)
84.27/49.99	   new_primPlusNat0(Succ(x0), Zero)
84.27/49.99	   new_sr3(x0, app(ty_Ratio, x1))
84.27/49.99	   new_sr8(x0, x1, ty_Integer)
84.27/49.99	   new_sr6(x0, ty_Float)
84.27/49.99	   new_sr17(x0)
84.27/49.99	   new_sr9(x0, x1, ty_Integer)
84.27/49.99	   new_sr7(x0, x1, ty_Double)
84.27/49.99	   new_sr2(x0, ty_Int)
84.27/49.99	   new_sr10(x0, ty_Double)
84.27/49.99	   new_sr5(x0, ty_Float)
84.27/49.99	   new_sr18(x0)
84.27/49.99	   new_sr4(x0, app(ty_Ratio, x1))
84.27/49.99	   new_primPlusNat0(Zero, Succ(x0))
84.27/49.99	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/49.99	   new_sr16(x0, x1, x2)
84.27/49.99	   new_sr1(x0, x1, ty_Double)
84.27/49.99	   new_primDivNatS01(Succ(Succ(x0)))
84.27/49.99	   new_sr19(x0)
84.27/49.99	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/49.99	   new_primDivNatS5(x0)
84.27/49.99	   new_sr5(x0, app(ty_Ratio, x1))
84.27/49.99	   new_primDivNatS3
84.27/49.99	   new_sr(x0, x1, ty_Double)
84.27/49.99	   new_sr0(x0, x1, ty_Float)
84.27/49.99	   new_sr1(x0, x1, ty_Int)
84.27/49.99	   new_sr15(x0, x1)
84.27/49.99	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_primDivNatS01(Zero)
84.27/49.99	   new_sr9(x0, x1, ty_Double)
84.27/49.99	   new_sr10(x0, ty_Float)
84.27/49.99	   new_sr10(x0, ty_Integer)
84.27/49.99	   new_sr4(x0, ty_Int)
84.27/49.99	   new_sr2(x0, app(ty_Ratio, x1))
84.27/49.99	   new_primMulNat0(Succ(x0), Zero)
84.27/49.99	   new_sr5(x0, ty_Double)
84.27/49.99	   new_primPlusNat0(Zero, Zero)
84.27/49.99	   new_sr8(x0, x1, ty_Int)
84.27/49.99	   new_sr14(x0, x1)
84.27/49.99	   new_sr3(x0, ty_Integer)
84.27/49.99	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/49.99	   new_sr3(x0, ty_Float)
84.27/49.99	   new_sr11(x0, ty_Int)
84.27/49.99	   new_new_pr2F0G12(Succ(Succ(x0)))
84.27/49.99	   anew_new_pr2F0G12(Succ(Succ(x0)))
84.27/49.99	   new_new_pr2F0G12(Succ(Zero))
84.27/49.99	   new_new_pr2F0G12(Zero)
84.27/49.99	   new_new_pr2F0G14(Succ(Succ(x0)))
84.27/49.99	   anew_new_pr2F0G14(Succ(Succ(x0)))
84.27/49.99	   new_new_pr2F0G14(Succ(Zero))
84.27/49.99	   new_new_pr2F0G14(Zero)
84.27/49.99	
84.27/49.99	We have to consider all minimal (P,Q,R)-chains.
84.27/49.99	----------------------------------------
84.27/49.99	
84.27/49.99	(40) MNOCProof (EQUIVALENT)
84.27/49.99	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
84.27/49.99	----------------------------------------
84.27/49.99	
84.27/49.99	(41)
84.27/49.99	Obligation:
84.27/49.99	Q DP problem:
84.27/49.99	The TRS P consists of the following rules:
84.27/49.99	
84.27/49.99	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/49.99	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/49.99	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/49.99	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/49.99	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/49.99	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/49.99	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/49.99	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/49.99	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/49.99	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> H'(vuz110, vuz111, vuz113, be, anew_new_pr2F0G14(vuz11400))
84.27/49.99	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be)
84.27/49.99	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be)
84.27/49.99	
84.27/49.99	The TRS R consists of the following rules:
84.27/49.99	
84.27/49.99	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.99	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/49.99	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/49.99	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/49.99	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/49.99	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/49.99	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.99	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/49.99	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/49.99	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/49.99	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.99	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/49.99	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/49.99	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/49.99	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/49.99	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/49.99	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.99	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/49.99	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.99	   new_sr13(vuz69, vuz20) -> error([])
84.27/49.99	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/49.99	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/49.99	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/49.99	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/49.99	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/49.99	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/49.99	   new_primMulNat0(Zero, Zero) -> Zero
84.27/49.99	   new_primDivNatS01(Zero) -> Zero
84.27/49.99	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.99	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_primDivNatS1(Zero) -> Zero
84.27/49.99	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/49.99	   new_primDivNatS3 -> Zero
84.27/49.99	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/49.99	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/49.99	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.99	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.99	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr15(vuz72, vuz20) -> error([])
84.27/49.99	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/49.99	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_fromInt -> Pos(Succ(Zero))
84.27/49.99	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/49.99	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/49.99	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/49.99	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/49.99	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/49.99	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/49.99	   new_sr14(vuz70, vuz20) -> error([])
84.27/49.99	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/49.99	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/49.99	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/49.99	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/49.99	   new_primDivNatS2 -> new_primDivNatS3
84.27/49.99	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/49.99	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/49.99	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/49.99	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/49.99	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/49.99	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/49.99	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/49.99	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/49.99	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/49.99	   anew_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.99	   new_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/49.99	   new_new_pr2F0G12(Succ(Zero)) -> cons_new_pr2F0G12(Succ(Zero))
84.27/49.99	   new_new_pr2F0G12(Zero) -> cons_new_pr2F0G12(Zero)
84.27/49.99	   anew_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/49.99	   new_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/49.99	   new_new_pr2F0G14(Succ(Zero)) -> cons_new_pr2F0G14(Succ(Zero))
84.27/49.99	   new_new_pr2F0G14(Zero) -> cons_new_pr2F0G14(Zero)
84.27/49.99	
84.27/49.99	Q is empty.
84.27/49.99	We have to consider all (P,Q,R)-chains.
84.27/49.99	----------------------------------------
84.27/49.99	
84.27/49.99	(42) InductionCalculusProof (EQUIVALENT)
84.27/49.99	Note that final constraints are written in bold face.
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G12(x4, x5, x6, Succ(Zero), x7) -> new_pr2F1(x4, x6, new_fromInt, x5, x7), new_pr2F1(x8, x9, x10, x11, x12) -> new_pr2F34(x9, x10, x8, new_sr9(x8, x11, x12), x12) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F1(x4, x6, new_fromInt, x5, x7)=new_pr2F1(x8, x9, x10, x11, x12)  ==>  new_pr2F0G12(x4, x5, x6, Succ(Zero), x7)_>=_new_pr2F1(x4, x6, new_fromInt, x5, x7))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F0G12(x4, x5, x6, Succ(Zero), x7)_>=_new_pr2F1(x4, x6, new_fromInt, x5, x7))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F1(x87, x88, x89, x90, x91) -> new_pr2F34(x88, x89, x87, new_sr9(x87, x90, x91), x91), new_pr2F34(x92, Pos(x93), x94, x95, x96) -> new_pr2F31(new_primPlusNat0(Succ(x92), x93), x94, new_primPlusNat0(Succ(x92), x93), x95, x96) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F34(x88, x89, x87, new_sr9(x87, x90, x91), x91)=new_pr2F34(x92, Pos(x93), x94, x95, x96)  ==>  new_pr2F1(x87, x88, x89, x90, x91)_>=_new_pr2F34(x88, x89, x87, new_sr9(x87, x90, x91), x91))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F1(x87, x88, Pos(x93), x90, x91)_>=_new_pr2F34(x88, Pos(x93), x87, new_sr9(x87, x90, x91), x91))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F34(x187, Pos(x188), x189, x190, x191) -> new_pr2F31(new_primPlusNat0(Succ(x187), x188), x189, new_primPlusNat0(Succ(x187), x188), x190, x191), new_pr2F31(Succ(x192), x193, Succ(Succ(x194)), x195, x196) -> new_pr2F0G12(x193, x195, Succ(x194), x194, x196) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F31(new_primPlusNat0(Succ(x187), x188), x189, new_primPlusNat0(Succ(x187), x188), x190, x191)=new_pr2F31(Succ(x192), x193, Succ(Succ(x194)), x195, x196)  ==>  new_pr2F34(x187, Pos(x188), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), x188), x189, new_primPlusNat0(Succ(x187), x188), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (Succ(x187)=x1577 & new_primPlusNat0(x1577, x188)=Succ(x192) & Succ(x187)=x1578 & new_primPlusNat0(x1578, x188)=Succ(Succ(x194))  ==>  new_pr2F34(x187, Pos(x188), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), x188), x189, new_primPlusNat0(Succ(x187), x188), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1577, x188)=Succ(x192) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Succ(Succ(new_primPlusNat0(x1580, x1579)))=Succ(x192) & Succ(x187)=Succ(x1580) & Succ(x187)=x1578 & new_primPlusNat0(x1578, Succ(x1579))=Succ(Succ(x194)) & (\/x1581,x1582,x1583,x1584,x1585,x1586,x1587:new_primPlusNat0(x1580, x1579)=Succ(x1581) & Succ(x1582)=x1580 & Succ(x1582)=x1583 & new_primPlusNat0(x1583, x1579)=Succ(Succ(x1584))  ==>  new_pr2F34(x1582, Pos(x1579), x1585, x1586, x1587)_>=_new_pr2F31(new_primPlusNat0(Succ(x1582), x1579), x1585, new_primPlusNat0(Succ(x1582), x1579), x1586, x1587))  ==>  new_pr2F34(x187, Pos(Succ(x1579)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1579)), x189, new_primPlusNat0(Succ(x187), Succ(x1579)), x190, x191))
84.27/49.99	
84.27/49.99	(4)    (Succ(x1588)=Succ(x192) & Succ(x187)=Succ(x1588) & Succ(x187)=x1578 & new_primPlusNat0(x1578, Zero)=Succ(Succ(x194))  ==>  new_pr2F34(x187, Pos(Zero), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Zero), x189, new_primPlusNat0(Succ(x187), Zero), x190, x191))
84.27/49.99	
84.27/49.99	(5)    (Succ(x1589)=Succ(x192) & Succ(x187)=Zero & Succ(x187)=x1578 & new_primPlusNat0(x1578, Succ(x1589))=Succ(Succ(x194))  ==>  new_pr2F34(x187, Pos(Succ(x1589)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1589)), x189, new_primPlusNat0(Succ(x187), Succ(x1589)), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Succ(x187)=x1578 & Succ(x1579)=x1590 & new_primPlusNat0(x1578, x1590)=Succ(Succ(x194)) & (\/x1581,x1582,x1583,x1584,x1585,x1586,x1587:new_primPlusNat0(x187, x1579)=Succ(x1581) & Succ(x1582)=x187 & Succ(x1582)=x1583 & new_primPlusNat0(x1583, x1579)=Succ(Succ(x1584))  ==>  new_pr2F34(x1582, Pos(x1579), x1585, x1586, x1587)_>=_new_pr2F31(new_primPlusNat0(Succ(x1582), x1579), x1585, new_primPlusNat0(Succ(x1582), x1579), x1586, x1587))  ==>  new_pr2F34(x187, Pos(Succ(x1579)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1579)), x189, new_primPlusNat0(Succ(x187), Succ(x1579)), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (Succ(x187)=x1578 & Zero=x1608 & new_primPlusNat0(x1578, x1608)=Succ(Succ(x194))  ==>  new_pr2F34(x187, Pos(Zero), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Zero), x189, new_primPlusNat0(Succ(x187), Zero), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1578, x1590)=Succ(Succ(x194)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(8)    (Succ(Succ(new_primPlusNat0(x1592, x1591)))=Succ(Succ(x194)) & Succ(x187)=Succ(x1592) & Succ(x1579)=Succ(x1591) & (\/x1581,x1582,x1583,x1584,x1585,x1586,x1587:new_primPlusNat0(x187, x1579)=Succ(x1581) & Succ(x1582)=x187 & Succ(x1582)=x1583 & new_primPlusNat0(x1583, x1579)=Succ(Succ(x1584))  ==>  new_pr2F34(x1582, Pos(x1579), x1585, x1586, x1587)_>=_new_pr2F31(new_primPlusNat0(Succ(x1582), x1579), x1585, new_primPlusNat0(Succ(x1582), x1579), x1586, x1587)) & (\/x1593,x1594,x1595,x1596,x1597,x1598,x1599,x1600,x1601,x1602,x1603,x1604,x1605:new_primPlusNat0(x1592, x1591)=Succ(Succ(x1593)) & Succ(x1594)=x1592 & Succ(x1595)=x1591 & (\/x1596,x1597,x1598,x1599,x1600,x1601,x1602:new_primPlusNat0(x1594, x1595)=Succ(x1596) & Succ(x1597)=x1594 & Succ(x1597)=x1598 & new_primPlusNat0(x1598, x1595)=Succ(Succ(x1599))  ==>  new_pr2F34(x1597, Pos(x1595), x1600, x1601, x1602)_>=_new_pr2F31(new_primPlusNat0(Succ(x1597), x1595), x1600, new_primPlusNat0(Succ(x1597), x1595), x1601, x1602))  ==>  new_pr2F34(x1594, Pos(Succ(x1595)), x1603, x1604, x1605)_>=_new_pr2F31(new_primPlusNat0(Succ(x1594), Succ(x1595)), x1603, new_primPlusNat0(Succ(x1594), Succ(x1595)), x1604, x1605))  ==>  new_pr2F34(x187, Pos(Succ(x1579)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1579)), x189, new_primPlusNat0(Succ(x187), Succ(x1579)), x190, x191))
84.27/49.99	
84.27/49.99	(9)    (Succ(x1606)=Succ(Succ(x194)) & Succ(x187)=Succ(x1606) & Succ(x1579)=Zero & (\/x1581,x1582,x1583,x1584,x1585,x1586,x1587:new_primPlusNat0(x187, x1579)=Succ(x1581) & Succ(x1582)=x187 & Succ(x1582)=x1583 & new_primPlusNat0(x1583, x1579)=Succ(Succ(x1584))  ==>  new_pr2F34(x1582, Pos(x1579), x1585, x1586, x1587)_>=_new_pr2F31(new_primPlusNat0(Succ(x1582), x1579), x1585, new_primPlusNat0(Succ(x1582), x1579), x1586, x1587))  ==>  new_pr2F34(x187, Pos(Succ(x1579)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1579)), x189, new_primPlusNat0(Succ(x187), Succ(x1579)), x190, x191))
84.27/49.99	
84.27/49.99	(10)    (Succ(x1607)=Succ(Succ(x194)) & Succ(x187)=Zero & Succ(x1579)=Succ(x1607) & (\/x1581,x1582,x1583,x1584,x1585,x1586,x1587:new_primPlusNat0(x187, x1579)=Succ(x1581) & Succ(x1582)=x187 & Succ(x1582)=x1583 & new_primPlusNat0(x1583, x1579)=Succ(Succ(x1584))  ==>  new_pr2F34(x1582, Pos(x1579), x1585, x1586, x1587)_>=_new_pr2F31(new_primPlusNat0(Succ(x1582), x1579), x1585, new_primPlusNat0(Succ(x1582), x1579), x1586, x1587))  ==>  new_pr2F34(x187, Pos(Succ(x1579)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1579)), x189, new_primPlusNat0(Succ(x187), Succ(x1579)), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (8) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(11)    (new_pr2F34(x187, Pos(Succ(x1579)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1579)), x189, new_primPlusNat0(Succ(x187), Succ(x1579)), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1578, x1608)=Succ(Succ(x194)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(12)    (Succ(Succ(new_primPlusNat0(x1610, x1609)))=Succ(Succ(x194)) & Succ(x187)=Succ(x1610) & Zero=Succ(x1609) & (\/x1611,x1612,x1613,x1614,x1615:new_primPlusNat0(x1610, x1609)=Succ(Succ(x1611)) & Succ(x1612)=x1610 & Zero=x1609  ==>  new_pr2F34(x1612, Pos(Zero), x1613, x1614, x1615)_>=_new_pr2F31(new_primPlusNat0(Succ(x1612), Zero), x1613, new_primPlusNat0(Succ(x1612), Zero), x1614, x1615))  ==>  new_pr2F34(x187, Pos(Zero), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Zero), x189, new_primPlusNat0(Succ(x187), Zero), x190, x191))
84.27/49.99	
84.27/49.99	(13)    (Succ(x1616)=Succ(Succ(x194)) & Succ(x187)=Succ(x1616) & Zero=Zero  ==>  new_pr2F34(x187, Pos(Zero), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Zero), x189, new_primPlusNat0(Succ(x187), Zero), x190, x191))
84.27/49.99	
84.27/49.99	(14)    (Succ(x1617)=Succ(Succ(x194)) & Succ(x187)=Zero & Zero=Succ(x1617)  ==>  new_pr2F34(x187, Pos(Zero), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Zero), x189, new_primPlusNat0(Succ(x187), Zero), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(15)    (new_pr2F34(Succ(x194), Pos(Zero), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x194)), Zero), x189, new_primPlusNat0(Succ(Succ(x194)), Zero), x190, x191))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (14) using rules (I), (II).
84.27/49.99	*We consider the chain new_pr2F34(x212, Pos(x213), x214, x215, x216) -> new_pr2F31(new_primPlusNat0(Succ(x212), x213), x214, new_primPlusNat0(Succ(x212), x213), x215, x216), new_pr2F31(Succ(x217), x218, Succ(Zero), x219, x220) -> new_pr2F1(x218, Zero, new_fromInt, x219, x220) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F31(new_primPlusNat0(Succ(x212), x213), x214, new_primPlusNat0(Succ(x212), x213), x215, x216)=new_pr2F31(Succ(x217), x218, Succ(Zero), x219, x220)  ==>  new_pr2F34(x212, Pos(x213), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), x213), x214, new_primPlusNat0(Succ(x212), x213), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (Succ(x212)=x1618 & new_primPlusNat0(x1618, x213)=Succ(x217) & Succ(x212)=x1619 & new_primPlusNat0(x1619, x213)=Succ(Zero)  ==>  new_pr2F34(x212, Pos(x213), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), x213), x214, new_primPlusNat0(Succ(x212), x213), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1618, x213)=Succ(x217) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Succ(Succ(new_primPlusNat0(x1621, x1620)))=Succ(x217) & Succ(x212)=Succ(x1621) & Succ(x212)=x1619 & new_primPlusNat0(x1619, Succ(x1620))=Succ(Zero) & (\/x1622,x1623,x1624,x1625,x1626,x1627:new_primPlusNat0(x1621, x1620)=Succ(x1622) & Succ(x1623)=x1621 & Succ(x1623)=x1624 & new_primPlusNat0(x1624, x1620)=Succ(Zero)  ==>  new_pr2F34(x1623, Pos(x1620), x1625, x1626, x1627)_>=_new_pr2F31(new_primPlusNat0(Succ(x1623), x1620), x1625, new_primPlusNat0(Succ(x1623), x1620), x1626, x1627))  ==>  new_pr2F34(x212, Pos(Succ(x1620)), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Succ(x1620)), x214, new_primPlusNat0(Succ(x212), Succ(x1620)), x215, x216))
84.27/49.99	
84.27/49.99	(4)    (Succ(x1628)=Succ(x217) & Succ(x212)=Succ(x1628) & Succ(x212)=x1619 & new_primPlusNat0(x1619, Zero)=Succ(Zero)  ==>  new_pr2F34(x212, Pos(Zero), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Zero), x214, new_primPlusNat0(Succ(x212), Zero), x215, x216))
84.27/49.99	
84.27/49.99	(5)    (Succ(x1629)=Succ(x217) & Succ(x212)=Zero & Succ(x212)=x1619 & new_primPlusNat0(x1619, Succ(x1629))=Succ(Zero)  ==>  new_pr2F34(x212, Pos(Succ(x1629)), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Succ(x1629)), x214, new_primPlusNat0(Succ(x212), Succ(x1629)), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Succ(x212)=x1619 & Succ(x1620)=x1630 & new_primPlusNat0(x1619, x1630)=Succ(Zero) & (\/x1622,x1623,x1624,x1625,x1626,x1627:new_primPlusNat0(x212, x1620)=Succ(x1622) & Succ(x1623)=x212 & Succ(x1623)=x1624 & new_primPlusNat0(x1624, x1620)=Succ(Zero)  ==>  new_pr2F34(x1623, Pos(x1620), x1625, x1626, x1627)_>=_new_pr2F31(new_primPlusNat0(Succ(x1623), x1620), x1625, new_primPlusNat0(Succ(x1623), x1620), x1626, x1627))  ==>  new_pr2F34(x212, Pos(Succ(x1620)), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Succ(x1620)), x214, new_primPlusNat0(Succ(x212), Succ(x1620)), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (Succ(x212)=x1619 & Zero=x1646 & new_primPlusNat0(x1619, x1646)=Succ(Zero)  ==>  new_pr2F34(x212, Pos(Zero), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Zero), x214, new_primPlusNat0(Succ(x212), Zero), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1619, x1630)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(8)    (Succ(Succ(new_primPlusNat0(x1632, x1631)))=Succ(Zero) & Succ(x212)=Succ(x1632) & Succ(x1620)=Succ(x1631) & (\/x1622,x1623,x1624,x1625,x1626,x1627:new_primPlusNat0(x212, x1620)=Succ(x1622) & Succ(x1623)=x212 & Succ(x1623)=x1624 & new_primPlusNat0(x1624, x1620)=Succ(Zero)  ==>  new_pr2F34(x1623, Pos(x1620), x1625, x1626, x1627)_>=_new_pr2F31(new_primPlusNat0(Succ(x1623), x1620), x1625, new_primPlusNat0(Succ(x1623), x1620), x1626, x1627)) & (\/x1633,x1634,x1635,x1636,x1637,x1638,x1639,x1640,x1641,x1642,x1643:new_primPlusNat0(x1632, x1631)=Succ(Zero) & Succ(x1633)=x1632 & Succ(x1634)=x1631 & (\/x1635,x1636,x1637,x1638,x1639,x1640:new_primPlusNat0(x1633, x1634)=Succ(x1635) & Succ(x1636)=x1633 & Succ(x1636)=x1637 & new_primPlusNat0(x1637, x1634)=Succ(Zero)  ==>  new_pr2F34(x1636, Pos(x1634), x1638, x1639, x1640)_>=_new_pr2F31(new_primPlusNat0(Succ(x1636), x1634), x1638, new_primPlusNat0(Succ(x1636), x1634), x1639, x1640))  ==>  new_pr2F34(x1633, Pos(Succ(x1634)), x1641, x1642, x1643)_>=_new_pr2F31(new_primPlusNat0(Succ(x1633), Succ(x1634)), x1641, new_primPlusNat0(Succ(x1633), Succ(x1634)), x1642, x1643))  ==>  new_pr2F34(x212, Pos(Succ(x1620)), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Succ(x1620)), x214, new_primPlusNat0(Succ(x212), Succ(x1620)), x215, x216))
84.27/49.99	
84.27/49.99	(9)    (Succ(x1644)=Succ(Zero) & Succ(x212)=Succ(x1644) & Succ(x1620)=Zero & (\/x1622,x1623,x1624,x1625,x1626,x1627:new_primPlusNat0(x212, x1620)=Succ(x1622) & Succ(x1623)=x212 & Succ(x1623)=x1624 & new_primPlusNat0(x1624, x1620)=Succ(Zero)  ==>  new_pr2F34(x1623, Pos(x1620), x1625, x1626, x1627)_>=_new_pr2F31(new_primPlusNat0(Succ(x1623), x1620), x1625, new_primPlusNat0(Succ(x1623), x1620), x1626, x1627))  ==>  new_pr2F34(x212, Pos(Succ(x1620)), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Succ(x1620)), x214, new_primPlusNat0(Succ(x212), Succ(x1620)), x215, x216))
84.27/49.99	
84.27/49.99	(10)    (Succ(x1645)=Succ(Zero) & Succ(x212)=Zero & Succ(x1620)=Succ(x1645) & (\/x1622,x1623,x1624,x1625,x1626,x1627:new_primPlusNat0(x212, x1620)=Succ(x1622) & Succ(x1623)=x212 & Succ(x1623)=x1624 & new_primPlusNat0(x1624, x1620)=Succ(Zero)  ==>  new_pr2F34(x1623, Pos(x1620), x1625, x1626, x1627)_>=_new_pr2F31(new_primPlusNat0(Succ(x1623), x1620), x1625, new_primPlusNat0(Succ(x1623), x1620), x1626, x1627))  ==>  new_pr2F34(x212, Pos(Succ(x1620)), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Succ(x1620)), x214, new_primPlusNat0(Succ(x212), Succ(x1620)), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1619, x1646)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(11)    (Succ(Succ(new_primPlusNat0(x1648, x1647)))=Succ(Zero) & Succ(x212)=Succ(x1648) & Zero=Succ(x1647) & (\/x1649,x1650,x1651,x1652:new_primPlusNat0(x1648, x1647)=Succ(Zero) & Succ(x1649)=x1648 & Zero=x1647  ==>  new_pr2F34(x1649, Pos(Zero), x1650, x1651, x1652)_>=_new_pr2F31(new_primPlusNat0(Succ(x1649), Zero), x1650, new_primPlusNat0(Succ(x1649), Zero), x1651, x1652))  ==>  new_pr2F34(x212, Pos(Zero), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Zero), x214, new_primPlusNat0(Succ(x212), Zero), x215, x216))
84.27/49.99	
84.27/49.99	(12)    (Succ(x1653)=Succ(Zero) & Succ(x212)=Succ(x1653) & Zero=Zero  ==>  new_pr2F34(x212, Pos(Zero), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Zero), x214, new_primPlusNat0(Succ(x212), Zero), x215, x216))
84.27/49.99	
84.27/49.99	(13)    (Succ(x1654)=Succ(Zero) & Succ(x212)=Zero & Zero=Succ(x1654)  ==>  new_pr2F34(x212, Pos(Zero), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(x212), Zero), x214, new_primPlusNat0(Succ(x212), Zero), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (11) using rules (I), (II).We simplified constraint (12) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(14)    (new_pr2F34(Zero, Pos(Zero), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), x214, new_primPlusNat0(Succ(Zero), Zero), x215, x216))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (13) using rules (I), (II).
84.27/49.99	*We consider the chain new_pr2F34(x241, Pos(x242), x243, x244, x245) -> new_pr2F31(new_primPlusNat0(Succ(x241), x242), x243, new_primPlusNat0(Succ(x241), x242), x244, x245), new_pr2F31(Succ(x246), x247, Succ(Succ(x248)), x249, x250) -> H(x247, x249, Succ(x248), x250, anew_new_pr2F0G12(x248)) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F31(new_primPlusNat0(Succ(x241), x242), x243, new_primPlusNat0(Succ(x241), x242), x244, x245)=new_pr2F31(Succ(x246), x247, Succ(Succ(x248)), x249, x250)  ==>  new_pr2F34(x241, Pos(x242), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), x242), x243, new_primPlusNat0(Succ(x241), x242), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (Succ(x241)=x1655 & new_primPlusNat0(x1655, x242)=Succ(x246) & Succ(x241)=x1656 & new_primPlusNat0(x1656, x242)=Succ(Succ(x248))  ==>  new_pr2F34(x241, Pos(x242), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), x242), x243, new_primPlusNat0(Succ(x241), x242), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1655, x242)=Succ(x246) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Succ(Succ(new_primPlusNat0(x1658, x1657)))=Succ(x246) & Succ(x241)=Succ(x1658) & Succ(x241)=x1656 & new_primPlusNat0(x1656, Succ(x1657))=Succ(Succ(x248)) & (\/x1659,x1660,x1661,x1662,x1663,x1664,x1665:new_primPlusNat0(x1658, x1657)=Succ(x1659) & Succ(x1660)=x1658 & Succ(x1660)=x1661 & new_primPlusNat0(x1661, x1657)=Succ(Succ(x1662))  ==>  new_pr2F34(x1660, Pos(x1657), x1663, x1664, x1665)_>=_new_pr2F31(new_primPlusNat0(Succ(x1660), x1657), x1663, new_primPlusNat0(Succ(x1660), x1657), x1664, x1665))  ==>  new_pr2F34(x241, Pos(Succ(x1657)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1657)), x243, new_primPlusNat0(Succ(x241), Succ(x1657)), x244, x245))
84.27/49.99	
84.27/49.99	(4)    (Succ(x1666)=Succ(x246) & Succ(x241)=Succ(x1666) & Succ(x241)=x1656 & new_primPlusNat0(x1656, Zero)=Succ(Succ(x248))  ==>  new_pr2F34(x241, Pos(Zero), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Zero), x243, new_primPlusNat0(Succ(x241), Zero), x244, x245))
84.27/49.99	
84.27/49.99	(5)    (Succ(x1667)=Succ(x246) & Succ(x241)=Zero & Succ(x241)=x1656 & new_primPlusNat0(x1656, Succ(x1667))=Succ(Succ(x248))  ==>  new_pr2F34(x241, Pos(Succ(x1667)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1667)), x243, new_primPlusNat0(Succ(x241), Succ(x1667)), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Succ(x241)=x1656 & Succ(x1657)=x1668 & new_primPlusNat0(x1656, x1668)=Succ(Succ(x248)) & (\/x1659,x1660,x1661,x1662,x1663,x1664,x1665:new_primPlusNat0(x241, x1657)=Succ(x1659) & Succ(x1660)=x241 & Succ(x1660)=x1661 & new_primPlusNat0(x1661, x1657)=Succ(Succ(x1662))  ==>  new_pr2F34(x1660, Pos(x1657), x1663, x1664, x1665)_>=_new_pr2F31(new_primPlusNat0(Succ(x1660), x1657), x1663, new_primPlusNat0(Succ(x1660), x1657), x1664, x1665))  ==>  new_pr2F34(x241, Pos(Succ(x1657)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1657)), x243, new_primPlusNat0(Succ(x241), Succ(x1657)), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (Succ(x241)=x1656 & Zero=x1686 & new_primPlusNat0(x1656, x1686)=Succ(Succ(x248))  ==>  new_pr2F34(x241, Pos(Zero), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Zero), x243, new_primPlusNat0(Succ(x241), Zero), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1656, x1668)=Succ(Succ(x248)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(8)    (Succ(Succ(new_primPlusNat0(x1670, x1669)))=Succ(Succ(x248)) & Succ(x241)=Succ(x1670) & Succ(x1657)=Succ(x1669) & (\/x1659,x1660,x1661,x1662,x1663,x1664,x1665:new_primPlusNat0(x241, x1657)=Succ(x1659) & Succ(x1660)=x241 & Succ(x1660)=x1661 & new_primPlusNat0(x1661, x1657)=Succ(Succ(x1662))  ==>  new_pr2F34(x1660, Pos(x1657), x1663, x1664, x1665)_>=_new_pr2F31(new_primPlusNat0(Succ(x1660), x1657), x1663, new_primPlusNat0(Succ(x1660), x1657), x1664, x1665)) & (\/x1671,x1672,x1673,x1674,x1675,x1676,x1677,x1678,x1679,x1680,x1681,x1682,x1683:new_primPlusNat0(x1670, x1669)=Succ(Succ(x1671)) & Succ(x1672)=x1670 & Succ(x1673)=x1669 & (\/x1674,x1675,x1676,x1677,x1678,x1679,x1680:new_primPlusNat0(x1672, x1673)=Succ(x1674) & Succ(x1675)=x1672 & Succ(x1675)=x1676 & new_primPlusNat0(x1676, x1673)=Succ(Succ(x1677))  ==>  new_pr2F34(x1675, Pos(x1673), x1678, x1679, x1680)_>=_new_pr2F31(new_primPlusNat0(Succ(x1675), x1673), x1678, new_primPlusNat0(Succ(x1675), x1673), x1679, x1680))  ==>  new_pr2F34(x1672, Pos(Succ(x1673)), x1681, x1682, x1683)_>=_new_pr2F31(new_primPlusNat0(Succ(x1672), Succ(x1673)), x1681, new_primPlusNat0(Succ(x1672), Succ(x1673)), x1682, x1683))  ==>  new_pr2F34(x241, Pos(Succ(x1657)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1657)), x243, new_primPlusNat0(Succ(x241), Succ(x1657)), x244, x245))
84.27/49.99	
84.27/49.99	(9)    (Succ(x1684)=Succ(Succ(x248)) & Succ(x241)=Succ(x1684) & Succ(x1657)=Zero & (\/x1659,x1660,x1661,x1662,x1663,x1664,x1665:new_primPlusNat0(x241, x1657)=Succ(x1659) & Succ(x1660)=x241 & Succ(x1660)=x1661 & new_primPlusNat0(x1661, x1657)=Succ(Succ(x1662))  ==>  new_pr2F34(x1660, Pos(x1657), x1663, x1664, x1665)_>=_new_pr2F31(new_primPlusNat0(Succ(x1660), x1657), x1663, new_primPlusNat0(Succ(x1660), x1657), x1664, x1665))  ==>  new_pr2F34(x241, Pos(Succ(x1657)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1657)), x243, new_primPlusNat0(Succ(x241), Succ(x1657)), x244, x245))
84.27/49.99	
84.27/49.99	(10)    (Succ(x1685)=Succ(Succ(x248)) & Succ(x241)=Zero & Succ(x1657)=Succ(x1685) & (\/x1659,x1660,x1661,x1662,x1663,x1664,x1665:new_primPlusNat0(x241, x1657)=Succ(x1659) & Succ(x1660)=x241 & Succ(x1660)=x1661 & new_primPlusNat0(x1661, x1657)=Succ(Succ(x1662))  ==>  new_pr2F34(x1660, Pos(x1657), x1663, x1664, x1665)_>=_new_pr2F31(new_primPlusNat0(Succ(x1660), x1657), x1663, new_primPlusNat0(Succ(x1660), x1657), x1664, x1665))  ==>  new_pr2F34(x241, Pos(Succ(x1657)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1657)), x243, new_primPlusNat0(Succ(x241), Succ(x1657)), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (8) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(11)    (new_pr2F34(x241, Pos(Succ(x1657)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1657)), x243, new_primPlusNat0(Succ(x241), Succ(x1657)), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1656, x1686)=Succ(Succ(x248)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(12)    (Succ(Succ(new_primPlusNat0(x1688, x1687)))=Succ(Succ(x248)) & Succ(x241)=Succ(x1688) & Zero=Succ(x1687) & (\/x1689,x1690,x1691,x1692,x1693:new_primPlusNat0(x1688, x1687)=Succ(Succ(x1689)) & Succ(x1690)=x1688 & Zero=x1687  ==>  new_pr2F34(x1690, Pos(Zero), x1691, x1692, x1693)_>=_new_pr2F31(new_primPlusNat0(Succ(x1690), Zero), x1691, new_primPlusNat0(Succ(x1690), Zero), x1692, x1693))  ==>  new_pr2F34(x241, Pos(Zero), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Zero), x243, new_primPlusNat0(Succ(x241), Zero), x244, x245))
84.27/49.99	
84.27/49.99	(13)    (Succ(x1694)=Succ(Succ(x248)) & Succ(x241)=Succ(x1694) & Zero=Zero  ==>  new_pr2F34(x241, Pos(Zero), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Zero), x243, new_primPlusNat0(Succ(x241), Zero), x244, x245))
84.27/49.99	
84.27/49.99	(14)    (Succ(x1695)=Succ(Succ(x248)) & Succ(x241)=Zero & Zero=Succ(x1695)  ==>  new_pr2F34(x241, Pos(Zero), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Zero), x243, new_primPlusNat0(Succ(x241), Zero), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(15)    (new_pr2F34(Succ(x248), Pos(Zero), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x248)), Zero), x243, new_primPlusNat0(Succ(Succ(x248)), Zero), x244, x245))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (14) using rules (I), (II).
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F31(Succ(x276), x277, Succ(Succ(x278)), x279, x280) -> new_pr2F0G12(x277, x279, Succ(x278), x278, x280), new_pr2F0G12(x281, x282, x283, Succ(Zero), x284) -> new_pr2F1(x281, x283, new_fromInt, x282, x284) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G12(x277, x279, Succ(x278), x278, x280)=new_pr2F0G12(x281, x282, x283, Succ(Zero), x284)  ==>  new_pr2F31(Succ(x276), x277, Succ(Succ(x278)), x279, x280)_>=_new_pr2F0G12(x277, x279, Succ(x278), x278, x280))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F31(Succ(x276), x277, Succ(Succ(Succ(Zero))), x279, x280)_>=_new_pr2F0G12(x277, x279, Succ(Succ(Zero)), Succ(Zero), x280))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F31(Succ(x300), x301, Succ(Succ(x302)), x303, x304) -> new_pr2F0G12(x301, x303, Succ(x302), x302, x304), new_pr2F0G12(x305, x306, x307, Zero, x308) -> new_pr2F0G13(new_sr8(x305, x306, x308), x305, new_primDivNatS1(Succ(x307)), new_primDivNatS1(Succ(x307)), x308) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G12(x301, x303, Succ(x302), x302, x304)=new_pr2F0G12(x305, x306, x307, Zero, x308)  ==>  new_pr2F31(Succ(x300), x301, Succ(Succ(x302)), x303, x304)_>=_new_pr2F0G12(x301, x303, Succ(x302), x302, x304))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_pr2F31(Succ(x300), x301, Succ(Succ(Zero)), x303, x304)_>=_new_pr2F0G12(x301, x303, Succ(Zero), Zero, x304))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G12(x394, x395, x396, Zero, x397) -> new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(x396)), new_primDivNatS1(Succ(x396)), x397), new_pr2F0G13(x398, x399, x400, Succ(Zero), x401) -> new_pr2F2(x399, x400, new_fromInt, x398, x401) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(x396)), new_primDivNatS1(Succ(x396)), x397)=new_pr2F0G13(x398, x399, x400, Succ(Zero), x401)  ==>  new_pr2F0G12(x394, x395, x396, Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(x396)), new_primDivNatS1(Succ(x396)), x397))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (Succ(x396)=x1696 & new_primDivNatS1(x1696)=Succ(Zero)  ==>  new_pr2F0G12(x394, x395, x396, Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(x396)), new_primDivNatS1(Succ(x396)), x397))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1696)=Succ(Zero) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_primDivNatS01(x1697)=Succ(Zero) & Succ(x396)=Succ(x1697)  ==>  new_pr2F0G12(x394, x395, x396, Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(x396)), new_primDivNatS1(Succ(x396)), x397))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(4)    (new_primDivNatS01(x1697)=Succ(Zero)  ==>  new_pr2F0G12(x394, x395, x1697, Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(x1697)), new_primDivNatS1(Succ(x1697)), x397))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1697)=Succ(Zero) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(5)    (Succ(new_primDivNatS4(x1698))=Succ(Zero)  ==>  new_pr2F0G12(x394, x395, Succ(Succ(x1698)), Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(Succ(Succ(x1698)))), new_primDivNatS1(Succ(Succ(Succ(x1698)))), x397))
84.27/49.99	
84.27/49.99	(6)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G12(x394, x395, Succ(Zero), Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x397))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G12(x394, x395, Succ(Succ(x1698)), Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(Succ(Succ(x1698)))), new_primDivNatS1(Succ(Succ(Succ(x1698)))), x397))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(8)    (new_pr2F0G12(x394, x395, Succ(Zero), Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x397))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G12(x410, x411, x412, Zero, x413) -> new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(x412)), new_primDivNatS1(Succ(x412)), x413), new_pr2F0G13(x414, x415, x416, Succ(Succ(x417)), x418) -> new_pr2F0G14(x414, x415, x416, x417, x418) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(x412)), new_primDivNatS1(Succ(x412)), x413)=new_pr2F0G13(x414, x415, x416, Succ(Succ(x417)), x418)  ==>  new_pr2F0G12(x410, x411, x412, Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(x412)), new_primDivNatS1(Succ(x412)), x413))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (Succ(x412)=x1699 & new_primDivNatS1(x1699)=Succ(Succ(x417))  ==>  new_pr2F0G12(x410, x411, x412, Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(x412)), new_primDivNatS1(Succ(x412)), x413))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1699)=Succ(Succ(x417)) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_primDivNatS01(x1700)=Succ(Succ(x417)) & Succ(x412)=Succ(x1700)  ==>  new_pr2F0G12(x410, x411, x412, Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(x412)), new_primDivNatS1(Succ(x412)), x413))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(4)    (new_primDivNatS01(x1700)=Succ(Succ(x417))  ==>  new_pr2F0G12(x410, x411, x1700, Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(x1700)), new_primDivNatS1(Succ(x1700)), x413))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1700)=Succ(Succ(x417)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(5)    (Succ(new_primDivNatS4(x1701))=Succ(Succ(x417))  ==>  new_pr2F0G12(x410, x411, Succ(Succ(x1701)), Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(Succ(Succ(x1701)))), new_primDivNatS1(Succ(Succ(Succ(x1701)))), x413))
84.27/49.99	
84.27/49.99	(6)    (Succ(new_primDivNatS2)=Succ(Succ(x417))  ==>  new_pr2F0G12(x410, x411, Succ(Zero), Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x413))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G12(x410, x411, Succ(Succ(x1701)), Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(Succ(Succ(x1701)))), new_primDivNatS1(Succ(Succ(Succ(x1701)))), x413))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(8)    (new_pr2F0G12(x410, x411, Succ(Zero), Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x413))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G12(x427, x428, x429, Zero, x430) -> new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(x429)), new_primDivNatS1(Succ(x429)), x430), new_pr2F0G13(x431, x432, x433, Zero, x434) -> new_pr2F0G13(x431, new_sr10(x432, x434), new_primDivNatS1(x433), new_primDivNatS1(x433), x434) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(x429)), new_primDivNatS1(Succ(x429)), x430)=new_pr2F0G13(x431, x432, x433, Zero, x434)  ==>  new_pr2F0G12(x427, x428, x429, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(x429)), new_primDivNatS1(Succ(x429)), x430))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (Succ(x429)=x1702 & new_primDivNatS1(x1702)=Zero  ==>  new_pr2F0G12(x427, x428, x429, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(x429)), new_primDivNatS1(Succ(x429)), x430))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1702)=Zero which results in the following new constraints:
84.27/49.99	
84.27/49.99	(3)    (Zero=Zero & Succ(x429)=Zero  ==>  new_pr2F0G12(x427, x428, x429, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(x429)), new_primDivNatS1(Succ(x429)), x430))
84.27/49.99	
84.27/49.99	(4)    (new_primDivNatS01(x1703)=Zero & Succ(x429)=Succ(x1703)  ==>  new_pr2F0G12(x427, x428, x429, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(x429)), new_primDivNatS1(Succ(x429)), x430))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(5)    (new_primDivNatS01(x1703)=Zero  ==>  new_pr2F0G12(x427, x428, x1703, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(x1703)), new_primDivNatS1(Succ(x1703)), x430))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1703)=Zero which results in the following new constraint:
84.27/49.99	
84.27/49.99	(6)    (Zero=Zero  ==>  new_pr2F0G12(x427, x428, Zero, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x430))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G12(x427, x428, Zero, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x430))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	*We consider the chain new_pr2F0G12(x447, x448, x449, Zero, x450) -> new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(x449)), new_primDivNatS1(Succ(x449)), x450), new_pr2F0G13(x451, x452, x453, Succ(Succ(x454)), x455) -> H'(x451, x452, x453, x455, anew_new_pr2F0G14(x454)) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(x449)), new_primDivNatS1(Succ(x449)), x450)=new_pr2F0G13(x451, x452, x453, Succ(Succ(x454)), x455)  ==>  new_pr2F0G12(x447, x448, x449, Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(x449)), new_primDivNatS1(Succ(x449)), x450))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (Succ(x449)=x1705 & new_primDivNatS1(x1705)=Succ(Succ(x454))  ==>  new_pr2F0G12(x447, x448, x449, Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(x449)), new_primDivNatS1(Succ(x449)), x450))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1705)=Succ(Succ(x454)) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (new_primDivNatS01(x1706)=Succ(Succ(x454)) & Succ(x449)=Succ(x1706)  ==>  new_pr2F0G12(x447, x448, x449, Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(x449)), new_primDivNatS1(Succ(x449)), x450))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(4)    (new_primDivNatS01(x1706)=Succ(Succ(x454))  ==>  new_pr2F0G12(x447, x448, x1706, Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(x1706)), new_primDivNatS1(Succ(x1706)), x450))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1706)=Succ(Succ(x454)) which results in the following new constraints:
84.27/49.99	
84.27/49.99	(5)    (Succ(new_primDivNatS4(x1707))=Succ(Succ(x454))  ==>  new_pr2F0G12(x447, x448, Succ(Succ(x1707)), Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(Succ(Succ(x1707)))), new_primDivNatS1(Succ(Succ(Succ(x1707)))), x450))
84.27/49.99	
84.27/49.99	(6)    (Succ(new_primDivNatS2)=Succ(Succ(x454))  ==>  new_pr2F0G12(x447, x448, Succ(Zero), Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x450))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(7)    (new_pr2F0G12(x447, x448, Succ(Succ(x1707)), Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(Succ(Succ(x1707)))), new_primDivNatS1(Succ(Succ(Succ(x1707)))), x450))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (6) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(8)    (new_pr2F0G12(x447, x448, Succ(Zero), Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x450))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be) the following chains were created:
84.27/49.99	*We consider the chain new_pr2F0G13(x488, x489, x490, Succ(Zero), x491) -> new_pr2F2(x489, x490, new_fromInt, x488, x491), new_pr2F2(x492, x493, Pos(x494), x495, x496) -> new_pr2F31(new_primPlusNat0(x493, x494), new_sr11(x492, x496), new_primPlusNat0(x493, x494), x495, x496) which results in the following constraint:
84.27/49.99	
84.27/49.99	(1)    (new_pr2F2(x489, x490, new_fromInt, x488, x491)=new_pr2F2(x492, x493, Pos(x494), x495, x496)  ==>  new_pr2F0G13(x488, x489, x490, Succ(Zero), x491)_>=_new_pr2F2(x489, x490, new_fromInt, x488, x491))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(2)    (new_fromInt=Pos(x494)  ==>  new_pr2F0G13(x488, x489, x490, Succ(Zero), x491)_>=_new_pr2F2(x489, x490, new_fromInt, x488, x491))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_fromInt=Pos(x494) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(3)    (Pos(Succ(Zero))=Pos(x494)  ==>  new_pr2F0G13(x488, x489, x490, Succ(Zero), x491)_>=_new_pr2F2(x489, x490, new_fromInt, x488, x491))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
84.27/49.99	
84.27/49.99	(4)    (new_pr2F0G13(x488, x489, x490, Succ(Zero), x491)_>=_new_pr2F2(x489, x490, new_fromInt, x488, x491))
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	
84.27/49.99	For Pair new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F2(x556, x557, Pos(x558), x559, x560) -> new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560), new_pr2F31(Succ(x561), x562, Succ(Succ(x563)), x564, x565) -> new_pr2F0G12(x562, x564, Succ(x563), x563, x565) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560)=new_pr2F31(Succ(x561), x562, Succ(Succ(x563)), x564, x565)  ==>  new_pr2F2(x556, x557, Pos(x558), x559, x560)_>=_new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primPlusNat0(x557, x558)=Succ(x561) & new_primPlusNat0(x557, x558)=Succ(Succ(x563))  ==>  new_pr2F2(x556, x557, Pos(x558), x559, x560)_>=_new_pr2F31(new_primPlusNat0(x557, x558), new_sr11(x556, x560), new_primPlusNat0(x557, x558), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x557, x558)=Succ(x561) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(3)    (Succ(Succ(new_primPlusNat0(x1709, x1708)))=Succ(x561) & new_primPlusNat0(Succ(x1709), Succ(x1708))=Succ(Succ(x563)) & (\/x1710,x1711,x1712,x1713,x1714:new_primPlusNat0(x1709, x1708)=Succ(x1710) & new_primPlusNat0(x1709, x1708)=Succ(Succ(x1711))  ==>  new_pr2F2(x1712, x1709, Pos(x1708), x1713, x1714)_>=_new_pr2F31(new_primPlusNat0(x1709, x1708), new_sr11(x1712, x1714), new_primPlusNat0(x1709, x1708), x1713, x1714))  ==>  new_pr2F2(x556, Succ(x1709), Pos(Succ(x1708)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1709), Succ(x1708)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1709), Succ(x1708)), x559, x560))
84.27/50.00	
84.27/50.00	(4)    (Succ(x1715)=Succ(x561) & new_primPlusNat0(Succ(x1715), Zero)=Succ(Succ(x563))  ==>  new_pr2F2(x556, Succ(x1715), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1715), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1715), Zero), x559, x560))
84.27/50.00	
84.27/50.00	(5)    (Succ(x1716)=Succ(x561) & new_primPlusNat0(Zero, Succ(x1716))=Succ(Succ(x563))  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1716)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1716)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1716)), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (Succ(x1709)=x1717 & Succ(x1708)=x1718 & new_primPlusNat0(x1717, x1718)=Succ(Succ(x563)) & (\/x1710,x1711,x1712,x1713,x1714:new_primPlusNat0(x1709, x1708)=Succ(x1710) & new_primPlusNat0(x1709, x1708)=Succ(Succ(x1711))  ==>  new_pr2F2(x1712, x1709, Pos(x1708), x1713, x1714)_>=_new_pr2F31(new_primPlusNat0(x1709, x1708), new_sr11(x1712, x1714), new_primPlusNat0(x1709, x1708), x1713, x1714))  ==>  new_pr2F2(x556, Succ(x1709), Pos(Succ(x1708)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1709), Succ(x1708)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1709), Succ(x1708)), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (Succ(x1715)=x1734 & Zero=x1735 & new_primPlusNat0(x1734, x1735)=Succ(Succ(x563))  ==>  new_pr2F2(x556, Succ(x1715), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1715), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1715), Zero), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(8)    (Zero=x1745 & Succ(x1716)=x1746 & new_primPlusNat0(x1745, x1746)=Succ(Succ(x563))  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1716)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1716)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1716)), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1717, x1718)=Succ(Succ(x563)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(9)    (Succ(Succ(new_primPlusNat0(x1720, x1719)))=Succ(Succ(x563)) & Succ(x1709)=Succ(x1720) & Succ(x1708)=Succ(x1719) & (\/x1710,x1711,x1712,x1713,x1714:new_primPlusNat0(x1709, x1708)=Succ(x1710) & new_primPlusNat0(x1709, x1708)=Succ(Succ(x1711))  ==>  new_pr2F2(x1712, x1709, Pos(x1708), x1713, x1714)_>=_new_pr2F31(new_primPlusNat0(x1709, x1708), new_sr11(x1712, x1714), new_primPlusNat0(x1709, x1708), x1713, x1714)) & (\/x1721,x1722,x1723,x1724,x1725,x1726,x1727,x1728,x1729,x1730,x1731:new_primPlusNat0(x1720, x1719)=Succ(Succ(x1721)) & Succ(x1722)=x1720 & Succ(x1723)=x1719 & (\/x1724,x1725,x1726,x1727,x1728:new_primPlusNat0(x1722, x1723)=Succ(x1724) & new_primPlusNat0(x1722, x1723)=Succ(Succ(x1725))  ==>  new_pr2F2(x1726, x1722, Pos(x1723), x1727, x1728)_>=_new_pr2F31(new_primPlusNat0(x1722, x1723), new_sr11(x1726, x1728), new_primPlusNat0(x1722, x1723), x1727, x1728))  ==>  new_pr2F2(x1729, Succ(x1722), Pos(Succ(x1723)), x1730, x1731)_>=_new_pr2F31(new_primPlusNat0(Succ(x1722), Succ(x1723)), new_sr11(x1729, x1731), new_primPlusNat0(Succ(x1722), Succ(x1723)), x1730, x1731))  ==>  new_pr2F2(x556, Succ(x1709), Pos(Succ(x1708)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1709), Succ(x1708)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1709), Succ(x1708)), x559, x560))
84.27/50.00	
84.27/50.00	(10)    (Succ(x1732)=Succ(Succ(x563)) & Succ(x1709)=Succ(x1732) & Succ(x1708)=Zero & (\/x1710,x1711,x1712,x1713,x1714:new_primPlusNat0(x1709, x1708)=Succ(x1710) & new_primPlusNat0(x1709, x1708)=Succ(Succ(x1711))  ==>  new_pr2F2(x1712, x1709, Pos(x1708), x1713, x1714)_>=_new_pr2F31(new_primPlusNat0(x1709, x1708), new_sr11(x1712, x1714), new_primPlusNat0(x1709, x1708), x1713, x1714))  ==>  new_pr2F2(x556, Succ(x1709), Pos(Succ(x1708)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1709), Succ(x1708)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1709), Succ(x1708)), x559, x560))
84.27/50.00	
84.27/50.00	(11)    (Succ(x1733)=Succ(Succ(x563)) & Succ(x1709)=Zero & Succ(x1708)=Succ(x1733) & (\/x1710,x1711,x1712,x1713,x1714:new_primPlusNat0(x1709, x1708)=Succ(x1710) & new_primPlusNat0(x1709, x1708)=Succ(Succ(x1711))  ==>  new_pr2F2(x1712, x1709, Pos(x1708), x1713, x1714)_>=_new_pr2F31(new_primPlusNat0(x1709, x1708), new_sr11(x1712, x1714), new_primPlusNat0(x1709, x1708), x1713, x1714))  ==>  new_pr2F2(x556, Succ(x1709), Pos(Succ(x1708)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1709), Succ(x1708)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1709), Succ(x1708)), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(12)    (new_pr2F2(x556, Succ(x1709), Pos(Succ(x1708)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1709), Succ(x1708)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1709), Succ(x1708)), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1734, x1735)=Succ(Succ(x563)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(13)    (Succ(Succ(new_primPlusNat0(x1737, x1736)))=Succ(Succ(x563)) & Succ(x1715)=Succ(x1737) & Zero=Succ(x1736) & (\/x1738,x1739,x1740,x1741,x1742:new_primPlusNat0(x1737, x1736)=Succ(Succ(x1738)) & Succ(x1739)=x1737 & Zero=x1736  ==>  new_pr2F2(x1740, Succ(x1739), Pos(Zero), x1741, x1742)_>=_new_pr2F31(new_primPlusNat0(Succ(x1739), Zero), new_sr11(x1740, x1742), new_primPlusNat0(Succ(x1739), Zero), x1741, x1742))  ==>  new_pr2F2(x556, Succ(x1715), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1715), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1715), Zero), x559, x560))
84.27/50.00	
84.27/50.00	(14)    (Succ(x1743)=Succ(Succ(x563)) & Succ(x1715)=Succ(x1743) & Zero=Zero  ==>  new_pr2F2(x556, Succ(x1715), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1715), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1715), Zero), x559, x560))
84.27/50.00	
84.27/50.00	(15)    (Succ(x1744)=Succ(Succ(x563)) & Succ(x1715)=Zero & Zero=Succ(x1744)  ==>  new_pr2F2(x556, Succ(x1715), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1715), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(x1715), Zero), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (13) using rules (I), (II).We simplified constraint (14) using rules (I), (II), (III) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(16)    (new_pr2F2(x556, Succ(Succ(x563)), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x563)), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(Succ(x563)), Zero), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (15) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1745, x1746)=Succ(Succ(x563)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(17)    (Succ(Succ(new_primPlusNat0(x1748, x1747)))=Succ(Succ(x563)) & Zero=Succ(x1748) & Succ(x1716)=Succ(x1747) & (\/x1749,x1750,x1751,x1752,x1753:new_primPlusNat0(x1748, x1747)=Succ(Succ(x1749)) & Zero=x1748 & Succ(x1750)=x1747  ==>  new_pr2F2(x1751, Zero, Pos(Succ(x1750)), x1752, x1753)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1750)), new_sr11(x1751, x1753), new_primPlusNat0(Zero, Succ(x1750)), x1752, x1753))  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1716)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1716)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1716)), x559, x560))
84.27/50.00	
84.27/50.00	(18)    (Succ(x1754)=Succ(Succ(x563)) & Zero=Succ(x1754) & Succ(x1716)=Zero  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1716)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1716)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1716)), x559, x560))
84.27/50.00	
84.27/50.00	(19)    (Succ(x1755)=Succ(Succ(x563)) & Zero=Zero & Succ(x1716)=Succ(x1755)  ==>  new_pr2F2(x556, Zero, Pos(Succ(x1716)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1716)), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(x1716)), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (17) using rules (I), (II).We solved constraint (18) using rules (I), (II).We simplified constraint (19) using rules (I), (II), (III) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(20)    (new_pr2F2(x556, Zero, Pos(Succ(Succ(x563))), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x563))), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(Succ(x563))), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F2(x581, x582, Pos(x583), x584, x585) -> new_pr2F31(new_primPlusNat0(x582, x583), new_sr11(x581, x585), new_primPlusNat0(x582, x583), x584, x585), new_pr2F31(Succ(x586), x587, Succ(Zero), x588, x589) -> new_pr2F1(x587, Zero, new_fromInt, x588, x589) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F31(new_primPlusNat0(x582, x583), new_sr11(x581, x585), new_primPlusNat0(x582, x583), x584, x585)=new_pr2F31(Succ(x586), x587, Succ(Zero), x588, x589)  ==>  new_pr2F2(x581, x582, Pos(x583), x584, x585)_>=_new_pr2F31(new_primPlusNat0(x582, x583), new_sr11(x581, x585), new_primPlusNat0(x582, x583), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primPlusNat0(x582, x583)=Succ(x586) & new_primPlusNat0(x582, x583)=Succ(Zero)  ==>  new_pr2F2(x581, x582, Pos(x583), x584, x585)_>=_new_pr2F31(new_primPlusNat0(x582, x583), new_sr11(x581, x585), new_primPlusNat0(x582, x583), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x582, x583)=Succ(x586) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(3)    (Succ(Succ(new_primPlusNat0(x1757, x1756)))=Succ(x586) & new_primPlusNat0(Succ(x1757), Succ(x1756))=Succ(Zero) & (\/x1758,x1759,x1760,x1761:new_primPlusNat0(x1757, x1756)=Succ(x1758) & new_primPlusNat0(x1757, x1756)=Succ(Zero)  ==>  new_pr2F2(x1759, x1757, Pos(x1756), x1760, x1761)_>=_new_pr2F31(new_primPlusNat0(x1757, x1756), new_sr11(x1759, x1761), new_primPlusNat0(x1757, x1756), x1760, x1761))  ==>  new_pr2F2(x581, Succ(x1757), Pos(Succ(x1756)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1757), Succ(x1756)), new_sr11(x581, x585), new_primPlusNat0(Succ(x1757), Succ(x1756)), x584, x585))
84.27/50.00	
84.27/50.00	(4)    (Succ(x1762)=Succ(x586) & new_primPlusNat0(Succ(x1762), Zero)=Succ(Zero)  ==>  new_pr2F2(x581, Succ(x1762), Pos(Zero), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1762), Zero), new_sr11(x581, x585), new_primPlusNat0(Succ(x1762), Zero), x584, x585))
84.27/50.00	
84.27/50.00	(5)    (Succ(x1763)=Succ(x586) & new_primPlusNat0(Zero, Succ(x1763))=Succ(Zero)  ==>  new_pr2F2(x581, Zero, Pos(Succ(x1763)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1763)), new_sr11(x581, x585), new_primPlusNat0(Zero, Succ(x1763)), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (Succ(x1757)=x1764 & Succ(x1756)=x1765 & new_primPlusNat0(x1764, x1765)=Succ(Zero) & (\/x1758,x1759,x1760,x1761:new_primPlusNat0(x1757, x1756)=Succ(x1758) & new_primPlusNat0(x1757, x1756)=Succ(Zero)  ==>  new_pr2F2(x1759, x1757, Pos(x1756), x1760, x1761)_>=_new_pr2F31(new_primPlusNat0(x1757, x1756), new_sr11(x1759, x1761), new_primPlusNat0(x1757, x1756), x1760, x1761))  ==>  new_pr2F2(x581, Succ(x1757), Pos(Succ(x1756)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1757), Succ(x1756)), new_sr11(x581, x585), new_primPlusNat0(Succ(x1757), Succ(x1756)), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (Succ(x1762)=x1779 & Zero=x1780 & new_primPlusNat0(x1779, x1780)=Succ(Zero)  ==>  new_pr2F2(x581, Succ(x1762), Pos(Zero), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1762), Zero), new_sr11(x581, x585), new_primPlusNat0(Succ(x1762), Zero), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(8)    (Zero=x1789 & Succ(x1763)=x1790 & new_primPlusNat0(x1789, x1790)=Succ(Zero)  ==>  new_pr2F2(x581, Zero, Pos(Succ(x1763)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1763)), new_sr11(x581, x585), new_primPlusNat0(Zero, Succ(x1763)), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1764, x1765)=Succ(Zero) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(9)    (Succ(Succ(new_primPlusNat0(x1767, x1766)))=Succ(Zero) & Succ(x1757)=Succ(x1767) & Succ(x1756)=Succ(x1766) & (\/x1758,x1759,x1760,x1761:new_primPlusNat0(x1757, x1756)=Succ(x1758) & new_primPlusNat0(x1757, x1756)=Succ(Zero)  ==>  new_pr2F2(x1759, x1757, Pos(x1756), x1760, x1761)_>=_new_pr2F31(new_primPlusNat0(x1757, x1756), new_sr11(x1759, x1761), new_primPlusNat0(x1757, x1756), x1760, x1761)) & (\/x1768,x1769,x1770,x1771,x1772,x1773,x1774,x1775,x1776:new_primPlusNat0(x1767, x1766)=Succ(Zero) & Succ(x1768)=x1767 & Succ(x1769)=x1766 & (\/x1770,x1771,x1772,x1773:new_primPlusNat0(x1768, x1769)=Succ(x1770) & new_primPlusNat0(x1768, x1769)=Succ(Zero)  ==>  new_pr2F2(x1771, x1768, Pos(x1769), x1772, x1773)_>=_new_pr2F31(new_primPlusNat0(x1768, x1769), new_sr11(x1771, x1773), new_primPlusNat0(x1768, x1769), x1772, x1773))  ==>  new_pr2F2(x1774, Succ(x1768), Pos(Succ(x1769)), x1775, x1776)_>=_new_pr2F31(new_primPlusNat0(Succ(x1768), Succ(x1769)), new_sr11(x1774, x1776), new_primPlusNat0(Succ(x1768), Succ(x1769)), x1775, x1776))  ==>  new_pr2F2(x581, Succ(x1757), Pos(Succ(x1756)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1757), Succ(x1756)), new_sr11(x581, x585), new_primPlusNat0(Succ(x1757), Succ(x1756)), x584, x585))
84.27/50.00	
84.27/50.00	(10)    (Succ(x1777)=Succ(Zero) & Succ(x1757)=Succ(x1777) & Succ(x1756)=Zero & (\/x1758,x1759,x1760,x1761:new_primPlusNat0(x1757, x1756)=Succ(x1758) & new_primPlusNat0(x1757, x1756)=Succ(Zero)  ==>  new_pr2F2(x1759, x1757, Pos(x1756), x1760, x1761)_>=_new_pr2F31(new_primPlusNat0(x1757, x1756), new_sr11(x1759, x1761), new_primPlusNat0(x1757, x1756), x1760, x1761))  ==>  new_pr2F2(x581, Succ(x1757), Pos(Succ(x1756)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1757), Succ(x1756)), new_sr11(x581, x585), new_primPlusNat0(Succ(x1757), Succ(x1756)), x584, x585))
84.27/50.00	
84.27/50.00	(11)    (Succ(x1778)=Succ(Zero) & Succ(x1757)=Zero & Succ(x1756)=Succ(x1778) & (\/x1758,x1759,x1760,x1761:new_primPlusNat0(x1757, x1756)=Succ(x1758) & new_primPlusNat0(x1757, x1756)=Succ(Zero)  ==>  new_pr2F2(x1759, x1757, Pos(x1756), x1760, x1761)_>=_new_pr2F31(new_primPlusNat0(x1757, x1756), new_sr11(x1759, x1761), new_primPlusNat0(x1757, x1756), x1760, x1761))  ==>  new_pr2F2(x581, Succ(x1757), Pos(Succ(x1756)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1757), Succ(x1756)), new_sr11(x581, x585), new_primPlusNat0(Succ(x1757), Succ(x1756)), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (9) using rules (I), (II).We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1779, x1780)=Succ(Zero) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(12)    (Succ(Succ(new_primPlusNat0(x1782, x1781)))=Succ(Zero) & Succ(x1762)=Succ(x1782) & Zero=Succ(x1781) & (\/x1783,x1784,x1785,x1786:new_primPlusNat0(x1782, x1781)=Succ(Zero) & Succ(x1783)=x1782 & Zero=x1781  ==>  new_pr2F2(x1784, Succ(x1783), Pos(Zero), x1785, x1786)_>=_new_pr2F31(new_primPlusNat0(Succ(x1783), Zero), new_sr11(x1784, x1786), new_primPlusNat0(Succ(x1783), Zero), x1785, x1786))  ==>  new_pr2F2(x581, Succ(x1762), Pos(Zero), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1762), Zero), new_sr11(x581, x585), new_primPlusNat0(Succ(x1762), Zero), x584, x585))
84.27/50.00	
84.27/50.00	(13)    (Succ(x1787)=Succ(Zero) & Succ(x1762)=Succ(x1787) & Zero=Zero  ==>  new_pr2F2(x581, Succ(x1762), Pos(Zero), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1762), Zero), new_sr11(x581, x585), new_primPlusNat0(Succ(x1762), Zero), x584, x585))
84.27/50.00	
84.27/50.00	(14)    (Succ(x1788)=Succ(Zero) & Succ(x1762)=Zero & Zero=Succ(x1788)  ==>  new_pr2F2(x581, Succ(x1762), Pos(Zero), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(x1762), Zero), new_sr11(x581, x585), new_primPlusNat0(Succ(x1762), Zero), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(15)    (new_pr2F2(x581, Succ(Zero), Pos(Zero), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), new_sr11(x581, x585), new_primPlusNat0(Succ(Zero), Zero), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (14) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1789, x1790)=Succ(Zero) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(16)    (Succ(Succ(new_primPlusNat0(x1792, x1791)))=Succ(Zero) & Zero=Succ(x1792) & Succ(x1763)=Succ(x1791) & (\/x1793,x1794,x1795,x1796:new_primPlusNat0(x1792, x1791)=Succ(Zero) & Zero=x1792 & Succ(x1793)=x1791  ==>  new_pr2F2(x1794, Zero, Pos(Succ(x1793)), x1795, x1796)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1793)), new_sr11(x1794, x1796), new_primPlusNat0(Zero, Succ(x1793)), x1795, x1796))  ==>  new_pr2F2(x581, Zero, Pos(Succ(x1763)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1763)), new_sr11(x581, x585), new_primPlusNat0(Zero, Succ(x1763)), x584, x585))
84.27/50.00	
84.27/50.00	(17)    (Succ(x1797)=Succ(Zero) & Zero=Succ(x1797) & Succ(x1763)=Zero  ==>  new_pr2F2(x581, Zero, Pos(Succ(x1763)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1763)), new_sr11(x581, x585), new_primPlusNat0(Zero, Succ(x1763)), x584, x585))
84.27/50.00	
84.27/50.00	(18)    (Succ(x1798)=Succ(Zero) & Zero=Zero & Succ(x1763)=Succ(x1798)  ==>  new_pr2F2(x581, Zero, Pos(Succ(x1763)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1763)), new_sr11(x581, x585), new_primPlusNat0(Zero, Succ(x1763)), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (16) using rules (I), (II).We solved constraint (17) using rules (I), (II).We simplified constraint (18) using rules (I), (II), (III) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(19)    (new_pr2F2(x581, Zero, Pos(Succ(Zero)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Zero)), new_sr11(x581, x585), new_primPlusNat0(Zero, Succ(Zero)), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F2(x610, x611, Pos(x612), x613, x614) -> new_pr2F31(new_primPlusNat0(x611, x612), new_sr11(x610, x614), new_primPlusNat0(x611, x612), x613, x614), new_pr2F31(Succ(x615), x616, Succ(Succ(x617)), x618, x619) -> H(x616, x618, Succ(x617), x619, anew_new_pr2F0G12(x617)) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F31(new_primPlusNat0(x611, x612), new_sr11(x610, x614), new_primPlusNat0(x611, x612), x613, x614)=new_pr2F31(Succ(x615), x616, Succ(Succ(x617)), x618, x619)  ==>  new_pr2F2(x610, x611, Pos(x612), x613, x614)_>=_new_pr2F31(new_primPlusNat0(x611, x612), new_sr11(x610, x614), new_primPlusNat0(x611, x612), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primPlusNat0(x611, x612)=Succ(x615) & new_primPlusNat0(x611, x612)=Succ(Succ(x617))  ==>  new_pr2F2(x610, x611, Pos(x612), x613, x614)_>=_new_pr2F31(new_primPlusNat0(x611, x612), new_sr11(x610, x614), new_primPlusNat0(x611, x612), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x611, x612)=Succ(x615) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(3)    (Succ(Succ(new_primPlusNat0(x1800, x1799)))=Succ(x615) & new_primPlusNat0(Succ(x1800), Succ(x1799))=Succ(Succ(x617)) & (\/x1801,x1802,x1803,x1804,x1805:new_primPlusNat0(x1800, x1799)=Succ(x1801) & new_primPlusNat0(x1800, x1799)=Succ(Succ(x1802))  ==>  new_pr2F2(x1803, x1800, Pos(x1799), x1804, x1805)_>=_new_pr2F31(new_primPlusNat0(x1800, x1799), new_sr11(x1803, x1805), new_primPlusNat0(x1800, x1799), x1804, x1805))  ==>  new_pr2F2(x610, Succ(x1800), Pos(Succ(x1799)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1800), Succ(x1799)), new_sr11(x610, x614), new_primPlusNat0(Succ(x1800), Succ(x1799)), x613, x614))
84.27/50.00	
84.27/50.00	(4)    (Succ(x1806)=Succ(x615) & new_primPlusNat0(Succ(x1806), Zero)=Succ(Succ(x617))  ==>  new_pr2F2(x610, Succ(x1806), Pos(Zero), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1806), Zero), new_sr11(x610, x614), new_primPlusNat0(Succ(x1806), Zero), x613, x614))
84.27/50.00	
84.27/50.00	(5)    (Succ(x1807)=Succ(x615) & new_primPlusNat0(Zero, Succ(x1807))=Succ(Succ(x617))  ==>  new_pr2F2(x610, Zero, Pos(Succ(x1807)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1807)), new_sr11(x610, x614), new_primPlusNat0(Zero, Succ(x1807)), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (Succ(x1800)=x1808 & Succ(x1799)=x1809 & new_primPlusNat0(x1808, x1809)=Succ(Succ(x617)) & (\/x1801,x1802,x1803,x1804,x1805:new_primPlusNat0(x1800, x1799)=Succ(x1801) & new_primPlusNat0(x1800, x1799)=Succ(Succ(x1802))  ==>  new_pr2F2(x1803, x1800, Pos(x1799), x1804, x1805)_>=_new_pr2F31(new_primPlusNat0(x1800, x1799), new_sr11(x1803, x1805), new_primPlusNat0(x1800, x1799), x1804, x1805))  ==>  new_pr2F2(x610, Succ(x1800), Pos(Succ(x1799)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1800), Succ(x1799)), new_sr11(x610, x614), new_primPlusNat0(Succ(x1800), Succ(x1799)), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (Succ(x1806)=x1825 & Zero=x1826 & new_primPlusNat0(x1825, x1826)=Succ(Succ(x617))  ==>  new_pr2F2(x610, Succ(x1806), Pos(Zero), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1806), Zero), new_sr11(x610, x614), new_primPlusNat0(Succ(x1806), Zero), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV), (VII) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(8)    (Zero=x1836 & Succ(x1807)=x1837 & new_primPlusNat0(x1836, x1837)=Succ(Succ(x617))  ==>  new_pr2F2(x610, Zero, Pos(Succ(x1807)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1807)), new_sr11(x610, x614), new_primPlusNat0(Zero, Succ(x1807)), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1808, x1809)=Succ(Succ(x617)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(9)    (Succ(Succ(new_primPlusNat0(x1811, x1810)))=Succ(Succ(x617)) & Succ(x1800)=Succ(x1811) & Succ(x1799)=Succ(x1810) & (\/x1801,x1802,x1803,x1804,x1805:new_primPlusNat0(x1800, x1799)=Succ(x1801) & new_primPlusNat0(x1800, x1799)=Succ(Succ(x1802))  ==>  new_pr2F2(x1803, x1800, Pos(x1799), x1804, x1805)_>=_new_pr2F31(new_primPlusNat0(x1800, x1799), new_sr11(x1803, x1805), new_primPlusNat0(x1800, x1799), x1804, x1805)) & (\/x1812,x1813,x1814,x1815,x1816,x1817,x1818,x1819,x1820,x1821,x1822:new_primPlusNat0(x1811, x1810)=Succ(Succ(x1812)) & Succ(x1813)=x1811 & Succ(x1814)=x1810 & (\/x1815,x1816,x1817,x1818,x1819:new_primPlusNat0(x1813, x1814)=Succ(x1815) & new_primPlusNat0(x1813, x1814)=Succ(Succ(x1816))  ==>  new_pr2F2(x1817, x1813, Pos(x1814), x1818, x1819)_>=_new_pr2F31(new_primPlusNat0(x1813, x1814), new_sr11(x1817, x1819), new_primPlusNat0(x1813, x1814), x1818, x1819))  ==>  new_pr2F2(x1820, Succ(x1813), Pos(Succ(x1814)), x1821, x1822)_>=_new_pr2F31(new_primPlusNat0(Succ(x1813), Succ(x1814)), new_sr11(x1820, x1822), new_primPlusNat0(Succ(x1813), Succ(x1814)), x1821, x1822))  ==>  new_pr2F2(x610, Succ(x1800), Pos(Succ(x1799)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1800), Succ(x1799)), new_sr11(x610, x614), new_primPlusNat0(Succ(x1800), Succ(x1799)), x613, x614))
84.27/50.00	
84.27/50.00	(10)    (Succ(x1823)=Succ(Succ(x617)) & Succ(x1800)=Succ(x1823) & Succ(x1799)=Zero & (\/x1801,x1802,x1803,x1804,x1805:new_primPlusNat0(x1800, x1799)=Succ(x1801) & new_primPlusNat0(x1800, x1799)=Succ(Succ(x1802))  ==>  new_pr2F2(x1803, x1800, Pos(x1799), x1804, x1805)_>=_new_pr2F31(new_primPlusNat0(x1800, x1799), new_sr11(x1803, x1805), new_primPlusNat0(x1800, x1799), x1804, x1805))  ==>  new_pr2F2(x610, Succ(x1800), Pos(Succ(x1799)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1800), Succ(x1799)), new_sr11(x610, x614), new_primPlusNat0(Succ(x1800), Succ(x1799)), x613, x614))
84.27/50.00	
84.27/50.00	(11)    (Succ(x1824)=Succ(Succ(x617)) & Succ(x1800)=Zero & Succ(x1799)=Succ(x1824) & (\/x1801,x1802,x1803,x1804,x1805:new_primPlusNat0(x1800, x1799)=Succ(x1801) & new_primPlusNat0(x1800, x1799)=Succ(Succ(x1802))  ==>  new_pr2F2(x1803, x1800, Pos(x1799), x1804, x1805)_>=_new_pr2F31(new_primPlusNat0(x1800, x1799), new_sr11(x1803, x1805), new_primPlusNat0(x1800, x1799), x1804, x1805))  ==>  new_pr2F2(x610, Succ(x1800), Pos(Succ(x1799)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1800), Succ(x1799)), new_sr11(x610, x614), new_primPlusNat0(Succ(x1800), Succ(x1799)), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(12)    (new_pr2F2(x610, Succ(x1800), Pos(Succ(x1799)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1800), Succ(x1799)), new_sr11(x610, x614), new_primPlusNat0(Succ(x1800), Succ(x1799)), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (10) using rules (I), (II).We solved constraint (11) using rules (I), (II).We simplified constraint (7) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1825, x1826)=Succ(Succ(x617)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(13)    (Succ(Succ(new_primPlusNat0(x1828, x1827)))=Succ(Succ(x617)) & Succ(x1806)=Succ(x1828) & Zero=Succ(x1827) & (\/x1829,x1830,x1831,x1832,x1833:new_primPlusNat0(x1828, x1827)=Succ(Succ(x1829)) & Succ(x1830)=x1828 & Zero=x1827  ==>  new_pr2F2(x1831, Succ(x1830), Pos(Zero), x1832, x1833)_>=_new_pr2F31(new_primPlusNat0(Succ(x1830), Zero), new_sr11(x1831, x1833), new_primPlusNat0(Succ(x1830), Zero), x1832, x1833))  ==>  new_pr2F2(x610, Succ(x1806), Pos(Zero), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1806), Zero), new_sr11(x610, x614), new_primPlusNat0(Succ(x1806), Zero), x613, x614))
84.27/50.00	
84.27/50.00	(14)    (Succ(x1834)=Succ(Succ(x617)) & Succ(x1806)=Succ(x1834) & Zero=Zero  ==>  new_pr2F2(x610, Succ(x1806), Pos(Zero), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1806), Zero), new_sr11(x610, x614), new_primPlusNat0(Succ(x1806), Zero), x613, x614))
84.27/50.00	
84.27/50.00	(15)    (Succ(x1835)=Succ(Succ(x617)) & Succ(x1806)=Zero & Zero=Succ(x1835)  ==>  new_pr2F2(x610, Succ(x1806), Pos(Zero), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1806), Zero), new_sr11(x610, x614), new_primPlusNat0(Succ(x1806), Zero), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (13) using rules (I), (II).We simplified constraint (14) using rules (I), (II), (III) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(16)    (new_pr2F2(x610, Succ(Succ(x617)), Pos(Zero), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x617)), Zero), new_sr11(x610, x614), new_primPlusNat0(Succ(Succ(x617)), Zero), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (15) using rules (I), (II).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primPlusNat0(x1836, x1837)=Succ(Succ(x617)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(17)    (Succ(Succ(new_primPlusNat0(x1839, x1838)))=Succ(Succ(x617)) & Zero=Succ(x1839) & Succ(x1807)=Succ(x1838) & (\/x1840,x1841,x1842,x1843,x1844:new_primPlusNat0(x1839, x1838)=Succ(Succ(x1840)) & Zero=x1839 & Succ(x1841)=x1838  ==>  new_pr2F2(x1842, Zero, Pos(Succ(x1841)), x1843, x1844)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1841)), new_sr11(x1842, x1844), new_primPlusNat0(Zero, Succ(x1841)), x1843, x1844))  ==>  new_pr2F2(x610, Zero, Pos(Succ(x1807)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1807)), new_sr11(x610, x614), new_primPlusNat0(Zero, Succ(x1807)), x613, x614))
84.27/50.00	
84.27/50.00	(18)    (Succ(x1845)=Succ(Succ(x617)) & Zero=Succ(x1845) & Succ(x1807)=Zero  ==>  new_pr2F2(x610, Zero, Pos(Succ(x1807)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1807)), new_sr11(x610, x614), new_primPlusNat0(Zero, Succ(x1807)), x613, x614))
84.27/50.00	
84.27/50.00	(19)    (Succ(x1846)=Succ(Succ(x617)) & Zero=Zero & Succ(x1807)=Succ(x1846)  ==>  new_pr2F2(x610, Zero, Pos(Succ(x1807)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(x1807)), new_sr11(x610, x614), new_primPlusNat0(Zero, Succ(x1807)), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (17) using rules (I), (II).We solved constraint (18) using rules (I), (II).We simplified constraint (19) using rules (I), (II), (III) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(20)    (new_pr2F2(x610, Zero, Pos(Succ(Succ(x617))), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x617))), new_sr11(x610, x614), new_primPlusNat0(Zero, Succ(Succ(x617))), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F31(Succ(x649), x650, Succ(Zero), x651, x652) -> new_pr2F1(x650, Zero, new_fromInt, x651, x652), new_pr2F1(x653, x654, x655, x656, x657) -> new_pr2F34(x654, x655, x653, new_sr9(x653, x656, x657), x657) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F1(x650, Zero, new_fromInt, x651, x652)=new_pr2F1(x653, x654, x655, x656, x657)  ==>  new_pr2F31(Succ(x649), x650, Succ(Zero), x651, x652)_>=_new_pr2F1(x650, Zero, new_fromInt, x651, x652))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_pr2F31(Succ(x649), x650, Succ(Zero), x651, x652)_>=_new_pr2F1(x650, Zero, new_fromInt, x651, x652))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F0G13(x767, x768, x769, Succ(Succ(x770)), x771) -> new_pr2F0G14(x767, x768, x769, x770, x771), new_pr2F0G14(x772, x773, x774, Succ(Zero), x775) -> new_pr2F2(x773, x774, new_fromInt, x772, x775) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G14(x767, x768, x769, x770, x771)=new_pr2F0G14(x772, x773, x774, Succ(Zero), x775)  ==>  new_pr2F0G13(x767, x768, x769, Succ(Succ(x770)), x771)_>=_new_pr2F0G14(x767, x768, x769, x770, x771))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_pr2F0G13(x767, x768, x769, Succ(Succ(Succ(Zero))), x771)_>=_new_pr2F0G14(x767, x768, x769, Succ(Zero), x771))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F0G13(x776, x777, x778, Succ(Succ(x779)), x780) -> new_pr2F0G14(x776, x777, x778, x779, x780), new_pr2F0G14(x781, x782, x783, Zero, x784) -> new_pr2F0G13(x781, new_sr10(x782, x784), new_primDivNatS1(x783), new_primDivNatS1(x783), x784) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G14(x776, x777, x778, x779, x780)=new_pr2F0G14(x781, x782, x783, Zero, x784)  ==>  new_pr2F0G13(x776, x777, x778, Succ(Succ(x779)), x780)_>=_new_pr2F0G14(x776, x777, x778, x779, x780))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_pr2F0G13(x776, x777, x778, Succ(Succ(Zero)), x780)_>=_new_pr2F0G14(x776, x777, x778, Zero, x780))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F0G14(x844, x845, x846, Succ(Zero), x847) -> new_pr2F2(x845, x846, new_fromInt, x844, x847), new_pr2F2(x848, x849, Pos(x850), x851, x852) -> new_pr2F31(new_primPlusNat0(x849, x850), new_sr11(x848, x852), new_primPlusNat0(x849, x850), x851, x852) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F2(x845, x846, new_fromInt, x844, x847)=new_pr2F2(x848, x849, Pos(x850), x851, x852)  ==>  new_pr2F0G14(x844, x845, x846, Succ(Zero), x847)_>=_new_pr2F2(x845, x846, new_fromInt, x844, x847))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_fromInt=Pos(x850)  ==>  new_pr2F0G14(x844, x845, x846, Succ(Zero), x847)_>=_new_pr2F2(x845, x846, new_fromInt, x844, x847))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_fromInt=Pos(x850) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (Pos(Succ(Zero))=Pos(x850)  ==>  new_pr2F0G14(x844, x845, x846, Succ(Zero), x847)_>=_new_pr2F2(x845, x846, new_fromInt, x844, x847))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(4)    (new_pr2F0G14(x844, x845, x846, Succ(Zero), x847)_>=_new_pr2F2(x845, x846, new_fromInt, x844, x847))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F0G14(x917, x918, x919, Zero, x920) -> new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(x919), new_primDivNatS1(x919), x920), new_pr2F0G13(x921, x922, x923, Succ(Zero), x924) -> new_pr2F2(x922, x923, new_fromInt, x921, x924) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(x919), new_primDivNatS1(x919), x920)=new_pr2F0G13(x921, x922, x923, Succ(Zero), x924)  ==>  new_pr2F0G14(x917, x918, x919, Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(x919), new_primDivNatS1(x919), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x919)=Succ(Zero)  ==>  new_pr2F0G14(x917, x918, x919, Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(x919), new_primDivNatS1(x919), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x919)=Succ(Zero) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_primDivNatS01(x1847)=Succ(Zero)  ==>  new_pr2F0G14(x917, x918, Succ(x1847), Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(Succ(x1847)), new_primDivNatS1(Succ(x1847)), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1847)=Succ(Zero) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (Succ(new_primDivNatS4(x1848))=Succ(Zero)  ==>  new_pr2F0G14(x917, x918, Succ(Succ(Succ(x1848))), Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(Succ(Succ(Succ(x1848)))), new_primDivNatS1(Succ(Succ(Succ(x1848)))), x920))
84.27/50.00	
84.27/50.00	(5)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G14(x917, x918, Succ(Succ(Zero)), Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (new_pr2F0G14(x917, x918, Succ(Succ(Succ(x1848))), Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(Succ(Succ(Succ(x1848)))), new_primDivNatS1(Succ(Succ(Succ(x1848)))), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G14(x917, x918, Succ(Succ(Zero)), Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F0G14(x933, x934, x935, Zero, x936) -> new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(x935), new_primDivNatS1(x935), x936), new_pr2F0G13(x937, x938, x939, Succ(Succ(x940)), x941) -> new_pr2F0G14(x937, x938, x939, x940, x941) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(x935), new_primDivNatS1(x935), x936)=new_pr2F0G13(x937, x938, x939, Succ(Succ(x940)), x941)  ==>  new_pr2F0G14(x933, x934, x935, Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(x935), new_primDivNatS1(x935), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x935)=Succ(Succ(x940))  ==>  new_pr2F0G14(x933, x934, x935, Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(x935), new_primDivNatS1(x935), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x935)=Succ(Succ(x940)) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_primDivNatS01(x1849)=Succ(Succ(x940))  ==>  new_pr2F0G14(x933, x934, Succ(x1849), Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(Succ(x1849)), new_primDivNatS1(Succ(x1849)), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1849)=Succ(Succ(x940)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (Succ(new_primDivNatS4(x1850))=Succ(Succ(x940))  ==>  new_pr2F0G14(x933, x934, Succ(Succ(Succ(x1850))), Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(Succ(Succ(Succ(x1850)))), new_primDivNatS1(Succ(Succ(Succ(x1850)))), x936))
84.27/50.00	
84.27/50.00	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x940))  ==>  new_pr2F0G14(x933, x934, Succ(Succ(Zero)), Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (new_pr2F0G14(x933, x934, Succ(Succ(Succ(x1850))), Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(Succ(Succ(Succ(x1850)))), new_primDivNatS1(Succ(Succ(Succ(x1850)))), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G14(x933, x934, Succ(Succ(Zero)), Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F0G14(x950, x951, x952, Zero, x953) -> new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(x952), new_primDivNatS1(x952), x953), new_pr2F0G13(x954, x955, x956, Zero, x957) -> new_pr2F0G13(x954, new_sr10(x955, x957), new_primDivNatS1(x956), new_primDivNatS1(x956), x957) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(x952), new_primDivNatS1(x952), x953)=new_pr2F0G13(x954, x955, x956, Zero, x957)  ==>  new_pr2F0G14(x950, x951, x952, Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(x952), new_primDivNatS1(x952), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x952)=Zero  ==>  new_pr2F0G14(x950, x951, x952, Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(x952), new_primDivNatS1(x952), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x952)=Zero which results in the following new constraints:
84.27/50.00	
84.27/50.00	(3)    (Zero=Zero  ==>  new_pr2F0G14(x950, x951, Zero, Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x953))
84.27/50.00	
84.27/50.00	(4)    (new_primDivNatS01(x1851)=Zero  ==>  new_pr2F0G14(x950, x951, Succ(x1851), Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(Succ(x1851)), new_primDivNatS1(Succ(x1851)), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(5)    (new_pr2F0G14(x950, x951, Zero, Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1851)=Zero which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (Zero=Zero  ==>  new_pr2F0G14(x950, x951, Succ(Zero), Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G14(x950, x951, Succ(Zero), Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F0G14(x970, x971, x972, Zero, x973) -> new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(x972), new_primDivNatS1(x972), x973), new_pr2F0G13(x974, x975, x976, Succ(Succ(x977)), x978) -> H'(x974, x975, x976, x978, anew_new_pr2F0G14(x977)) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(x972), new_primDivNatS1(x972), x973)=new_pr2F0G13(x974, x975, x976, Succ(Succ(x977)), x978)  ==>  new_pr2F0G14(x970, x971, x972, Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(x972), new_primDivNatS1(x972), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x972)=Succ(Succ(x977))  ==>  new_pr2F0G14(x970, x971, x972, Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(x972), new_primDivNatS1(x972), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x972)=Succ(Succ(x977)) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_primDivNatS01(x1853)=Succ(Succ(x977))  ==>  new_pr2F0G14(x970, x971, Succ(x1853), Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(Succ(x1853)), new_primDivNatS1(Succ(x1853)), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1853)=Succ(Succ(x977)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (Succ(new_primDivNatS4(x1854))=Succ(Succ(x977))  ==>  new_pr2F0G14(x970, x971, Succ(Succ(Succ(x1854))), Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(Succ(Succ(Succ(x1854)))), new_primDivNatS1(Succ(Succ(Succ(x1854)))), x973))
84.27/50.00	
84.27/50.00	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x977))  ==>  new_pr2F0G14(x970, x971, Succ(Succ(Zero)), Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (new_pr2F0G14(x970, x971, Succ(Succ(Succ(x1854))), Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(Succ(Succ(Succ(x1854)))), new_primDivNatS1(Succ(Succ(Succ(x1854)))), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G14(x970, x971, Succ(Succ(Zero)), Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F0G13(x1007, x1008, x1009, Zero, x1010) -> new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(x1009), new_primDivNatS1(x1009), x1010), new_pr2F0G13(x1011, x1012, x1013, Succ(Zero), x1014) -> new_pr2F2(x1012, x1013, new_fromInt, x1011, x1014) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(x1009), new_primDivNatS1(x1009), x1010)=new_pr2F0G13(x1011, x1012, x1013, Succ(Zero), x1014)  ==>  new_pr2F0G13(x1007, x1008, x1009, Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(x1009), new_primDivNatS1(x1009), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x1009)=Succ(Zero)  ==>  new_pr2F0G13(x1007, x1008, x1009, Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(x1009), new_primDivNatS1(x1009), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1009)=Succ(Zero) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_primDivNatS01(x1855)=Succ(Zero)  ==>  new_pr2F0G13(x1007, x1008, Succ(x1855), Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(Succ(x1855)), new_primDivNatS1(Succ(x1855)), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1855)=Succ(Zero) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (Succ(new_primDivNatS4(x1856))=Succ(Zero)  ==>  new_pr2F0G13(x1007, x1008, Succ(Succ(Succ(x1856))), Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(Succ(Succ(Succ(x1856)))), new_primDivNatS1(Succ(Succ(Succ(x1856)))), x1010))
84.27/50.00	
84.27/50.00	(5)    (Succ(new_primDivNatS2)=Succ(Zero)  ==>  new_pr2F0G13(x1007, x1008, Succ(Succ(Zero)), Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (new_pr2F0G13(x1007, x1008, Succ(Succ(Succ(x1856))), Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(Succ(Succ(Succ(x1856)))), new_primDivNatS1(Succ(Succ(Succ(x1856)))), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G13(x1007, x1008, Succ(Succ(Zero)), Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F0G13(x1023, x1024, x1025, Zero, x1026) -> new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(x1025), new_primDivNatS1(x1025), x1026), new_pr2F0G13(x1027, x1028, x1029, Succ(Succ(x1030)), x1031) -> new_pr2F0G14(x1027, x1028, x1029, x1030, x1031) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(x1025), new_primDivNatS1(x1025), x1026)=new_pr2F0G13(x1027, x1028, x1029, Succ(Succ(x1030)), x1031)  ==>  new_pr2F0G13(x1023, x1024, x1025, Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(x1025), new_primDivNatS1(x1025), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x1025)=Succ(Succ(x1030))  ==>  new_pr2F0G13(x1023, x1024, x1025, Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(x1025), new_primDivNatS1(x1025), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1025)=Succ(Succ(x1030)) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_primDivNatS01(x1857)=Succ(Succ(x1030))  ==>  new_pr2F0G13(x1023, x1024, Succ(x1857), Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(Succ(x1857)), new_primDivNatS1(Succ(x1857)), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1857)=Succ(Succ(x1030)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (Succ(new_primDivNatS4(x1858))=Succ(Succ(x1030))  ==>  new_pr2F0G13(x1023, x1024, Succ(Succ(Succ(x1858))), Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(Succ(Succ(Succ(x1858)))), new_primDivNatS1(Succ(Succ(Succ(x1858)))), x1026))
84.27/50.00	
84.27/50.00	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x1030))  ==>  new_pr2F0G13(x1023, x1024, Succ(Succ(Zero)), Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (new_pr2F0G13(x1023, x1024, Succ(Succ(Succ(x1858))), Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(Succ(Succ(Succ(x1858)))), new_primDivNatS1(Succ(Succ(Succ(x1858)))), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G13(x1023, x1024, Succ(Succ(Zero)), Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F0G13(x1040, x1041, x1042, Zero, x1043) -> new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(x1042), new_primDivNatS1(x1042), x1043), new_pr2F0G13(x1044, x1045, x1046, Zero, x1047) -> new_pr2F0G13(x1044, new_sr10(x1045, x1047), new_primDivNatS1(x1046), new_primDivNatS1(x1046), x1047) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(x1042), new_primDivNatS1(x1042), x1043)=new_pr2F0G13(x1044, x1045, x1046, Zero, x1047)  ==>  new_pr2F0G13(x1040, x1041, x1042, Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(x1042), new_primDivNatS1(x1042), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x1042)=Zero  ==>  new_pr2F0G13(x1040, x1041, x1042, Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(x1042), new_primDivNatS1(x1042), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1042)=Zero which results in the following new constraints:
84.27/50.00	
84.27/50.00	(3)    (Zero=Zero  ==>  new_pr2F0G13(x1040, x1041, Zero, Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1043))
84.27/50.00	
84.27/50.00	(4)    (new_primDivNatS01(x1859)=Zero  ==>  new_pr2F0G13(x1040, x1041, Succ(x1859), Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(Succ(x1859)), new_primDivNatS1(Succ(x1859)), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(5)    (new_pr2F0G13(x1040, x1041, Zero, Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1859)=Zero which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (Zero=Zero  ==>  new_pr2F0G13(x1040, x1041, Succ(Zero), Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G13(x1040, x1041, Succ(Zero), Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*We consider the chain new_pr2F0G13(x1060, x1061, x1062, Zero, x1063) -> new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(x1062), new_primDivNatS1(x1062), x1063), new_pr2F0G13(x1064, x1065, x1066, Succ(Succ(x1067)), x1068) -> H'(x1064, x1065, x1066, x1068, anew_new_pr2F0G14(x1067)) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(x1062), new_primDivNatS1(x1062), x1063)=new_pr2F0G13(x1064, x1065, x1066, Succ(Succ(x1067)), x1068)  ==>  new_pr2F0G13(x1060, x1061, x1062, Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(x1062), new_primDivNatS1(x1062), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (new_primDivNatS1(x1062)=Succ(Succ(x1067))  ==>  new_pr2F0G13(x1060, x1061, x1062, Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(x1062), new_primDivNatS1(x1062), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x1062)=Succ(Succ(x1067)) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_primDivNatS01(x1861)=Succ(Succ(x1067))  ==>  new_pr2F0G13(x1060, x1061, Succ(x1861), Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(Succ(x1861)), new_primDivNatS1(Succ(x1861)), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x1861)=Succ(Succ(x1067)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (Succ(new_primDivNatS4(x1862))=Succ(Succ(x1067))  ==>  new_pr2F0G13(x1060, x1061, Succ(Succ(Succ(x1862))), Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(Succ(Succ(Succ(x1862)))), new_primDivNatS1(Succ(Succ(Succ(x1862)))), x1063))
84.27/50.00	
84.27/50.00	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x1067))  ==>  new_pr2F0G13(x1060, x1061, Succ(Succ(Zero)), Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(6)    (new_pr2F0G13(x1060, x1061, Succ(Succ(Succ(x1862))), Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(Succ(Succ(Succ(x1862)))), new_primDivNatS1(Succ(Succ(Succ(x1862)))), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G13(x1060, x1061, Succ(Succ(Zero)), Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800)) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F31(Succ(x1142), x1143, Succ(Succ(x1144)), x1145, x1146) -> H(x1143, x1145, Succ(x1144), x1146, anew_new_pr2F0G12(x1144)), H(x1147, x1148, x1149, x1150, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(x1147, x1148, x1149, Succ(Zero), x1150) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (H(x1143, x1145, Succ(x1144), x1146, anew_new_pr2F0G12(x1144))=H(x1147, x1148, x1149, x1150, cons_new_pr2F0G12(Succ(Zero)))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(x1144)), x1145, x1146)_>=_H(x1143, x1145, Succ(x1144), x1146, anew_new_pr2F0G12(x1144)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (anew_new_pr2F0G12(x1144)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(x1144)), x1145, x1146)_>=_H(x1143, x1145, Succ(x1144), x1146, anew_new_pr2F0G12(x1144)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on anew_new_pr2F0G12(x1144)=cons_new_pr2F0G12(Succ(Zero)) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_new_pr2F0G12(x1863)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(x1863)))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(x1863))), x1146, anew_new_pr2F0G12(Succ(Succ(x1863)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_new_pr2F0G12(x1863)=cons_new_pr2F0G12(Succ(Zero)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (new_new_pr2F0G12(x1864)=cons_new_pr2F0G12(Succ(Zero)) & (\/x1865,x1866,x1867,x1868:new_new_pr2F0G12(x1864)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1865), x1866, Succ(Succ(Succ(Succ(x1864)))), x1867, x1868)_>=_H(x1866, x1867, Succ(Succ(Succ(x1864))), x1868, anew_new_pr2F0G12(Succ(Succ(x1864)))))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(Succ(Succ(x1864)))))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(Succ(Succ(x1864))))), x1146, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1864)))))))
84.27/50.00	
84.27/50.00	(5)    (cons_new_pr2F0G12(Succ(Zero))=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(Succ(Zero))))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(Succ(Zero)))), x1146, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	(6)    (cons_new_pr2F0G12(Zero)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(Zero)))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(Zero))), x1146, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rule (VI) where we applied the induction hypothesis (\/x1865,x1866,x1867,x1868:new_new_pr2F0G12(x1864)=cons_new_pr2F0G12(Succ(Zero))  ==>  new_pr2F31(Succ(x1865), x1866, Succ(Succ(Succ(Succ(x1864)))), x1867, x1868)_>=_H(x1866, x1867, Succ(Succ(Succ(x1864))), x1868, anew_new_pr2F0G12(Succ(Succ(x1864))))) with sigma = [x1865 / x1142, x1866 / x1143, x1867 / x1145, x1868 / x1146] which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(x1864)))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(x1864))), x1146, anew_new_pr2F0G12(Succ(Succ(x1864))))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(Succ(Succ(x1864)))))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(Succ(Succ(x1864))))), x1146, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1864)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(8)    (new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(Succ(Zero))))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(Succ(Zero)))), x1146, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (6) using rules (I), (II).
84.27/50.00	*We consider the chain new_pr2F31(Succ(x1151), x1152, Succ(Succ(x1153)), x1154, x1155) -> H(x1152, x1154, Succ(x1153), x1155, anew_new_pr2F0G12(x1153)), H(x1156, x1157, x1158, x1159, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(x1156, x1157, x1158, Zero, x1159) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (H(x1152, x1154, Succ(x1153), x1155, anew_new_pr2F0G12(x1153))=H(x1156, x1157, x1158, x1159, cons_new_pr2F0G12(Zero))  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(x1153)), x1154, x1155)_>=_H(x1152, x1154, Succ(x1153), x1155, anew_new_pr2F0G12(x1153)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (anew_new_pr2F0G12(x1153)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(x1153)), x1154, x1155)_>=_H(x1152, x1154, Succ(x1153), x1155, anew_new_pr2F0G12(x1153)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on anew_new_pr2F0G12(x1153)=cons_new_pr2F0G12(Zero) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_new_pr2F0G12(x1869)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(x1869)))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(x1869))), x1155, anew_new_pr2F0G12(Succ(Succ(x1869)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_new_pr2F0G12(x1869)=cons_new_pr2F0G12(Zero) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (new_new_pr2F0G12(x1870)=cons_new_pr2F0G12(Zero) & (\/x1871,x1872,x1873,x1874:new_new_pr2F0G12(x1870)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1871), x1872, Succ(Succ(Succ(Succ(x1870)))), x1873, x1874)_>=_H(x1872, x1873, Succ(Succ(Succ(x1870))), x1874, anew_new_pr2F0G12(Succ(Succ(x1870)))))  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(Succ(Succ(x1870)))))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(Succ(Succ(x1870))))), x1155, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1870)))))))
84.27/50.00	
84.27/50.00	(5)    (cons_new_pr2F0G12(Succ(Zero))=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(Succ(Zero))))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(Succ(Zero)))), x1155, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	(6)    (cons_new_pr2F0G12(Zero)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(Zero)))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(Zero))), x1155, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rule (VI) where we applied the induction hypothesis (\/x1871,x1872,x1873,x1874:new_new_pr2F0G12(x1870)=cons_new_pr2F0G12(Zero)  ==>  new_pr2F31(Succ(x1871), x1872, Succ(Succ(Succ(Succ(x1870)))), x1873, x1874)_>=_H(x1872, x1873, Succ(Succ(Succ(x1870))), x1874, anew_new_pr2F0G12(Succ(Succ(x1870))))) with sigma = [x1871 / x1151, x1872 / x1152, x1873 / x1154, x1874 / x1155] which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(x1870)))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(x1870))), x1155, anew_new_pr2F0G12(Succ(Succ(x1870))))  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(Succ(Succ(x1870)))))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(Succ(Succ(x1870))))), x1155, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1870)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(8)    (new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(Zero)))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(Zero))), x1155, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) the following chains were created:
84.27/50.00	*We consider the chain H(x1175, x1176, x1177, x1178, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(x1175, x1176, x1177, Succ(Zero), x1178), new_pr2F0G12(x1179, x1180, x1181, Succ(Zero), x1182) -> new_pr2F1(x1179, x1181, new_fromInt, x1180, x1182) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G12(x1175, x1176, x1177, Succ(Zero), x1178)=new_pr2F0G12(x1179, x1180, x1181, Succ(Zero), x1182)  ==>  H(x1175, x1176, x1177, x1178, cons_new_pr2F0G12(Succ(Zero)))_>=_new_pr2F0G12(x1175, x1176, x1177, Succ(Zero), x1178))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (H(x1175, x1176, x1177, x1178, cons_new_pr2F0G12(Succ(Zero)))_>=_new_pr2F0G12(x1175, x1176, x1177, Succ(Zero), x1178))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) the following chains were created:
84.27/50.00	*We consider the chain H(x1267, x1268, x1269, x1270, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(x1267, x1268, x1269, Zero, x1270), new_pr2F0G12(x1271, x1272, x1273, Zero, x1274) -> new_pr2F0G13(new_sr8(x1271, x1272, x1274), x1271, new_primDivNatS1(Succ(x1273)), new_primDivNatS1(Succ(x1273)), x1274) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G12(x1267, x1268, x1269, Zero, x1270)=new_pr2F0G12(x1271, x1272, x1273, Zero, x1274)  ==>  H(x1267, x1268, x1269, x1270, cons_new_pr2F0G12(Zero))_>=_new_pr2F0G12(x1267, x1268, x1269, Zero, x1270))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (H(x1267, x1268, x1269, x1270, cons_new_pr2F0G12(Zero))_>=_new_pr2F0G12(x1267, x1268, x1269, Zero, x1270))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> H'(vuz110, vuz111, vuz113, be, anew_new_pr2F0G14(vuz11400)) the following chains were created:
84.27/50.00	*We consider the chain new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(x1410)), x1411) -> H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(x1410)), H'(x1412, x1413, x1414, x1415, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(x1412, x1413, x1414, Succ(Zero), x1415) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(x1410))=H'(x1412, x1413, x1414, x1415, cons_new_pr2F0G14(Succ(Zero)))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(x1410)), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(x1410)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (anew_new_pr2F0G14(x1410)=cons_new_pr2F0G14(Succ(Zero))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(x1410)), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(x1410)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on anew_new_pr2F0G14(x1410)=cons_new_pr2F0G14(Succ(Zero)) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_new_pr2F0G14(x1875)=cons_new_pr2F0G14(Succ(Zero))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(x1875)))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(x1875)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_new_pr2F0G14(x1875)=cons_new_pr2F0G14(Succ(Zero)) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (new_new_pr2F0G14(x1876)=cons_new_pr2F0G14(Succ(Zero)) & (\/x1877,x1878,x1879,x1880:new_new_pr2F0G14(x1876)=cons_new_pr2F0G14(Succ(Zero))  ==>  new_pr2F0G13(x1877, x1878, x1879, Succ(Succ(Succ(Succ(x1876)))), x1880)_>=_H'(x1877, x1878, x1879, x1880, anew_new_pr2F0G14(Succ(Succ(x1876)))))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(Succ(Succ(x1876)))))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(Succ(Succ(x1876)))))))
84.27/50.00	
84.27/50.00	(5)    (cons_new_pr2F0G14(Succ(Zero))=cons_new_pr2F0G14(Succ(Zero))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(Succ(Zero))))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	(6)    (cons_new_pr2F0G14(Zero)=cons_new_pr2F0G14(Succ(Zero))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(Zero)))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rule (VI) where we applied the induction hypothesis (\/x1877,x1878,x1879,x1880:new_new_pr2F0G14(x1876)=cons_new_pr2F0G14(Succ(Zero))  ==>  new_pr2F0G13(x1877, x1878, x1879, Succ(Succ(Succ(Succ(x1876)))), x1880)_>=_H'(x1877, x1878, x1879, x1880, anew_new_pr2F0G14(Succ(Succ(x1876))))) with sigma = [x1877 / x1407, x1878 / x1408, x1879 / x1409, x1880 / x1411] which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(x1876)))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(x1876))))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(Succ(Succ(x1876)))))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(Succ(Succ(x1876)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(8)    (new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(Succ(Zero))))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (6) using rules (I), (II).
84.27/50.00	*We consider the chain new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(x1419)), x1420) -> H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(x1419)), H'(x1421, x1422, x1423, x1424, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(x1421, x1422, x1423, Zero, x1424) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(x1419))=H'(x1421, x1422, x1423, x1424, cons_new_pr2F0G14(Zero))  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(x1419)), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(x1419)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (anew_new_pr2F0G14(x1419)=cons_new_pr2F0G14(Zero)  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(x1419)), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(x1419)))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on anew_new_pr2F0G14(x1419)=cons_new_pr2F0G14(Zero) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(3)    (new_new_pr2F0G14(x1881)=cons_new_pr2F0G14(Zero)  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(x1881)))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(x1881)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_new_pr2F0G14(x1881)=cons_new_pr2F0G14(Zero) which results in the following new constraints:
84.27/50.00	
84.27/50.00	(4)    (new_new_pr2F0G14(x1882)=cons_new_pr2F0G14(Zero) & (\/x1883,x1884,x1885,x1886:new_new_pr2F0G14(x1882)=cons_new_pr2F0G14(Zero)  ==>  new_pr2F0G13(x1883, x1884, x1885, Succ(Succ(Succ(Succ(x1882)))), x1886)_>=_H'(x1883, x1884, x1885, x1886, anew_new_pr2F0G14(Succ(Succ(x1882)))))  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(Succ(Succ(x1882)))))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(Succ(Succ(x1882)))))))
84.27/50.00	
84.27/50.00	(5)    (cons_new_pr2F0G14(Succ(Zero))=cons_new_pr2F0G14(Zero)  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(Succ(Zero))))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	(6)    (cons_new_pr2F0G14(Zero)=cons_new_pr2F0G14(Zero)  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(Zero)))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (4) using rule (VI) where we applied the induction hypothesis (\/x1883,x1884,x1885,x1886:new_new_pr2F0G14(x1882)=cons_new_pr2F0G14(Zero)  ==>  new_pr2F0G13(x1883, x1884, x1885, Succ(Succ(Succ(Succ(x1882)))), x1886)_>=_H'(x1883, x1884, x1885, x1886, anew_new_pr2F0G14(Succ(Succ(x1882))))) with sigma = [x1883 / x1416, x1884 / x1417, x1885 / x1418, x1886 / x1420] which results in the following new constraint:
84.27/50.00	
84.27/50.00	(7)    (new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(x1882)))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(x1882))))  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(Succ(Succ(x1882)))))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(Succ(Succ(x1882)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(8)    (new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(Zero)))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) the following chains were created:
84.27/50.00	*We consider the chain H'(x1461, x1462, x1463, x1464, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(x1461, x1462, x1463, Succ(Zero), x1464), new_pr2F0G14(x1465, x1466, x1467, Succ(Zero), x1468) -> new_pr2F2(x1466, x1467, new_fromInt, x1465, x1468) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G14(x1461, x1462, x1463, Succ(Zero), x1464)=new_pr2F0G14(x1465, x1466, x1467, Succ(Zero), x1468)  ==>  H'(x1461, x1462, x1463, x1464, cons_new_pr2F0G14(Succ(Zero)))_>=_new_pr2F0G14(x1461, x1462, x1463, Succ(Zero), x1464))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (H'(x1461, x1462, x1463, x1464, cons_new_pr2F0G14(Succ(Zero)))_>=_new_pr2F0G14(x1461, x1462, x1463, Succ(Zero), x1464))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	For Pair H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) the following chains were created:
84.27/50.00	*We consider the chain H'(x1541, x1542, x1543, x1544, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(x1541, x1542, x1543, Zero, x1544), new_pr2F0G14(x1545, x1546, x1547, Zero, x1548) -> new_pr2F0G13(x1545, new_sr10(x1546, x1548), new_primDivNatS1(x1547), new_primDivNatS1(x1547), x1548) which results in the following constraint:
84.27/50.00	
84.27/50.00	(1)    (new_pr2F0G14(x1541, x1542, x1543, Zero, x1544)=new_pr2F0G14(x1545, x1546, x1547, Zero, x1548)  ==>  H'(x1541, x1542, x1543, x1544, cons_new_pr2F0G14(Zero))_>=_new_pr2F0G14(x1541, x1542, x1543, Zero, x1544))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.00	
84.27/50.00	(2)    (H'(x1541, x1542, x1543, x1544, cons_new_pr2F0G14(Zero))_>=_new_pr2F0G14(x1541, x1542, x1543, Zero, x1544))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	To summarize, we get the following constraints P__>=_ for the following pairs.
84.27/50.00	
84.27/50.00	*new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x4, x5, x6, Succ(Zero), x7)_>=_new_pr2F1(x4, x6, new_fromInt, x5, x7))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/50.00	
84.27/50.00	*(new_pr2F1(x87, x88, Pos(x93), x90, x91)_>=_new_pr2F34(x88, Pos(x93), x87, new_sr9(x87, x90, x91), x91))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/50.00	
84.27/50.00	*(new_pr2F34(Succ(x194), Pos(Zero), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x194)), Zero), x189, new_primPlusNat0(Succ(Succ(x194)), Zero), x190, x191))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F34(x187, Pos(Succ(x1579)), x189, x190, x191)_>=_new_pr2F31(new_primPlusNat0(Succ(x187), Succ(x1579)), x189, new_primPlusNat0(Succ(x187), Succ(x1579)), x190, x191))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F34(Zero, Pos(Zero), x214, x215, x216)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), x214, new_primPlusNat0(Succ(Zero), Zero), x215, x216))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F34(Succ(x248), Pos(Zero), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x248)), Zero), x243, new_primPlusNat0(Succ(Succ(x248)), Zero), x244, x245))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F34(x241, Pos(Succ(x1657)), x243, x244, x245)_>=_new_pr2F31(new_primPlusNat0(Succ(x241), Succ(x1657)), x243, new_primPlusNat0(Succ(x241), Succ(x1657)), x244, x245))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/50.00	
84.27/50.00	*(new_pr2F31(Succ(x276), x277, Succ(Succ(Succ(Zero))), x279, x280)_>=_new_pr2F0G12(x277, x279, Succ(Succ(Zero)), Succ(Zero), x280))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F31(Succ(x300), x301, Succ(Succ(Zero)), x303, x304)_>=_new_pr2F0G12(x301, x303, Succ(Zero), Zero, x304))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x394, x395, Succ(Succ(x1698)), Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(Succ(Succ(x1698)))), new_primDivNatS1(Succ(Succ(Succ(x1698)))), x397))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x394, x395, Succ(Zero), Zero, x397)_>=_new_pr2F0G13(new_sr8(x394, x395, x397), x394, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x397))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x410, x411, Succ(Succ(x1701)), Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(Succ(Succ(x1701)))), new_primDivNatS1(Succ(Succ(Succ(x1701)))), x413))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x410, x411, Succ(Zero), Zero, x413)_>=_new_pr2F0G13(new_sr8(x410, x411, x413), x410, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x413))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x427, x428, Zero, Zero, x430)_>=_new_pr2F0G13(new_sr8(x427, x428, x430), x427, new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x430))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x447, x448, Succ(Succ(x1707)), Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(Succ(Succ(x1707)))), new_primDivNatS1(Succ(Succ(Succ(x1707)))), x450))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G12(x447, x448, Succ(Zero), Zero, x450)_>=_new_pr2F0G13(new_sr8(x447, x448, x450), x447, new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x450))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x488, x489, x490, Succ(Zero), x491)_>=_new_pr2F2(x489, x490, new_fromInt, x488, x491))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/50.00	
84.27/50.00	*(new_pr2F2(x556, Succ(Succ(x563)), Pos(Zero), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x563)), Zero), new_sr11(x556, x560), new_primPlusNat0(Succ(Succ(x563)), Zero), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F2(x556, Zero, Pos(Succ(Succ(x563))), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x563))), new_sr11(x556, x560), new_primPlusNat0(Zero, Succ(Succ(x563))), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F2(x556, Succ(x1709), Pos(Succ(x1708)), x559, x560)_>=_new_pr2F31(new_primPlusNat0(Succ(x1709), Succ(x1708)), new_sr11(x556, x560), new_primPlusNat0(Succ(x1709), Succ(x1708)), x559, x560))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F2(x581, Succ(Zero), Pos(Zero), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Succ(Zero), Zero), new_sr11(x581, x585), new_primPlusNat0(Succ(Zero), Zero), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F2(x581, Zero, Pos(Succ(Zero)), x584, x585)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Zero)), new_sr11(x581, x585), new_primPlusNat0(Zero, Succ(Zero)), x584, x585))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F2(x610, Succ(Succ(x617)), Pos(Zero), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(Succ(x617)), Zero), new_sr11(x610, x614), new_primPlusNat0(Succ(Succ(x617)), Zero), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F2(x610, Zero, Pos(Succ(Succ(x617))), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Zero, Succ(Succ(x617))), new_sr11(x610, x614), new_primPlusNat0(Zero, Succ(Succ(x617))), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F2(x610, Succ(x1800), Pos(Succ(x1799)), x613, x614)_>=_new_pr2F31(new_primPlusNat0(Succ(x1800), Succ(x1799)), new_sr11(x610, x614), new_primPlusNat0(Succ(x1800), Succ(x1799)), x613, x614))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/50.00	
84.27/50.00	*(new_pr2F31(Succ(x649), x650, Succ(Zero), x651, x652)_>=_new_pr2F1(x650, Zero, new_fromInt, x651, x652))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x767, x768, x769, Succ(Succ(Succ(Zero))), x771)_>=_new_pr2F0G14(x767, x768, x769, Succ(Zero), x771))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x776, x777, x778, Succ(Succ(Zero)), x780)_>=_new_pr2F0G14(x776, x777, x778, Zero, x780))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x844, x845, x846, Succ(Zero), x847)_>=_new_pr2F2(x845, x846, new_fromInt, x844, x847))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x917, x918, Succ(Succ(Succ(x1848))), Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(Succ(Succ(Succ(x1848)))), new_primDivNatS1(Succ(Succ(Succ(x1848)))), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x917, x918, Succ(Succ(Zero)), Zero, x920)_>=_new_pr2F0G13(x917, new_sr10(x918, x920), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x920))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x933, x934, Succ(Succ(Succ(x1850))), Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(Succ(Succ(Succ(x1850)))), new_primDivNatS1(Succ(Succ(Succ(x1850)))), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x933, x934, Succ(Succ(Zero)), Zero, x936)_>=_new_pr2F0G13(x933, new_sr10(x934, x936), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x936))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x950, x951, Zero, Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x950, x951, Succ(Zero), Zero, x953)_>=_new_pr2F0G13(x950, new_sr10(x951, x953), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x953))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x970, x971, Succ(Succ(Succ(x1854))), Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(Succ(Succ(Succ(x1854)))), new_primDivNatS1(Succ(Succ(Succ(x1854)))), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G14(x970, x971, Succ(Succ(Zero)), Zero, x973)_>=_new_pr2F0G13(x970, new_sr10(x971, x973), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x973))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1007, x1008, Succ(Succ(Succ(x1856))), Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(Succ(Succ(Succ(x1856)))), new_primDivNatS1(Succ(Succ(Succ(x1856)))), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1007, x1008, Succ(Succ(Zero)), Zero, x1010)_>=_new_pr2F0G13(x1007, new_sr10(x1008, x1010), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1010))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1023, x1024, Succ(Succ(Succ(x1858))), Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(Succ(Succ(Succ(x1858)))), new_primDivNatS1(Succ(Succ(Succ(x1858)))), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1023, x1024, Succ(Succ(Zero)), Zero, x1026)_>=_new_pr2F0G13(x1023, new_sr10(x1024, x1026), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1026))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1040, x1041, Zero, Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1040, x1041, Succ(Zero), Zero, x1043)_>=_new_pr2F0G13(x1040, new_sr10(x1041, x1043), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x1043))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1060, x1061, Succ(Succ(Succ(x1862))), Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(Succ(Succ(Succ(x1862)))), new_primDivNatS1(Succ(Succ(Succ(x1862)))), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1060, x1061, Succ(Succ(Zero)), Zero, x1063)_>=_new_pr2F0G13(x1060, new_sr10(x1061, x1063), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x1063))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/50.00	
84.27/50.00	*(new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(x1864)))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(x1864))), x1146, anew_new_pr2F0G12(Succ(Succ(x1864))))  ==>  new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(Succ(Succ(x1864)))))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(Succ(Succ(x1864))))), x1146, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1864)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F31(Succ(x1142), x1143, Succ(Succ(Succ(Succ(Succ(Zero))))), x1145, x1146)_>=_H(x1143, x1145, Succ(Succ(Succ(Succ(Zero)))), x1146, anew_new_pr2F0G12(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(x1870)))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(x1870))), x1155, anew_new_pr2F0G12(Succ(Succ(x1870))))  ==>  new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(Succ(Succ(x1870)))))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(Succ(Succ(x1870))))), x1155, anew_new_pr2F0G12(Succ(Succ(Succ(Succ(x1870)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F31(Succ(x1151), x1152, Succ(Succ(Succ(Succ(Zero)))), x1154, x1155)_>=_H(x1152, x1154, Succ(Succ(Succ(Zero))), x1155, anew_new_pr2F0G12(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/50.00	
84.27/50.00	*(H(x1175, x1176, x1177, x1178, cons_new_pr2F0G12(Succ(Zero)))_>=_new_pr2F0G12(x1175, x1176, x1177, Succ(Zero), x1178))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/50.00	
84.27/50.00	*(H(x1267, x1268, x1269, x1270, cons_new_pr2F0G12(Zero))_>=_new_pr2F0G12(x1267, x1268, x1269, Zero, x1270))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> H'(vuz110, vuz111, vuz113, be, anew_new_pr2F0G14(vuz11400))
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(x1876)))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(x1876))))  ==>  new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(Succ(Succ(x1876)))))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(Succ(Succ(x1876)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1407, x1408, x1409, Succ(Succ(Succ(Succ(Succ(Zero))))), x1411)_>=_H'(x1407, x1408, x1409, x1411, anew_new_pr2F0G14(Succ(Succ(Succ(Zero))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(x1882)))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(x1882))))  ==>  new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(Succ(Succ(x1882)))))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(Succ(Succ(x1882)))))))
84.27/50.00	
84.27/50.00	
84.27/50.00	*(new_pr2F0G13(x1416, x1417, x1418, Succ(Succ(Succ(Succ(Zero)))), x1420)_>=_H'(x1416, x1417, x1418, x1420, anew_new_pr2F0G14(Succ(Succ(Zero)))))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be)
84.27/50.00	
84.27/50.00	*(H'(x1461, x1462, x1463, x1464, cons_new_pr2F0G14(Succ(Zero)))_>=_new_pr2F0G14(x1461, x1462, x1463, Succ(Zero), x1464))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	*H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be)
84.27/50.00	
84.27/50.00	*(H'(x1541, x1542, x1543, x1544, cons_new_pr2F0G14(Zero))_>=_new_pr2F0G14(x1541, x1542, x1543, Zero, x1544))
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	
84.27/50.00	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. 
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(43)
84.27/50.00	Obligation:
84.27/50.00	Q DP problem:
84.27/50.00	The TRS P consists of the following rules:
84.27/50.00	
84.27/50.00	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd) -> new_pr2F1(vuz228, vuz230, new_fromInt, vuz229, bd)
84.27/50.00	   new_pr2F1(vuz228, vuz230, vuz233, vuz229, bd) -> new_pr2F34(vuz230, vuz233, vuz228, new_sr9(vuz228, vuz229, bd), bd)
84.27/50.00	   new_pr2F34(vuz214, Pos(vuz2150), vuz216, vuz217, bc) -> new_pr2F31(new_primPlusNat0(Succ(vuz214), vuz2150), vuz216, new_primPlusNat0(Succ(vuz214), vuz2150), vuz217, bc)
84.27/50.00	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> new_pr2F0G12(vuz216, vuz217, Succ(vuz21800), vuz21800, bc)
84.27/50.00	   new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd) -> new_pr2F0G13(new_sr8(vuz228, vuz229, bd), vuz228, new_primDivNatS1(Succ(vuz230)), new_primDivNatS1(Succ(vuz230)), bd)
84.27/50.00	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/50.00	   new_pr2F2(vuz111, vuz113, Pos(vuz1160), vuz110, be) -> new_pr2F31(new_primPlusNat0(vuz113, vuz1160), new_sr11(vuz111, be), new_primPlusNat0(vuz113, vuz1160), vuz110, be)
84.27/50.00	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Zero), vuz217, bc) -> new_pr2F1(vuz216, Zero, new_fromInt, vuz217, bc)
84.27/50.00	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/50.00	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be) -> new_pr2F2(vuz111, vuz113, new_fromInt, vuz110, be)
84.27/50.00	   new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/50.00	   new_pr2F0G13(vuz110, vuz111, vuz113, Zero, be) -> new_pr2F0G13(vuz110, new_sr10(vuz111, be), new_primDivNatS1(vuz113), new_primDivNatS1(vuz113), be)
84.27/50.00	   new_pr2F31(Succ(vuz2190), vuz216, Succ(Succ(vuz21800)), vuz217, bc) -> H(vuz216, vuz217, Succ(vuz21800), bc, anew_new_pr2F0G12(vuz21800))
84.27/50.00	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Succ(Zero))) -> new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Zero), bd)
84.27/50.00	   H(vuz228, vuz229, vuz230, bd, cons_new_pr2F0G12(Zero)) -> new_pr2F0G12(vuz228, vuz229, vuz230, Zero, bd)
84.27/50.00	   new_pr2F0G13(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> H'(vuz110, vuz111, vuz113, be, anew_new_pr2F0G14(vuz11400))
84.27/50.00	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Succ(Zero))) -> new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Zero), be)
84.27/50.00	   H'(vuz110, vuz111, vuz113, be, cons_new_pr2F0G14(Zero)) -> new_pr2F0G14(vuz110, vuz111, vuz113, Zero, be)
84.27/50.00	
84.27/50.00	The TRS R consists of the following rules:
84.27/50.00	
84.27/50.00	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.00	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/50.00	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.00	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/50.00	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/50.00	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.00	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/50.00	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/50.00	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.00	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.00	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.00	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.00	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/50.00	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/50.00	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.00	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.00	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/50.00	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.00	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.00	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.00	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.00	   new_primDivNatS01(Zero) -> Zero
84.27/50.00	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_primDivNatS1(Zero) -> Zero
84.27/50.00	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_primDivNatS3 -> Zero
84.27/50.00	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.00	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/50.00	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/50.00	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/50.00	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.00	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/50.00	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_fromInt -> Pos(Succ(Zero))
84.27/50.00	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/50.00	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/50.00	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.00	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.00	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/50.00	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/50.00	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/50.00	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.00	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/50.00	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/50.00	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/50.00	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.00	   anew_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/50.00	   new_new_pr2F0G12(Succ(Succ(vuz23100))) -> new_new_pr2F0G12(vuz23100)
84.27/50.00	   new_new_pr2F0G12(Succ(Zero)) -> cons_new_pr2F0G12(Succ(Zero))
84.27/50.00	   new_new_pr2F0G12(Zero) -> cons_new_pr2F0G12(Zero)
84.27/50.00	   anew_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/50.00	   new_new_pr2F0G14(Succ(Succ(vuz11400))) -> new_new_pr2F0G14(vuz11400)
84.27/50.00	   new_new_pr2F0G14(Succ(Zero)) -> cons_new_pr2F0G14(Succ(Zero))
84.27/50.00	   new_new_pr2F0G14(Zero) -> cons_new_pr2F0G14(Zero)
84.27/50.00	
84.27/50.00	The set Q consists of the following terms:
84.27/50.00	
84.27/50.00	   new_sr1(x0, x1, ty_Integer)
84.27/50.00	   new_sr(x0, x1, ty_Integer)
84.27/50.00	   new_sr6(x0, ty_Int)
84.27/50.00	   new_sr12(Pos(x0), Neg(x1))
84.27/50.00	   new_sr12(Neg(x0), Pos(x1))
84.27/50.00	   new_sr7(x0, x1, ty_Int)
84.27/50.00	   new_sr9(x0, x1, ty_Float)
84.27/50.00	   new_sr5(x0, ty_Integer)
84.27/50.00	   new_sr10(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr4(x0, ty_Integer)
84.27/50.00	   new_sr0(x0, x1, ty_Integer)
84.27/50.00	   new_sr2(x0, ty_Double)
84.27/50.00	   new_sr2(x0, ty_Float)
84.27/50.00	   new_sr12(Neg(x0), Neg(x1))
84.27/50.00	   new_sr(x0, x1, ty_Int)
84.27/50.00	   new_sr5(x0, ty_Int)
84.27/50.00	   new_primDivNatS1(Zero)
84.27/50.00	   new_sr6(x0, ty_Integer)
84.27/50.00	   new_sr11(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr3(x0, ty_Double)
84.27/50.00	   new_sr13(x0, x1)
84.27/50.00	   new_sr4(x0, ty_Float)
84.27/50.00	   new_sr0(x0, x1, ty_Int)
84.27/50.00	   new_primMulNat0(Zero, Zero)
84.27/50.00	   new_sr11(x0, ty_Float)
84.27/50.00	   new_sr20(x0)
84.27/50.00	   new_sr11(x0, ty_Double)
84.27/50.00	   new_sr3(x0, ty_Int)
84.27/50.00	   new_sr0(x0, x1, ty_Double)
84.27/50.00	   new_sr8(x0, x1, ty_Double)
84.27/50.00	   new_fromInt
84.27/50.00	   new_sr6(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr(x0, x1, ty_Float)
84.27/50.00	   new_primDivNatS4(x0)
84.27/50.00	   new_sr4(x0, ty_Double)
84.27/50.00	   new_sr10(x0, ty_Int)
84.27/50.00	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr2(x0, ty_Integer)
84.27/50.00	   new_sr21(x0, x1)
84.27/50.00	   new_primMulNat0(Zero, Succ(x0))
84.27/50.00	   new_primDivNatS2
84.27/50.00	   new_primDivNatS1(Succ(x0))
84.27/50.00	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr6(x0, ty_Double)
84.27/50.00	   new_sr12(Pos(x0), Pos(x1))
84.27/50.00	   new_sr8(x0, x1, ty_Float)
84.27/50.00	   new_sr11(x0, ty_Integer)
84.27/50.00	   new_sr7(x0, x1, ty_Float)
84.27/50.00	   new_sr7(x0, x1, ty_Integer)
84.27/50.00	   new_sr1(x0, x1, ty_Float)
84.27/50.00	   new_primDivNatS01(Succ(Zero))
84.27/50.00	   new_sr9(x0, x1, ty_Int)
84.27/50.00	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.00	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr8(x0, x1, ty_Integer)
84.27/50.00	   new_sr6(x0, ty_Float)
84.27/50.00	   new_sr17(x0)
84.27/50.00	   new_sr9(x0, x1, ty_Integer)
84.27/50.00	   new_sr7(x0, x1, ty_Double)
84.27/50.00	   new_sr2(x0, ty_Int)
84.27/50.00	   new_sr10(x0, ty_Double)
84.27/50.00	   new_sr5(x0, ty_Float)
84.27/50.00	   new_sr18(x0)
84.27/50.00	   new_sr4(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.00	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.00	   new_sr16(x0, x1, x2)
84.27/50.00	   new_sr1(x0, x1, ty_Double)
84.27/50.00	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.00	   new_sr19(x0)
84.27/50.00	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.00	   new_primDivNatS5(x0)
84.27/50.00	   new_sr5(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primDivNatS3
84.27/50.00	   new_sr(x0, x1, ty_Double)
84.27/50.00	   new_sr0(x0, x1, ty_Float)
84.27/50.00	   new_sr1(x0, x1, ty_Int)
84.27/50.00	   new_sr15(x0, x1)
84.27/50.00	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_primDivNatS01(Zero)
84.27/50.00	   new_sr9(x0, x1, ty_Double)
84.27/50.00	   new_sr10(x0, ty_Float)
84.27/50.00	   new_sr10(x0, ty_Integer)
84.27/50.00	   new_sr4(x0, ty_Int)
84.27/50.00	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primMulNat0(Succ(x0), Zero)
84.27/50.00	   new_sr5(x0, ty_Double)
84.27/50.00	   new_primPlusNat0(Zero, Zero)
84.27/50.00	   new_sr8(x0, x1, ty_Int)
84.27/50.00	   new_sr14(x0, x1)
84.27/50.00	   new_sr3(x0, ty_Integer)
84.27/50.00	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr3(x0, ty_Float)
84.27/50.00	   new_sr11(x0, ty_Int)
84.27/50.00	   new_new_pr2F0G12(Succ(Succ(x0)))
84.27/50.00	   anew_new_pr2F0G12(Succ(Succ(x0)))
84.27/50.00	   new_new_pr2F0G12(Succ(Zero))
84.27/50.00	   new_new_pr2F0G12(Zero)
84.27/50.00	   new_new_pr2F0G14(Succ(Succ(x0)))
84.27/50.00	   anew_new_pr2F0G14(Succ(Succ(x0)))
84.27/50.00	   new_new_pr2F0G14(Succ(Zero))
84.27/50.00	   new_new_pr2F0G14(Zero)
84.27/50.00	
84.27/50.00	We have to consider all minimal (P,Q,R)-chains.
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(44)
84.27/50.00	Obligation:
84.27/50.00	Q DP problem:
84.27/50.00	The TRS P consists of the following rules:
84.27/50.00	
84.27/50.00	   new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/50.00	
84.27/50.00	R is empty.
84.27/50.00	Q is empty.
84.27/50.00	We have to consider all minimal (P,Q,R)-chains.
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(45) QDPSizeChangeProof (EQUIVALENT)
84.27/50.00	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. 
84.27/50.00	
84.27/50.00	From the DPs we obtained the following set of size-change graphs:
84.27/50.00	*new_pr2F0G14(vuz110, vuz111, vuz113, Succ(Succ(vuz11400)), be) -> new_pr2F0G14(vuz110, vuz111, vuz113, vuz11400, be)
84.27/50.00	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5
84.27/50.00	
84.27/50.00	
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(46)
84.27/50.00	YES
84.27/50.00	
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(47)
84.27/50.00	Obligation:
84.27/50.00	Q DP problem:
84.27/50.00	The TRS P consists of the following rules:
84.27/50.00	
84.27/50.00	   new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.27/50.00	
84.27/50.00	R is empty.
84.27/50.00	Q is empty.
84.27/50.00	We have to consider all minimal (P,Q,R)-chains.
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(48) QDPSizeChangeProof (EQUIVALENT)
84.27/50.00	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. 
84.27/50.00	
84.27/50.00	From the DPs we obtained the following set of size-change graphs:
84.27/50.00	*new_pr2F0G12(vuz228, vuz229, vuz230, Succ(Succ(vuz23100)), bd) -> new_pr2F0G12(vuz228, vuz229, vuz230, vuz23100, bd)
84.27/50.00	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5
84.27/50.00	
84.27/50.00	
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(49)
84.27/50.00	YES
84.27/50.00	
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(50)
84.27/50.00	Obligation:
84.27/50.00	Q DP problem:
84.27/50.00	The TRS P consists of the following rules:
84.27/50.00	
84.27/50.00	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.00	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.00	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Zero), vuz205, h) -> new_pr2F(vuz204, Zero, new_fromInt, vuz205, h)
84.27/50.00	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.00	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.00	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.00	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.00	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.00	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.00	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.00	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.00	
84.27/50.00	The TRS R consists of the following rules:
84.27/50.00	
84.27/50.00	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.00	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/50.00	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.00	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/50.00	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/50.00	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.00	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/50.00	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/50.00	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.00	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.00	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.00	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.00	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/50.00	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/50.00	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.00	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.00	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/50.00	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.00	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.00	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.00	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.00	   new_primDivNatS01(Zero) -> Zero
84.27/50.00	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_primDivNatS1(Zero) -> Zero
84.27/50.00	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_primDivNatS3 -> Zero
84.27/50.00	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.00	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/50.00	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/50.00	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/50.00	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.00	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/50.00	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_fromInt -> Pos(Succ(Zero))
84.27/50.00	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/50.00	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/50.00	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.00	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.00	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/50.00	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/50.00	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/50.00	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.00	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/50.00	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/50.00	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/50.00	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.00	
84.27/50.00	The set Q consists of the following terms:
84.27/50.00	
84.27/50.00	   new_sr1(x0, x1, ty_Integer)
84.27/50.00	   new_sr(x0, x1, ty_Integer)
84.27/50.00	   new_sr6(x0, ty_Int)
84.27/50.00	   new_sr12(Pos(x0), Neg(x1))
84.27/50.00	   new_sr12(Neg(x0), Pos(x1))
84.27/50.00	   new_sr7(x0, x1, ty_Int)
84.27/50.00	   new_sr9(x0, x1, ty_Float)
84.27/50.00	   new_sr5(x0, ty_Integer)
84.27/50.00	   new_sr10(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr4(x0, ty_Integer)
84.27/50.00	   new_sr0(x0, x1, ty_Integer)
84.27/50.00	   new_sr2(x0, ty_Double)
84.27/50.00	   new_sr2(x0, ty_Float)
84.27/50.00	   new_sr12(Neg(x0), Neg(x1))
84.27/50.00	   new_sr(x0, x1, ty_Int)
84.27/50.00	   new_sr5(x0, ty_Int)
84.27/50.00	   new_primDivNatS1(Zero)
84.27/50.00	   new_sr6(x0, ty_Integer)
84.27/50.00	   new_sr11(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr3(x0, ty_Double)
84.27/50.00	   new_sr13(x0, x1)
84.27/50.00	   new_sr4(x0, ty_Float)
84.27/50.00	   new_sr0(x0, x1, ty_Int)
84.27/50.00	   new_primMulNat0(Zero, Zero)
84.27/50.00	   new_sr11(x0, ty_Float)
84.27/50.00	   new_sr20(x0)
84.27/50.00	   new_sr11(x0, ty_Double)
84.27/50.00	   new_sr3(x0, ty_Int)
84.27/50.00	   new_sr0(x0, x1, ty_Double)
84.27/50.00	   new_sr8(x0, x1, ty_Double)
84.27/50.00	   new_fromInt
84.27/50.00	   new_sr6(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr(x0, x1, ty_Float)
84.27/50.00	   new_primDivNatS4(x0)
84.27/50.00	   new_sr4(x0, ty_Double)
84.27/50.00	   new_sr10(x0, ty_Int)
84.27/50.00	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr2(x0, ty_Integer)
84.27/50.00	   new_sr21(x0, x1)
84.27/50.00	   new_primMulNat0(Zero, Succ(x0))
84.27/50.00	   new_primDivNatS2
84.27/50.00	   new_primDivNatS1(Succ(x0))
84.27/50.00	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr6(x0, ty_Double)
84.27/50.00	   new_sr12(Pos(x0), Pos(x1))
84.27/50.00	   new_sr8(x0, x1, ty_Float)
84.27/50.00	   new_sr11(x0, ty_Integer)
84.27/50.00	   new_sr7(x0, x1, ty_Float)
84.27/50.00	   new_sr7(x0, x1, ty_Integer)
84.27/50.00	   new_sr1(x0, x1, ty_Float)
84.27/50.00	   new_primDivNatS01(Succ(Zero))
84.27/50.00	   new_sr9(x0, x1, ty_Int)
84.27/50.00	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.00	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr8(x0, x1, ty_Integer)
84.27/50.00	   new_sr6(x0, ty_Float)
84.27/50.00	   new_sr17(x0)
84.27/50.00	   new_sr9(x0, x1, ty_Integer)
84.27/50.00	   new_sr7(x0, x1, ty_Double)
84.27/50.00	   new_sr2(x0, ty_Int)
84.27/50.00	   new_sr10(x0, ty_Double)
84.27/50.00	   new_sr5(x0, ty_Float)
84.27/50.00	   new_sr18(x0)
84.27/50.00	   new_sr4(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.00	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.00	   new_sr16(x0, x1, x2)
84.27/50.00	   new_sr1(x0, x1, ty_Double)
84.27/50.00	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.00	   new_sr19(x0)
84.27/50.00	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.00	   new_primDivNatS5(x0)
84.27/50.00	   new_sr5(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primDivNatS3
84.27/50.00	   new_sr(x0, x1, ty_Double)
84.27/50.00	   new_sr0(x0, x1, ty_Float)
84.27/50.00	   new_sr1(x0, x1, ty_Int)
84.27/50.00	   new_sr15(x0, x1)
84.27/50.00	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_primDivNatS01(Zero)
84.27/50.00	   new_sr9(x0, x1, ty_Double)
84.27/50.00	   new_sr10(x0, ty_Float)
84.27/50.00	   new_sr10(x0, ty_Integer)
84.27/50.00	   new_sr4(x0, ty_Int)
84.27/50.00	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primMulNat0(Succ(x0), Zero)
84.27/50.00	   new_sr5(x0, ty_Double)
84.27/50.00	   new_primPlusNat0(Zero, Zero)
84.27/50.00	   new_sr8(x0, x1, ty_Int)
84.27/50.00	   new_sr14(x0, x1)
84.27/50.00	   new_sr3(x0, ty_Integer)
84.27/50.00	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr3(x0, ty_Float)
84.27/50.00	   new_sr11(x0, ty_Int)
84.27/50.00	
84.27/50.00	We have to consider all minimal (P,Q,R)-chains.
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(51) TransformationProof (EQUIVALENT)
84.27/50.00	By instantiating [LPAR04] the rule new_pr2F30(Succ(vuz2120), vuz204, Succ(Zero), vuz205, h) -> new_pr2F(vuz204, Zero, new_fromInt, vuz205, h) we obtained the following new rules [LPAR04]:
84.27/50.00	
84.27/50.00	   (new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3),new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3))
84.27/50.00	
84.27/50.00	
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(52)
84.27/50.00	Obligation:
84.27/50.00	Q DP problem:
84.27/50.00	The TRS P consists of the following rules:
84.27/50.00	
84.27/50.00	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.00	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.00	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.00	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.00	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.00	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.00	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.00	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.00	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.00	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.00	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3)
84.27/50.00	
84.27/50.00	The TRS R consists of the following rules:
84.27/50.00	
84.27/50.00	   new_sr6(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr11(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.00	   new_sr(vuz204, vuz205, ty_Double) -> new_sr13(vuz204, vuz205)
84.27/50.00	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.00	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr10(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Integer) -> new_sr14(vuz216, vuz217)
84.27/50.00	   new_sr5(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_sr6(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/50.00	   new_sr10(vuz111, ty_Integer) -> new_sr18(vuz111)
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.00	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Integer) -> new_sr14(vuz204, vuz205)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Double) -> new_sr13(vuz228, vuz229)
84.27/50.00	   new_sr11(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/50.00	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.00	   new_sr4(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.00	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.00	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.00	   new_sr11(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Float) -> new_sr15(vuz216, vuz217)
84.27/50.00	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/50.00	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.00	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.00	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Int) -> new_sr12(vuz216, vuz217)
84.27/50.00	   new_sr9(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Float) -> new_sr15(vuz204, vuz205)
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.00	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.00	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.00	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.00	   new_primDivNatS01(Zero) -> Zero
84.27/50.00	   new_sr11(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr4(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_primDivNatS1(Zero) -> Zero
84.27/50.00	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_primDivNatS3 -> Zero
84.27/50.00	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr5(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.00	   new_sr8(vuz228, vuz229, app(ty_Ratio, ca)) -> new_sr16(vuz228, vuz229, ca)
84.27/50.00	   new_sr6(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/50.00	   new_sr(vuz204, vuz205, app(ty_Ratio, cc)) -> new_sr16(vuz204, vuz205, cc)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/50.00	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.00	   new_sr5(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr10(vuz111, app(ty_Ratio, cd)) -> new_sr21(vuz111, cd)
84.27/50.00	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr4(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_fromInt -> Pos(Succ(Zero))
84.27/50.00	   new_sr7(vuz216, vuz217, app(ty_Ratio, bg)) -> new_sr16(vuz216, vuz217, bg)
84.27/50.00	   new_sr5(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr5(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr8(vuz228, vuz229, ty_Float) -> new_sr15(vuz228, vuz229)
84.27/50.00	   new_sr4(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.00	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.00	   new_sr10(vuz111, ty_Double) -> new_sr17(vuz111)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Int) -> new_sr12(vuz228, vuz229)
84.27/50.00	   new_sr4(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr9(vuz228, vuz229, ty_Integer) -> new_sr14(vuz228, vuz229)
84.27/50.00	   new_sr10(vuz111, ty_Float) -> new_sr20(vuz111)
84.27/50.00	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.00	   new_sr6(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.00	   new_sr(vuz204, vuz205, ty_Int) -> new_sr12(vuz204, vuz205)
84.27/50.00	   new_sr6(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr7(vuz216, vuz217, ty_Double) -> new_sr13(vuz216, vuz217)
84.27/50.00	   new_sr11(vuz111, ty_Int) -> new_sr19(vuz111)
84.27/50.00	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.00	
84.27/50.00	The set Q consists of the following terms:
84.27/50.00	
84.27/50.00	   new_sr1(x0, x1, ty_Integer)
84.27/50.00	   new_sr(x0, x1, ty_Integer)
84.27/50.00	   new_sr6(x0, ty_Int)
84.27/50.00	   new_sr12(Pos(x0), Neg(x1))
84.27/50.00	   new_sr12(Neg(x0), Pos(x1))
84.27/50.00	   new_sr7(x0, x1, ty_Int)
84.27/50.00	   new_sr9(x0, x1, ty_Float)
84.27/50.00	   new_sr5(x0, ty_Integer)
84.27/50.00	   new_sr10(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr4(x0, ty_Integer)
84.27/50.00	   new_sr0(x0, x1, ty_Integer)
84.27/50.00	   new_sr2(x0, ty_Double)
84.27/50.00	   new_sr2(x0, ty_Float)
84.27/50.00	   new_sr12(Neg(x0), Neg(x1))
84.27/50.00	   new_sr(x0, x1, ty_Int)
84.27/50.00	   new_sr5(x0, ty_Int)
84.27/50.00	   new_primDivNatS1(Zero)
84.27/50.00	   new_sr6(x0, ty_Integer)
84.27/50.00	   new_sr11(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr3(x0, ty_Double)
84.27/50.00	   new_sr13(x0, x1)
84.27/50.00	   new_sr4(x0, ty_Float)
84.27/50.00	   new_sr0(x0, x1, ty_Int)
84.27/50.00	   new_primMulNat0(Zero, Zero)
84.27/50.00	   new_sr11(x0, ty_Float)
84.27/50.00	   new_sr20(x0)
84.27/50.00	   new_sr11(x0, ty_Double)
84.27/50.00	   new_sr3(x0, ty_Int)
84.27/50.00	   new_sr0(x0, x1, ty_Double)
84.27/50.00	   new_sr8(x0, x1, ty_Double)
84.27/50.00	   new_fromInt
84.27/50.00	   new_sr6(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr(x0, x1, ty_Float)
84.27/50.00	   new_primDivNatS4(x0)
84.27/50.00	   new_sr4(x0, ty_Double)
84.27/50.00	   new_sr10(x0, ty_Int)
84.27/50.00	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr2(x0, ty_Integer)
84.27/50.00	   new_sr21(x0, x1)
84.27/50.00	   new_primMulNat0(Zero, Succ(x0))
84.27/50.00	   new_primDivNatS2
84.27/50.00	   new_primDivNatS1(Succ(x0))
84.27/50.00	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr6(x0, ty_Double)
84.27/50.00	   new_sr12(Pos(x0), Pos(x1))
84.27/50.00	   new_sr8(x0, x1, ty_Float)
84.27/50.00	   new_sr11(x0, ty_Integer)
84.27/50.00	   new_sr7(x0, x1, ty_Float)
84.27/50.00	   new_sr7(x0, x1, ty_Integer)
84.27/50.00	   new_sr1(x0, x1, ty_Float)
84.27/50.00	   new_primDivNatS01(Succ(Zero))
84.27/50.00	   new_sr9(x0, x1, ty_Int)
84.27/50.00	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.00	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.00	   new_sr8(x0, x1, ty_Integer)
84.27/50.00	   new_sr6(x0, ty_Float)
84.27/50.00	   new_sr17(x0)
84.27/50.00	   new_sr9(x0, x1, ty_Integer)
84.27/50.00	   new_sr7(x0, x1, ty_Double)
84.27/50.00	   new_sr2(x0, ty_Int)
84.27/50.00	   new_sr10(x0, ty_Double)
84.27/50.00	   new_sr5(x0, ty_Float)
84.27/50.00	   new_sr18(x0)
84.27/50.00	   new_sr4(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.00	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.00	   new_sr16(x0, x1, x2)
84.27/50.00	   new_sr1(x0, x1, ty_Double)
84.27/50.00	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.00	   new_sr19(x0)
84.27/50.00	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.00	   new_primDivNatS5(x0)
84.27/50.00	   new_sr5(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primDivNatS3
84.27/50.00	   new_sr(x0, x1, ty_Double)
84.27/50.00	   new_sr0(x0, x1, ty_Float)
84.27/50.00	   new_sr1(x0, x1, ty_Int)
84.27/50.00	   new_sr15(x0, x1)
84.27/50.00	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_primDivNatS01(Zero)
84.27/50.00	   new_sr9(x0, x1, ty_Double)
84.27/50.00	   new_sr10(x0, ty_Float)
84.27/50.00	   new_sr10(x0, ty_Integer)
84.27/50.00	   new_sr4(x0, ty_Int)
84.27/50.00	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.00	   new_primMulNat0(Succ(x0), Zero)
84.27/50.00	   new_sr5(x0, ty_Double)
84.27/50.00	   new_primPlusNat0(Zero, Zero)
84.27/50.00	   new_sr8(x0, x1, ty_Int)
84.27/50.00	   new_sr14(x0, x1)
84.27/50.00	   new_sr3(x0, ty_Integer)
84.27/50.00	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/50.00	   new_sr3(x0, ty_Float)
84.27/50.00	   new_sr11(x0, ty_Int)
84.27/50.00	
84.27/50.00	We have to consider all minimal (P,Q,R)-chains.
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(53) UsableRulesProof (EQUIVALENT)
84.27/50.00	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.
84.27/50.00	----------------------------------------
84.27/50.00	
84.27/50.00	(54)
84.27/50.00	Obligation:
84.27/50.00	Q DP problem:
84.27/50.00	The TRS P consists of the following rules:
84.27/50.00	
84.27/50.00	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.00	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.00	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.00	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.00	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.00	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.00	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.00	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.00	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.00	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.00	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.00	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.00	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.00	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3)
84.27/50.00	
84.27/50.00	The TRS R consists of the following rules:
84.27/50.00	
84.27/50.00	   new_fromInt -> Pos(Succ(Zero))
84.27/50.00	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_primDivNatS1(Zero) -> Zero
84.27/50.00	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.00	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.00	   new_primDivNatS01(Zero) -> Zero
84.27/50.00	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.00	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.00	   new_primDivNatS3 -> Zero
84.27/50.00	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.00	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.00	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.00	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.00	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.00	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.00	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.00	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.00	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.00	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.00	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.00	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.00	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.00	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.00	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.00	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.00	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.00	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.00	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.00	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.00	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.00	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.00	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.00	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.00	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.00	
84.27/50.00	The set Q consists of the following terms:
84.27/50.00	
84.27/50.00	   new_sr1(x0, x1, ty_Integer)
84.27/50.00	   new_sr(x0, x1, ty_Integer)
84.27/50.00	   new_sr6(x0, ty_Int)
84.27/50.00	   new_sr12(Pos(x0), Neg(x1))
84.27/50.00	   new_sr12(Neg(x0), Pos(x1))
84.27/50.00	   new_sr7(x0, x1, ty_Int)
84.27/50.00	   new_sr9(x0, x1, ty_Float)
84.27/50.00	   new_sr5(x0, ty_Integer)
84.27/50.00	   new_sr10(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr4(x0, ty_Integer)
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_sr(x0, x1, ty_Int)
84.27/50.01	   new_sr5(x0, ty_Int)
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr6(x0, ty_Integer)
84.27/50.01	   new_sr11(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr4(x0, ty_Float)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr11(x0, ty_Float)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr11(x0, ty_Double)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_sr8(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_sr6(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr4(x0, ty_Double)
84.27/50.01	   new_sr10(x0, ty_Int)
84.27/50.01	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr6(x0, ty_Double)
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr8(x0, x1, ty_Float)
84.27/50.01	   new_sr11(x0, ty_Integer)
84.27/50.01	   new_sr7(x0, x1, ty_Float)
84.27/50.01	   new_sr7(x0, x1, ty_Integer)
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_sr9(x0, x1, ty_Int)
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr8(x0, x1, ty_Integer)
84.27/50.01	   new_sr6(x0, ty_Float)
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr9(x0, x1, ty_Integer)
84.27/50.01	   new_sr7(x0, x1, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr10(x0, ty_Double)
84.27/50.01	   new_sr5(x0, ty_Float)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_sr4(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_sr5(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr(x0, x1, ty_Double)
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr9(x0, x1, ty_Double)
84.27/50.01	   new_sr10(x0, ty_Float)
84.27/50.01	   new_sr10(x0, ty_Integer)
84.27/50.01	   new_sr4(x0, ty_Int)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_sr5(x0, ty_Double)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr8(x0, x1, ty_Int)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	   new_sr11(x0, ty_Int)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(55) QReductionProof (EQUIVALENT)
84.27/50.01	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
84.27/50.01	
84.27/50.01	   new_sr(x0, x1, ty_Integer)
84.27/50.01	   new_sr6(x0, ty_Int)
84.27/50.01	   new_sr7(x0, x1, ty_Int)
84.27/50.01	   new_sr9(x0, x1, ty_Float)
84.27/50.01	   new_sr5(x0, ty_Integer)
84.27/50.01	   new_sr10(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr4(x0, ty_Integer)
84.27/50.01	   new_sr(x0, x1, ty_Int)
84.27/50.01	   new_sr5(x0, ty_Int)
84.27/50.01	   new_sr6(x0, ty_Integer)
84.27/50.01	   new_sr11(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr4(x0, ty_Float)
84.27/50.01	   new_sr11(x0, ty_Float)
84.27/50.01	   new_sr11(x0, ty_Double)
84.27/50.01	   new_sr8(x0, x1, ty_Double)
84.27/50.01	   new_sr6(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr(x0, x1, ty_Float)
84.27/50.01	   new_sr4(x0, ty_Double)
84.27/50.01	   new_sr10(x0, ty_Int)
84.27/50.01	   new_sr8(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr6(x0, ty_Double)
84.27/50.01	   new_sr8(x0, x1, ty_Float)
84.27/50.01	   new_sr11(x0, ty_Integer)
84.27/50.01	   new_sr7(x0, x1, ty_Float)
84.27/50.01	   new_sr7(x0, x1, ty_Integer)
84.27/50.01	   new_sr9(x0, x1, ty_Int)
84.27/50.01	   new_sr8(x0, x1, ty_Integer)
84.27/50.01	   new_sr6(x0, ty_Float)
84.27/50.01	   new_sr9(x0, x1, ty_Integer)
84.27/50.01	   new_sr7(x0, x1, ty_Double)
84.27/50.01	   new_sr10(x0, ty_Double)
84.27/50.01	   new_sr5(x0, ty_Float)
84.27/50.01	   new_sr4(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr5(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr(x0, x1, ty_Double)
84.27/50.01	   new_sr7(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr9(x0, x1, ty_Double)
84.27/50.01	   new_sr10(x0, ty_Float)
84.27/50.01	   new_sr10(x0, ty_Integer)
84.27/50.01	   new_sr4(x0, ty_Int)
84.27/50.01	   new_sr5(x0, ty_Double)
84.27/50.01	   new_sr8(x0, x1, ty_Int)
84.27/50.01	   new_sr9(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr11(x0, ty_Int)
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(56)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_fromInt -> Pos(Succ(Zero))
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(57) TransformationProof (EQUIVALENT)
84.27/50.01	By rewriting [LPAR04] the rule new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, new_fromInt, vuz223, ba) at position [2] we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba),new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(58)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_fromInt -> Pos(Succ(Zero))
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(59) TransformationProof (EQUIVALENT)
84.27/50.01	By rewriting [LPAR04] the rule new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS1(Succ(vuz224)), new_primDivNatS1(Succ(vuz224)), ba) at position [2] we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba),new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(60)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_fromInt -> Pos(Succ(Zero))
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(61) TransformationProof (EQUIVALENT)
84.27/50.01	By rewriting [LPAR04] the rule new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb) at position [2] we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb),new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(62)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_fromInt -> Pos(Succ(Zero))
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(63) TransformationProof (EQUIVALENT)
84.27/50.01	By rewriting [LPAR04] the rule new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, new_fromInt, vuz102, bb) at position [2] we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb),new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(64)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_fromInt -> Pos(Succ(Zero))
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(65) TransformationProof (EQUIVALENT)
84.27/50.01	By rewriting [LPAR04] the rule new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, new_fromInt, z2, z3) at position [2] we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3),new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(66)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_fromInt -> Pos(Succ(Zero))
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(67) UsableRulesProof (EQUIVALENT)
84.27/50.01	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.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(68)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_fromInt
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(69) QReductionProof (EQUIVALENT)
84.27/50.01	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
84.27/50.01	
84.27/50.01	   new_fromInt
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(70)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(71) TransformationProof (EQUIVALENT)
84.27/50.01	By rewriting [LPAR04] the rule new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS1(Succ(vuz224)), ba) at position [3] we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba),new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(72)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(73) TransformationProof (EQUIVALENT)
84.27/50.01	By instantiating [LPAR04] the rule new_pr2F0(vuz103, Succ(vuz1050), Pos(Succ(vuz11500)), vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb) we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3),new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(74)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba)
84.27/50.01	   new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(75) DependencyGraphProof (EQUIVALENT)
84.27/50.01	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(76)
84.27/50.01	Complex Obligation (AND)
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(77)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(78) TransformationProof (EQUIVALENT)
84.27/50.01	By instantiating [LPAR04] the rule new_pr2F30(Succ(vuz2120), vuz204, Succ(Succ(vuz21100)), vuz205, h) -> new_pr2F0G1(vuz204, vuz205, Succ(vuz21100), vuz21100, h) we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F30(Succ(Succ(x2)), z1, Succ(Succ(x2)), z2, z3) -> new_pr2F0G1(z1, z2, Succ(x2), x2, z3),new_pr2F30(Succ(Succ(x2)), z1, Succ(Succ(x2)), z2, z3) -> new_pr2F0G1(z1, z2, Succ(x2), x2, z3))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(79)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Succ(x2)), z1, Succ(Succ(x2)), z2, z3) -> new_pr2F0G1(z1, z2, Succ(x2), x2, z3)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(80) TransformationProof (EQUIVALENT)
84.27/50.01	By instantiating [LPAR04] the rule new_pr2F(vuz222, vuz224, vuz232, vuz223, ba) -> new_pr2F32(vuz224, vuz232, vuz222, new_sr1(vuz222, vuz223, ba), ba) we obtained the following new rules [LPAR04]:
84.27/50.01	
84.27/50.01	   (new_pr2F(z0, z2, Pos(Succ(Zero)), z1, z3) -> new_pr2F32(z2, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z3), z3),new_pr2F(z0, z2, Pos(Succ(Zero)), z1, z3) -> new_pr2F32(z2, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z3), z3))
84.27/50.01	   (new_pr2F(z0, Zero, Pos(Succ(Zero)), z1, z2) -> new_pr2F32(Zero, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z2), z2),new_pr2F(z0, Zero, Pos(Succ(Zero)), z1, z2) -> new_pr2F32(Zero, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z2), z2))
84.27/50.01	
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(81)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Succ(vuz203000))), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.01	   new_pr2F3(Succ(vuz2020), Zero, vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F32(vuz202, Pos(Zero), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz202), vuz204, Succ(vuz202), vuz205, h)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F30(Succ(Succ(x2)), z1, Succ(Succ(x2)), z2, z3) -> new_pr2F0G1(z1, z2, Succ(x2), x2, z3)
84.27/50.01	   new_pr2F(z0, z2, Pos(Succ(Zero)), z1, z3) -> new_pr2F32(z2, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z3), z3)
84.27/50.01	   new_pr2F(z0, Zero, Pos(Succ(Zero)), z1, z2) -> new_pr2F32(Zero, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z2), z2)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.01	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.01	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.01	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.01	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_primDivNatS1(Zero) -> Zero
84.27/50.01	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.01	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.01	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.01	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.01	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.01	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.01	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.01	
84.27/50.01	The set Q consists of the following terms:
84.27/50.01	
84.27/50.01	   new_sr1(x0, x1, ty_Integer)
84.27/50.01	   new_sr12(Pos(x0), Neg(x1))
84.27/50.01	   new_sr12(Neg(x0), Pos(x1))
84.27/50.01	   new_sr0(x0, x1, ty_Integer)
84.27/50.01	   new_sr2(x0, ty_Double)
84.27/50.01	   new_sr2(x0, ty_Float)
84.27/50.01	   new_sr12(Neg(x0), Neg(x1))
84.27/50.01	   new_primDivNatS1(Zero)
84.27/50.01	   new_sr3(x0, ty_Double)
84.27/50.01	   new_sr13(x0, x1)
84.27/50.01	   new_sr0(x0, x1, ty_Int)
84.27/50.01	   new_primMulNat0(Zero, Zero)
84.27/50.01	   new_sr20(x0)
84.27/50.01	   new_sr3(x0, ty_Int)
84.27/50.01	   new_sr0(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS4(x0)
84.27/50.01	   new_sr2(x0, ty_Integer)
84.27/50.01	   new_sr21(x0, x1)
84.27/50.01	   new_primMulNat0(Zero, Succ(x0))
84.27/50.01	   new_primDivNatS2
84.27/50.01	   new_primDivNatS1(Succ(x0))
84.27/50.01	   new_sr12(Pos(x0), Pos(x1))
84.27/50.01	   new_sr1(x0, x1, ty_Float)
84.27/50.01	   new_primDivNatS01(Succ(Zero))
84.27/50.01	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.01	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.01	   new_sr17(x0)
84.27/50.01	   new_sr2(x0, ty_Int)
84.27/50.01	   new_sr18(x0)
84.27/50.01	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.01	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.01	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_sr16(x0, x1, x2)
84.27/50.01	   new_sr1(x0, x1, ty_Double)
84.27/50.01	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.01	   new_sr19(x0)
84.27/50.01	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.01	   new_primDivNatS5(x0)
84.27/50.01	   new_primDivNatS3
84.27/50.01	   new_sr0(x0, x1, ty_Float)
84.27/50.01	   new_sr1(x0, x1, ty_Int)
84.27/50.01	   new_sr15(x0, x1)
84.27/50.01	   new_primDivNatS01(Zero)
84.27/50.01	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.01	   new_primMulNat0(Succ(x0), Zero)
84.27/50.01	   new_primPlusNat0(Zero, Zero)
84.27/50.01	   new_sr14(x0, x1)
84.27/50.01	   new_sr3(x0, ty_Integer)
84.27/50.01	   new_sr3(x0, ty_Float)
84.27/50.01	
84.27/50.01	We have to consider all minimal (P,Q,R)-chains.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(82) DependencyGraphProof (EQUIVALENT)
84.27/50.01	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 4 less nodes.
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(83)
84.27/50.01	Complex Obligation (AND)
84.27/50.01	
84.27/50.01	----------------------------------------
84.27/50.01	
84.27/50.01	(84)
84.27/50.01	Obligation:
84.27/50.01	Q DP problem:
84.27/50.01	The TRS P consists of the following rules:
84.27/50.01	
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.01	   new_pr2F(z0, z2, Pos(Succ(Zero)), z1, z3) -> new_pr2F32(z2, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z3), z3)
84.27/50.01	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.01	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.01	   new_pr2F30(Succ(Succ(x2)), z1, Succ(Succ(x2)), z2, z3) -> new_pr2F0G1(z1, z2, Succ(x2), x2, z3)
84.27/50.01	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.01	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	   new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3)
84.27/50.01	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.01	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.01	
84.27/50.01	The TRS R consists of the following rules:
84.27/50.01	
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.01	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.01	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.01	   new_primDivNatS01(Zero) -> Zero
84.27/50.01	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.01	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.01	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.01	   new_primDivNatS3 -> Zero
84.27/50.01	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.01	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.01	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.01	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.01	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.01	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.01	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.01	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	
84.27/50.02	The set Q consists of the following terms:
84.27/50.02	
84.27/50.02	   new_sr1(x0, x1, ty_Integer)
84.27/50.02	   new_sr12(Pos(x0), Neg(x1))
84.27/50.02	   new_sr12(Neg(x0), Pos(x1))
84.27/50.02	   new_sr0(x0, x1, ty_Integer)
84.27/50.02	   new_sr2(x0, ty_Double)
84.27/50.02	   new_sr2(x0, ty_Float)
84.27/50.02	   new_sr12(Neg(x0), Neg(x1))
84.27/50.02	   new_primDivNatS1(Zero)
84.27/50.02	   new_sr3(x0, ty_Double)
84.27/50.02	   new_sr13(x0, x1)
84.27/50.02	   new_sr0(x0, x1, ty_Int)
84.27/50.02	   new_primMulNat0(Zero, Zero)
84.27/50.02	   new_sr20(x0)
84.27/50.02	   new_sr3(x0, ty_Int)
84.27/50.02	   new_sr0(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS4(x0)
84.27/50.02	   new_sr2(x0, ty_Integer)
84.27/50.02	   new_sr21(x0, x1)
84.27/50.02	   new_primMulNat0(Zero, Succ(x0))
84.27/50.02	   new_primDivNatS2
84.27/50.02	   new_primDivNatS1(Succ(x0))
84.27/50.02	   new_sr12(Pos(x0), Pos(x1))
84.27/50.02	   new_sr1(x0, x1, ty_Float)
84.27/50.02	   new_primDivNatS01(Succ(Zero))
84.27/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.02	   new_sr17(x0)
84.27/50.02	   new_sr2(x0, ty_Int)
84.27/50.02	   new_sr18(x0)
84.27/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_sr16(x0, x1, x2)
84.27/50.02	   new_sr1(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.02	   new_sr19(x0)
84.27/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_primDivNatS5(x0)
84.27/50.02	   new_primDivNatS3
84.27/50.02	   new_sr0(x0, x1, ty_Float)
84.27/50.02	   new_sr1(x0, x1, ty_Int)
84.27/50.02	   new_sr15(x0, x1)
84.27/50.02	   new_primDivNatS01(Zero)
84.27/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.02	   new_primMulNat0(Succ(x0), Zero)
84.27/50.02	   new_primPlusNat0(Zero, Zero)
84.27/50.02	   new_sr14(x0, x1)
84.27/50.02	   new_sr3(x0, ty_Integer)
84.27/50.02	   new_sr3(x0, ty_Float)
84.27/50.02	
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(85) QDPOrderProof (EQUIVALENT)
84.27/50.02	We use the reduction pair processor [LPAR04,JAR06].
84.27/50.02	
84.27/50.02	
84.27/50.02	The following pairs can be oriented strictly and are deleted.
84.27/50.02	
84.27/50.02	   new_pr2F32(Succ(vuz2020), Pos(Succ(Zero)), vuz204, vuz205, h) -> new_pr2F30(Succ(vuz2020), vuz204, Succ(vuz2020), vuz205, h)
84.27/50.02	   new_pr2F0G1(vuz222, vuz223, vuz224, Zero, ba) -> new_pr2F0G10(new_sr0(vuz222, vuz223, ba), vuz222, new_primDivNatS01(vuz224), new_primDivNatS01(vuz224), ba)
84.27/50.02	The remaining pairs can at least be oriented weakly.
84.27/50.02	Used ordering:  Polynomial interpretation [POLO]:
84.27/50.02	
84.27/50.02	   POL(Neg(x_1)) = 0
84.27/50.02	   POL(Pos(x_1)) = 1
84.27/50.02	   POL(Succ(x_1)) = 1 + x_1
84.27/50.02	   POL(Zero) = 0
84.27/50.02	   POL([]) = 1
84.27/50.02	   POL(app(x_1, x_2)) = 1 + x_1 + x_2
84.27/50.02	   POL(error(x_1)) = x_1
84.27/50.02	   POL(new_pr2F(x_1, x_2, x_3, x_4, x_5)) = 1 + x_1 + x_2 + x_5
84.27/50.02	   POL(new_pr2F0(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_5
84.27/50.02	   POL(new_pr2F0G1(x_1, x_2, x_3, x_4, x_5)) = 1 + x_1 + x_3 + x_5
84.27/50.02	   POL(new_pr2F0G10(x_1, x_2, x_3, x_4, x_5)) = x_3 + x_5
84.27/50.02	   POL(new_pr2F0G11(x_1, x_2, x_3, x_4, x_5)) = x_3 + x_5
84.27/50.02	   POL(new_pr2F30(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_3 + x_5
84.27/50.02	   POL(new_pr2F32(x_1, x_2, x_3, x_4, x_5)) = x_1 + x_2 + x_3 + x_5
84.27/50.02	   POL(new_pr2F33(x_1, x_2, x_3, x_4, x_5)) = 1 + x_1 + x_2 + x_5
84.27/50.02	   POL(new_primDivNatS01(x_1)) = x_1
84.27/50.02	   POL(new_primDivNatS1(x_1)) = x_1
84.27/50.02	   POL(new_primDivNatS2) = 0
84.27/50.02	   POL(new_primDivNatS3) = 0
84.27/50.02	   POL(new_primDivNatS4(x_1)) = 1 + x_1
84.27/50.02	   POL(new_primDivNatS5(x_1)) = 1 + x_1
84.27/50.02	   POL(new_primMulNat0(x_1, x_2)) = 0
84.27/50.02	   POL(new_primPlusNat0(x_1, x_2)) = 0
84.27/50.02	   POL(new_sr0(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
84.27/50.02	   POL(new_sr1(x_1, x_2, x_3)) = x_1 + x_2 + x_3
84.27/50.02	   POL(new_sr12(x_1, x_2)) = 1
84.27/50.02	   POL(new_sr13(x_1, x_2)) = 1
84.27/50.02	   POL(new_sr14(x_1, x_2)) = 1
84.27/50.02	   POL(new_sr15(x_1, x_2)) = 1
84.27/50.02	   POL(new_sr16(x_1, x_2, x_3)) = 1
84.27/50.02	   POL(new_sr17(x_1)) = 1
84.27/50.02	   POL(new_sr18(x_1)) = 1
84.27/50.02	   POL(new_sr19(x_1)) = 1
84.27/50.02	   POL(new_sr2(x_1, x_2)) = x_1 + x_2
84.27/50.02	   POL(new_sr20(x_1)) = 1
84.27/50.02	   POL(new_sr21(x_1, x_2)) = 1
84.27/50.02	   POL(new_sr3(x_1, x_2)) = 1
84.27/50.02	   POL(ty_Double) = 1
84.27/50.02	   POL(ty_Float) = 1
84.27/50.02	   POL(ty_Int) = 1
84.27/50.02	   POL(ty_Integer) = 1
84.27/50.02	   POL(ty_Ratio) = 1
84.27/50.02	
84.27/50.02	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
84.27/50.02	
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(86)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.02	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Zero), ba) -> new_pr2F(vuz222, vuz224, Pos(Succ(Zero)), vuz223, ba)
84.27/50.02	   new_pr2F(z0, z2, Pos(Succ(Zero)), z1, z3) -> new_pr2F32(z2, Pos(Succ(Zero)), z0, new_sr1(z0, z1, z3), z3)
84.27/50.02	   new_pr2F30(Succ(Zero), y_0, Succ(Zero), z2, z3) -> new_pr2F(y_0, Zero, Pos(Succ(Zero)), z2, z3)
84.27/50.02	   new_pr2F30(Succ(Succ(x2)), z1, Succ(Succ(x2)), z2, z3) -> new_pr2F0G1(z1, z2, Succ(x2), x2, z3)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.02	   new_pr2F0(z1, Succ(x1), Pos(Succ(Zero)), z0, z3) -> new_pr2F33(x1, Zero, z1, z0, z3)
84.27/50.02	   new_pr2F33(Succ(vuz1050), Zero, vuz103, vuz102, bb) -> new_pr2F30(Succ(vuz1050), new_sr3(vuz103, bb), Succ(vuz1050), vuz102, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Zero), bb) -> new_pr2F0(vuz103, vuz105, Pos(Succ(Zero)), vuz102, bb)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	
84.27/50.02	The set Q consists of the following terms:
84.27/50.02	
84.27/50.02	   new_sr1(x0, x1, ty_Integer)
84.27/50.02	   new_sr12(Pos(x0), Neg(x1))
84.27/50.02	   new_sr12(Neg(x0), Pos(x1))
84.27/50.02	   new_sr0(x0, x1, ty_Integer)
84.27/50.02	   new_sr2(x0, ty_Double)
84.27/50.02	   new_sr2(x0, ty_Float)
84.27/50.02	   new_sr12(Neg(x0), Neg(x1))
84.27/50.02	   new_primDivNatS1(Zero)
84.27/50.02	   new_sr3(x0, ty_Double)
84.27/50.02	   new_sr13(x0, x1)
84.27/50.02	   new_sr0(x0, x1, ty_Int)
84.27/50.02	   new_primMulNat0(Zero, Zero)
84.27/50.02	   new_sr20(x0)
84.27/50.02	   new_sr3(x0, ty_Int)
84.27/50.02	   new_sr0(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS4(x0)
84.27/50.02	   new_sr2(x0, ty_Integer)
84.27/50.02	   new_sr21(x0, x1)
84.27/50.02	   new_primMulNat0(Zero, Succ(x0))
84.27/50.02	   new_primDivNatS2
84.27/50.02	   new_primDivNatS1(Succ(x0))
84.27/50.02	   new_sr12(Pos(x0), Pos(x1))
84.27/50.02	   new_sr1(x0, x1, ty_Float)
84.27/50.02	   new_primDivNatS01(Succ(Zero))
84.27/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.02	   new_sr17(x0)
84.27/50.02	   new_sr2(x0, ty_Int)
84.27/50.02	   new_sr18(x0)
84.27/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_sr16(x0, x1, x2)
84.27/50.02	   new_sr1(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.02	   new_sr19(x0)
84.27/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_primDivNatS5(x0)
84.27/50.02	   new_primDivNatS3
84.27/50.02	   new_sr0(x0, x1, ty_Float)
84.27/50.02	   new_sr1(x0, x1, ty_Int)
84.27/50.02	   new_sr15(x0, x1)
84.27/50.02	   new_primDivNatS01(Zero)
84.27/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.02	   new_primMulNat0(Succ(x0), Zero)
84.27/50.02	   new_primPlusNat0(Zero, Zero)
84.27/50.02	   new_sr14(x0, x1)
84.27/50.02	   new_sr3(x0, ty_Integer)
84.27/50.02	   new_sr3(x0, ty_Float)
84.27/50.02	
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(87) DependencyGraphProof (EQUIVALENT)
84.27/50.02	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 8 less nodes.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(88)
84.27/50.02	Complex Obligation (AND)
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(89)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	
84.27/50.02	The set Q consists of the following terms:
84.27/50.02	
84.27/50.02	   new_sr1(x0, x1, ty_Integer)
84.27/50.02	   new_sr12(Pos(x0), Neg(x1))
84.27/50.02	   new_sr12(Neg(x0), Pos(x1))
84.27/50.02	   new_sr0(x0, x1, ty_Integer)
84.27/50.02	   new_sr2(x0, ty_Double)
84.27/50.02	   new_sr2(x0, ty_Float)
84.27/50.02	   new_sr12(Neg(x0), Neg(x1))
84.27/50.02	   new_primDivNatS1(Zero)
84.27/50.02	   new_sr3(x0, ty_Double)
84.27/50.02	   new_sr13(x0, x1)
84.27/50.02	   new_sr0(x0, x1, ty_Int)
84.27/50.02	   new_primMulNat0(Zero, Zero)
84.27/50.02	   new_sr20(x0)
84.27/50.02	   new_sr3(x0, ty_Int)
84.27/50.02	   new_sr0(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS4(x0)
84.27/50.02	   new_sr2(x0, ty_Integer)
84.27/50.02	   new_sr21(x0, x1)
84.27/50.02	   new_primMulNat0(Zero, Succ(x0))
84.27/50.02	   new_primDivNatS2
84.27/50.02	   new_primDivNatS1(Succ(x0))
84.27/50.02	   new_sr12(Pos(x0), Pos(x1))
84.27/50.02	   new_sr1(x0, x1, ty_Float)
84.27/50.02	   new_primDivNatS01(Succ(Zero))
84.27/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.02	   new_sr17(x0)
84.27/50.02	   new_sr2(x0, ty_Int)
84.27/50.02	   new_sr18(x0)
84.27/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_sr16(x0, x1, x2)
84.27/50.02	   new_sr1(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.02	   new_sr19(x0)
84.27/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_primDivNatS5(x0)
84.27/50.02	   new_primDivNatS3
84.27/50.02	   new_sr0(x0, x1, ty_Float)
84.27/50.02	   new_sr1(x0, x1, ty_Int)
84.27/50.02	   new_sr15(x0, x1)
84.27/50.02	   new_primDivNatS01(Zero)
84.27/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.02	   new_primMulNat0(Succ(x0), Zero)
84.27/50.02	   new_primPlusNat0(Zero, Zero)
84.27/50.02	   new_sr14(x0, x1)
84.27/50.02	   new_sr3(x0, ty_Integer)
84.27/50.02	   new_sr3(x0, ty_Float)
84.27/50.02	
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(90) QDPSizeChangeProof (EQUIVALENT)
84.27/50.02	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. 
84.27/50.02	
84.27/50.02	From the DPs we obtained the following set of size-change graphs:
84.27/50.02	*new_pr2F0G1(vuz222, vuz223, vuz224, Succ(Succ(vuz22500)), ba) -> new_pr2F0G1(vuz222, vuz223, vuz224, vuz22500, ba)
84.27/50.02	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5
84.27/50.02	
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(91)
84.27/50.02	YES
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(92)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	
84.27/50.02	The set Q consists of the following terms:
84.27/50.02	
84.27/50.02	   new_sr1(x0, x1, ty_Integer)
84.27/50.02	   new_sr12(Pos(x0), Neg(x1))
84.27/50.02	   new_sr12(Neg(x0), Pos(x1))
84.27/50.02	   new_sr0(x0, x1, ty_Integer)
84.27/50.02	   new_sr2(x0, ty_Double)
84.27/50.02	   new_sr2(x0, ty_Float)
84.27/50.02	   new_sr12(Neg(x0), Neg(x1))
84.27/50.02	   new_primDivNatS1(Zero)
84.27/50.02	   new_sr3(x0, ty_Double)
84.27/50.02	   new_sr13(x0, x1)
84.27/50.02	   new_sr0(x0, x1, ty_Int)
84.27/50.02	   new_primMulNat0(Zero, Zero)
84.27/50.02	   new_sr20(x0)
84.27/50.02	   new_sr3(x0, ty_Int)
84.27/50.02	   new_sr0(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS4(x0)
84.27/50.02	   new_sr2(x0, ty_Integer)
84.27/50.02	   new_sr21(x0, x1)
84.27/50.02	   new_primMulNat0(Zero, Succ(x0))
84.27/50.02	   new_primDivNatS2
84.27/50.02	   new_primDivNatS1(Succ(x0))
84.27/50.02	   new_sr12(Pos(x0), Pos(x1))
84.27/50.02	   new_sr1(x0, x1, ty_Float)
84.27/50.02	   new_primDivNatS01(Succ(Zero))
84.27/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.02	   new_sr17(x0)
84.27/50.02	   new_sr2(x0, ty_Int)
84.27/50.02	   new_sr18(x0)
84.27/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_sr16(x0, x1, x2)
84.27/50.02	   new_sr1(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.02	   new_sr19(x0)
84.27/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_primDivNatS5(x0)
84.27/50.02	   new_primDivNatS3
84.27/50.02	   new_sr0(x0, x1, ty_Float)
84.27/50.02	   new_sr1(x0, x1, ty_Int)
84.27/50.02	   new_sr15(x0, x1)
84.27/50.02	   new_primDivNatS01(Zero)
84.27/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.02	   new_primMulNat0(Succ(x0), Zero)
84.27/50.02	   new_primPlusNat0(Zero, Zero)
84.27/50.02	   new_sr14(x0, x1)
84.27/50.02	   new_sr3(x0, ty_Integer)
84.27/50.02	   new_sr3(x0, ty_Float)
84.27/50.02	
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(93) MNOCProof (EQUIVALENT)
84.27/50.02	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(94)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	
84.27/50.02	Q is empty.
84.27/50.02	We have to consider all (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(95) InductionCalculusProof (EQUIVALENT)
84.27/50.02	Note that final constraints are written in bold face.
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G10(x5, x6, x7, Succ(Succ(x8)), x9) -> new_pr2F0G11(x5, x6, x7, x8, x9), new_pr2F0G11(x10, x11, x12, Succ(Succ(x13)), x14) -> new_pr2F0G11(x10, x11, x12, x13, x14) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G11(x5, x6, x7, x8, x9)=new_pr2F0G11(x10, x11, x12, Succ(Succ(x13)), x14)  ==>  new_pr2F0G10(x5, x6, x7, Succ(Succ(x8)), x9)_>=_new_pr2F0G11(x5, x6, x7, x8, x9))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_pr2F0G10(x5, x6, x7, Succ(Succ(Succ(Succ(x13)))), x9)_>=_new_pr2F0G11(x5, x6, x7, Succ(Succ(x13)), x9))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G10(x15, x16, x17, Succ(Succ(x18)), x19) -> new_pr2F0G11(x15, x16, x17, x18, x19), new_pr2F0G11(x20, x21, x22, Zero, x23) -> new_pr2F0G10(x20, new_sr2(x21, x23), new_primDivNatS1(x22), new_primDivNatS1(x22), x23) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G11(x15, x16, x17, x18, x19)=new_pr2F0G11(x20, x21, x22, Zero, x23)  ==>  new_pr2F0G10(x15, x16, x17, Succ(Succ(x18)), x19)_>=_new_pr2F0G11(x15, x16, x17, x18, x19))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_pr2F0G10(x15, x16, x17, Succ(Succ(Zero)), x19)_>=_new_pr2F0G11(x15, x16, x17, Zero, x19))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G11(x34, x35, x36, Succ(Succ(x37)), x38) -> new_pr2F0G11(x34, x35, x36, x37, x38), new_pr2F0G11(x39, x40, x41, Succ(Succ(x42)), x43) -> new_pr2F0G11(x39, x40, x41, x42, x43) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G11(x34, x35, x36, x37, x38)=new_pr2F0G11(x39, x40, x41, Succ(Succ(x42)), x43)  ==>  new_pr2F0G11(x34, x35, x36, Succ(Succ(x37)), x38)_>=_new_pr2F0G11(x34, x35, x36, x37, x38))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_pr2F0G11(x34, x35, x36, Succ(Succ(Succ(Succ(x42)))), x38)_>=_new_pr2F0G11(x34, x35, x36, Succ(Succ(x42)), x38))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G11(x44, x45, x46, Succ(Succ(x47)), x48) -> new_pr2F0G11(x44, x45, x46, x47, x48), new_pr2F0G11(x49, x50, x51, Zero, x52) -> new_pr2F0G10(x49, new_sr2(x50, x52), new_primDivNatS1(x51), new_primDivNatS1(x51), x52) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G11(x44, x45, x46, x47, x48)=new_pr2F0G11(x49, x50, x51, Zero, x52)  ==>  new_pr2F0G11(x44, x45, x46, Succ(Succ(x47)), x48)_>=_new_pr2F0G11(x44, x45, x46, x47, x48))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_pr2F0G11(x44, x45, x46, Succ(Succ(Zero)), x48)_>=_new_pr2F0G11(x44, x45, x46, Zero, x48))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G11(x58, x59, x60, Zero, x61) -> new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(x60), new_primDivNatS1(x60), x61), new_pr2F0G10(x62, x63, x64, Succ(Succ(x65)), x66) -> new_pr2F0G11(x62, x63, x64, x65, x66) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(x60), new_primDivNatS1(x60), x61)=new_pr2F0G10(x62, x63, x64, Succ(Succ(x65)), x66)  ==>  new_pr2F0G11(x58, x59, x60, Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(x60), new_primDivNatS1(x60), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x60)=Succ(Succ(x65))  ==>  new_pr2F0G11(x58, x59, x60, Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(x60), new_primDivNatS1(x60), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x60)=Succ(Succ(x65)) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x108)=Succ(Succ(x65))  ==>  new_pr2F0G11(x58, x59, Succ(x108), Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(Succ(x108)), new_primDivNatS1(Succ(x108)), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x108)=Succ(Succ(x65)) which results in the following new constraints:
84.27/50.02	
84.27/50.02	(4)    (Succ(new_primDivNatS4(x109))=Succ(Succ(x65))  ==>  new_pr2F0G11(x58, x59, Succ(Succ(Succ(x109))), Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(Succ(Succ(Succ(x109)))), new_primDivNatS1(Succ(Succ(Succ(x109)))), x61))
84.27/50.02	
84.27/50.02	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x65))  ==>  new_pr2F0G11(x58, x59, Succ(Succ(Zero)), Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G11(x58, x59, Succ(Succ(Succ(x109))), Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(Succ(Succ(Succ(x109)))), new_primDivNatS1(Succ(Succ(Succ(x109)))), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G11(x58, x59, Succ(Succ(Zero)), Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G11(x75, x76, x77, Zero, x78) -> new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(x77), new_primDivNatS1(x77), x78), new_pr2F0G10(x79, x80, x81, Zero, x82) -> new_pr2F0G10(x79, new_sr2(x80, x82), new_primDivNatS1(x81), new_primDivNatS1(x81), x82) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(x77), new_primDivNatS1(x77), x78)=new_pr2F0G10(x79, x80, x81, Zero, x82)  ==>  new_pr2F0G11(x75, x76, x77, Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(x77), new_primDivNatS1(x77), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x77)=Zero  ==>  new_pr2F0G11(x75, x76, x77, Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(x77), new_primDivNatS1(x77), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x77)=Zero which results in the following new constraints:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x110)=Zero  ==>  new_pr2F0G11(x75, x76, Succ(x110), Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(Succ(x110)), new_primDivNatS1(Succ(x110)), x78))
84.27/50.02	
84.27/50.02	(4)    (Zero=Zero  ==>  new_pr2F0G11(x75, x76, Zero, Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x110)=Zero which results in the following new constraint:
84.27/50.02	
84.27/50.02	(5)    (Zero=Zero  ==>  new_pr2F0G11(x75, x76, Succ(Zero), Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G11(x75, x76, Zero, Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G11(x75, x76, Succ(Zero), Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G10(x83, x84, x85, Zero, x86) -> new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(x85), new_primDivNatS1(x85), x86), new_pr2F0G10(x87, x88, x89, Succ(Succ(x90)), x91) -> new_pr2F0G11(x87, x88, x89, x90, x91) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(x85), new_primDivNatS1(x85), x86)=new_pr2F0G10(x87, x88, x89, Succ(Succ(x90)), x91)  ==>  new_pr2F0G10(x83, x84, x85, Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(x85), new_primDivNatS1(x85), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x85)=Succ(Succ(x90))  ==>  new_pr2F0G10(x83, x84, x85, Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(x85), new_primDivNatS1(x85), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x85)=Succ(Succ(x90)) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x112)=Succ(Succ(x90))  ==>  new_pr2F0G10(x83, x84, Succ(x112), Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(Succ(x112)), new_primDivNatS1(Succ(x112)), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x112)=Succ(Succ(x90)) which results in the following new constraints:
84.27/50.02	
84.27/50.02	(4)    (Succ(new_primDivNatS4(x113))=Succ(Succ(x90))  ==>  new_pr2F0G10(x83, x84, Succ(Succ(Succ(x113))), Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(Succ(Succ(Succ(x113)))), new_primDivNatS1(Succ(Succ(Succ(x113)))), x86))
84.27/50.02	
84.27/50.02	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x90))  ==>  new_pr2F0G10(x83, x84, Succ(Succ(Zero)), Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G10(x83, x84, Succ(Succ(Succ(x113))), Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(Succ(Succ(Succ(x113)))), new_primDivNatS1(Succ(Succ(Succ(x113)))), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G10(x83, x84, Succ(Succ(Zero)), Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G10(x100, x101, x102, Zero, x103) -> new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(x102), new_primDivNatS1(x102), x103), new_pr2F0G10(x104, x105, x106, Zero, x107) -> new_pr2F0G10(x104, new_sr2(x105, x107), new_primDivNatS1(x106), new_primDivNatS1(x106), x107) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(x102), new_primDivNatS1(x102), x103)=new_pr2F0G10(x104, x105, x106, Zero, x107)  ==>  new_pr2F0G10(x100, x101, x102, Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(x102), new_primDivNatS1(x102), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x102)=Zero  ==>  new_pr2F0G10(x100, x101, x102, Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(x102), new_primDivNatS1(x102), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x102)=Zero which results in the following new constraints:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x114)=Zero  ==>  new_pr2F0G10(x100, x101, Succ(x114), Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(Succ(x114)), new_primDivNatS1(Succ(x114)), x103))
84.27/50.02	
84.27/50.02	(4)    (Zero=Zero  ==>  new_pr2F0G10(x100, x101, Zero, Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x114)=Zero which results in the following new constraint:
84.27/50.02	
84.27/50.02	(5)    (Zero=Zero  ==>  new_pr2F0G10(x100, x101, Succ(Zero), Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G10(x100, x101, Zero, Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G10(x100, x101, Succ(Zero), Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	To summarize, we get the following constraints P__>=_ for the following pairs.
84.27/50.02	
84.27/50.02	*new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x5, x6, x7, Succ(Succ(Succ(Succ(x13)))), x9)_>=_new_pr2F0G11(x5, x6, x7, Succ(Succ(x13)), x9))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x15, x16, x17, Succ(Succ(Zero)), x19)_>=_new_pr2F0G11(x15, x16, x17, Zero, x19))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x34, x35, x36, Succ(Succ(Succ(Succ(x42)))), x38)_>=_new_pr2F0G11(x34, x35, x36, Succ(Succ(x42)), x38))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x44, x45, x46, Succ(Succ(Zero)), x48)_>=_new_pr2F0G11(x44, x45, x46, Zero, x48))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x58, x59, Succ(Succ(Succ(x109))), Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(Succ(Succ(Succ(x109)))), new_primDivNatS1(Succ(Succ(Succ(x109)))), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x58, x59, Succ(Succ(Zero)), Zero, x61)_>=_new_pr2F0G10(x58, new_sr2(x59, x61), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x61))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x75, x76, Succ(Zero), Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x75, x76, Zero, Zero, x78)_>=_new_pr2F0G10(x75, new_sr2(x76, x78), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x78))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x83, x84, Succ(Succ(Succ(x113))), Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(Succ(Succ(Succ(x113)))), new_primDivNatS1(Succ(Succ(Succ(x113)))), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x83, x84, Succ(Succ(Zero)), Zero, x86)_>=_new_pr2F0G10(x83, new_sr2(x84, x86), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x86))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x100, x101, Succ(Zero), Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x100, x101, Zero, Zero, x103)_>=_new_pr2F0G10(x100, new_sr2(x101, x103), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x103))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	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. 
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(96)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	
84.27/50.02	The set Q consists of the following terms:
84.27/50.02	
84.27/50.02	   new_sr1(x0, x1, ty_Integer)
84.27/50.02	   new_sr12(Pos(x0), Neg(x1))
84.27/50.02	   new_sr12(Neg(x0), Pos(x1))
84.27/50.02	   new_sr0(x0, x1, ty_Integer)
84.27/50.02	   new_sr2(x0, ty_Double)
84.27/50.02	   new_sr2(x0, ty_Float)
84.27/50.02	   new_sr12(Neg(x0), Neg(x1))
84.27/50.02	   new_primDivNatS1(Zero)
84.27/50.02	   new_sr3(x0, ty_Double)
84.27/50.02	   new_sr13(x0, x1)
84.27/50.02	   new_sr0(x0, x1, ty_Int)
84.27/50.02	   new_primMulNat0(Zero, Zero)
84.27/50.02	   new_sr20(x0)
84.27/50.02	   new_sr3(x0, ty_Int)
84.27/50.02	   new_sr0(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS4(x0)
84.27/50.02	   new_sr2(x0, ty_Integer)
84.27/50.02	   new_sr21(x0, x1)
84.27/50.02	   new_primMulNat0(Zero, Succ(x0))
84.27/50.02	   new_primDivNatS2
84.27/50.02	   new_primDivNatS1(Succ(x0))
84.27/50.02	   new_sr12(Pos(x0), Pos(x1))
84.27/50.02	   new_sr1(x0, x1, ty_Float)
84.27/50.02	   new_primDivNatS01(Succ(Zero))
84.27/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.02	   new_sr17(x0)
84.27/50.02	   new_sr2(x0, ty_Int)
84.27/50.02	   new_sr18(x0)
84.27/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_sr16(x0, x1, x2)
84.27/50.02	   new_sr1(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.02	   new_sr19(x0)
84.27/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_primDivNatS5(x0)
84.27/50.02	   new_primDivNatS3
84.27/50.02	   new_sr0(x0, x1, ty_Float)
84.27/50.02	   new_sr1(x0, x1, ty_Int)
84.27/50.02	   new_sr15(x0, x1)
84.27/50.02	   new_primDivNatS01(Zero)
84.27/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.02	   new_primMulNat0(Succ(x0), Zero)
84.27/50.02	   new_primPlusNat0(Zero, Zero)
84.27/50.02	   new_sr14(x0, x1)
84.27/50.02	   new_sr3(x0, ty_Integer)
84.27/50.02	   new_sr3(x0, ty_Float)
84.27/50.02	
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(97) QDPPairToRuleProof (EQUIVALENT)
84.27/50.02	The dependency pair new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb) was transformed to the following new rules:
84.27/50.02	   anew_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Zero) -> cons_new_pr2F0G11(Zero)
84.27/50.02	
84.27/50.02	the following new pairs maintain the fan-in:
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> H(vuz102, vuz103, vuz105, bb, anew_new_pr2F0G11(vuz10600))
84.27/50.02	
84.27/50.02	the following new pairs maintain the fan-out:
84.27/50.02	   H(vuz102, vuz103, vuz105, bb, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb)
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(98)
84.27/50.02	Complex Obligation (AND)
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(99)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> H(vuz102, vuz103, vuz105, bb, anew_new_pr2F0G11(vuz10600))
84.27/50.02	   H(vuz102, vuz103, vuz105, bb, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   anew_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Zero) -> cons_new_pr2F0G11(Zero)
84.27/50.02	
84.27/50.02	The set Q consists of the following terms:
84.27/50.02	
84.27/50.02	   new_sr1(x0, x1, ty_Integer)
84.27/50.02	   new_sr12(Pos(x0), Neg(x1))
84.27/50.02	   new_sr12(Neg(x0), Pos(x1))
84.27/50.02	   new_sr0(x0, x1, ty_Integer)
84.27/50.02	   new_sr2(x0, ty_Double)
84.27/50.02	   new_sr2(x0, ty_Float)
84.27/50.02	   new_sr12(Neg(x0), Neg(x1))
84.27/50.02	   new_primDivNatS1(Zero)
84.27/50.02	   new_sr3(x0, ty_Double)
84.27/50.02	   new_sr13(x0, x1)
84.27/50.02	   new_sr0(x0, x1, ty_Int)
84.27/50.02	   new_primMulNat0(Zero, Zero)
84.27/50.02	   new_sr20(x0)
84.27/50.02	   new_sr3(x0, ty_Int)
84.27/50.02	   new_sr0(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS4(x0)
84.27/50.02	   new_sr2(x0, ty_Integer)
84.27/50.02	   new_sr21(x0, x1)
84.27/50.02	   new_primMulNat0(Zero, Succ(x0))
84.27/50.02	   new_primDivNatS2
84.27/50.02	   new_primDivNatS1(Succ(x0))
84.27/50.02	   new_sr12(Pos(x0), Pos(x1))
84.27/50.02	   new_sr1(x0, x1, ty_Float)
84.27/50.02	   new_primDivNatS01(Succ(Zero))
84.27/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.02	   new_sr17(x0)
84.27/50.02	   new_sr2(x0, ty_Int)
84.27/50.02	   new_sr18(x0)
84.27/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_sr16(x0, x1, x2)
84.27/50.02	   new_sr1(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.02	   new_sr19(x0)
84.27/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_primDivNatS5(x0)
84.27/50.02	   new_primDivNatS3
84.27/50.02	   new_sr0(x0, x1, ty_Float)
84.27/50.02	   new_sr1(x0, x1, ty_Int)
84.27/50.02	   new_sr15(x0, x1)
84.27/50.02	   new_primDivNatS01(Zero)
84.27/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.02	   new_primMulNat0(Succ(x0), Zero)
84.27/50.02	   new_primPlusNat0(Zero, Zero)
84.27/50.02	   new_sr14(x0, x1)
84.27/50.02	   new_sr3(x0, ty_Integer)
84.27/50.02	   new_sr3(x0, ty_Float)
84.27/50.02	   new_new_pr2F0G11(Succ(Succ(x0)))
84.27/50.02	   anew_new_pr2F0G11(Succ(Succ(x0)))
84.27/50.02	   new_new_pr2F0G11(Zero)
84.27/50.02	
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(100) MNOCProof (EQUIVALENT)
84.27/50.02	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(101)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> H(vuz102, vuz103, vuz105, bb, anew_new_pr2F0G11(vuz10600))
84.27/50.02	   H(vuz102, vuz103, vuz105, bb, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   anew_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Zero) -> cons_new_pr2F0G11(Zero)
84.27/50.02	
84.27/50.02	Q is empty.
84.27/50.02	We have to consider all (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(102) InductionCalculusProof (EQUIVALENT)
84.27/50.02	Note that final constraints are written in bold face.
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G10(x5, x6, x7, Succ(Succ(x8)), x9) -> new_pr2F0G11(x5, x6, x7, x8, x9), new_pr2F0G11(x10, x11, x12, Zero, x13) -> new_pr2F0G10(x10, new_sr2(x11, x13), new_primDivNatS1(x12), new_primDivNatS1(x12), x13) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G11(x5, x6, x7, x8, x9)=new_pr2F0G11(x10, x11, x12, Zero, x13)  ==>  new_pr2F0G10(x5, x6, x7, Succ(Succ(x8)), x9)_>=_new_pr2F0G11(x5, x6, x7, x8, x9))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_pr2F0G10(x5, x6, x7, Succ(Succ(Zero)), x9)_>=_new_pr2F0G11(x5, x6, x7, Zero, x9))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G11(x29, x30, x31, Zero, x32) -> new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(x31), new_primDivNatS1(x31), x32), new_pr2F0G10(x33, x34, x35, Succ(Succ(x36)), x37) -> new_pr2F0G11(x33, x34, x35, x36, x37) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(x31), new_primDivNatS1(x31), x32)=new_pr2F0G10(x33, x34, x35, Succ(Succ(x36)), x37)  ==>  new_pr2F0G11(x29, x30, x31, Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(x31), new_primDivNatS1(x31), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x31)=Succ(Succ(x36))  ==>  new_pr2F0G11(x29, x30, x31, Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(x31), new_primDivNatS1(x31), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x31)=Succ(Succ(x36)) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x150)=Succ(Succ(x36))  ==>  new_pr2F0G11(x29, x30, Succ(x150), Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(Succ(x150)), new_primDivNatS1(Succ(x150)), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x150)=Succ(Succ(x36)) which results in the following new constraints:
84.27/50.02	
84.27/50.02	(4)    (Succ(new_primDivNatS4(x151))=Succ(Succ(x36))  ==>  new_pr2F0G11(x29, x30, Succ(Succ(Succ(x151))), Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(Succ(Succ(Succ(x151)))), new_primDivNatS1(Succ(Succ(Succ(x151)))), x32))
84.27/50.02	
84.27/50.02	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x36))  ==>  new_pr2F0G11(x29, x30, Succ(Succ(Zero)), Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G11(x29, x30, Succ(Succ(Succ(x151))), Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(Succ(Succ(Succ(x151)))), new_primDivNatS1(Succ(Succ(Succ(x151)))), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G11(x29, x30, Succ(Succ(Zero)), Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G11(x42, x43, x44, Zero, x45) -> new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(x44), new_primDivNatS1(x44), x45), new_pr2F0G10(x46, x47, x48, Zero, x49) -> new_pr2F0G10(x46, new_sr2(x47, x49), new_primDivNatS1(x48), new_primDivNatS1(x48), x49) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(x44), new_primDivNatS1(x44), x45)=new_pr2F0G10(x46, x47, x48, Zero, x49)  ==>  new_pr2F0G11(x42, x43, x44, Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(x44), new_primDivNatS1(x44), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x44)=Zero  ==>  new_pr2F0G11(x42, x43, x44, Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(x44), new_primDivNatS1(x44), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x44)=Zero which results in the following new constraints:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x152)=Zero  ==>  new_pr2F0G11(x42, x43, Succ(x152), Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(Succ(x152)), new_primDivNatS1(Succ(x152)), x45))
84.27/50.02	
84.27/50.02	(4)    (Zero=Zero  ==>  new_pr2F0G11(x42, x43, Zero, Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x152)=Zero which results in the following new constraint:
84.27/50.02	
84.27/50.02	(5)    (Zero=Zero  ==>  new_pr2F0G11(x42, x43, Succ(Zero), Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G11(x42, x43, Zero, Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G11(x42, x43, Succ(Zero), Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G11(x50, x51, x52, Zero, x53) -> new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(x52), new_primDivNatS1(x52), x53), new_pr2F0G10(x54, x55, x56, Succ(Succ(x57)), x58) -> H(x54, x55, x56, x58, anew_new_pr2F0G11(x57)) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(x52), new_primDivNatS1(x52), x53)=new_pr2F0G10(x54, x55, x56, Succ(Succ(x57)), x58)  ==>  new_pr2F0G11(x50, x51, x52, Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(x52), new_primDivNatS1(x52), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x52)=Succ(Succ(x57))  ==>  new_pr2F0G11(x50, x51, x52, Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(x52), new_primDivNatS1(x52), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x52)=Succ(Succ(x57)) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x154)=Succ(Succ(x57))  ==>  new_pr2F0G11(x50, x51, Succ(x154), Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(Succ(x154)), new_primDivNatS1(Succ(x154)), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x154)=Succ(Succ(x57)) which results in the following new constraints:
84.27/50.02	
84.27/50.02	(4)    (Succ(new_primDivNatS4(x155))=Succ(Succ(x57))  ==>  new_pr2F0G11(x50, x51, Succ(Succ(Succ(x155))), Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(Succ(Succ(Succ(x155)))), new_primDivNatS1(Succ(Succ(Succ(x155)))), x53))
84.27/50.02	
84.27/50.02	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x57))  ==>  new_pr2F0G11(x50, x51, Succ(Succ(Zero)), Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G11(x50, x51, Succ(Succ(Succ(x155))), Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(Succ(Succ(Succ(x155)))), new_primDivNatS1(Succ(Succ(Succ(x155)))), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G11(x50, x51, Succ(Succ(Zero)), Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G10(x63, x64, x65, Zero, x66) -> new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(x65), new_primDivNatS1(x65), x66), new_pr2F0G10(x67, x68, x69, Succ(Succ(x70)), x71) -> new_pr2F0G11(x67, x68, x69, x70, x71) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(x65), new_primDivNatS1(x65), x66)=new_pr2F0G10(x67, x68, x69, Succ(Succ(x70)), x71)  ==>  new_pr2F0G10(x63, x64, x65, Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(x65), new_primDivNatS1(x65), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x65)=Succ(Succ(x70))  ==>  new_pr2F0G10(x63, x64, x65, Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(x65), new_primDivNatS1(x65), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x65)=Succ(Succ(x70)) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x156)=Succ(Succ(x70))  ==>  new_pr2F0G10(x63, x64, Succ(x156), Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(Succ(x156)), new_primDivNatS1(Succ(x156)), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x156)=Succ(Succ(x70)) which results in the following new constraints:
84.27/50.02	
84.27/50.02	(4)    (Succ(new_primDivNatS4(x157))=Succ(Succ(x70))  ==>  new_pr2F0G10(x63, x64, Succ(Succ(Succ(x157))), Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(Succ(Succ(Succ(x157)))), new_primDivNatS1(Succ(Succ(Succ(x157)))), x66))
84.27/50.02	
84.27/50.02	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x70))  ==>  new_pr2F0G10(x63, x64, Succ(Succ(Zero)), Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G10(x63, x64, Succ(Succ(Succ(x157))), Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(Succ(Succ(Succ(x157)))), new_primDivNatS1(Succ(Succ(Succ(x157)))), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G10(x63, x64, Succ(Succ(Zero)), Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G10(x76, x77, x78, Zero, x79) -> new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(x78), new_primDivNatS1(x78), x79), new_pr2F0G10(x80, x81, x82, Zero, x83) -> new_pr2F0G10(x80, new_sr2(x81, x83), new_primDivNatS1(x82), new_primDivNatS1(x82), x83) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(x78), new_primDivNatS1(x78), x79)=new_pr2F0G10(x80, x81, x82, Zero, x83)  ==>  new_pr2F0G10(x76, x77, x78, Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(x78), new_primDivNatS1(x78), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x78)=Zero  ==>  new_pr2F0G10(x76, x77, x78, Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(x78), new_primDivNatS1(x78), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x78)=Zero which results in the following new constraints:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x158)=Zero  ==>  new_pr2F0G10(x76, x77, Succ(x158), Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(Succ(x158)), new_primDivNatS1(Succ(x158)), x79))
84.27/50.02	
84.27/50.02	(4)    (Zero=Zero  ==>  new_pr2F0G10(x76, x77, Zero, Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x158)=Zero which results in the following new constraint:
84.27/50.02	
84.27/50.02	(5)    (Zero=Zero  ==>  new_pr2F0G10(x76, x77, Succ(Zero), Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G10(x76, x77, Zero, Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G10(x76, x77, Succ(Zero), Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*We consider the chain new_pr2F0G10(x84, x85, x86, Zero, x87) -> new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(x86), new_primDivNatS1(x86), x87), new_pr2F0G10(x88, x89, x90, Succ(Succ(x91)), x92) -> H(x88, x89, x90, x92, anew_new_pr2F0G11(x91)) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(x86), new_primDivNatS1(x86), x87)=new_pr2F0G10(x88, x89, x90, Succ(Succ(x91)), x92)  ==>  new_pr2F0G10(x84, x85, x86, Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(x86), new_primDivNatS1(x86), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (new_primDivNatS1(x86)=Succ(Succ(x91))  ==>  new_pr2F0G10(x84, x85, x86, Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(x86), new_primDivNatS1(x86), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS1(x86)=Succ(Succ(x91)) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(3)    (new_primDivNatS01(x160)=Succ(Succ(x91))  ==>  new_pr2F0G10(x84, x85, Succ(x160), Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(Succ(x160)), new_primDivNatS1(Succ(x160)), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x160)=Succ(Succ(x91)) which results in the following new constraints:
84.27/50.02	
84.27/50.02	(4)    (Succ(new_primDivNatS4(x161))=Succ(Succ(x91))  ==>  new_pr2F0G10(x84, x85, Succ(Succ(Succ(x161))), Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(Succ(Succ(Succ(x161)))), new_primDivNatS1(Succ(Succ(Succ(x161)))), x87))
84.27/50.02	
84.27/50.02	(5)    (Succ(new_primDivNatS2)=Succ(Succ(x91))  ==>  new_pr2F0G10(x84, x85, Succ(Succ(Zero)), Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G10(x84, x85, Succ(Succ(Succ(x161))), Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(Succ(Succ(Succ(x161)))), new_primDivNatS1(Succ(Succ(Succ(x161)))), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G10(x84, x85, Succ(Succ(Zero)), Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> H(vuz102, vuz103, vuz105, bb, anew_new_pr2F0G11(vuz10600)) the following chains were created:
84.27/50.02	*We consider the chain new_pr2F0G10(x117, x118, x119, Succ(Succ(x120)), x121) -> H(x117, x118, x119, x121, anew_new_pr2F0G11(x120)), H(x122, x123, x124, x125, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(x122, x123, x124, Zero, x125) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (H(x117, x118, x119, x121, anew_new_pr2F0G11(x120))=H(x122, x123, x124, x125, cons_new_pr2F0G11(Zero))  ==>  new_pr2F0G10(x117, x118, x119, Succ(Succ(x120)), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(x120)))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (anew_new_pr2F0G11(x120)=cons_new_pr2F0G11(Zero)  ==>  new_pr2F0G10(x117, x118, x119, Succ(Succ(x120)), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(x120)))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on anew_new_pr2F0G11(x120)=cons_new_pr2F0G11(Zero) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(3)    (new_new_pr2F0G11(x162)=cons_new_pr2F0G11(Zero)  ==>  new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(x162)))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(x162)))))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_new_pr2F0G11(x162)=cons_new_pr2F0G11(Zero) which results in the following new constraints:
84.27/50.02	
84.27/50.02	(4)    (new_new_pr2F0G11(x163)=cons_new_pr2F0G11(Zero) & (\/x164,x165,x166,x167:new_new_pr2F0G11(x163)=cons_new_pr2F0G11(Zero)  ==>  new_pr2F0G10(x164, x165, x166, Succ(Succ(Succ(Succ(x163)))), x167)_>=_H(x164, x165, x166, x167, anew_new_pr2F0G11(Succ(Succ(x163)))))  ==>  new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(Succ(Succ(x163)))))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(Succ(Succ(x163)))))))
84.27/50.02	
84.27/50.02	(5)    (cons_new_pr2F0G11(Zero)=cons_new_pr2F0G11(Zero)  ==>  new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(Zero)))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(Zero)))))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (4) using rule (VI) where we applied the induction hypothesis (\/x164,x165,x166,x167:new_new_pr2F0G11(x163)=cons_new_pr2F0G11(Zero)  ==>  new_pr2F0G10(x164, x165, x166, Succ(Succ(Succ(Succ(x163)))), x167)_>=_H(x164, x165, x166, x167, anew_new_pr2F0G11(Succ(Succ(x163))))) with sigma = [x164 / x117, x165 / x118, x166 / x119, x167 / x121] which results in the following new constraint:
84.27/50.02	
84.27/50.02	(6)    (new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(x163)))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(x163))))  ==>  new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(Succ(Succ(x163)))))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(Succ(Succ(x163)))))))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (5) using rules (I), (II) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(7)    (new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(Zero)))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(Zero)))))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	For Pair H(vuz102, vuz103, vuz105, bb, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) the following chains were created:
84.27/50.02	*We consider the chain H(x130, x131, x132, x133, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(x130, x131, x132, Zero, x133), new_pr2F0G11(x134, x135, x136, Zero, x137) -> new_pr2F0G10(x134, new_sr2(x135, x137), new_primDivNatS1(x136), new_primDivNatS1(x136), x137) which results in the following constraint:
84.27/50.02	
84.27/50.02	(1)    (new_pr2F0G11(x130, x131, x132, Zero, x133)=new_pr2F0G11(x134, x135, x136, Zero, x137)  ==>  H(x130, x131, x132, x133, cons_new_pr2F0G11(Zero))_>=_new_pr2F0G11(x130, x131, x132, Zero, x133))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
84.27/50.02	
84.27/50.02	(2)    (H(x130, x131, x132, x133, cons_new_pr2F0G11(Zero))_>=_new_pr2F0G11(x130, x131, x132, Zero, x133))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	To summarize, we get the following constraints P__>=_ for the following pairs.
84.27/50.02	
84.27/50.02	*new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x5, x6, x7, Succ(Succ(Zero)), x9)_>=_new_pr2F0G11(x5, x6, x7, Zero, x9))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x29, x30, Succ(Succ(Succ(x151))), Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(Succ(Succ(Succ(x151)))), new_primDivNatS1(Succ(Succ(Succ(x151)))), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x29, x30, Succ(Succ(Zero)), Zero, x32)_>=_new_pr2F0G10(x29, new_sr2(x30, x32), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x32))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x42, x43, Succ(Zero), Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x42, x43, Zero, Zero, x45)_>=_new_pr2F0G10(x42, new_sr2(x43, x45), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x45))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x50, x51, Succ(Succ(Succ(x155))), Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(Succ(Succ(Succ(x155)))), new_primDivNatS1(Succ(Succ(Succ(x155)))), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G11(x50, x51, Succ(Succ(Zero)), Zero, x53)_>=_new_pr2F0G10(x50, new_sr2(x51, x53), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x53))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x63, x64, Succ(Succ(Succ(x157))), Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(Succ(Succ(Succ(x157)))), new_primDivNatS1(Succ(Succ(Succ(x157)))), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x63, x64, Succ(Succ(Zero)), Zero, x66)_>=_new_pr2F0G10(x63, new_sr2(x64, x66), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x66))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x76, x77, Succ(Zero), Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(Succ(Zero)), new_primDivNatS1(Succ(Zero)), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x76, x77, Zero, Zero, x79)_>=_new_pr2F0G10(x76, new_sr2(x77, x79), new_primDivNatS1(Zero), new_primDivNatS1(Zero), x79))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x84, x85, Succ(Succ(Succ(x161))), Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(Succ(Succ(Succ(x161)))), new_primDivNatS1(Succ(Succ(Succ(x161)))), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x84, x85, Succ(Succ(Zero)), Zero, x87)_>=_new_pr2F0G10(x84, new_sr2(x85, x87), new_primDivNatS1(Succ(Succ(Zero))), new_primDivNatS1(Succ(Succ(Zero))), x87))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> H(vuz102, vuz103, vuz105, bb, anew_new_pr2F0G11(vuz10600))
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(x163)))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(x163))))  ==>  new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(Succ(Succ(x163)))))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(Succ(Succ(x163)))))))
84.27/50.02	
84.27/50.02	
84.27/50.02	*(new_pr2F0G10(x117, x118, x119, Succ(Succ(Succ(Succ(Zero)))), x121)_>=_H(x117, x118, x119, x121, anew_new_pr2F0G11(Succ(Succ(Zero)))))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	*H(vuz102, vuz103, vuz105, bb, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb)
84.27/50.02	
84.27/50.02	*(H(x130, x131, x132, x133, cons_new_pr2F0G11(Zero))_>=_new_pr2F0G11(x130, x131, x132, Zero, x133))
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	
84.27/50.02	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. 
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(103)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Zero, bb) -> new_pr2F0G10(vuz102, new_sr2(vuz103, bb), new_primDivNatS1(vuz105), new_primDivNatS1(vuz105), bb)
84.27/50.02	   new_pr2F0G10(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> H(vuz102, vuz103, vuz105, bb, anew_new_pr2F0G11(vuz10600))
84.27/50.02	   H(vuz102, vuz103, vuz105, bb, cons_new_pr2F0G11(Zero)) -> new_pr2F0G11(vuz102, vuz103, vuz105, Zero, bb)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_primDivNatS1(Zero) -> Zero
84.27/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.27/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.27/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.27/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.27/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   anew_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Succ(Succ(vuz10600))) -> new_new_pr2F0G11(vuz10600)
84.27/50.02	   new_new_pr2F0G11(Zero) -> cons_new_pr2F0G11(Zero)
84.27/50.02	
84.27/50.02	The set Q consists of the following terms:
84.27/50.02	
84.27/50.02	   new_sr1(x0, x1, ty_Integer)
84.27/50.02	   new_sr12(Pos(x0), Neg(x1))
84.27/50.02	   new_sr12(Neg(x0), Pos(x1))
84.27/50.02	   new_sr0(x0, x1, ty_Integer)
84.27/50.02	   new_sr2(x0, ty_Double)
84.27/50.02	   new_sr2(x0, ty_Float)
84.27/50.02	   new_sr12(Neg(x0), Neg(x1))
84.27/50.02	   new_primDivNatS1(Zero)
84.27/50.02	   new_sr3(x0, ty_Double)
84.27/50.02	   new_sr13(x0, x1)
84.27/50.02	   new_sr0(x0, x1, ty_Int)
84.27/50.02	   new_primMulNat0(Zero, Zero)
84.27/50.02	   new_sr20(x0)
84.27/50.02	   new_sr3(x0, ty_Int)
84.27/50.02	   new_sr0(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS4(x0)
84.27/50.02	   new_sr2(x0, ty_Integer)
84.27/50.02	   new_sr21(x0, x1)
84.27/50.02	   new_primMulNat0(Zero, Succ(x0))
84.27/50.02	   new_primDivNatS2
84.27/50.02	   new_primDivNatS1(Succ(x0))
84.27/50.02	   new_sr12(Pos(x0), Pos(x1))
84.27/50.02	   new_sr1(x0, x1, ty_Float)
84.27/50.02	   new_primDivNatS01(Succ(Zero))
84.27/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.27/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.27/50.02	   new_sr17(x0)
84.27/50.02	   new_sr2(x0, ty_Int)
84.27/50.02	   new_sr18(x0)
84.27/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.27/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.27/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_sr16(x0, x1, x2)
84.27/50.02	   new_sr1(x0, x1, ty_Double)
84.27/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.27/50.02	   new_sr19(x0)
84.27/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.27/50.02	   new_primDivNatS5(x0)
84.27/50.02	   new_primDivNatS3
84.27/50.02	   new_sr0(x0, x1, ty_Float)
84.27/50.02	   new_sr1(x0, x1, ty_Int)
84.27/50.02	   new_sr15(x0, x1)
84.27/50.02	   new_primDivNatS01(Zero)
84.27/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.27/50.02	   new_primMulNat0(Succ(x0), Zero)
84.27/50.02	   new_primPlusNat0(Zero, Zero)
84.27/50.02	   new_sr14(x0, x1)
84.27/50.02	   new_sr3(x0, ty_Integer)
84.27/50.02	   new_sr3(x0, ty_Float)
84.27/50.02	   new_new_pr2F0G11(Succ(Succ(x0)))
84.27/50.02	   anew_new_pr2F0G11(Succ(Succ(x0)))
84.27/50.02	   new_new_pr2F0G11(Zero)
84.27/50.02	
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(104)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	
84.27/50.02	R is empty.
84.27/50.02	Q is empty.
84.27/50.02	We have to consider all minimal (P,Q,R)-chains.
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(105) QDPSizeChangeProof (EQUIVALENT)
84.27/50.02	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. 
84.27/50.02	
84.27/50.02	From the DPs we obtained the following set of size-change graphs:
84.27/50.02	*new_pr2F0G11(vuz102, vuz103, vuz105, Succ(Succ(vuz10600)), bb) -> new_pr2F0G11(vuz102, vuz103, vuz105, vuz10600, bb)
84.27/50.02	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5
84.27/50.02	
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(106)
84.27/50.02	YES
84.27/50.02	
84.27/50.02	----------------------------------------
84.27/50.02	
84.27/50.02	(107)
84.27/50.02	Obligation:
84.27/50.02	Q DP problem:
84.27/50.02	The TRS P consists of the following rules:
84.27/50.02	
84.27/50.02	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.27/50.02	
84.27/50.02	The TRS R consists of the following rules:
84.27/50.02	
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.27/50.02	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.27/50.02	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.27/50.02	   new_primDivNatS01(Zero) -> Zero
84.27/50.02	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.27/50.02	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.27/50.02	   new_primDivNatS2 -> new_primDivNatS3
84.27/50.02	   new_primDivNatS3 -> Zero
84.27/50.02	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.27/50.02	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.27/50.02	   new_sr15(vuz72, vuz20) -> error([])
84.27/50.02	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.27/50.02	   new_primMulNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.27/50.02	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.27/50.02	   new_primPlusNat0(Zero, Zero) -> Zero
84.27/50.02	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.27/50.02	   new_sr16(vuz73, vuz20, ce) -> error([])
84.27/50.02	   new_sr14(vuz70, vuz20) -> error([])
84.27/50.02	   new_sr13(vuz69, vuz20) -> error([])
84.27/50.02	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.27/50.02	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.27/50.02	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.37/50.02	   new_primDivNatS1(Zero) -> Zero
84.37/50.02	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.37/50.02	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.37/50.02	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.37/50.02	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.37/50.02	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.37/50.02	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.37/50.02	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.37/50.02	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.37/50.02	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.37/50.02	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.37/50.02	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.37/50.02	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.37/50.02	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.37/50.02	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.37/50.02	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.37/50.02	
84.37/50.02	The set Q consists of the following terms:
84.37/50.02	
84.37/50.02	   new_sr1(x0, x1, ty_Integer)
84.37/50.02	   new_sr12(Pos(x0), Neg(x1))
84.37/50.02	   new_sr12(Neg(x0), Pos(x1))
84.37/50.02	   new_sr0(x0, x1, ty_Integer)
84.37/50.02	   new_sr2(x0, ty_Double)
84.37/50.02	   new_sr2(x0, ty_Float)
84.37/50.02	   new_sr12(Neg(x0), Neg(x1))
84.37/50.02	   new_primDivNatS1(Zero)
84.37/50.02	   new_sr3(x0, ty_Double)
84.37/50.02	   new_sr13(x0, x1)
84.37/50.02	   new_sr0(x0, x1, ty_Int)
84.37/50.02	   new_primMulNat0(Zero, Zero)
84.37/50.02	   new_sr20(x0)
84.37/50.02	   new_sr3(x0, ty_Int)
84.37/50.02	   new_sr0(x0, x1, ty_Double)
84.37/50.02	   new_primDivNatS4(x0)
84.37/50.02	   new_sr2(x0, ty_Integer)
84.37/50.02	   new_sr21(x0, x1)
84.37/50.02	   new_primMulNat0(Zero, Succ(x0))
84.37/50.02	   new_primDivNatS2
84.37/50.02	   new_primDivNatS1(Succ(x0))
84.37/50.02	   new_sr12(Pos(x0), Pos(x1))
84.37/50.02	   new_sr1(x0, x1, ty_Float)
84.37/50.02	   new_primDivNatS01(Succ(Zero))
84.37/50.02	   new_primPlusNat0(Succ(x0), Zero)
84.37/50.02	   new_sr3(x0, app(ty_Ratio, x1))
84.37/50.02	   new_sr17(x0)
84.37/50.02	   new_sr2(x0, ty_Int)
84.37/50.02	   new_sr18(x0)
84.37/50.02	   new_primPlusNat0(Zero, Succ(x0))
84.37/50.02	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.37/50.02	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.37/50.02	   new_primMulNat0(Succ(x0), Succ(x1))
84.37/50.02	   new_sr16(x0, x1, x2)
84.37/50.02	   new_sr1(x0, x1, ty_Double)
84.37/50.02	   new_primDivNatS01(Succ(Succ(x0)))
84.37/50.02	   new_sr19(x0)
84.37/50.02	   new_primPlusNat0(Succ(x0), Succ(x1))
84.37/50.02	   new_primDivNatS5(x0)
84.37/50.02	   new_primDivNatS3
84.37/50.02	   new_sr0(x0, x1, ty_Float)
84.37/50.02	   new_sr1(x0, x1, ty_Int)
84.37/50.02	   new_sr15(x0, x1)
84.37/50.02	   new_primDivNatS01(Zero)
84.37/50.02	   new_sr2(x0, app(ty_Ratio, x1))
84.37/50.02	   new_primMulNat0(Succ(x0), Zero)
84.37/50.02	   new_primPlusNat0(Zero, Zero)
84.37/50.02	   new_sr14(x0, x1)
84.37/50.02	   new_sr3(x0, ty_Integer)
84.37/50.02	   new_sr3(x0, ty_Float)
84.37/50.02	
84.37/50.02	We have to consider all minimal (P,Q,R)-chains.
84.37/50.02	----------------------------------------
84.37/50.02	
84.37/50.02	(108) UsableRulesProof (EQUIVALENT)
84.37/50.02	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.
84.37/50.02	----------------------------------------
84.37/50.02	
84.37/50.02	(109)
84.37/50.02	Obligation:
84.37/50.02	Q DP problem:
84.37/50.02	The TRS P consists of the following rules:
84.37/50.02	
84.37/50.02	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.37/50.02	
84.37/50.02	R is empty.
84.37/50.02	The set Q consists of the following terms:
84.37/50.02	
84.37/50.02	   new_sr1(x0, x1, ty_Integer)
84.37/50.02	   new_sr12(Pos(x0), Neg(x1))
84.37/50.02	   new_sr12(Neg(x0), Pos(x1))
84.37/50.02	   new_sr0(x0, x1, ty_Integer)
84.37/50.02	   new_sr2(x0, ty_Double)
84.37/50.03	   new_sr2(x0, ty_Float)
84.37/50.03	   new_sr12(Neg(x0), Neg(x1))
84.37/50.03	   new_primDivNatS1(Zero)
84.37/50.03	   new_sr3(x0, ty_Double)
84.37/50.03	   new_sr13(x0, x1)
84.37/50.03	   new_sr0(x0, x1, ty_Int)
84.37/50.03	   new_primMulNat0(Zero, Zero)
84.37/50.03	   new_sr20(x0)
84.37/50.03	   new_sr3(x0, ty_Int)
84.37/50.03	   new_sr0(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS4(x0)
84.37/50.03	   new_sr2(x0, ty_Integer)
84.37/50.03	   new_sr21(x0, x1)
84.37/50.03	   new_primMulNat0(Zero, Succ(x0))
84.37/50.03	   new_primDivNatS2
84.37/50.03	   new_primDivNatS1(Succ(x0))
84.37/50.03	   new_sr12(Pos(x0), Pos(x1))
84.37/50.03	   new_sr1(x0, x1, ty_Float)
84.37/50.03	   new_primDivNatS01(Succ(Zero))
84.37/50.03	   new_primPlusNat0(Succ(x0), Zero)
84.37/50.03	   new_sr3(x0, app(ty_Ratio, x1))
84.37/50.03	   new_sr17(x0)
84.37/50.03	   new_sr2(x0, ty_Int)
84.37/50.03	   new_sr18(x0)
84.37/50.03	   new_primPlusNat0(Zero, Succ(x0))
84.37/50.03	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_primMulNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_sr16(x0, x1, x2)
84.37/50.03	   new_sr1(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS01(Succ(Succ(x0)))
84.37/50.03	   new_sr19(x0)
84.37/50.03	   new_primPlusNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_primDivNatS5(x0)
84.37/50.03	   new_primDivNatS3
84.37/50.03	   new_sr0(x0, x1, ty_Float)
84.37/50.03	   new_sr1(x0, x1, ty_Int)
84.37/50.03	   new_sr15(x0, x1)
84.37/50.03	   new_primDivNatS01(Zero)
84.37/50.03	   new_sr2(x0, app(ty_Ratio, x1))
84.37/50.03	   new_primMulNat0(Succ(x0), Zero)
84.37/50.03	   new_primPlusNat0(Zero, Zero)
84.37/50.03	   new_sr14(x0, x1)
84.37/50.03	   new_sr3(x0, ty_Integer)
84.37/50.03	   new_sr3(x0, ty_Float)
84.37/50.03	
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(110) QReductionProof (EQUIVALENT)
84.37/50.03	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
84.37/50.03	
84.37/50.03	   new_sr1(x0, x1, ty_Integer)
84.37/50.03	   new_sr12(Pos(x0), Neg(x1))
84.37/50.03	   new_sr12(Neg(x0), Pos(x1))
84.37/50.03	   new_sr0(x0, x1, ty_Integer)
84.37/50.03	   new_sr2(x0, ty_Double)
84.37/50.03	   new_sr2(x0, ty_Float)
84.37/50.03	   new_sr12(Neg(x0), Neg(x1))
84.37/50.03	   new_primDivNatS1(Zero)
84.37/50.03	   new_sr3(x0, ty_Double)
84.37/50.03	   new_sr13(x0, x1)
84.37/50.03	   new_sr0(x0, x1, ty_Int)
84.37/50.03	   new_primMulNat0(Zero, Zero)
84.37/50.03	   new_sr20(x0)
84.37/50.03	   new_sr3(x0, ty_Int)
84.37/50.03	   new_sr0(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS4(x0)
84.37/50.03	   new_sr2(x0, ty_Integer)
84.37/50.03	   new_sr21(x0, x1)
84.37/50.03	   new_primMulNat0(Zero, Succ(x0))
84.37/50.03	   new_primDivNatS2
84.37/50.03	   new_primDivNatS1(Succ(x0))
84.37/50.03	   new_sr12(Pos(x0), Pos(x1))
84.37/50.03	   new_sr1(x0, x1, ty_Float)
84.37/50.03	   new_primDivNatS01(Succ(Zero))
84.37/50.03	   new_primPlusNat0(Succ(x0), Zero)
84.37/50.03	   new_sr3(x0, app(ty_Ratio, x1))
84.37/50.03	   new_sr17(x0)
84.37/50.03	   new_sr2(x0, ty_Int)
84.37/50.03	   new_sr18(x0)
84.37/50.03	   new_primPlusNat0(Zero, Succ(x0))
84.37/50.03	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_primMulNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_sr16(x0, x1, x2)
84.37/50.03	   new_sr1(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS01(Succ(Succ(x0)))
84.37/50.03	   new_sr19(x0)
84.37/50.03	   new_primPlusNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_primDivNatS5(x0)
84.37/50.03	   new_primDivNatS3
84.37/50.03	   new_sr0(x0, x1, ty_Float)
84.37/50.03	   new_sr1(x0, x1, ty_Int)
84.37/50.03	   new_sr15(x0, x1)
84.37/50.03	   new_primDivNatS01(Zero)
84.37/50.03	   new_sr2(x0, app(ty_Ratio, x1))
84.37/50.03	   new_primMulNat0(Succ(x0), Zero)
84.37/50.03	   new_primPlusNat0(Zero, Zero)
84.37/50.03	   new_sr14(x0, x1)
84.37/50.03	   new_sr3(x0, ty_Integer)
84.37/50.03	   new_sr3(x0, ty_Float)
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(111)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(112) QDPSizeChangeProof (EQUIVALENT)
84.37/50.03	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. 
84.37/50.03	
84.37/50.03	From the DPs we obtained the following set of size-change graphs:
84.37/50.03	*new_pr2F3(Succ(vuz2020), Succ(vuz203000), vuz204, vuz205, h) -> new_pr2F3(vuz2020, vuz203000, vuz204, vuz205, h)
84.37/50.03	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(113)
84.37/50.03	YES
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(114)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.37/50.03	
84.37/50.03	The TRS R consists of the following rules:
84.37/50.03	
84.37/50.03	   new_sr0(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.37/50.03	   new_sr0(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.37/50.03	   new_sr0(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.37/50.03	   new_sr0(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.37/50.03	   new_sr0(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.37/50.03	   new_primDivNatS01(Succ(Succ(vuz130000))) -> Succ(new_primDivNatS4(vuz130000))
84.37/50.03	   new_primDivNatS01(Zero) -> Zero
84.37/50.03	   new_primDivNatS01(Succ(Zero)) -> Succ(new_primDivNatS2)
84.37/50.03	   new_primDivNatS1(Succ(vuz550)) -> new_primDivNatS01(vuz550)
84.37/50.03	   new_primDivNatS2 -> new_primDivNatS3
84.37/50.03	   new_primDivNatS3 -> Zero
84.37/50.03	   new_primDivNatS4(vuz1300) -> new_primDivNatS5(vuz1300)
84.37/50.03	   new_primDivNatS5(vuz1300) -> new_primDivNatS01(vuz1300)
84.37/50.03	   new_sr15(vuz72, vuz20) -> error([])
84.37/50.03	   new_sr12(Neg(vuz710), Neg(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.37/50.03	   new_sr12(Pos(vuz710), Pos(vuz200)) -> Pos(new_primMulNat0(vuz710, vuz200))
84.37/50.03	   new_sr12(Pos(vuz710), Neg(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.37/50.03	   new_sr12(Neg(vuz710), Pos(vuz200)) -> Neg(new_primMulNat0(vuz710, vuz200))
84.37/50.03	   new_primMulNat0(Succ(vuz7100), Zero) -> Zero
84.37/50.03	   new_primMulNat0(Zero, Succ(vuz2000)) -> Zero
84.37/50.03	   new_primMulNat0(Zero, Zero) -> Zero
84.37/50.03	   new_primMulNat0(Succ(vuz7100), Succ(vuz2000)) -> new_primPlusNat0(new_primMulNat0(vuz7100, Succ(vuz2000)), Succ(vuz2000))
84.37/50.03	   new_primPlusNat0(Succ(vuz4000), Succ(vuz5000)) -> Succ(Succ(new_primPlusNat0(vuz4000, vuz5000)))
84.37/50.03	   new_primPlusNat0(Zero, Succ(vuz5000)) -> Succ(vuz5000)
84.37/50.03	   new_primPlusNat0(Zero, Zero) -> Zero
84.37/50.03	   new_primPlusNat0(Succ(vuz4000), Zero) -> Succ(vuz4000)
84.37/50.03	   new_sr16(vuz73, vuz20, ce) -> error([])
84.37/50.03	   new_sr14(vuz70, vuz20) -> error([])
84.37/50.03	   new_sr13(vuz69, vuz20) -> error([])
84.37/50.03	   new_sr2(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.37/50.03	   new_sr2(vuz103, ty_Double) -> new_sr17(vuz103)
84.37/50.03	   new_sr2(vuz103, ty_Float) -> new_sr20(vuz103)
84.37/50.03	   new_sr2(vuz103, ty_Int) -> new_sr19(vuz103)
84.37/50.03	   new_sr2(vuz103, ty_Integer) -> new_sr18(vuz103)
84.37/50.03	   new_primDivNatS1(Zero) -> Zero
84.37/50.03	   new_sr18(vuz12) -> new_sr14(vuz12, vuz12)
84.37/50.03	   new_sr19(vuz12) -> new_sr12(vuz12, vuz12)
84.37/50.03	   new_sr20(vuz12) -> new_sr15(vuz12, vuz12)
84.37/50.03	   new_sr17(vuz12) -> new_sr13(vuz12, vuz12)
84.37/50.03	   new_sr21(vuz12, cb) -> new_sr16(vuz12, vuz12, cb)
84.37/50.03	   new_sr1(vuz222, vuz223, ty_Int) -> new_sr12(vuz222, vuz223)
84.37/50.03	   new_sr1(vuz222, vuz223, ty_Double) -> new_sr13(vuz222, vuz223)
84.37/50.03	   new_sr1(vuz222, vuz223, app(ty_Ratio, bf)) -> new_sr16(vuz222, vuz223, bf)
84.37/50.03	   new_sr1(vuz222, vuz223, ty_Float) -> new_sr15(vuz222, vuz223)
84.37/50.03	   new_sr1(vuz222, vuz223, ty_Integer) -> new_sr14(vuz222, vuz223)
84.37/50.03	   new_sr3(vuz103, app(ty_Ratio, bh)) -> new_sr21(vuz103, bh)
84.37/50.03	   new_sr3(vuz103, ty_Int) -> new_sr19(vuz103)
84.37/50.03	   new_sr3(vuz103, ty_Integer) -> new_sr18(vuz103)
84.37/50.03	   new_sr3(vuz103, ty_Float) -> new_sr20(vuz103)
84.37/50.03	   new_sr3(vuz103, ty_Double) -> new_sr17(vuz103)
84.37/50.03	
84.37/50.03	The set Q consists of the following terms:
84.37/50.03	
84.37/50.03	   new_sr1(x0, x1, ty_Integer)
84.37/50.03	   new_sr12(Pos(x0), Neg(x1))
84.37/50.03	   new_sr12(Neg(x0), Pos(x1))
84.37/50.03	   new_sr0(x0, x1, ty_Integer)
84.37/50.03	   new_sr2(x0, ty_Double)
84.37/50.03	   new_sr2(x0, ty_Float)
84.37/50.03	   new_sr12(Neg(x0), Neg(x1))
84.37/50.03	   new_primDivNatS1(Zero)
84.37/50.03	   new_sr3(x0, ty_Double)
84.37/50.03	   new_sr13(x0, x1)
84.37/50.03	   new_sr0(x0, x1, ty_Int)
84.37/50.03	   new_primMulNat0(Zero, Zero)
84.37/50.03	   new_sr20(x0)
84.37/50.03	   new_sr3(x0, ty_Int)
84.37/50.03	   new_sr0(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS4(x0)
84.37/50.03	   new_sr2(x0, ty_Integer)
84.37/50.03	   new_sr21(x0, x1)
84.37/50.03	   new_primMulNat0(Zero, Succ(x0))
84.37/50.03	   new_primDivNatS2
84.37/50.03	   new_primDivNatS1(Succ(x0))
84.37/50.03	   new_sr12(Pos(x0), Pos(x1))
84.37/50.03	   new_sr1(x0, x1, ty_Float)
84.37/50.03	   new_primDivNatS01(Succ(Zero))
84.37/50.03	   new_primPlusNat0(Succ(x0), Zero)
84.37/50.03	   new_sr3(x0, app(ty_Ratio, x1))
84.37/50.03	   new_sr17(x0)
84.37/50.03	   new_sr2(x0, ty_Int)
84.37/50.03	   new_sr18(x0)
84.37/50.03	   new_primPlusNat0(Zero, Succ(x0))
84.37/50.03	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_primMulNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_sr16(x0, x1, x2)
84.37/50.03	   new_sr1(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS01(Succ(Succ(x0)))
84.37/50.03	   new_sr19(x0)
84.37/50.03	   new_primPlusNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_primDivNatS5(x0)
84.37/50.03	   new_primDivNatS3
84.37/50.03	   new_sr0(x0, x1, ty_Float)
84.37/50.03	   new_sr1(x0, x1, ty_Int)
84.37/50.03	   new_sr15(x0, x1)
84.37/50.03	   new_primDivNatS01(Zero)
84.37/50.03	   new_sr2(x0, app(ty_Ratio, x1))
84.37/50.03	   new_primMulNat0(Succ(x0), Zero)
84.37/50.03	   new_primPlusNat0(Zero, Zero)
84.37/50.03	   new_sr14(x0, x1)
84.37/50.03	   new_sr3(x0, ty_Integer)
84.37/50.03	   new_sr3(x0, ty_Float)
84.37/50.03	
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(115) UsableRulesProof (EQUIVALENT)
84.37/50.03	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.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(116)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	The set Q consists of the following terms:
84.37/50.03	
84.37/50.03	   new_sr1(x0, x1, ty_Integer)
84.37/50.03	   new_sr12(Pos(x0), Neg(x1))
84.37/50.03	   new_sr12(Neg(x0), Pos(x1))
84.37/50.03	   new_sr0(x0, x1, ty_Integer)
84.37/50.03	   new_sr2(x0, ty_Double)
84.37/50.03	   new_sr2(x0, ty_Float)
84.37/50.03	   new_sr12(Neg(x0), Neg(x1))
84.37/50.03	   new_primDivNatS1(Zero)
84.37/50.03	   new_sr3(x0, ty_Double)
84.37/50.03	   new_sr13(x0, x1)
84.37/50.03	   new_sr0(x0, x1, ty_Int)
84.37/50.03	   new_primMulNat0(Zero, Zero)
84.37/50.03	   new_sr20(x0)
84.37/50.03	   new_sr3(x0, ty_Int)
84.37/50.03	   new_sr0(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS4(x0)
84.37/50.03	   new_sr2(x0, ty_Integer)
84.37/50.03	   new_sr21(x0, x1)
84.37/50.03	   new_primMulNat0(Zero, Succ(x0))
84.37/50.03	   new_primDivNatS2
84.37/50.03	   new_primDivNatS1(Succ(x0))
84.37/50.03	   new_sr12(Pos(x0), Pos(x1))
84.37/50.03	   new_sr1(x0, x1, ty_Float)
84.37/50.03	   new_primDivNatS01(Succ(Zero))
84.37/50.03	   new_primPlusNat0(Succ(x0), Zero)
84.37/50.03	   new_sr3(x0, app(ty_Ratio, x1))
84.37/50.03	   new_sr17(x0)
84.37/50.03	   new_sr2(x0, ty_Int)
84.37/50.03	   new_sr18(x0)
84.37/50.03	   new_primPlusNat0(Zero, Succ(x0))
84.37/50.03	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_primMulNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_sr16(x0, x1, x2)
84.37/50.03	   new_sr1(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS01(Succ(Succ(x0)))
84.37/50.03	   new_sr19(x0)
84.37/50.03	   new_primPlusNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_primDivNatS5(x0)
84.37/50.03	   new_primDivNatS3
84.37/50.03	   new_sr0(x0, x1, ty_Float)
84.37/50.03	   new_sr1(x0, x1, ty_Int)
84.37/50.03	   new_sr15(x0, x1)
84.37/50.03	   new_primDivNatS01(Zero)
84.37/50.03	   new_sr2(x0, app(ty_Ratio, x1))
84.37/50.03	   new_primMulNat0(Succ(x0), Zero)
84.37/50.03	   new_primPlusNat0(Zero, Zero)
84.37/50.03	   new_sr14(x0, x1)
84.37/50.03	   new_sr3(x0, ty_Integer)
84.37/50.03	   new_sr3(x0, ty_Float)
84.37/50.03	
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(117) QReductionProof (EQUIVALENT)
84.37/50.03	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
84.37/50.03	
84.37/50.03	   new_sr1(x0, x1, ty_Integer)
84.37/50.03	   new_sr12(Pos(x0), Neg(x1))
84.37/50.03	   new_sr12(Neg(x0), Pos(x1))
84.37/50.03	   new_sr0(x0, x1, ty_Integer)
84.37/50.03	   new_sr2(x0, ty_Double)
84.37/50.03	   new_sr2(x0, ty_Float)
84.37/50.03	   new_sr12(Neg(x0), Neg(x1))
84.37/50.03	   new_primDivNatS1(Zero)
84.37/50.03	   new_sr3(x0, ty_Double)
84.37/50.03	   new_sr13(x0, x1)
84.37/50.03	   new_sr0(x0, x1, ty_Int)
84.37/50.03	   new_primMulNat0(Zero, Zero)
84.37/50.03	   new_sr20(x0)
84.37/50.03	   new_sr3(x0, ty_Int)
84.37/50.03	   new_sr0(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS4(x0)
84.37/50.03	   new_sr2(x0, ty_Integer)
84.37/50.03	   new_sr21(x0, x1)
84.37/50.03	   new_primMulNat0(Zero, Succ(x0))
84.37/50.03	   new_primDivNatS2
84.37/50.03	   new_primDivNatS1(Succ(x0))
84.37/50.03	   new_sr12(Pos(x0), Pos(x1))
84.37/50.03	   new_sr1(x0, x1, ty_Float)
84.37/50.03	   new_primDivNatS01(Succ(Zero))
84.37/50.03	   new_primPlusNat0(Succ(x0), Zero)
84.37/50.03	   new_sr3(x0, app(ty_Ratio, x1))
84.37/50.03	   new_sr17(x0)
84.37/50.03	   new_sr2(x0, ty_Int)
84.37/50.03	   new_sr18(x0)
84.37/50.03	   new_primPlusNat0(Zero, Succ(x0))
84.37/50.03	   new_sr1(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_sr0(x0, x1, app(ty_Ratio, x2))
84.37/50.03	   new_primMulNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_sr16(x0, x1, x2)
84.37/50.03	   new_sr1(x0, x1, ty_Double)
84.37/50.03	   new_primDivNatS01(Succ(Succ(x0)))
84.37/50.03	   new_sr19(x0)
84.37/50.03	   new_primPlusNat0(Succ(x0), Succ(x1))
84.37/50.03	   new_primDivNatS5(x0)
84.37/50.03	   new_primDivNatS3
84.37/50.03	   new_sr0(x0, x1, ty_Float)
84.37/50.03	   new_sr1(x0, x1, ty_Int)
84.37/50.03	   new_sr15(x0, x1)
84.37/50.03	   new_primDivNatS01(Zero)
84.37/50.03	   new_sr2(x0, app(ty_Ratio, x1))
84.37/50.03	   new_primMulNat0(Succ(x0), Zero)
84.37/50.03	   new_primPlusNat0(Zero, Zero)
84.37/50.03	   new_sr14(x0, x1)
84.37/50.03	   new_sr3(x0, ty_Integer)
84.37/50.03	   new_sr3(x0, ty_Float)
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(118)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(119) QDPSizeChangeProof (EQUIVALENT)
84.37/50.03	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. 
84.37/50.03	
84.37/50.03	From the DPs we obtained the following set of size-change graphs:
84.37/50.03	*new_pr2F33(Succ(vuz1050), Succ(vuz11500), vuz103, vuz102, bb) -> new_pr2F33(vuz1050, vuz11500, vuz103, vuz102, bb)
84.37/50.03	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(120)
84.37/50.03	YES
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(121)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_pr2F0G16(vuz20, vuz21, Succ(Succ(vuz2200)), h) -> new_pr2F0G16(vuz20, vuz21, vuz2200, h)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(122) QDPSizeChangeProof (EQUIVALENT)
84.37/50.03	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. 
84.37/50.03	
84.37/50.03	From the DPs we obtained the following set of size-change graphs:
84.37/50.03	*new_pr2F0G16(vuz20, vuz21, Succ(Succ(vuz2200)), h) -> new_pr2F0G16(vuz20, vuz21, vuz2200, h)
84.37/50.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(123)
84.37/50.03	YES
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(124)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_primDivNatS(Succ(Succ(vuz130000))) -> new_primDivNatS(vuz130000)
84.37/50.03	   new_primDivNatS00(Succ(Succ(vuz130000))) -> new_primDivNatS(vuz130000)
84.37/50.03	   new_primDivNatS0(Succ(Succ(vuz130000))) -> new_primDivNatS(vuz130000)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(125) DependencyGraphProof (EQUIVALENT)
84.37/50.03	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(126)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_primDivNatS(Succ(Succ(vuz130000))) -> new_primDivNatS(vuz130000)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(127) QDPSizeChangeProof (EQUIVALENT)
84.37/50.03	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. 
84.37/50.03	
84.37/50.03	From the DPs we obtained the following set of size-change graphs:
84.37/50.03	*new_primDivNatS(Succ(Succ(vuz130000))) -> new_primDivNatS(vuz130000)
84.37/50.03	The graph contains the following edges 1 > 1
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(128)
84.37/50.03	YES
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(129)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_primMulNat(Succ(vuz7100), Succ(vuz2000)) -> new_primMulNat(vuz7100, Succ(vuz2000))
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(130) QDPSizeChangeProof (EQUIVALENT)
84.37/50.03	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. 
84.37/50.03	
84.37/50.03	From the DPs we obtained the following set of size-change graphs:
84.37/50.03	*new_primMulNat(Succ(vuz7100), Succ(vuz2000)) -> new_primMulNat(vuz7100, Succ(vuz2000))
84.37/50.03	The graph contains the following edges 1 > 1, 2 >= 2
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(131)
84.37/50.03	YES
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(132)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_pr2F0G15(vuz12, vuz13, Succ(Succ(vuz1400)), h) -> new_pr2F0G15(vuz12, vuz13, vuz1400, h)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(133) QDPSizeChangeProof (EQUIVALENT)
84.37/50.03	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. 
84.37/50.03	
84.37/50.03	From the DPs we obtained the following set of size-change graphs:
84.37/50.03	*new_pr2F0G15(vuz12, vuz13, Succ(Succ(vuz1400)), h) -> new_pr2F0G15(vuz12, vuz13, vuz1400, h)
84.37/50.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(134)
84.37/50.03	YES
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(135)
84.37/50.03	Obligation:
84.37/50.03	Q DP problem:
84.37/50.03	The TRS P consists of the following rules:
84.37/50.03	
84.37/50.03	   new_primPlusNat(Succ(vuz4000), Succ(vuz5000)) -> new_primPlusNat(vuz4000, vuz5000)
84.37/50.03	
84.37/50.03	R is empty.
84.37/50.03	Q is empty.
84.37/50.03	We have to consider all minimal (P,Q,R)-chains.
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(136) QDPSizeChangeProof (EQUIVALENT)
84.37/50.03	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. 
84.37/50.03	
84.37/50.03	From the DPs we obtained the following set of size-change graphs:
84.37/50.03	*new_primPlusNat(Succ(vuz4000), Succ(vuz5000)) -> new_primPlusNat(vuz4000, vuz5000)
84.37/50.03	The graph contains the following edges 1 > 1, 2 > 2
84.37/50.03	
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(137)
84.37/50.03	YES
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(138) Narrow (COMPLETE)
84.37/50.03	Haskell To QDPs
84.37/50.03	
84.37/50.03	digraph dp_graph {
84.37/50.03	node [outthreshold=100, inthreshold=100];1[label="(^)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
84.37/50.03	3[label="(^) vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
84.37/50.03	4[label="(^) vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
84.37/50.03	5[label="pr4 vuz3 vuz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
84.37/50.03	6[label="pr3 (vuz4 == fromInt (Pos Zero)) vuz3 vuz4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
84.37/50.03	7[label="pr3 (primEqInt vuz4 (fromInt (Pos Zero))) vuz3 vuz4",fontsize=16,color="burlywood",shape="box"];4738[label="vuz4/Pos vuz40",fontsize=10,color="white",style="solid",shape="box"];7 -> 4738[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4738 -> 8[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4739[label="vuz4/Neg vuz40",fontsize=10,color="white",style="solid",shape="box"];7 -> 4739[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4739 -> 9[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	8[label="pr3 (primEqInt (Pos vuz40) (fromInt (Pos Zero))) vuz3 (Pos vuz40)",fontsize=16,color="burlywood",shape="box"];4740[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];8 -> 4740[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4740 -> 10[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4741[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 4741[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4741 -> 11[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	9[label="pr3 (primEqInt (Neg vuz40) (fromInt (Pos Zero))) vuz3 (Neg vuz40)",fontsize=16,color="burlywood",shape="box"];4742[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 4742[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4742 -> 12[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4743[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 4743[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4743 -> 13[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	10[label="pr3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
84.37/50.03	11[label="pr3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
84.37/50.03	12[label="pr3 (primEqInt (Neg (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
84.37/50.03	13[label="pr3 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
84.37/50.03	14[label="pr3 (primEqInt (Pos (Succ vuz400)) (Pos Zero)) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
84.37/50.03	15[label="pr3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
84.37/50.03	16[label="pr3 (primEqInt (Neg (Succ vuz400)) (Pos Zero)) vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
84.37/50.03	17[label="pr3 (primEqInt (Neg Zero) (Pos Zero)) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
84.37/50.03	18[label="pr3 False vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
84.37/50.03	19[label="pr3 True vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
84.37/50.03	20[label="pr3 False vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
84.37/50.03	21[label="pr3 True vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
84.37/50.03	22[label="pr2 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
84.37/50.03	23[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];23 -> 27[label="",style="solid", color="black", weight=3];
84.37/50.03	24[label="pr2 vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
84.37/50.03	25 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	25[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];26[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (Pos (Succ vuz400) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];26 -> 29[label="",style="solid", color="black", weight=3];
84.37/50.03	27[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];28[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (Neg (Succ vuz400) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
84.37/50.03	29[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (compare (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
84.37/50.03	30[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (compare (Neg (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
84.37/50.03	31[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
84.37/50.03	32[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (primCmpInt (Neg (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
84.37/50.03	33[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
84.37/50.03	34[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (primCmpInt (Neg (Succ vuz400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];34 -> 36[label="",style="solid", color="black", weight=3];
84.37/50.03	35[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpNat (Succ vuz400) Zero == GT)",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
84.37/50.03	36[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) (LT == GT)",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3];
84.37/50.03	37[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (GT == GT)",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
84.37/50.03	38[label="pr2Pr1 vuz3 (Neg (Succ vuz400)) False",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
84.37/50.03	39[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) True",fontsize=16,color="black",shape="box"];39 -> 41[label="",style="solid", color="black", weight=3];
84.37/50.03	40[label="pr0 vuz3 (Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];40 -> 42[label="",style="solid", color="black", weight=3];
84.37/50.03	41 -> 43[label="",style="dashed", color="red", weight=0];
84.37/50.03	41[label="pr2F vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="magenta"];41 -> 44[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	42[label="error []",fontsize=16,color="black",shape="box"];42 -> 45[label="",style="solid", color="black", weight=3];
84.37/50.03	44 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	44[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];43[label="pr2F vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="triangle"];43 -> 46[label="",style="solid", color="black", weight=3];
84.37/50.03	45[label="error []",fontsize=16,color="red",shape="box"];46[label="pr2F4 vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="box"];46 -> 47[label="",style="solid", color="black", weight=3];
84.37/50.03	47[label="pr2F3 (Pos (Succ vuz400) - vuz5 == fromInt (Pos Zero)) vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="box"];47 -> 48[label="",style="solid", color="black", weight=3];
84.37/50.03	48[label="pr2F3 (primEqInt (Pos (Succ vuz400) - vuz5) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400) - vuz5) vuz3",fontsize=16,color="black",shape="box"];48 -> 49[label="",style="solid", color="black", weight=3];
84.37/50.03	49[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) vuz5) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) vuz5) vuz3",fontsize=16,color="burlywood",shape="box"];4744[label="vuz5/Pos vuz50",fontsize=10,color="white",style="solid",shape="box"];49 -> 4744[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4744 -> 50[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4745[label="vuz5/Neg vuz50",fontsize=10,color="white",style="solid",shape="box"];49 -> 4745[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4745 -> 51[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	50[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (Pos vuz50)) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (Pos vuz50)) vuz3",fontsize=16,color="black",shape="box"];50 -> 52[label="",style="solid", color="black", weight=3];
84.37/50.03	51[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (Neg vuz50)) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (Neg vuz50)) vuz3",fontsize=16,color="black",shape="box"];51 -> 53[label="",style="solid", color="black", weight=3];
84.37/50.03	52[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) vuz50) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) vuz50) vuz3",fontsize=16,color="burlywood",shape="box"];4746[label="vuz50/Succ vuz500",fontsize=10,color="white",style="solid",shape="box"];52 -> 4746[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4746 -> 54[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4747[label="vuz50/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 4747[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4747 -> 55[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	53[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz400) vuz50)) (fromInt (Pos Zero))) vuz3 (Pos (primPlusNat (Succ vuz400) vuz50)) vuz3",fontsize=16,color="burlywood",shape="box"];4748[label="vuz50/Succ vuz500",fontsize=10,color="white",style="solid",shape="box"];53 -> 4748[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4748 -> 56[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4749[label="vuz50/Zero",fontsize=10,color="white",style="solid",shape="box"];53 -> 4749[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4749 -> 57[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	54[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) (Succ vuz500)) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) (Succ vuz500)) vuz3",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
84.37/50.03	55[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) Zero) vuz3",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
84.37/50.03	56[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz400) (Succ vuz500))) (fromInt (Pos Zero))) vuz3 (Pos (primPlusNat (Succ vuz400) (Succ vuz500))) vuz3",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
84.37/50.03	57[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz400) Zero)) (fromInt (Pos Zero))) vuz3 (Pos (primPlusNat (Succ vuz400) Zero)) vuz3",fontsize=16,color="black",shape="box"];57 -> 61[label="",style="solid", color="black", weight=3];
84.37/50.03	58[label="pr2F3 (primEqInt (primMinusNat vuz400 vuz500) (fromInt (Pos Zero))) vuz3 (primMinusNat vuz400 vuz500) vuz3",fontsize=16,color="burlywood",shape="triangle"];4750[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];58 -> 4750[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4750 -> 62[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4751[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 4751[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4751 -> 63[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	59[label="pr2F3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="triangle"];59 -> 64[label="",style="solid", color="black", weight=3];
84.37/50.03	60 -> 59[label="",style="dashed", color="red", weight=0];
84.37/50.03	60[label="pr2F3 (primEqInt (Pos (Succ (Succ (primPlusNat vuz400 vuz500)))) (fromInt (Pos Zero))) vuz3 (Pos (Succ (Succ (primPlusNat vuz400 vuz500)))) vuz3",fontsize=16,color="magenta"];60 -> 65[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	61 -> 59[label="",style="dashed", color="red", weight=0];
84.37/50.03	61[label="pr2F3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="magenta"];62[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) vuz500) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) vuz500) vuz3",fontsize=16,color="burlywood",shape="box"];4752[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];62 -> 4752[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4752 -> 66[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4753[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];62 -> 4753[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4753 -> 67[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	63[label="pr2F3 (primEqInt (primMinusNat Zero vuz500) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero vuz500) vuz3",fontsize=16,color="burlywood",shape="box"];4754[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];63 -> 4754[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4754 -> 68[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4755[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];63 -> 4755[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4755 -> 69[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	64[label="pr2F3 (primEqInt (Pos (Succ vuz400)) (Pos Zero)) vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="box"];64 -> 70[label="",style="solid", color="black", weight=3];
84.37/50.03	65[label="Succ (primPlusNat vuz400 vuz500)",fontsize=16,color="green",shape="box"];65 -> 71[label="",style="dashed", color="green", weight=3];
84.37/50.03	66[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) (Succ vuz5000)) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];66 -> 72[label="",style="solid", color="black", weight=3];
84.37/50.03	67[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) Zero) vuz3",fontsize=16,color="black",shape="box"];67 -> 73[label="",style="solid", color="black", weight=3];
84.37/50.03	68[label="pr2F3 (primEqInt (primMinusNat Zero (Succ vuz5000)) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];68 -> 74[label="",style="solid", color="black", weight=3];
84.37/50.03	69[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero Zero) vuz3",fontsize=16,color="black",shape="box"];69 -> 75[label="",style="solid", color="black", weight=3];
84.37/50.03	70[label="pr2F3 False vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="box"];70 -> 76[label="",style="solid", color="black", weight=3];
84.37/50.03	71[label="primPlusNat vuz400 vuz500",fontsize=16,color="burlywood",shape="triangle"];4756[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];71 -> 4756[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4756 -> 77[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4757[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];71 -> 4757[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4757 -> 78[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	72 -> 58[label="",style="dashed", color="red", weight=0];
84.37/50.03	72[label="pr2F3 (primEqInt (primMinusNat vuz4000 vuz5000) (fromInt (Pos Zero))) vuz3 (primMinusNat vuz4000 vuz5000) vuz3",fontsize=16,color="magenta"];72 -> 79[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	72 -> 80[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	73 -> 59[label="",style="dashed", color="red", weight=0];
84.37/50.03	73[label="pr2F3 (primEqInt (Pos (Succ vuz4000)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="magenta"];73 -> 81[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	74[label="pr2F3 (primEqInt (Neg (Succ vuz5000)) (fromInt (Pos Zero))) vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];74 -> 82[label="",style="solid", color="black", weight=3];
84.37/50.03	75[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];75 -> 83[label="",style="solid", color="black", weight=3];
84.37/50.03	76[label="pr2F0 vuz3 (Pos (Succ vuz400)) vuz3",fontsize=16,color="black",shape="box"];76 -> 84[label="",style="solid", color="black", weight=3];
84.37/50.03	77[label="primPlusNat (Succ vuz4000) vuz500",fontsize=16,color="burlywood",shape="box"];4758[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];77 -> 4758[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4758 -> 85[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4759[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];77 -> 4759[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4759 -> 86[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	78[label="primPlusNat Zero vuz500",fontsize=16,color="burlywood",shape="box"];4760[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];78 -> 4760[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4760 -> 87[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4761[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];78 -> 4761[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4761 -> 88[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	79[label="vuz4000",fontsize=16,color="green",shape="box"];80[label="vuz5000",fontsize=16,color="green",shape="box"];81[label="vuz4000",fontsize=16,color="green",shape="box"];82[label="pr2F3 (primEqInt (Neg (Succ vuz5000)) (Pos Zero)) vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];82 -> 89[label="",style="solid", color="black", weight=3];
84.37/50.03	83[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];83 -> 90[label="",style="solid", color="black", weight=3];
84.37/50.03	84[label="pr2F0G vuz3 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];84 -> 91[label="",style="solid", color="black", weight=3];
84.37/50.03	85[label="primPlusNat (Succ vuz4000) (Succ vuz5000)",fontsize=16,color="black",shape="box"];85 -> 92[label="",style="solid", color="black", weight=3];
84.37/50.03	86[label="primPlusNat (Succ vuz4000) Zero",fontsize=16,color="black",shape="box"];86 -> 93[label="",style="solid", color="black", weight=3];
84.37/50.03	87[label="primPlusNat Zero (Succ vuz5000)",fontsize=16,color="black",shape="box"];87 -> 94[label="",style="solid", color="black", weight=3];
84.37/50.03	88[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];88 -> 95[label="",style="solid", color="black", weight=3];
84.37/50.03	89[label="pr2F3 False vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];89 -> 96[label="",style="solid", color="black", weight=3];
84.37/50.03	90[label="pr2F3 True vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];90 -> 97[label="",style="solid", color="black", weight=3];
84.37/50.03	91[label="pr2F0G2 vuz3 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];91 -> 98[label="",style="solid", color="black", weight=3];
84.37/50.03	92[label="Succ (Succ (primPlusNat vuz4000 vuz5000))",fontsize=16,color="green",shape="box"];92 -> 99[label="",style="dashed", color="green", weight=3];
84.37/50.03	93[label="Succ vuz4000",fontsize=16,color="green",shape="box"];94[label="Succ vuz5000",fontsize=16,color="green",shape="box"];95[label="Zero",fontsize=16,color="green",shape="box"];96[label="pr2F0 vuz3 (Neg (Succ vuz5000)) vuz3",fontsize=16,color="black",shape="box"];96 -> 100[label="",style="solid", color="black", weight=3];
84.37/50.03	97[label="vuz3",fontsize=16,color="green",shape="box"];98[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz400)) (even (Pos (Succ vuz400)))",fontsize=16,color="black",shape="box"];98 -> 101[label="",style="solid", color="black", weight=3];
84.37/50.03	99 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	99[label="primPlusNat vuz4000 vuz5000",fontsize=16,color="magenta"];99 -> 102[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	99 -> 103[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	100[label="pr2F0G vuz3 vuz3 (Neg (Succ vuz5000))",fontsize=16,color="black",shape="box"];100 -> 104[label="",style="solid", color="black", weight=3];
84.37/50.03	101[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz400)) (primEvenInt (Pos (Succ vuz400)))",fontsize=16,color="black",shape="box"];101 -> 105[label="",style="solid", color="black", weight=3];
84.37/50.03	102[label="vuz4000",fontsize=16,color="green",shape="box"];103[label="vuz5000",fontsize=16,color="green",shape="box"];104[label="pr2F0G2 vuz3 vuz3 (Neg (Succ vuz5000))",fontsize=16,color="black",shape="box"];104 -> 106[label="",style="solid", color="black", weight=3];
84.37/50.03	105 -> 256[label="",style="dashed", color="red", weight=0];
84.37/50.03	105[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz400)) (primEvenNat (Succ vuz400))",fontsize=16,color="magenta"];105 -> 257[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	105 -> 258[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	105 -> 259[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	106[label="pr2F0G1 vuz3 vuz3 (Neg (Succ vuz5000)) (even (Neg (Succ vuz5000)))",fontsize=16,color="black",shape="box"];106 -> 109[label="",style="solid", color="black", weight=3];
84.37/50.03	257[label="vuz3",fontsize=16,color="green",shape="box"];258[label="vuz400",fontsize=16,color="green",shape="box"];259[label="Succ vuz400",fontsize=16,color="green",shape="box"];256[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat vuz22)",fontsize=16,color="burlywood",shape="triangle"];4762[label="vuz22/Succ vuz220",fontsize=10,color="white",style="solid",shape="box"];256 -> 4762[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4762 -> 275[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4763[label="vuz22/Zero",fontsize=10,color="white",style="solid",shape="box"];256 -> 4763[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4763 -> 276[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	109[label="pr2F0G1 vuz3 vuz3 (Neg (Succ vuz5000)) (primEvenInt (Neg (Succ vuz5000)))",fontsize=16,color="black",shape="box"];109 -> 112[label="",style="solid", color="black", weight=3];
84.37/50.03	275[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat (Succ vuz220))",fontsize=16,color="burlywood",shape="box"];4764[label="vuz220/Succ vuz2200",fontsize=10,color="white",style="solid",shape="box"];275 -> 4764[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4764 -> 279[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4765[label="vuz220/Zero",fontsize=10,color="white",style="solid",shape="box"];275 -> 4765[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4765 -> 280[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	276[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];276 -> 281[label="",style="solid", color="black", weight=3];
84.37/50.03	112 -> 199[label="",style="dashed", color="red", weight=0];
84.37/50.03	112[label="pr2F0G1 vuz3 vuz3 (Neg (Succ vuz5000)) (primEvenNat (Succ vuz5000))",fontsize=16,color="magenta"];112 -> 200[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	112 -> 201[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	112 -> 202[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	279[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat (Succ (Succ vuz2200)))",fontsize=16,color="black",shape="box"];279 -> 284[label="",style="solid", color="black", weight=3];
84.37/50.03	280[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];280 -> 285[label="",style="solid", color="black", weight=3];
84.37/50.03	281[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) True",fontsize=16,color="black",shape="box"];281 -> 286[label="",style="solid", color="black", weight=3];
84.37/50.03	200[label="vuz3",fontsize=16,color="green",shape="box"];201[label="vuz5000",fontsize=16,color="green",shape="box"];202[label="Succ vuz5000",fontsize=16,color="green",shape="box"];199[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat vuz14)",fontsize=16,color="burlywood",shape="triangle"];4766[label="vuz14/Succ vuz140",fontsize=10,color="white",style="solid",shape="box"];199 -> 4766[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4766 -> 212[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4767[label="vuz14/Zero",fontsize=10,color="white",style="solid",shape="box"];199 -> 4767[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4767 -> 213[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	284 -> 256[label="",style="dashed", color="red", weight=0];
84.37/50.03	284[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) (primEvenNat vuz2200)",fontsize=16,color="magenta"];284 -> 289[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	285[label="pr2F0G1 vuz20 vuz20 (Pos (Succ vuz21)) False",fontsize=16,color="black",shape="box"];285 -> 290[label="",style="solid", color="black", weight=3];
84.37/50.03	286[label="pr2F0G vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];286 -> 291[label="",style="solid", color="black", weight=3];
84.37/50.03	212[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat (Succ vuz140))",fontsize=16,color="burlywood",shape="box"];4768[label="vuz140/Succ vuz1400",fontsize=10,color="white",style="solid",shape="box"];212 -> 4768[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4768 -> 216[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4769[label="vuz140/Zero",fontsize=10,color="white",style="solid",shape="box"];212 -> 4769[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4769 -> 217[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	213[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];213 -> 218[label="",style="solid", color="black", weight=3];
84.37/50.03	289[label="vuz2200",fontsize=16,color="green",shape="box"];290[label="pr2F0G0 vuz20 vuz20 (Pos (Succ vuz21)) otherwise",fontsize=16,color="black",shape="box"];290 -> 294[label="",style="solid", color="black", weight=3];
84.37/50.03	291[label="pr2F0G2 vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];291 -> 295[label="",style="solid", color="black", weight=3];
84.37/50.03	216[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat (Succ (Succ vuz1400)))",fontsize=16,color="black",shape="box"];216 -> 227[label="",style="solid", color="black", weight=3];
84.37/50.03	217[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];217 -> 228[label="",style="solid", color="black", weight=3];
84.37/50.03	218[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) True",fontsize=16,color="black",shape="box"];218 -> 229[label="",style="solid", color="black", weight=3];
84.37/50.03	294[label="pr2F0G0 vuz20 vuz20 (Pos (Succ vuz21)) True",fontsize=16,color="black",shape="box"];294 -> 298[label="",style="solid", color="black", weight=3];
84.37/50.03	295[label="pr2F0G1 vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];295 -> 299[label="",style="solid", color="black", weight=3];
84.37/50.03	227 -> 199[label="",style="dashed", color="red", weight=0];
84.37/50.03	227[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) (primEvenNat vuz1400)",fontsize=16,color="magenta"];227 -> 237[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	228[label="pr2F0G1 vuz12 vuz12 (Neg (Succ vuz13)) False",fontsize=16,color="black",shape="box"];228 -> 238[label="",style="solid", color="black", weight=3];
84.37/50.03	229[label="pr2F0G vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];229 -> 239[label="",style="solid", color="black", weight=3];
84.37/50.03	298 -> 302[label="",style="dashed", color="red", weight=0];
84.37/50.03	298[label="pr2F vuz20 (Pos (Succ vuz21) - fromInt (Pos (Succ Zero))) (vuz20 * vuz20)",fontsize=16,color="magenta"];298 -> 303[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	299[label="pr2F0G1 vuz20 (vuz20 * vuz20) (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz21) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];299 -> 304[label="",style="solid", color="black", weight=3];
84.37/50.03	237[label="vuz1400",fontsize=16,color="green",shape="box"];238[label="pr2F0G0 vuz12 vuz12 (Neg (Succ vuz13)) otherwise",fontsize=16,color="black",shape="box"];238 -> 253[label="",style="solid", color="black", weight=3];
84.37/50.03	239[label="pr2F0G2 vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];239 -> 254[label="",style="solid", color="black", weight=3];
84.37/50.03	303 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	303[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];302[label="pr2F vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="black",shape="triangle"];302 -> 305[label="",style="solid", color="black", weight=3];
84.37/50.03	304[label="pr2F0G1 vuz20 (vuz20 * vuz20) (primQuotInt (Pos (Succ vuz21)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz21)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];304 -> 309[label="",style="solid", color="black", weight=3];
84.37/50.03	253[label="pr2F0G0 vuz12 vuz12 (Neg (Succ vuz13)) True",fontsize=16,color="black",shape="box"];253 -> 277[label="",style="solid", color="black", weight=3];
84.37/50.03	254[label="pr2F0G1 vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];254 -> 278[label="",style="solid", color="black", weight=3];
84.37/50.03	305[label="pr2F4 vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="black",shape="box"];305 -> 310[label="",style="solid", color="black", weight=3];
84.37/50.03	309[label="pr2F0G1 vuz20 (vuz20 * vuz20) (primQuotInt (Pos (Succ vuz21)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz21)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];309 -> 315[label="",style="solid", color="black", weight=3];
84.37/50.03	277 -> 282[label="",style="dashed", color="red", weight=0];
84.37/50.03	277[label="pr2F vuz12 (Neg (Succ vuz13) - fromInt (Pos (Succ Zero))) (vuz12 * vuz12)",fontsize=16,color="magenta"];277 -> 283[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	278[label="pr2F0G1 vuz12 (vuz12 * vuz12) (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg (Succ vuz13) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];278 -> 287[label="",style="solid", color="black", weight=3];
84.37/50.03	310[label="pr2F3 (Pos (Succ vuz21) - vuz24 == fromInt (Pos Zero)) vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="black",shape="box"];310 -> 316[label="",style="solid", color="black", weight=3];
84.37/50.03	315 -> 1605[label="",style="dashed", color="red", weight=0];
84.37/50.03	315[label="pr2F0G1 vuz20 (vuz20 * vuz20) (Pos (primDivNatS (Succ vuz21) (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS (Succ vuz21) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];315 -> 1606[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	315 -> 1607[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	315 -> 1608[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	315 -> 1609[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	283 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	283[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];282[label="pr2F vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="black",shape="triangle"];282 -> 288[label="",style="solid", color="black", weight=3];
84.37/50.03	287[label="pr2F0G1 vuz12 (vuz12 * vuz12) (primQuotInt (Neg (Succ vuz13)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg (Succ vuz13)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];287 -> 292[label="",style="solid", color="black", weight=3];
84.37/50.03	316 -> 3789[label="",style="dashed", color="red", weight=0];
84.37/50.03	316[label="pr2F3 (primEqInt (Pos (Succ vuz21) - vuz24) (fromInt (Pos Zero))) vuz20 (Pos (Succ vuz21) - vuz24) (vuz20 * vuz20)",fontsize=16,color="magenta"];316 -> 3790[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	316 -> 3791[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	316 -> 3792[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	316 -> 3793[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1606[label="vuz20",fontsize=16,color="green",shape="box"];1607 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1607[label="primDivNatS (Succ vuz21) (Succ (Succ Zero))",fontsize=16,color="magenta"];1607 -> 1624[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1608[label="vuz20",fontsize=16,color="green",shape="box"];1609 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1609[label="primDivNatS (Succ vuz21) (Succ (Succ Zero))",fontsize=16,color="magenta"];1609 -> 1625[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1605[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenInt (Pos vuz106))",fontsize=16,color="black",shape="triangle"];1605 -> 1626[label="",style="solid", color="black", weight=3];
84.37/50.03	288[label="pr2F4 vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="black",shape="box"];288 -> 293[label="",style="solid", color="black", weight=3];
84.37/50.03	292[label="pr2F0G1 vuz12 (vuz12 * vuz12) (primQuotInt (Neg (Succ vuz13)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg (Succ vuz13)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];292 -> 296[label="",style="solid", color="black", weight=3];
84.37/50.03	3790[label="vuz20",fontsize=16,color="green",shape="box"];3791[label="vuz21",fontsize=16,color="green",shape="box"];3792[label="vuz20",fontsize=16,color="green",shape="box"];3793[label="vuz24",fontsize=16,color="green",shape="box"];3789[label="pr2F3 (primEqInt (Pos (Succ vuz202) - vuz203) (fromInt (Pos Zero))) vuz204 (Pos (Succ vuz202) - vuz203) (vuz204 * vuz205)",fontsize=16,color="black",shape="triangle"];3789 -> 3814[label="",style="solid", color="black", weight=3];
84.37/50.03	1624[label="Succ vuz21",fontsize=16,color="green",shape="box"];1222[label="primDivNatS vuz55 (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];4770[label="vuz55/Succ vuz550",fontsize=10,color="white",style="solid",shape="box"];1222 -> 4770[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4770 -> 1237[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4771[label="vuz55/Zero",fontsize=10,color="white",style="solid",shape="box"];1222 -> 4771[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4771 -> 1238[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1625[label="Succ vuz21",fontsize=16,color="green",shape="box"];1626[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat vuz106)",fontsize=16,color="burlywood",shape="triangle"];4772[label="vuz106/Succ vuz1060",fontsize=10,color="white",style="solid",shape="box"];1626 -> 4772[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4772 -> 1659[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4773[label="vuz106/Zero",fontsize=10,color="white",style="solid",shape="box"];1626 -> 4773[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4773 -> 1660[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	293[label="pr2F3 (Neg (Succ vuz13) - vuz23 == fromInt (Pos Zero)) vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="black",shape="box"];293 -> 297[label="",style="solid", color="black", weight=3];
84.37/50.03	296 -> 1755[label="",style="dashed", color="red", weight=0];
84.37/50.03	296[label="pr2F0G1 vuz12 (vuz12 * vuz12) (Neg (primDivNatS (Succ vuz13) (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS (Succ vuz13) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];296 -> 1756[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	296 -> 1757[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	296 -> 1758[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	296 -> 1759[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	3814[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz202)) vuz203) (fromInt (Pos Zero))) vuz204 (primMinusInt (Pos (Succ vuz202)) vuz203) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4774[label="vuz203/Pos vuz2030",fontsize=10,color="white",style="solid",shape="box"];3814 -> 4774[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4774 -> 3843[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4775[label="vuz203/Neg vuz2030",fontsize=10,color="white",style="solid",shape="box"];3814 -> 4775[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4775 -> 3844[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1237[label="primDivNatS (Succ vuz550) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1237 -> 1285[label="",style="solid", color="black", weight=3];
84.37/50.03	1238[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1238 -> 1286[label="",style="solid", color="black", weight=3];
84.37/50.03	1659[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat (Succ vuz1060))",fontsize=16,color="burlywood",shape="box"];4776[label="vuz1060/Succ vuz10600",fontsize=10,color="white",style="solid",shape="box"];1659 -> 4776[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4776 -> 1713[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4777[label="vuz1060/Zero",fontsize=10,color="white",style="solid",shape="box"];1659 -> 4777[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4777 -> 1714[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1660[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];1660 -> 1715[label="",style="solid", color="black", weight=3];
84.37/50.03	297 -> 4256[label="",style="dashed", color="red", weight=0];
84.37/50.03	297[label="pr2F3 (primEqInt (Neg (Succ vuz13) - vuz23) (fromInt (Pos Zero))) vuz12 (Neg (Succ vuz13) - vuz23) (vuz12 * vuz12)",fontsize=16,color="magenta"];297 -> 4257[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	297 -> 4258[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	297 -> 4259[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	297 -> 4260[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1756 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1756[label="primDivNatS (Succ vuz13) (Succ (Succ Zero))",fontsize=16,color="magenta"];1756 -> 1770[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1757 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1757[label="primDivNatS (Succ vuz13) (Succ (Succ Zero))",fontsize=16,color="magenta"];1757 -> 1771[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1758[label="vuz12",fontsize=16,color="green",shape="box"];1759[label="vuz12",fontsize=16,color="green",shape="box"];1755[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenInt (Neg vuz114))",fontsize=16,color="black",shape="triangle"];1755 -> 1772[label="",style="solid", color="black", weight=3];
84.37/50.03	3843[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz202)) (Pos vuz2030)) (fromInt (Pos Zero))) vuz204 (primMinusInt (Pos (Succ vuz202)) (Pos vuz2030)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];3843 -> 3919[label="",style="solid", color="black", weight=3];
84.37/50.03	3844[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz202)) (Neg vuz2030)) (fromInt (Pos Zero))) vuz204 (primMinusInt (Pos (Succ vuz202)) (Neg vuz2030)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];3844 -> 3920[label="",style="solid", color="black", weight=3];
84.37/50.03	1285 -> 562[label="",style="dashed", color="red", weight=0];
84.37/50.03	1285[label="primDivNatS0 vuz550 (Succ Zero) (primGEqNatS vuz550 (Succ Zero))",fontsize=16,color="magenta"];1285 -> 1313[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1286[label="Zero",fontsize=16,color="green",shape="box"];1713[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat (Succ (Succ vuz10600)))",fontsize=16,color="black",shape="box"];1713 -> 1773[label="",style="solid", color="black", weight=3];
84.37/50.03	1714[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];1714 -> 1774[label="",style="solid", color="black", weight=3];
84.37/50.03	1715[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) True",fontsize=16,color="black",shape="box"];1715 -> 1775[label="",style="solid", color="black", weight=3];
84.37/50.03	4257[label="vuz13",fontsize=16,color="green",shape="box"];4258[label="vuz12",fontsize=16,color="green",shape="box"];4259[label="vuz12",fontsize=16,color="green",shape="box"];4260[label="vuz23",fontsize=16,color="green",shape="box"];4256[label="pr2F3 (primEqInt (Neg (Succ vuz214) - vuz215) (fromInt (Pos Zero))) vuz216 (Neg (Succ vuz214) - vuz215) (vuz216 * vuz217)",fontsize=16,color="black",shape="triangle"];4256 -> 4281[label="",style="solid", color="black", weight=3];
84.37/50.03	1770[label="Succ vuz13",fontsize=16,color="green",shape="box"];1771[label="Succ vuz13",fontsize=16,color="green",shape="box"];1772[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat vuz114)",fontsize=16,color="burlywood",shape="triangle"];4778[label="vuz114/Succ vuz1140",fontsize=10,color="white",style="solid",shape="box"];1772 -> 4778[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4778 -> 1793[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4779[label="vuz114/Zero",fontsize=10,color="white",style="solid",shape="box"];1772 -> 4779[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4779 -> 1794[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	3919[label="pr2F3 (primEqInt (primMinusNat (Succ vuz202) vuz2030) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz202) vuz2030) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4780[label="vuz2030/Succ vuz20300",fontsize=10,color="white",style="solid",shape="box"];3919 -> 4780[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4780 -> 4005[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4781[label="vuz2030/Zero",fontsize=10,color="white",style="solid",shape="box"];3919 -> 4781[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4781 -> 4006[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	3920 -> 4007[label="",style="dashed", color="red", weight=0];
84.37/50.03	3920[label="pr2F3 (primEqInt (Pos (primPlusNat (Succ vuz202) vuz2030)) (fromInt (Pos Zero))) vuz204 (Pos (primPlusNat (Succ vuz202) vuz2030)) (vuz204 * vuz205)",fontsize=16,color="magenta"];3920 -> 4008[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	3920 -> 4009[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1313[label="vuz550",fontsize=16,color="green",shape="box"];562[label="primDivNatS0 vuz1300 (Succ Zero) (primGEqNatS vuz1300 (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];4782[label="vuz1300/Succ vuz13000",fontsize=10,color="white",style="solid",shape="box"];562 -> 4782[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4782 -> 570[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4783[label="vuz1300/Zero",fontsize=10,color="white",style="solid",shape="box"];562 -> 4783[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4783 -> 571[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1773 -> 1626[label="",style="dashed", color="red", weight=0];
84.37/50.03	1773[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) (primEvenNat vuz10600)",fontsize=16,color="magenta"];1773 -> 1795[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1774[label="pr2F0G1 vuz102 (vuz103 * vuz103) (Pos vuz105) False",fontsize=16,color="black",shape="box"];1774 -> 1796[label="",style="solid", color="black", weight=3];
84.37/50.03	1775[label="pr2F0G vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1775 -> 1797[label="",style="solid", color="black", weight=3];
84.37/50.03	4281[label="pr2F3 (primEqInt (primMinusInt (Neg (Succ vuz214)) vuz215) (fromInt (Pos Zero))) vuz216 (primMinusInt (Neg (Succ vuz214)) vuz215) (vuz216 * vuz217)",fontsize=16,color="burlywood",shape="box"];4784[label="vuz215/Pos vuz2150",fontsize=10,color="white",style="solid",shape="box"];4281 -> 4784[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4784 -> 4288[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4785[label="vuz215/Neg vuz2150",fontsize=10,color="white",style="solid",shape="box"];4281 -> 4785[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4785 -> 4289[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1793[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat (Succ vuz1140))",fontsize=16,color="burlywood",shape="box"];4786[label="vuz1140/Succ vuz11400",fontsize=10,color="white",style="solid",shape="box"];1793 -> 4786[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4786 -> 1807[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4787[label="vuz1140/Zero",fontsize=10,color="white",style="solid",shape="box"];1793 -> 4787[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4787 -> 1808[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1794[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];1794 -> 1809[label="",style="solid", color="black", weight=3];
84.37/50.03	4005[label="pr2F3 (primEqInt (primMinusNat (Succ vuz202) (Succ vuz20300)) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz202) (Succ vuz20300)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4005 -> 4086[label="",style="solid", color="black", weight=3];
84.37/50.03	4006[label="pr2F3 (primEqInt (primMinusNat (Succ vuz202) Zero) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz202) Zero) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4006 -> 4087[label="",style="solid", color="black", weight=3];
84.37/50.03	4008 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4008[label="primPlusNat (Succ vuz202) vuz2030",fontsize=16,color="magenta"];4008 -> 4088[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4008 -> 4089[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4009 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4009[label="primPlusNat (Succ vuz202) vuz2030",fontsize=16,color="magenta"];4009 -> 4090[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4009 -> 4091[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4007[label="pr2F3 (primEqInt (Pos vuz212) (fromInt (Pos Zero))) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="triangle"];4788[label="vuz212/Succ vuz2120",fontsize=10,color="white",style="solid",shape="box"];4007 -> 4788[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4788 -> 4092[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4789[label="vuz212/Zero",fontsize=10,color="white",style="solid",shape="box"];4007 -> 4789[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4789 -> 4093[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	570[label="primDivNatS0 (Succ vuz13000) (Succ Zero) (primGEqNatS (Succ vuz13000) (Succ Zero))",fontsize=16,color="black",shape="box"];570 -> 584[label="",style="solid", color="black", weight=3];
84.37/50.03	571[label="primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero))",fontsize=16,color="black",shape="box"];571 -> 585[label="",style="solid", color="black", weight=3];
84.37/50.03	1795[label="vuz10600",fontsize=16,color="green",shape="box"];1796[label="pr2F0G0 vuz102 (vuz103 * vuz103) (Pos vuz105) otherwise",fontsize=16,color="black",shape="box"];1796 -> 1810[label="",style="solid", color="black", weight=3];
84.37/50.03	1797[label="pr2F0G2 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1797 -> 1811[label="",style="solid", color="black", weight=3];
84.37/50.03	4288[label="pr2F3 (primEqInt (primMinusInt (Neg (Succ vuz214)) (Pos vuz2150)) (fromInt (Pos Zero))) vuz216 (primMinusInt (Neg (Succ vuz214)) (Pos vuz2150)) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4288 -> 4296[label="",style="solid", color="black", weight=3];
84.37/50.03	4289[label="pr2F3 (primEqInt (primMinusInt (Neg (Succ vuz214)) (Neg vuz2150)) (fromInt (Pos Zero))) vuz216 (primMinusInt (Neg (Succ vuz214)) (Neg vuz2150)) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4289 -> 4297[label="",style="solid", color="black", weight=3];
84.37/50.03	1807[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat (Succ (Succ vuz11400)))",fontsize=16,color="black",shape="box"];1807 -> 1817[label="",style="solid", color="black", weight=3];
84.37/50.03	1808[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];1808 -> 1818[label="",style="solid", color="black", weight=3];
84.37/50.03	1809[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) True",fontsize=16,color="black",shape="box"];1809 -> 1819[label="",style="solid", color="black", weight=3];
84.37/50.03	4086[label="pr2F3 (primEqInt (primMinusNat vuz202 vuz20300) (fromInt (Pos Zero))) vuz204 (primMinusNat vuz202 vuz20300) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="triangle"];4790[label="vuz202/Succ vuz2020",fontsize=10,color="white",style="solid",shape="box"];4086 -> 4790[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4790 -> 4165[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4791[label="vuz202/Zero",fontsize=10,color="white",style="solid",shape="box"];4086 -> 4791[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4791 -> 4166[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4087 -> 4007[label="",style="dashed", color="red", weight=0];
84.37/50.03	4087[label="pr2F3 (primEqInt (Pos (Succ vuz202)) (fromInt (Pos Zero))) vuz204 (Pos (Succ vuz202)) (vuz204 * vuz205)",fontsize=16,color="magenta"];4087 -> 4167[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4087 -> 4168[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4088[label="Succ vuz202",fontsize=16,color="green",shape="box"];4089[label="vuz2030",fontsize=16,color="green",shape="box"];4090[label="Succ vuz202",fontsize=16,color="green",shape="box"];4091[label="vuz2030",fontsize=16,color="green",shape="box"];4092[label="pr2F3 (primEqInt (Pos (Succ vuz2120)) (fromInt (Pos Zero))) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4092 -> 4169[label="",style="solid", color="black", weight=3];
84.37/50.03	4093[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4093 -> 4170[label="",style="solid", color="black", weight=3];
84.37/50.03	584[label="primDivNatS0 (Succ vuz13000) (Succ Zero) (primGEqNatS vuz13000 Zero)",fontsize=16,color="burlywood",shape="box"];4792[label="vuz13000/Succ vuz130000",fontsize=10,color="white",style="solid",shape="box"];584 -> 4792[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4792 -> 606[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4793[label="vuz13000/Zero",fontsize=10,color="white",style="solid",shape="box"];584 -> 4793[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4793 -> 607[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	585[label="primDivNatS0 Zero (Succ Zero) False",fontsize=16,color="black",shape="box"];585 -> 608[label="",style="solid", color="black", weight=3];
84.37/50.03	1810[label="pr2F0G0 vuz102 (vuz103 * vuz103) (Pos vuz105) True",fontsize=16,color="black",shape="box"];1810 -> 1820[label="",style="solid", color="black", weight=3];
84.37/50.03	1811[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1811 -> 1821[label="",style="solid", color="black", weight=3];
84.37/50.03	4296 -> 4311[label="",style="dashed", color="red", weight=0];
84.37/50.03	4296[label="pr2F3 (primEqInt (Neg (primPlusNat (Succ vuz214) vuz2150)) (fromInt (Pos Zero))) vuz216 (Neg (primPlusNat (Succ vuz214) vuz2150)) (vuz216 * vuz217)",fontsize=16,color="magenta"];4296 -> 4312[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4296 -> 4313[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4297 -> 4086[label="",style="dashed", color="red", weight=0];
84.37/50.03	4297[label="pr2F3 (primEqInt (primMinusNat vuz2150 (Succ vuz214)) (fromInt (Pos Zero))) vuz216 (primMinusNat vuz2150 (Succ vuz214)) (vuz216 * vuz217)",fontsize=16,color="magenta"];4297 -> 4330[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4297 -> 4331[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4297 -> 4332[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4297 -> 4333[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1817 -> 1772[label="",style="dashed", color="red", weight=0];
84.37/50.03	1817[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) (primEvenNat vuz11400)",fontsize=16,color="magenta"];1817 -> 1829[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1818[label="pr2F0G1 vuz110 (vuz111 * vuz111) (Neg vuz113) False",fontsize=16,color="black",shape="box"];1818 -> 1830[label="",style="solid", color="black", weight=3];
84.37/50.03	1819[label="pr2F0G vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1819 -> 1831[label="",style="solid", color="black", weight=3];
84.37/50.03	4165[label="pr2F3 (primEqInt (primMinusNat (Succ vuz2020) vuz20300) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz2020) vuz20300) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4794[label="vuz20300/Succ vuz203000",fontsize=10,color="white",style="solid",shape="box"];4165 -> 4794[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4794 -> 4282[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4795[label="vuz20300/Zero",fontsize=10,color="white",style="solid",shape="box"];4165 -> 4795[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4795 -> 4283[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4166[label="pr2F3 (primEqInt (primMinusNat Zero vuz20300) (fromInt (Pos Zero))) vuz204 (primMinusNat Zero vuz20300) (vuz204 * vuz205)",fontsize=16,color="burlywood",shape="box"];4796[label="vuz20300/Succ vuz203000",fontsize=10,color="white",style="solid",shape="box"];4166 -> 4796[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4796 -> 4284[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4797[label="vuz20300/Zero",fontsize=10,color="white",style="solid",shape="box"];4166 -> 4797[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4797 -> 4285[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4167[label="Succ vuz202",fontsize=16,color="green",shape="box"];4168[label="Succ vuz202",fontsize=16,color="green",shape="box"];4169[label="pr2F3 (primEqInt (Pos (Succ vuz2120)) (Pos Zero)) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4169 -> 4286[label="",style="solid", color="black", weight=3];
84.37/50.03	4170[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4170 -> 4287[label="",style="solid", color="black", weight=3];
84.37/50.03	606[label="primDivNatS0 (Succ (Succ vuz130000)) (Succ Zero) (primGEqNatS (Succ vuz130000) Zero)",fontsize=16,color="black",shape="box"];606 -> 619[label="",style="solid", color="black", weight=3];
84.37/50.03	607[label="primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];607 -> 620[label="",style="solid", color="black", weight=3];
84.37/50.03	608[label="Zero",fontsize=16,color="green",shape="box"];1820 -> 1832[label="",style="dashed", color="red", weight=0];
84.37/50.03	1820[label="pr2F (vuz103 * vuz103) (Pos vuz105 - fromInt (Pos (Succ Zero))) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1820 -> 1833[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1821[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos vuz105 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1821 -> 1834[label="",style="solid", color="black", weight=3];
84.37/50.03	4312 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4312[label="primPlusNat (Succ vuz214) vuz2150",fontsize=16,color="magenta"];4312 -> 4334[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4312 -> 4335[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4313 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4313[label="primPlusNat (Succ vuz214) vuz2150",fontsize=16,color="magenta"];4313 -> 4336[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4313 -> 4337[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4311[label="pr2F3 (primEqInt (Neg vuz219) (fromInt (Pos Zero))) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="burlywood",shape="triangle"];4798[label="vuz219/Succ vuz2190",fontsize=10,color="white",style="solid",shape="box"];4311 -> 4798[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4798 -> 4338[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4799[label="vuz219/Zero",fontsize=10,color="white",style="solid",shape="box"];4311 -> 4799[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4799 -> 4339[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4330[label="vuz216",fontsize=16,color="green",shape="box"];4331[label="vuz2150",fontsize=16,color="green",shape="box"];4332[label="vuz217",fontsize=16,color="green",shape="box"];4333[label="Succ vuz214",fontsize=16,color="green",shape="box"];1829[label="vuz11400",fontsize=16,color="green",shape="box"];1830[label="pr2F0G0 vuz110 (vuz111 * vuz111) (Neg vuz113) otherwise",fontsize=16,color="black",shape="box"];1830 -> 1835[label="",style="solid", color="black", weight=3];
84.37/50.03	1831[label="pr2F0G2 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1831 -> 1836[label="",style="solid", color="black", weight=3];
84.37/50.03	4282[label="pr2F3 (primEqInt (primMinusNat (Succ vuz2020) (Succ vuz203000)) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz2020) (Succ vuz203000)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4282 -> 4290[label="",style="solid", color="black", weight=3];
84.37/50.03	4283[label="pr2F3 (primEqInt (primMinusNat (Succ vuz2020) Zero) (fromInt (Pos Zero))) vuz204 (primMinusNat (Succ vuz2020) Zero) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4283 -> 4291[label="",style="solid", color="black", weight=3];
84.37/50.03	4284[label="pr2F3 (primEqInt (primMinusNat Zero (Succ vuz203000)) (fromInt (Pos Zero))) vuz204 (primMinusNat Zero (Succ vuz203000)) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4284 -> 4292[label="",style="solid", color="black", weight=3];
84.37/50.03	4285[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz204 (primMinusNat Zero Zero) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4285 -> 4293[label="",style="solid", color="black", weight=3];
84.37/50.03	4286[label="pr2F3 False vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4286 -> 4294[label="",style="solid", color="black", weight=3];
84.37/50.03	4287[label="pr2F3 True vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4287 -> 4295[label="",style="solid", color="black", weight=3];
84.37/50.03	619[label="primDivNatS0 (Succ (Succ vuz130000)) (Succ Zero) True",fontsize=16,color="black",shape="box"];619 -> 645[label="",style="solid", color="black", weight=3];
84.37/50.03	620[label="primDivNatS0 (Succ Zero) (Succ Zero) True",fontsize=16,color="black",shape="box"];620 -> 646[label="",style="solid", color="black", weight=3];
84.37/50.03	1833 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	1833[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];1832[label="pr2F (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="triangle"];1832 -> 1837[label="",style="solid", color="black", weight=3];
84.37/50.03	1834[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (primQuotInt (Pos vuz105) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos vuz105) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1834 -> 1846[label="",style="solid", color="black", weight=3];
84.37/50.03	4334[label="Succ vuz214",fontsize=16,color="green",shape="box"];4335[label="vuz2150",fontsize=16,color="green",shape="box"];4336[label="Succ vuz214",fontsize=16,color="green",shape="box"];4337[label="vuz2150",fontsize=16,color="green",shape="box"];4338[label="pr2F3 (primEqInt (Neg (Succ vuz2190)) (fromInt (Pos Zero))) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4338 -> 4365[label="",style="solid", color="black", weight=3];
84.37/50.03	4339[label="pr2F3 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4339 -> 4366[label="",style="solid", color="black", weight=3];
84.37/50.03	1835[label="pr2F0G0 vuz110 (vuz111 * vuz111) (Neg vuz113) True",fontsize=16,color="black",shape="box"];1835 -> 1847[label="",style="solid", color="black", weight=3];
84.37/50.03	1836[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1836 -> 1848[label="",style="solid", color="black", weight=3];
84.37/50.03	4290 -> 4086[label="",style="dashed", color="red", weight=0];
84.37/50.03	4290[label="pr2F3 (primEqInt (primMinusNat vuz2020 vuz203000) (fromInt (Pos Zero))) vuz204 (primMinusNat vuz2020 vuz203000) (vuz204 * vuz205)",fontsize=16,color="magenta"];4290 -> 4298[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4290 -> 4299[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4291 -> 4007[label="",style="dashed", color="red", weight=0];
84.37/50.03	4291[label="pr2F3 (primEqInt (Pos (Succ vuz2020)) (fromInt (Pos Zero))) vuz204 (Pos (Succ vuz2020)) (vuz204 * vuz205)",fontsize=16,color="magenta"];4291 -> 4300[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4291 -> 4301[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4292 -> 4311[label="",style="dashed", color="red", weight=0];
84.37/50.03	4292[label="pr2F3 (primEqInt (Neg (Succ vuz203000)) (fromInt (Pos Zero))) vuz204 (Neg (Succ vuz203000)) (vuz204 * vuz205)",fontsize=16,color="magenta"];4292 -> 4314[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4292 -> 4315[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4292 -> 4316[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4292 -> 4317[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4293 -> 4007[label="",style="dashed", color="red", weight=0];
84.37/50.03	4293[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz204 (Pos Zero) (vuz204 * vuz205)",fontsize=16,color="magenta"];4293 -> 4303[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4293 -> 4304[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4294[label="pr2F0 vuz204 (Pos vuz211) (vuz204 * vuz205)",fontsize=16,color="black",shape="box"];4294 -> 4305[label="",style="solid", color="black", weight=3];
84.37/50.03	4295[label="vuz204 * vuz205",fontsize=16,color="blue",shape="box"];4800[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4800[label="",style="solid", color="blue", weight=9];
84.37/50.03	4800 -> 4306[label="",style="solid", color="blue", weight=3];
84.37/50.03	4801[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4801[label="",style="solid", color="blue", weight=9];
84.37/50.03	4801 -> 4307[label="",style="solid", color="blue", weight=3];
84.37/50.03	4802[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4802[label="",style="solid", color="blue", weight=9];
84.37/50.03	4802 -> 4308[label="",style="solid", color="blue", weight=3];
84.37/50.03	4803[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4803[label="",style="solid", color="blue", weight=9];
84.37/50.03	4803 -> 4309[label="",style="solid", color="blue", weight=3];
84.37/50.03	4804[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4295 -> 4804[label="",style="solid", color="blue", weight=9];
84.37/50.03	4804 -> 4310[label="",style="solid", color="blue", weight=3];
84.37/50.03	645[label="Succ (primDivNatS (primMinusNatS (Succ (Succ vuz130000)) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];645 -> 673[label="",style="dashed", color="green", weight=3];
84.37/50.03	646[label="Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];646 -> 674[label="",style="dashed", color="green", weight=3];
84.37/50.03	1837[label="pr2F4 (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1837 -> 1849[label="",style="solid", color="black", weight=3];
84.37/50.03	1846[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (primQuotInt (Pos vuz105) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos vuz105) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1846 -> 1859[label="",style="solid", color="black", weight=3];
84.37/50.03	4365[label="pr2F3 (primEqInt (Neg (Succ vuz2190)) (Pos Zero)) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4365 -> 4378[label="",style="solid", color="black", weight=3];
84.37/50.03	4366[label="pr2F3 (primEqInt (Neg Zero) (Pos Zero)) vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4366 -> 4379[label="",style="solid", color="black", weight=3];
84.37/50.03	1847 -> 1860[label="",style="dashed", color="red", weight=0];
84.37/50.03	1847[label="pr2F (vuz111 * vuz111) (Neg vuz113 - fromInt (Pos (Succ Zero))) (vuz111 * vuz111 * vuz110)",fontsize=16,color="magenta"];1847 -> 1861[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1848[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg vuz113 `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1848 -> 1862[label="",style="solid", color="black", weight=3];
84.37/50.03	4298[label="vuz2020",fontsize=16,color="green",shape="box"];4299[label="vuz203000",fontsize=16,color="green",shape="box"];4300[label="Succ vuz2020",fontsize=16,color="green",shape="box"];4301[label="Succ vuz2020",fontsize=16,color="green",shape="box"];4314[label="vuz204",fontsize=16,color="green",shape="box"];4315[label="Succ vuz203000",fontsize=16,color="green",shape="box"];4316[label="Succ vuz203000",fontsize=16,color="green",shape="box"];4317[label="vuz205",fontsize=16,color="green",shape="box"];4303[label="Zero",fontsize=16,color="green",shape="box"];4304[label="Zero",fontsize=16,color="green",shape="box"];4305[label="pr2F0G (vuz204 * vuz205) vuz204 (Pos vuz211)",fontsize=16,color="black",shape="box"];4305 -> 4340[label="",style="solid", color="black", weight=3];
84.37/50.03	4306 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4306[label="vuz204 * vuz205",fontsize=16,color="magenta"];4306 -> 4341[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4306 -> 4342[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4307 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4307[label="vuz204 * vuz205",fontsize=16,color="magenta"];4307 -> 4343[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4307 -> 4344[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4308 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4308[label="vuz204 * vuz205",fontsize=16,color="magenta"];4308 -> 4345[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4308 -> 4346[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4309 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4309[label="vuz204 * vuz205",fontsize=16,color="magenta"];4309 -> 4347[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4309 -> 4348[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4310 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4310[label="vuz204 * vuz205",fontsize=16,color="magenta"];4310 -> 4349[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4310 -> 4350[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	673 -> 508[label="",style="dashed", color="red", weight=0];
84.37/50.03	673[label="primDivNatS (primMinusNatS (Succ (Succ vuz130000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];673 -> 739[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	674 -> 510[label="",style="dashed", color="red", weight=0];
84.37/50.03	674[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1849[label="pr2F3 (Pos vuz105 - vuz115 == fromInt (Pos Zero)) (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1849 -> 1863[label="",style="solid", color="black", weight=3];
84.37/50.03	1859 -> 1605[label="",style="dashed", color="red", weight=0];
84.37/50.03	1859[label="pr2F0G1 vuz102 (vuz103 * vuz103 * (vuz103 * vuz103)) (Pos (primDivNatS vuz105 (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS vuz105 (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1859 -> 1864[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1859 -> 1865[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1859 -> 1866[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4378[label="pr2F3 False vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4378 -> 4381[label="",style="solid", color="black", weight=3];
84.37/50.03	4379[label="pr2F3 True vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4379 -> 4382[label="",style="solid", color="black", weight=3];
84.37/50.03	1861 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	1861[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];1860[label="pr2F (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="triangle"];1860 -> 1867[label="",style="solid", color="black", weight=3];
84.37/50.03	1862[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (primQuotInt (Neg vuz113) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg vuz113) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1862 -> 1874[label="",style="solid", color="black", weight=3];
84.37/50.03	4340[label="pr2F0G2 (vuz204 * vuz205) vuz204 (Pos vuz211)",fontsize=16,color="black",shape="box"];4340 -> 4367[label="",style="solid", color="black", weight=3];
84.37/50.03	4341[label="vuz204",fontsize=16,color="green",shape="box"];4342[label="vuz205",fontsize=16,color="green",shape="box"];1024[label="vuz69 * vuz20",fontsize=16,color="black",shape="triangle"];1024 -> 1029[label="",style="solid", color="black", weight=3];
84.37/50.03	4343[label="vuz204",fontsize=16,color="green",shape="box"];4344[label="vuz205",fontsize=16,color="green",shape="box"];1041[label="vuz70 * vuz20",fontsize=16,color="black",shape="triangle"];1041 -> 1046[label="",style="solid", color="black", weight=3];
84.37/50.03	4345[label="vuz205",fontsize=16,color="green",shape="box"];4346[label="vuz204",fontsize=16,color="green",shape="box"];1051[label="vuz71 * vuz20",fontsize=16,color="black",shape="triangle"];1051 -> 1056[label="",style="solid", color="black", weight=3];
84.37/50.03	4347[label="vuz205",fontsize=16,color="green",shape="box"];4348[label="vuz204",fontsize=16,color="green",shape="box"];1059[label="vuz72 * vuz20",fontsize=16,color="black",shape="triangle"];1059 -> 1064[label="",style="solid", color="black", weight=3];
84.37/50.03	4349[label="vuz204",fontsize=16,color="green",shape="box"];4350[label="vuz205",fontsize=16,color="green",shape="box"];1069[label="vuz73 * vuz20",fontsize=16,color="black",shape="triangle"];1069 -> 1074[label="",style="solid", color="black", weight=3];
84.37/50.03	739[label="vuz130000",fontsize=16,color="green",shape="box"];508[label="primDivNatS (primMinusNatS (Succ (Succ vuz1300)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];508 -> 538[label="",style="solid", color="black", weight=3];
84.37/50.03	510[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];510 -> 541[label="",style="solid", color="black", weight=3];
84.37/50.03	1863[label="pr2F3 (primEqInt (Pos vuz105 - vuz115) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos vuz105 - vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1863 -> 1875[label="",style="solid", color="black", weight=3];
84.37/50.03	1864[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4805[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4805[label="",style="solid", color="blue", weight=9];
84.37/50.03	4805 -> 1876[label="",style="solid", color="blue", weight=3];
84.37/50.03	4806[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4806[label="",style="solid", color="blue", weight=9];
84.37/50.03	4806 -> 1877[label="",style="solid", color="blue", weight=3];
84.37/50.03	4807[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4807[label="",style="solid", color="blue", weight=9];
84.37/50.03	4807 -> 1878[label="",style="solid", color="blue", weight=3];
84.37/50.03	4808[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4808[label="",style="solid", color="blue", weight=9];
84.37/50.03	4808 -> 1879[label="",style="solid", color="blue", weight=3];
84.37/50.03	4809[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1864 -> 4809[label="",style="solid", color="blue", weight=9];
84.37/50.03	4809 -> 1880[label="",style="solid", color="blue", weight=3];
84.37/50.03	1865 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1865[label="primDivNatS vuz105 (Succ (Succ Zero))",fontsize=16,color="magenta"];1865 -> 1881[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1866 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1866[label="primDivNatS vuz105 (Succ (Succ Zero))",fontsize=16,color="magenta"];1866 -> 1882[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4381[label="pr2F0 vuz216 (Neg vuz218) (vuz216 * vuz217)",fontsize=16,color="black",shape="box"];4381 -> 4384[label="",style="solid", color="black", weight=3];
84.37/50.03	4382[label="vuz216 * vuz217",fontsize=16,color="blue",shape="box"];4810[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4810[label="",style="solid", color="blue", weight=9];
84.37/50.03	4810 -> 4385[label="",style="solid", color="blue", weight=3];
84.37/50.03	4811[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4811[label="",style="solid", color="blue", weight=9];
84.37/50.03	4811 -> 4386[label="",style="solid", color="blue", weight=3];
84.37/50.03	4812[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4812[label="",style="solid", color="blue", weight=9];
84.37/50.03	4812 -> 4387[label="",style="solid", color="blue", weight=3];
84.37/50.03	4813[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4813[label="",style="solid", color="blue", weight=9];
84.37/50.03	4813 -> 4388[label="",style="solid", color="blue", weight=3];
84.37/50.03	4814[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4382 -> 4814[label="",style="solid", color="blue", weight=9];
84.37/50.03	4814 -> 4389[label="",style="solid", color="blue", weight=3];
84.37/50.03	1867[label="pr2F4 (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1867 -> 1883[label="",style="solid", color="black", weight=3];
84.37/50.03	1874[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (primQuotInt (Neg vuz113) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg vuz113) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1874 -> 1896[label="",style="solid", color="black", weight=3];
84.37/50.03	4367[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos vuz211) (even (Pos vuz211))",fontsize=16,color="black",shape="box"];4367 -> 4380[label="",style="solid", color="black", weight=3];
84.37/50.03	1029[label="error []",fontsize=16,color="red",shape="box"];1046[label="error []",fontsize=16,color="red",shape="box"];1056[label="primMulInt vuz71 vuz20",fontsize=16,color="burlywood",shape="box"];4815[label="vuz71/Pos vuz710",fontsize=10,color="white",style="solid",shape="box"];1056 -> 4815[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4815 -> 1065[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4816[label="vuz71/Neg vuz710",fontsize=10,color="white",style="solid",shape="box"];1056 -> 4816[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4816 -> 1066[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1064[label="error []",fontsize=16,color="red",shape="box"];1074[label="error []",fontsize=16,color="red",shape="box"];538[label="primDivNatS (primMinusNatS (Succ vuz1300) Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];538 -> 554[label="",style="solid", color="black", weight=3];
84.37/50.03	541[label="primDivNatS (primMinusNatS Zero Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];541 -> 557[label="",style="solid", color="black", weight=3];
84.37/50.03	1875[label="pr2F3 (primEqInt (primMinusInt (Pos vuz105) vuz115) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusInt (Pos vuz105) vuz115) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="box"];4817[label="vuz115/Pos vuz1150",fontsize=10,color="white",style="solid",shape="box"];1875 -> 4817[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4817 -> 1897[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4818[label="vuz115/Neg vuz1150",fontsize=10,color="white",style="solid",shape="box"];1875 -> 4818[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4818 -> 1898[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1876 -> 397[label="",style="dashed", color="red", weight=0];
84.37/50.03	1876[label="vuz103 * vuz103",fontsize=16,color="magenta"];1876 -> 1899[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1877 -> 398[label="",style="dashed", color="red", weight=0];
84.37/50.03	1877[label="vuz103 * vuz103",fontsize=16,color="magenta"];1877 -> 1900[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1878 -> 399[label="",style="dashed", color="red", weight=0];
84.37/50.03	1878[label="vuz103 * vuz103",fontsize=16,color="magenta"];1878 -> 1901[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1879 -> 400[label="",style="dashed", color="red", weight=0];
84.37/50.03	1879[label="vuz103 * vuz103",fontsize=16,color="magenta"];1879 -> 1902[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1880 -> 401[label="",style="dashed", color="red", weight=0];
84.37/50.03	1880[label="vuz103 * vuz103",fontsize=16,color="magenta"];1880 -> 1903[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1881[label="vuz105",fontsize=16,color="green",shape="box"];1882[label="vuz105",fontsize=16,color="green",shape="box"];4384[label="pr2F0G (vuz216 * vuz217) vuz216 (Neg vuz218)",fontsize=16,color="black",shape="box"];4384 -> 4392[label="",style="solid", color="black", weight=3];
84.37/50.03	4385 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4385[label="vuz216 * vuz217",fontsize=16,color="magenta"];4385 -> 4393[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4385 -> 4394[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4386 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4386[label="vuz216 * vuz217",fontsize=16,color="magenta"];4386 -> 4395[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4386 -> 4396[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4387 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4387[label="vuz216 * vuz217",fontsize=16,color="magenta"];4387 -> 4397[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4387 -> 4398[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4388 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4388[label="vuz216 * vuz217",fontsize=16,color="magenta"];4388 -> 4399[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4388 -> 4400[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4389 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4389[label="vuz216 * vuz217",fontsize=16,color="magenta"];4389 -> 4401[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4389 -> 4402[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1883[label="pr2F3 (Neg vuz113 - vuz116 == fromInt (Pos Zero)) (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1883 -> 1904[label="",style="solid", color="black", weight=3];
84.37/50.03	1896 -> 1755[label="",style="dashed", color="red", weight=0];
84.37/50.03	1896[label="pr2F0G1 vuz110 (vuz111 * vuz111 * (vuz111 * vuz111)) (Neg (primDivNatS vuz113 (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS vuz113 (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1896 -> 1917[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1896 -> 1918[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1896 -> 1919[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4380[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos vuz211) (primEvenInt (Pos vuz211))",fontsize=16,color="black",shape="box"];4380 -> 4383[label="",style="solid", color="black", weight=3];
84.37/50.03	1065[label="primMulInt (Pos vuz710) vuz20",fontsize=16,color="burlywood",shape="box"];4819[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];1065 -> 4819[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4819 -> 1075[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4820[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];1065 -> 4820[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4820 -> 1076[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1066[label="primMulInt (Neg vuz710) vuz20",fontsize=16,color="burlywood",shape="box"];4821[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];1066 -> 4821[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4821 -> 1077[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4822[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];1066 -> 4822[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4822 -> 1078[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	554[label="primDivNatS (Succ vuz1300) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];554 -> 562[label="",style="solid", color="black", weight=3];
84.37/50.03	557[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];557 -> 566[label="",style="solid", color="black", weight=3];
84.37/50.03	1897[label="pr2F3 (primEqInt (primMinusInt (Pos vuz105) (Pos vuz1150)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusInt (Pos vuz105) (Pos vuz1150)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1897 -> 1920[label="",style="solid", color="black", weight=3];
84.37/50.03	1898[label="pr2F3 (primEqInt (primMinusInt (Pos vuz105) (Neg vuz1150)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusInt (Pos vuz105) (Neg vuz1150)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1898 -> 1921[label="",style="solid", color="black", weight=3];
84.37/50.03	1899[label="vuz103",fontsize=16,color="green",shape="box"];397 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	397[label="vuz12 * vuz12",fontsize=16,color="magenta"];397 -> 1026[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	397 -> 1027[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1900[label="vuz103",fontsize=16,color="green",shape="box"];398 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	398[label="vuz12 * vuz12",fontsize=16,color="magenta"];398 -> 1043[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	398 -> 1044[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1901[label="vuz103",fontsize=16,color="green",shape="box"];399 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	399[label="vuz12 * vuz12",fontsize=16,color="magenta"];399 -> 1053[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	399 -> 1054[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1902[label="vuz103",fontsize=16,color="green",shape="box"];400 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	400[label="vuz12 * vuz12",fontsize=16,color="magenta"];400 -> 1061[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	400 -> 1062[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1903[label="vuz103",fontsize=16,color="green",shape="box"];401 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	401[label="vuz12 * vuz12",fontsize=16,color="magenta"];401 -> 1071[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	401 -> 1072[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4392[label="pr2F0G2 (vuz216 * vuz217) vuz216 (Neg vuz218)",fontsize=16,color="black",shape="box"];4392 -> 4406[label="",style="solid", color="black", weight=3];
84.37/50.03	4393[label="vuz216",fontsize=16,color="green",shape="box"];4394[label="vuz217",fontsize=16,color="green",shape="box"];4395[label="vuz216",fontsize=16,color="green",shape="box"];4396[label="vuz217",fontsize=16,color="green",shape="box"];4397[label="vuz217",fontsize=16,color="green",shape="box"];4398[label="vuz216",fontsize=16,color="green",shape="box"];4399[label="vuz217",fontsize=16,color="green",shape="box"];4400[label="vuz216",fontsize=16,color="green",shape="box"];4401[label="vuz216",fontsize=16,color="green",shape="box"];4402[label="vuz217",fontsize=16,color="green",shape="box"];1904[label="pr2F3 (primEqInt (Neg vuz113 - vuz116) (fromInt (Pos Zero))) (vuz111 * vuz111) (Neg vuz113 - vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1904 -> 1922[label="",style="solid", color="black", weight=3];
84.37/50.03	1917 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1917[label="primDivNatS vuz113 (Succ (Succ Zero))",fontsize=16,color="magenta"];1917 -> 1930[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1918 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	1918[label="primDivNatS vuz113 (Succ (Succ Zero))",fontsize=16,color="magenta"];1918 -> 1931[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1919[label="vuz111 * vuz111",fontsize=16,color="blue",shape="box"];4823[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4823[label="",style="solid", color="blue", weight=9];
84.37/50.03	4823 -> 1932[label="",style="solid", color="blue", weight=3];
84.37/50.03	4824[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4824[label="",style="solid", color="blue", weight=9];
84.37/50.03	4824 -> 1933[label="",style="solid", color="blue", weight=3];
84.37/50.03	4825[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4825[label="",style="solid", color="blue", weight=9];
84.37/50.03	4825 -> 1934[label="",style="solid", color="blue", weight=3];
84.37/50.03	4826[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4826[label="",style="solid", color="blue", weight=9];
84.37/50.03	4826 -> 1935[label="",style="solid", color="blue", weight=3];
84.37/50.03	4827[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1919 -> 4827[label="",style="solid", color="blue", weight=9];
84.37/50.03	4827 -> 1936[label="",style="solid", color="blue", weight=3];
84.37/50.03	4383[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos vuz211) (primEvenNat vuz211)",fontsize=16,color="burlywood",shape="box"];4828[label="vuz211/Succ vuz2110",fontsize=10,color="white",style="solid",shape="box"];4383 -> 4828[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4828 -> 4390[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4829[label="vuz211/Zero",fontsize=10,color="white",style="solid",shape="box"];4383 -> 4829[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4829 -> 4391[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1075[label="primMulInt (Pos vuz710) (Pos vuz200)",fontsize=16,color="black",shape="box"];1075 -> 1081[label="",style="solid", color="black", weight=3];
84.37/50.03	1076[label="primMulInt (Pos vuz710) (Neg vuz200)",fontsize=16,color="black",shape="box"];1076 -> 1082[label="",style="solid", color="black", weight=3];
84.37/50.03	1077[label="primMulInt (Neg vuz710) (Pos vuz200)",fontsize=16,color="black",shape="box"];1077 -> 1083[label="",style="solid", color="black", weight=3];
84.37/50.03	1078[label="primMulInt (Neg vuz710) (Neg vuz200)",fontsize=16,color="black",shape="box"];1078 -> 1084[label="",style="solid", color="black", weight=3];
84.37/50.03	566[label="Zero",fontsize=16,color="green",shape="box"];1920[label="pr2F3 (primEqInt (primMinusNat vuz105 vuz1150) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat vuz105 vuz1150) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="triangle"];4830[label="vuz105/Succ vuz1050",fontsize=10,color="white",style="solid",shape="box"];1920 -> 4830[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4830 -> 1937[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4831[label="vuz105/Zero",fontsize=10,color="white",style="solid",shape="box"];1920 -> 4831[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4831 -> 1938[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1921 -> 4007[label="",style="dashed", color="red", weight=0];
84.37/50.03	1921[label="pr2F3 (primEqInt (Pos (primPlusNat vuz105 vuz1150)) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos (primPlusNat vuz105 vuz1150)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1921 -> 4022[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1921 -> 4023[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1921 -> 4024[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1921 -> 4025[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1026[label="vuz12",fontsize=16,color="green",shape="box"];1027[label="vuz12",fontsize=16,color="green",shape="box"];1043[label="vuz12",fontsize=16,color="green",shape="box"];1044[label="vuz12",fontsize=16,color="green",shape="box"];1053[label="vuz12",fontsize=16,color="green",shape="box"];1054[label="vuz12",fontsize=16,color="green",shape="box"];1061[label="vuz12",fontsize=16,color="green",shape="box"];1062[label="vuz12",fontsize=16,color="green",shape="box"];1071[label="vuz12",fontsize=16,color="green",shape="box"];1072[label="vuz12",fontsize=16,color="green",shape="box"];4406[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg vuz218) (even (Neg vuz218))",fontsize=16,color="black",shape="box"];4406 -> 4410[label="",style="solid", color="black", weight=3];
84.37/50.03	1922[label="pr2F3 (primEqInt (primMinusInt (Neg vuz113) vuz116) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusInt (Neg vuz113) vuz116) (vuz111 * vuz111 * vuz110)",fontsize=16,color="burlywood",shape="box"];4832[label="vuz116/Pos vuz1160",fontsize=10,color="white",style="solid",shape="box"];1922 -> 4832[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4832 -> 1942[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4833[label="vuz116/Neg vuz1160",fontsize=10,color="white",style="solid",shape="box"];1922 -> 4833[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4833 -> 1943[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1930[label="vuz113",fontsize=16,color="green",shape="box"];1931[label="vuz113",fontsize=16,color="green",shape="box"];1932 -> 397[label="",style="dashed", color="red", weight=0];
84.37/50.03	1932[label="vuz111 * vuz111",fontsize=16,color="magenta"];1932 -> 1944[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1933 -> 398[label="",style="dashed", color="red", weight=0];
84.37/50.03	1933[label="vuz111 * vuz111",fontsize=16,color="magenta"];1933 -> 1945[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1934 -> 399[label="",style="dashed", color="red", weight=0];
84.37/50.03	1934[label="vuz111 * vuz111",fontsize=16,color="magenta"];1934 -> 1946[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1935 -> 400[label="",style="dashed", color="red", weight=0];
84.37/50.03	1935[label="vuz111 * vuz111",fontsize=16,color="magenta"];1935 -> 1947[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1936 -> 401[label="",style="dashed", color="red", weight=0];
84.37/50.03	1936[label="vuz111 * vuz111",fontsize=16,color="magenta"];1936 -> 1948[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4390[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ vuz2110)) (primEvenNat (Succ vuz2110))",fontsize=16,color="burlywood",shape="box"];4834[label="vuz2110/Succ vuz21100",fontsize=10,color="white",style="solid",shape="box"];4390 -> 4834[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4834 -> 4403[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4835[label="vuz2110/Zero",fontsize=10,color="white",style="solid",shape="box"];4390 -> 4835[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4835 -> 4404[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4391[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos Zero) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4391 -> 4405[label="",style="solid", color="black", weight=3];
84.37/50.03	1081[label="Pos (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1081 -> 1107[label="",style="dashed", color="green", weight=3];
84.37/50.03	1082[label="Neg (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1082 -> 1108[label="",style="dashed", color="green", weight=3];
84.37/50.03	1083[label="Neg (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1083 -> 1109[label="",style="dashed", color="green", weight=3];
84.37/50.03	1084[label="Pos (primMulNat vuz710 vuz200)",fontsize=16,color="green",shape="box"];1084 -> 1110[label="",style="dashed", color="green", weight=3];
84.37/50.03	1937[label="pr2F3 (primEqInt (primMinusNat (Succ vuz1050) vuz1150) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat (Succ vuz1050) vuz1150) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="box"];4836[label="vuz1150/Succ vuz11500",fontsize=10,color="white",style="solid",shape="box"];1937 -> 4836[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4836 -> 1949[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4837[label="vuz1150/Zero",fontsize=10,color="white",style="solid",shape="box"];1937 -> 4837[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4837 -> 1950[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1938[label="pr2F3 (primEqInt (primMinusNat Zero vuz1150) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat Zero vuz1150) (vuz103 * vuz103 * vuz102)",fontsize=16,color="burlywood",shape="box"];4838[label="vuz1150/Succ vuz11500",fontsize=10,color="white",style="solid",shape="box"];1938 -> 4838[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4838 -> 1951[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4839[label="vuz1150/Zero",fontsize=10,color="white",style="solid",shape="box"];1938 -> 4839[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4839 -> 1952[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4022[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4840[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4840[label="",style="solid", color="blue", weight=9];
84.37/50.03	4840 -> 4094[label="",style="solid", color="blue", weight=3];
84.37/50.03	4841[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4841[label="",style="solid", color="blue", weight=9];
84.37/50.03	4841 -> 4095[label="",style="solid", color="blue", weight=3];
84.37/50.03	4842[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4842[label="",style="solid", color="blue", weight=9];
84.37/50.03	4842 -> 4096[label="",style="solid", color="blue", weight=3];
84.37/50.03	4843[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4843[label="",style="solid", color="blue", weight=9];
84.37/50.03	4843 -> 4097[label="",style="solid", color="blue", weight=3];
84.37/50.03	4844[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4022 -> 4844[label="",style="solid", color="blue", weight=9];
84.37/50.03	4844 -> 4098[label="",style="solid", color="blue", weight=3];
84.37/50.03	4023[label="vuz102",fontsize=16,color="green",shape="box"];4024 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4024[label="primPlusNat vuz105 vuz1150",fontsize=16,color="magenta"];4024 -> 4099[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4024 -> 4100[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4025 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4025[label="primPlusNat vuz105 vuz1150",fontsize=16,color="magenta"];4025 -> 4101[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4025 -> 4102[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4410[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg vuz218) (primEvenInt (Neg vuz218))",fontsize=16,color="black",shape="box"];4410 -> 4415[label="",style="solid", color="black", weight=3];
84.37/50.03	1942[label="pr2F3 (primEqInt (primMinusInt (Neg vuz113) (Pos vuz1160)) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusInt (Neg vuz113) (Pos vuz1160)) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1942 -> 1969[label="",style="solid", color="black", weight=3];
84.37/50.03	1943[label="pr2F3 (primEqInt (primMinusInt (Neg vuz113) (Neg vuz1160)) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusInt (Neg vuz113) (Neg vuz1160)) (vuz111 * vuz111 * vuz110)",fontsize=16,color="black",shape="box"];1943 -> 1970[label="",style="solid", color="black", weight=3];
84.37/50.03	1944[label="vuz111",fontsize=16,color="green",shape="box"];1945[label="vuz111",fontsize=16,color="green",shape="box"];1946[label="vuz111",fontsize=16,color="green",shape="box"];1947[label="vuz111",fontsize=16,color="green",shape="box"];1948[label="vuz111",fontsize=16,color="green",shape="box"];4403[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ (Succ vuz21100))) (primEvenNat (Succ (Succ vuz21100)))",fontsize=16,color="black",shape="box"];4403 -> 4407[label="",style="solid", color="black", weight=3];
84.37/50.03	4404[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4404 -> 4408[label="",style="solid", color="black", weight=3];
84.37/50.03	4405[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos Zero) True",fontsize=16,color="black",shape="box"];4405 -> 4409[label="",style="solid", color="black", weight=3];
84.37/50.03	1107[label="primMulNat vuz710 vuz200",fontsize=16,color="burlywood",shape="triangle"];4845[label="vuz710/Succ vuz7100",fontsize=10,color="white",style="solid",shape="box"];1107 -> 4845[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4845 -> 1173[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4846[label="vuz710/Zero",fontsize=10,color="white",style="solid",shape="box"];1107 -> 4846[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4846 -> 1174[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1108 -> 1107[label="",style="dashed", color="red", weight=0];
84.37/50.03	1108[label="primMulNat vuz710 vuz200",fontsize=16,color="magenta"];1108 -> 1175[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1109 -> 1107[label="",style="dashed", color="red", weight=0];
84.37/50.03	1109[label="primMulNat vuz710 vuz200",fontsize=16,color="magenta"];1109 -> 1176[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1110 -> 1107[label="",style="dashed", color="red", weight=0];
84.37/50.03	1110[label="primMulNat vuz710 vuz200",fontsize=16,color="magenta"];1110 -> 1177[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1110 -> 1178[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1949[label="pr2F3 (primEqInt (primMinusNat (Succ vuz1050) (Succ vuz11500)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat (Succ vuz1050) (Succ vuz11500)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1949 -> 1971[label="",style="solid", color="black", weight=3];
84.37/50.03	1950[label="pr2F3 (primEqInt (primMinusNat (Succ vuz1050) Zero) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat (Succ vuz1050) Zero) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1950 -> 1972[label="",style="solid", color="black", weight=3];
84.37/50.03	1951[label="pr2F3 (primEqInt (primMinusNat Zero (Succ vuz11500)) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat Zero (Succ vuz11500)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1951 -> 1973[label="",style="solid", color="black", weight=3];
84.37/50.03	1952[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat Zero Zero) (vuz103 * vuz103 * vuz102)",fontsize=16,color="black",shape="box"];1952 -> 1974[label="",style="solid", color="black", weight=3];
84.37/50.03	4094 -> 397[label="",style="dashed", color="red", weight=0];
84.37/50.03	4094[label="vuz103 * vuz103",fontsize=16,color="magenta"];4094 -> 4171[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4095 -> 398[label="",style="dashed", color="red", weight=0];
84.37/50.03	4095[label="vuz103 * vuz103",fontsize=16,color="magenta"];4095 -> 4172[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4096 -> 399[label="",style="dashed", color="red", weight=0];
84.37/50.03	4096[label="vuz103 * vuz103",fontsize=16,color="magenta"];4096 -> 4173[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4097 -> 400[label="",style="dashed", color="red", weight=0];
84.37/50.03	4097[label="vuz103 * vuz103",fontsize=16,color="magenta"];4097 -> 4174[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4098 -> 401[label="",style="dashed", color="red", weight=0];
84.37/50.03	4098[label="vuz103 * vuz103",fontsize=16,color="magenta"];4098 -> 4175[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4099[label="vuz105",fontsize=16,color="green",shape="box"];4100[label="vuz1150",fontsize=16,color="green",shape="box"];4101[label="vuz105",fontsize=16,color="green",shape="box"];4102[label="vuz1150",fontsize=16,color="green",shape="box"];4415[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg vuz218) (primEvenNat vuz218)",fontsize=16,color="burlywood",shape="box"];4847[label="vuz218/Succ vuz2180",fontsize=10,color="white",style="solid",shape="box"];4415 -> 4847[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4847 -> 4421[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4848[label="vuz218/Zero",fontsize=10,color="white",style="solid",shape="box"];4415 -> 4848[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4848 -> 4422[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1969 -> 4311[label="",style="dashed", color="red", weight=0];
84.37/50.03	1969[label="pr2F3 (primEqInt (Neg (primPlusNat vuz113 vuz1160)) (fromInt (Pos Zero))) (vuz111 * vuz111) (Neg (primPlusNat vuz113 vuz1160)) (vuz111 * vuz111 * vuz110)",fontsize=16,color="magenta"];1969 -> 4318[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1969 -> 4319[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1969 -> 4320[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1969 -> 4321[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1970 -> 1920[label="",style="dashed", color="red", weight=0];
84.37/50.03	1970[label="pr2F3 (primEqInt (primMinusNat vuz1160 vuz113) (fromInt (Pos Zero))) (vuz111 * vuz111) (primMinusNat vuz1160 vuz113) (vuz111 * vuz111 * vuz110)",fontsize=16,color="magenta"];1970 -> 2001[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1970 -> 2002[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1970 -> 2003[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1970 -> 2004[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4407 -> 4464[label="",style="dashed", color="red", weight=0];
84.37/50.03	4407[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ (Succ vuz21100))) (primEvenNat vuz21100)",fontsize=16,color="magenta"];4407 -> 4465[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4407 -> 4466[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4407 -> 4467[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4407 -> 4468[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4408[label="pr2F0G1 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) False",fontsize=16,color="black",shape="box"];4408 -> 4413[label="",style="solid", color="black", weight=3];
84.37/50.03	4409[label="pr2F0G (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4409 -> 4414[label="",style="solid", color="black", weight=3];
84.37/50.03	1173[label="primMulNat (Succ vuz7100) vuz200",fontsize=16,color="burlywood",shape="box"];4849[label="vuz200/Succ vuz2000",fontsize=10,color="white",style="solid",shape="box"];1173 -> 4849[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4849 -> 1228[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4850[label="vuz200/Zero",fontsize=10,color="white",style="solid",shape="box"];1173 -> 4850[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4850 -> 1229[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1174[label="primMulNat Zero vuz200",fontsize=16,color="burlywood",shape="box"];4851[label="vuz200/Succ vuz2000",fontsize=10,color="white",style="solid",shape="box"];1174 -> 4851[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4851 -> 1230[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4852[label="vuz200/Zero",fontsize=10,color="white",style="solid",shape="box"];1174 -> 4852[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4852 -> 1231[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	1175[label="vuz200",fontsize=16,color="green",shape="box"];1176[label="vuz710",fontsize=16,color="green",shape="box"];1177[label="vuz200",fontsize=16,color="green",shape="box"];1178[label="vuz710",fontsize=16,color="green",shape="box"];1971 -> 1920[label="",style="dashed", color="red", weight=0];
84.37/50.03	1971[label="pr2F3 (primEqInt (primMinusNat vuz1050 vuz11500) (fromInt (Pos Zero))) (vuz103 * vuz103) (primMinusNat vuz1050 vuz11500) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1971 -> 2005[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1971 -> 2006[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1972 -> 4007[label="",style="dashed", color="red", weight=0];
84.37/50.03	1972[label="pr2F3 (primEqInt (Pos (Succ vuz1050)) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos (Succ vuz1050)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1972 -> 4030[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1972 -> 4031[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1972 -> 4032[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1972 -> 4033[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1973 -> 4311[label="",style="dashed", color="red", weight=0];
84.37/50.03	1973[label="pr2F3 (primEqInt (Neg (Succ vuz11500)) (fromInt (Pos Zero))) (vuz103 * vuz103) (Neg (Succ vuz11500)) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1973 -> 4322[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1973 -> 4323[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1973 -> 4324[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1973 -> 4325[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1974 -> 4007[label="",style="dashed", color="red", weight=0];
84.37/50.03	1974[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (vuz103 * vuz103) (Pos Zero) (vuz103 * vuz103 * vuz102)",fontsize=16,color="magenta"];1974 -> 4034[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1974 -> 4035[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1974 -> 4036[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1974 -> 4037[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4171[label="vuz103",fontsize=16,color="green",shape="box"];4172[label="vuz103",fontsize=16,color="green",shape="box"];4173[label="vuz103",fontsize=16,color="green",shape="box"];4174[label="vuz103",fontsize=16,color="green",shape="box"];4175[label="vuz103",fontsize=16,color="green",shape="box"];4421[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ vuz2180)) (primEvenNat (Succ vuz2180))",fontsize=16,color="burlywood",shape="box"];4853[label="vuz2180/Succ vuz21800",fontsize=10,color="white",style="solid",shape="box"];4421 -> 4853[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4853 -> 4428[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4854[label="vuz2180/Zero",fontsize=10,color="white",style="solid",shape="box"];4421 -> 4854[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4854 -> 4429[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4422[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg Zero) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4422 -> 4430[label="",style="solid", color="black", weight=3];
84.37/50.03	4318[label="vuz111 * vuz111",fontsize=16,color="blue",shape="box"];4855[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4855[label="",style="solid", color="blue", weight=9];
84.37/50.03	4855 -> 4351[label="",style="solid", color="blue", weight=3];
84.37/50.03	4856[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4856[label="",style="solid", color="blue", weight=9];
84.37/50.03	4856 -> 4352[label="",style="solid", color="blue", weight=3];
84.37/50.03	4857[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4857[label="",style="solid", color="blue", weight=9];
84.37/50.03	4857 -> 4353[label="",style="solid", color="blue", weight=3];
84.37/50.03	4858[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4858[label="",style="solid", color="blue", weight=9];
84.37/50.03	4858 -> 4354[label="",style="solid", color="blue", weight=3];
84.37/50.03	4859[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4318 -> 4859[label="",style="solid", color="blue", weight=9];
84.37/50.03	4859 -> 4355[label="",style="solid", color="blue", weight=3];
84.37/50.03	4319 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4319[label="primPlusNat vuz113 vuz1160",fontsize=16,color="magenta"];4319 -> 4356[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4319 -> 4357[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4320 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	4320[label="primPlusNat vuz113 vuz1160",fontsize=16,color="magenta"];4320 -> 4358[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4320 -> 4359[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4321[label="vuz110",fontsize=16,color="green",shape="box"];2001[label="vuz111",fontsize=16,color="green",shape="box"];2002[label="vuz1160",fontsize=16,color="green",shape="box"];2003[label="vuz110",fontsize=16,color="green",shape="box"];2004[label="vuz113",fontsize=16,color="green",shape="box"];4465[label="vuz204",fontsize=16,color="green",shape="box"];4466[label="vuz205",fontsize=16,color="green",shape="box"];4467[label="Succ vuz21100",fontsize=16,color="green",shape="box"];4468[label="vuz21100",fontsize=16,color="green",shape="box"];4464[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat vuz225)",fontsize=16,color="burlywood",shape="triangle"];4860[label="vuz225/Succ vuz2250",fontsize=10,color="white",style="solid",shape="box"];4464 -> 4860[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4860 -> 4477[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4861[label="vuz225/Zero",fontsize=10,color="white",style="solid",shape="box"];4464 -> 4861[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4861 -> 4478[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4413[label="pr2F0G0 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) otherwise",fontsize=16,color="black",shape="box"];4413 -> 4419[label="",style="solid", color="black", weight=3];
84.37/50.03	4414[label="pr2F0G2 (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4414 -> 4420[label="",style="solid", color="black", weight=3];
84.37/50.03	1228[label="primMulNat (Succ vuz7100) (Succ vuz2000)",fontsize=16,color="black",shape="box"];1228 -> 1263[label="",style="solid", color="black", weight=3];
84.37/50.03	1229[label="primMulNat (Succ vuz7100) Zero",fontsize=16,color="black",shape="box"];1229 -> 1264[label="",style="solid", color="black", weight=3];
84.37/50.03	1230[label="primMulNat Zero (Succ vuz2000)",fontsize=16,color="black",shape="box"];1230 -> 1265[label="",style="solid", color="black", weight=3];
84.37/50.03	1231[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1231 -> 1266[label="",style="solid", color="black", weight=3];
84.37/50.03	2005[label="vuz1050",fontsize=16,color="green",shape="box"];2006[label="vuz11500",fontsize=16,color="green",shape="box"];4030[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4862[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4862[label="",style="solid", color="blue", weight=9];
84.37/50.03	4862 -> 4103[label="",style="solid", color="blue", weight=3];
84.37/50.03	4863[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4863[label="",style="solid", color="blue", weight=9];
84.37/50.03	4863 -> 4104[label="",style="solid", color="blue", weight=3];
84.37/50.03	4864[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4864[label="",style="solid", color="blue", weight=9];
84.37/50.03	4864 -> 4105[label="",style="solid", color="blue", weight=3];
84.37/50.03	4865[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4865[label="",style="solid", color="blue", weight=9];
84.37/50.03	4865 -> 4106[label="",style="solid", color="blue", weight=3];
84.37/50.03	4866[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4866[label="",style="solid", color="blue", weight=9];
84.37/50.03	4866 -> 4107[label="",style="solid", color="blue", weight=3];
84.37/50.03	4031[label="vuz102",fontsize=16,color="green",shape="box"];4032[label="Succ vuz1050",fontsize=16,color="green",shape="box"];4033[label="Succ vuz1050",fontsize=16,color="green",shape="box"];4322[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4867[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4867[label="",style="solid", color="blue", weight=9];
84.37/50.03	4867 -> 4360[label="",style="solid", color="blue", weight=3];
84.37/50.03	4868[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4868[label="",style="solid", color="blue", weight=9];
84.37/50.03	4868 -> 4361[label="",style="solid", color="blue", weight=3];
84.37/50.03	4869[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4869[label="",style="solid", color="blue", weight=9];
84.37/50.03	4869 -> 4362[label="",style="solid", color="blue", weight=3];
84.37/50.03	4870[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4870[label="",style="solid", color="blue", weight=9];
84.37/50.03	4870 -> 4363[label="",style="solid", color="blue", weight=3];
84.37/50.03	4871[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4871[label="",style="solid", color="blue", weight=9];
84.37/50.03	4871 -> 4364[label="",style="solid", color="blue", weight=3];
84.37/50.03	4323[label="Succ vuz11500",fontsize=16,color="green",shape="box"];4324[label="Succ vuz11500",fontsize=16,color="green",shape="box"];4325[label="vuz102",fontsize=16,color="green",shape="box"];4034[label="vuz103 * vuz103",fontsize=16,color="blue",shape="box"];4872[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4872[label="",style="solid", color="blue", weight=9];
84.37/50.03	4872 -> 4108[label="",style="solid", color="blue", weight=3];
84.37/50.03	4873[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4873[label="",style="solid", color="blue", weight=9];
84.37/50.03	4873 -> 4109[label="",style="solid", color="blue", weight=3];
84.37/50.03	4874[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4874[label="",style="solid", color="blue", weight=9];
84.37/50.03	4874 -> 4110[label="",style="solid", color="blue", weight=3];
84.37/50.03	4875[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4875[label="",style="solid", color="blue", weight=9];
84.37/50.03	4875 -> 4111[label="",style="solid", color="blue", weight=3];
84.37/50.03	4876[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4034 -> 4876[label="",style="solid", color="blue", weight=9];
84.37/50.03	4876 -> 4112[label="",style="solid", color="blue", weight=3];
84.37/50.03	4035[label="vuz102",fontsize=16,color="green",shape="box"];4036[label="Zero",fontsize=16,color="green",shape="box"];4037[label="Zero",fontsize=16,color="green",shape="box"];4428[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ (Succ vuz21800))) (primEvenNat (Succ (Succ vuz21800)))",fontsize=16,color="black",shape="box"];4428 -> 4437[label="",style="solid", color="black", weight=3];
84.37/50.03	4429[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4429 -> 4438[label="",style="solid", color="black", weight=3];
84.37/50.03	4430[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg Zero) True",fontsize=16,color="black",shape="box"];4430 -> 4439[label="",style="solid", color="black", weight=3];
84.37/50.03	4351 -> 397[label="",style="dashed", color="red", weight=0];
84.37/50.03	4351[label="vuz111 * vuz111",fontsize=16,color="magenta"];4351 -> 4368[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4352 -> 398[label="",style="dashed", color="red", weight=0];
84.37/50.03	4352[label="vuz111 * vuz111",fontsize=16,color="magenta"];4352 -> 4369[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4353 -> 399[label="",style="dashed", color="red", weight=0];
84.37/50.03	4353[label="vuz111 * vuz111",fontsize=16,color="magenta"];4353 -> 4370[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4354 -> 400[label="",style="dashed", color="red", weight=0];
84.37/50.03	4354[label="vuz111 * vuz111",fontsize=16,color="magenta"];4354 -> 4371[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4355 -> 401[label="",style="dashed", color="red", weight=0];
84.37/50.03	4355[label="vuz111 * vuz111",fontsize=16,color="magenta"];4355 -> 4372[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4356[label="vuz113",fontsize=16,color="green",shape="box"];4357[label="vuz1160",fontsize=16,color="green",shape="box"];4358[label="vuz113",fontsize=16,color="green",shape="box"];4359[label="vuz1160",fontsize=16,color="green",shape="box"];4477[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat (Succ vuz2250))",fontsize=16,color="burlywood",shape="box"];4877[label="vuz2250/Succ vuz22500",fontsize=10,color="white",style="solid",shape="box"];4477 -> 4877[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4877 -> 4489[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4878[label="vuz2250/Zero",fontsize=10,color="white",style="solid",shape="box"];4477 -> 4878[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4878 -> 4490[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4478[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4478 -> 4491[label="",style="solid", color="black", weight=3];
84.37/50.03	4419[label="pr2F0G0 (vuz204 * vuz205) vuz204 (Pos (Succ Zero)) True",fontsize=16,color="black",shape="box"];4419 -> 4426[label="",style="solid", color="black", weight=3];
84.37/50.03	4420[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4420 -> 4427[label="",style="solid", color="black", weight=3];
84.37/50.03	1263 -> 71[label="",style="dashed", color="red", weight=0];
84.37/50.03	1263[label="primPlusNat (primMulNat vuz7100 (Succ vuz2000)) (Succ vuz2000)",fontsize=16,color="magenta"];1263 -> 1273[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1263 -> 1274[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1264[label="Zero",fontsize=16,color="green",shape="box"];1265[label="Zero",fontsize=16,color="green",shape="box"];1266[label="Zero",fontsize=16,color="green",shape="box"];4103 -> 397[label="",style="dashed", color="red", weight=0];
84.37/50.03	4103[label="vuz103 * vuz103",fontsize=16,color="magenta"];4103 -> 4176[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4104 -> 398[label="",style="dashed", color="red", weight=0];
84.37/50.03	4104[label="vuz103 * vuz103",fontsize=16,color="magenta"];4104 -> 4177[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4105 -> 399[label="",style="dashed", color="red", weight=0];
84.37/50.03	4105[label="vuz103 * vuz103",fontsize=16,color="magenta"];4105 -> 4178[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4106 -> 400[label="",style="dashed", color="red", weight=0];
84.37/50.03	4106[label="vuz103 * vuz103",fontsize=16,color="magenta"];4106 -> 4179[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4107 -> 401[label="",style="dashed", color="red", weight=0];
84.37/50.03	4107[label="vuz103 * vuz103",fontsize=16,color="magenta"];4107 -> 4180[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4360 -> 397[label="",style="dashed", color="red", weight=0];
84.37/50.03	4360[label="vuz103 * vuz103",fontsize=16,color="magenta"];4360 -> 4373[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4361 -> 398[label="",style="dashed", color="red", weight=0];
84.37/50.03	4361[label="vuz103 * vuz103",fontsize=16,color="magenta"];4361 -> 4374[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4362 -> 399[label="",style="dashed", color="red", weight=0];
84.37/50.03	4362[label="vuz103 * vuz103",fontsize=16,color="magenta"];4362 -> 4375[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4363 -> 400[label="",style="dashed", color="red", weight=0];
84.37/50.03	4363[label="vuz103 * vuz103",fontsize=16,color="magenta"];4363 -> 4376[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4364 -> 401[label="",style="dashed", color="red", weight=0];
84.37/50.03	4364[label="vuz103 * vuz103",fontsize=16,color="magenta"];4364 -> 4377[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4108 -> 397[label="",style="dashed", color="red", weight=0];
84.37/50.03	4108[label="vuz103 * vuz103",fontsize=16,color="magenta"];4108 -> 4181[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4109 -> 398[label="",style="dashed", color="red", weight=0];
84.37/50.03	4109[label="vuz103 * vuz103",fontsize=16,color="magenta"];4109 -> 4182[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4110 -> 399[label="",style="dashed", color="red", weight=0];
84.37/50.03	4110[label="vuz103 * vuz103",fontsize=16,color="magenta"];4110 -> 4183[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4111 -> 400[label="",style="dashed", color="red", weight=0];
84.37/50.03	4111[label="vuz103 * vuz103",fontsize=16,color="magenta"];4111 -> 4184[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4112 -> 401[label="",style="dashed", color="red", weight=0];
84.37/50.03	4112[label="vuz103 * vuz103",fontsize=16,color="magenta"];4112 -> 4185[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4437 -> 4546[label="",style="dashed", color="red", weight=0];
84.37/50.03	4437[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ (Succ vuz21800))) (primEvenNat vuz21800)",fontsize=16,color="magenta"];4437 -> 4547[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4437 -> 4548[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4437 -> 4549[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4437 -> 4550[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4438[label="pr2F0G1 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) False",fontsize=16,color="black",shape="box"];4438 -> 4449[label="",style="solid", color="black", weight=3];
84.37/50.03	4439[label="pr2F0G (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4439 -> 4450[label="",style="solid", color="black", weight=3];
84.37/50.03	4368[label="vuz111",fontsize=16,color="green",shape="box"];4369[label="vuz111",fontsize=16,color="green",shape="box"];4370[label="vuz111",fontsize=16,color="green",shape="box"];4371[label="vuz111",fontsize=16,color="green",shape="box"];4372[label="vuz111",fontsize=16,color="green",shape="box"];4489[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat (Succ (Succ vuz22500)))",fontsize=16,color="black",shape="box"];4489 -> 4498[label="",style="solid", color="black", weight=3];
84.37/50.03	4490[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4490 -> 4499[label="",style="solid", color="black", weight=3];
84.37/50.03	4491[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) True",fontsize=16,color="black",shape="box"];4491 -> 4500[label="",style="solid", color="black", weight=3];
84.37/50.03	4426 -> 4581[label="",style="dashed", color="red", weight=0];
84.37/50.03	4426[label="pr2F vuz204 (Pos (Succ Zero) - fromInt (Pos (Succ Zero))) (vuz204 * (vuz204 * vuz205))",fontsize=16,color="magenta"];4426 -> 4582[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4426 -> 4583[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4426 -> 4584[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4426 -> 4585[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4427[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4427 -> 4440[label="",style="solid", color="black", weight=3];
84.37/50.03	1273 -> 1107[label="",style="dashed", color="red", weight=0];
84.37/50.03	1273[label="primMulNat vuz7100 (Succ vuz2000)",fontsize=16,color="magenta"];1273 -> 1305[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1273 -> 1306[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	1274[label="Succ vuz2000",fontsize=16,color="green",shape="box"];4176[label="vuz103",fontsize=16,color="green",shape="box"];4177[label="vuz103",fontsize=16,color="green",shape="box"];4178[label="vuz103",fontsize=16,color="green",shape="box"];4179[label="vuz103",fontsize=16,color="green",shape="box"];4180[label="vuz103",fontsize=16,color="green",shape="box"];4373[label="vuz103",fontsize=16,color="green",shape="box"];4374[label="vuz103",fontsize=16,color="green",shape="box"];4375[label="vuz103",fontsize=16,color="green",shape="box"];4376[label="vuz103",fontsize=16,color="green",shape="box"];4377[label="vuz103",fontsize=16,color="green",shape="box"];4181[label="vuz103",fontsize=16,color="green",shape="box"];4182[label="vuz103",fontsize=16,color="green",shape="box"];4183[label="vuz103",fontsize=16,color="green",shape="box"];4184[label="vuz103",fontsize=16,color="green",shape="box"];4185[label="vuz103",fontsize=16,color="green",shape="box"];4547[label="vuz217",fontsize=16,color="green",shape="box"];4548[label="vuz21800",fontsize=16,color="green",shape="box"];4549[label="vuz216",fontsize=16,color="green",shape="box"];4550[label="Succ vuz21800",fontsize=16,color="green",shape="box"];4546[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat vuz231)",fontsize=16,color="burlywood",shape="triangle"];4879[label="vuz231/Succ vuz2310",fontsize=10,color="white",style="solid",shape="box"];4546 -> 4879[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4879 -> 4559[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4880[label="vuz231/Zero",fontsize=10,color="white",style="solid",shape="box"];4546 -> 4880[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4880 -> 4560[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4449[label="pr2F0G0 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) otherwise",fontsize=16,color="black",shape="box"];4449 -> 4461[label="",style="solid", color="black", weight=3];
84.37/50.03	4450[label="pr2F0G2 (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4450 -> 4462[label="",style="solid", color="black", weight=3];
84.37/50.03	4498 -> 4464[label="",style="dashed", color="red", weight=0];
84.37/50.03	4498[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) (primEvenNat vuz22500)",fontsize=16,color="magenta"];4498 -> 4518[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4499[label="pr2F0G1 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) False",fontsize=16,color="black",shape="box"];4499 -> 4519[label="",style="solid", color="black", weight=3];
84.37/50.03	4500[label="pr2F0G (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4500 -> 4520[label="",style="solid", color="black", weight=3];
84.37/50.03	4582[label="vuz204",fontsize=16,color="green",shape="box"];4583[label="vuz205",fontsize=16,color="green",shape="box"];4584[label="Zero",fontsize=16,color="green",shape="box"];4585 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	4585[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4581[label="pr2F vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="black",shape="triangle"];4581 -> 4591[label="",style="solid", color="black", weight=3];
84.37/50.03	4440[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4440 -> 4451[label="",style="solid", color="black", weight=3];
84.37/50.03	1305[label="Succ vuz2000",fontsize=16,color="green",shape="box"];1306[label="vuz7100",fontsize=16,color="green",shape="box"];4559[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat (Succ vuz2310))",fontsize=16,color="burlywood",shape="box"];4881[label="vuz2310/Succ vuz23100",fontsize=10,color="white",style="solid",shape="box"];4559 -> 4881[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4881 -> 4578[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4882[label="vuz2310/Zero",fontsize=10,color="white",style="solid",shape="box"];4559 -> 4882[label="",style="solid", color="burlywood", weight=9];
84.37/50.03	4882 -> 4579[label="",style="solid", color="burlywood", weight=3];
84.37/50.03	4560[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];4560 -> 4580[label="",style="solid", color="black", weight=3];
84.37/50.03	4461[label="pr2F0G0 (vuz216 * vuz217) vuz216 (Neg (Succ Zero)) True",fontsize=16,color="black",shape="box"];4461 -> 4482[label="",style="solid", color="black", weight=3];
84.37/50.03	4462[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4462 -> 4483[label="",style="solid", color="black", weight=3];
84.37/50.03	4518[label="vuz22500",fontsize=16,color="green",shape="box"];4519[label="pr2F0G0 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) otherwise",fontsize=16,color="black",shape="box"];4519 -> 4543[label="",style="solid", color="black", weight=3];
84.37/50.03	4520[label="pr2F0G2 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4520 -> 4544[label="",style="solid", color="black", weight=3];
84.37/50.03	4591[label="pr2F4 vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="black",shape="box"];4591 -> 4606[label="",style="solid", color="black", weight=3];
84.37/50.03	4451[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4451 -> 4463[label="",style="solid", color="black", weight=3];
84.37/50.03	4578[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat (Succ (Succ vuz23100)))",fontsize=16,color="black",shape="box"];4578 -> 4592[label="",style="solid", color="black", weight=3];
84.37/50.03	4579[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];4579 -> 4593[label="",style="solid", color="black", weight=3];
84.37/50.03	4580[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) True",fontsize=16,color="black",shape="box"];4580 -> 4594[label="",style="solid", color="black", weight=3];
84.37/50.03	4482 -> 4655[label="",style="dashed", color="red", weight=0];
84.37/50.03	4482[label="pr2F vuz216 (Neg (Succ Zero) - fromInt (Pos (Succ Zero))) (vuz216 * (vuz216 * vuz217))",fontsize=16,color="magenta"];4482 -> 4656[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4482 -> 4657[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4482 -> 4658[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4482 -> 4659[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4483[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4483 -> 4501[label="",style="solid", color="black", weight=3];
84.37/50.03	4543[label="pr2F0G0 (vuz222 * vuz223) vuz222 (Pos (Succ vuz224)) True",fontsize=16,color="black",shape="box"];4543 -> 4561[label="",style="solid", color="black", weight=3];
84.37/50.03	4544[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4544 -> 4562[label="",style="solid", color="black", weight=3];
84.37/50.03	4606[label="pr2F3 (Pos (Succ vuz224) - vuz232 == fromInt (Pos Zero)) vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="black",shape="box"];4606 -> 4626[label="",style="solid", color="black", weight=3];
84.37/50.03	4463 -> 1605[label="",style="dashed", color="red", weight=0];
84.37/50.03	4463[label="pr2F0G1 (vuz204 * vuz205) (vuz204 * vuz204) (Pos (primDivNatS Zero (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS Zero (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4463 -> 4485[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4463 -> 4486[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4463 -> 4487[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4463 -> 4488[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4592 -> 4546[label="",style="dashed", color="red", weight=0];
84.37/50.03	4592[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) (primEvenNat vuz23100)",fontsize=16,color="magenta"];4592 -> 4607[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4593[label="pr2F0G1 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) False",fontsize=16,color="black",shape="box"];4593 -> 4608[label="",style="solid", color="black", weight=3];
84.37/50.03	4594[label="pr2F0G (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4594 -> 4609[label="",style="solid", color="black", weight=3];
84.37/50.03	4656[label="vuz217",fontsize=16,color="green",shape="box"];4657[label="vuz216",fontsize=16,color="green",shape="box"];4658 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	4658[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4659[label="Zero",fontsize=16,color="green",shape="box"];4655[label="pr2F vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="black",shape="triangle"];4655 -> 4665[label="",style="solid", color="black", weight=3];
84.37/50.03	4501[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (primQuotInt (Neg Zero) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg Zero) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4501 -> 4521[label="",style="solid", color="black", weight=3];
84.37/50.03	4561 -> 4581[label="",style="dashed", color="red", weight=0];
84.37/50.03	4561[label="pr2F vuz222 (Pos (Succ vuz224) - fromInt (Pos (Succ Zero))) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="magenta"];4561 -> 4590[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4562[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz224) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4562 -> 4595[label="",style="solid", color="black", weight=3];
84.37/50.03	4626 -> 3789[label="",style="dashed", color="red", weight=0];
84.37/50.03	4626[label="pr2F3 (primEqInt (Pos (Succ vuz224) - vuz232) (fromInt (Pos Zero))) vuz222 (Pos (Succ vuz224) - vuz232) (vuz222 * (vuz222 * vuz223))",fontsize=16,color="magenta"];4626 -> 4640[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4626 -> 4641[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4626 -> 4642[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4626 -> 4643[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4485[label="vuz204",fontsize=16,color="green",shape="box"];4486 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4486[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4486 -> 4511[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4487[label="vuz204 * vuz205",fontsize=16,color="blue",shape="box"];4883[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4883[label="",style="solid", color="blue", weight=9];
84.37/50.03	4883 -> 4512[label="",style="solid", color="blue", weight=3];
84.37/50.03	4884[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4884[label="",style="solid", color="blue", weight=9];
84.37/50.03	4884 -> 4513[label="",style="solid", color="blue", weight=3];
84.37/50.03	4885[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4885[label="",style="solid", color="blue", weight=9];
84.37/50.03	4885 -> 4514[label="",style="solid", color="blue", weight=3];
84.37/50.03	4886[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4886[label="",style="solid", color="blue", weight=9];
84.37/50.03	4886 -> 4515[label="",style="solid", color="blue", weight=3];
84.37/50.03	4887[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4487 -> 4887[label="",style="solid", color="blue", weight=9];
84.37/50.03	4887 -> 4516[label="",style="solid", color="blue", weight=3];
84.37/50.03	4488 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4488[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4488 -> 4517[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4607[label="vuz23100",fontsize=16,color="green",shape="box"];4608[label="pr2F0G0 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) otherwise",fontsize=16,color="black",shape="box"];4608 -> 4627[label="",style="solid", color="black", weight=3];
84.37/50.03	4609[label="pr2F0G2 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];4609 -> 4628[label="",style="solid", color="black", weight=3];
84.37/50.03	4665[label="pr2F4 vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="black",shape="box"];4665 -> 4684[label="",style="solid", color="black", weight=3];
84.37/50.03	4521[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (primQuotInt (Neg Zero) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg Zero) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4521 -> 4545[label="",style="solid", color="black", weight=3];
84.37/50.03	4590 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	4590[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4595[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (primQuotInt (Pos (Succ vuz224)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz224)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4595 -> 4610[label="",style="solid", color="black", weight=3];
84.37/50.03	4640[label="vuz222",fontsize=16,color="green",shape="box"];4641[label="vuz224",fontsize=16,color="green",shape="box"];4642[label="vuz222 * vuz223",fontsize=16,color="blue",shape="box"];4888[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4888[label="",style="solid", color="blue", weight=9];
84.37/50.03	4888 -> 4650[label="",style="solid", color="blue", weight=3];
84.37/50.03	4889[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4889[label="",style="solid", color="blue", weight=9];
84.37/50.03	4889 -> 4651[label="",style="solid", color="blue", weight=3];
84.37/50.03	4890[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4890[label="",style="solid", color="blue", weight=9];
84.37/50.03	4890 -> 4652[label="",style="solid", color="blue", weight=3];
84.37/50.03	4891[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4891[label="",style="solid", color="blue", weight=9];
84.37/50.03	4891 -> 4653[label="",style="solid", color="blue", weight=3];
84.37/50.03	4892[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4642 -> 4892[label="",style="solid", color="blue", weight=9];
84.37/50.03	4892 -> 4654[label="",style="solid", color="blue", weight=3];
84.37/50.03	4643[label="vuz232",fontsize=16,color="green",shape="box"];4511[label="Zero",fontsize=16,color="green",shape="box"];4512 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4512[label="vuz204 * vuz205",fontsize=16,color="magenta"];4512 -> 4533[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4512 -> 4534[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4513 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4513[label="vuz204 * vuz205",fontsize=16,color="magenta"];4513 -> 4535[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4513 -> 4536[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4514 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4514[label="vuz204 * vuz205",fontsize=16,color="magenta"];4514 -> 4537[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4514 -> 4538[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4515 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4515[label="vuz204 * vuz205",fontsize=16,color="magenta"];4515 -> 4539[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4515 -> 4540[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4516 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4516[label="vuz204 * vuz205",fontsize=16,color="magenta"];4516 -> 4541[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4516 -> 4542[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4517[label="Zero",fontsize=16,color="green",shape="box"];4627[label="pr2F0G0 (vuz228 * vuz229) vuz228 (Neg (Succ vuz230)) True",fontsize=16,color="black",shape="box"];4627 -> 4644[label="",style="solid", color="black", weight=3];
84.37/50.03	4628[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4628 -> 4645[label="",style="solid", color="black", weight=3];
84.37/50.03	4684[label="pr2F3 (Neg (Succ vuz230) - vuz233 == fromInt (Pos Zero)) vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="black",shape="box"];4684 -> 4696[label="",style="solid", color="black", weight=3];
84.37/50.03	4545 -> 1755[label="",style="dashed", color="red", weight=0];
84.37/50.03	4545[label="pr2F0G1 (vuz216 * vuz217) (vuz216 * vuz216) (Neg (primDivNatS Zero (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS Zero (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4545 -> 4564[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4545 -> 4565[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4545 -> 4566[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4545 -> 4567[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4610[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (primQuotInt (Pos (Succ vuz224)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz224)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4610 -> 4629[label="",style="solid", color="black", weight=3];
84.37/50.03	4650 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4650[label="vuz222 * vuz223",fontsize=16,color="magenta"];4650 -> 4666[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4650 -> 4667[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4651 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4651[label="vuz222 * vuz223",fontsize=16,color="magenta"];4651 -> 4668[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4651 -> 4669[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4652 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4652[label="vuz222 * vuz223",fontsize=16,color="magenta"];4652 -> 4670[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4652 -> 4671[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4653 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4653[label="vuz222 * vuz223",fontsize=16,color="magenta"];4653 -> 4672[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4653 -> 4673[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4654 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4654[label="vuz222 * vuz223",fontsize=16,color="magenta"];4654 -> 4674[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4654 -> 4675[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4533[label="vuz204",fontsize=16,color="green",shape="box"];4534[label="vuz205",fontsize=16,color="green",shape="box"];4535[label="vuz204",fontsize=16,color="green",shape="box"];4536[label="vuz205",fontsize=16,color="green",shape="box"];4537[label="vuz205",fontsize=16,color="green",shape="box"];4538[label="vuz204",fontsize=16,color="green",shape="box"];4539[label="vuz205",fontsize=16,color="green",shape="box"];4540[label="vuz204",fontsize=16,color="green",shape="box"];4541[label="vuz204",fontsize=16,color="green",shape="box"];4542[label="vuz205",fontsize=16,color="green",shape="box"];4644 -> 4655[label="",style="dashed", color="red", weight=0];
84.37/50.03	4644[label="pr2F vuz228 (Neg (Succ vuz230) - fromInt (Pos (Succ Zero))) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="magenta"];4644 -> 4664[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4645[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Neg (Succ vuz230) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4645 -> 4676[label="",style="solid", color="black", weight=3];
84.37/50.03	4696 -> 4256[label="",style="dashed", color="red", weight=0];
84.37/50.03	4696[label="pr2F3 (primEqInt (Neg (Succ vuz230) - vuz233) (fromInt (Pos Zero))) vuz228 (Neg (Succ vuz230) - vuz233) (vuz228 * (vuz228 * vuz229))",fontsize=16,color="magenta"];4696 -> 4698[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4696 -> 4699[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4696 -> 4700[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4696 -> 4701[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4564 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4564[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4564 -> 4599[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4565 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4565[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];4565 -> 4600[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4566[label="vuz216 * vuz217",fontsize=16,color="blue",shape="box"];4893[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4893[label="",style="solid", color="blue", weight=9];
84.37/50.03	4893 -> 4601[label="",style="solid", color="blue", weight=3];
84.37/50.03	4894[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4894[label="",style="solid", color="blue", weight=9];
84.37/50.03	4894 -> 4602[label="",style="solid", color="blue", weight=3];
84.37/50.03	4895[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4895[label="",style="solid", color="blue", weight=9];
84.37/50.03	4895 -> 4603[label="",style="solid", color="blue", weight=3];
84.37/50.03	4896[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4896[label="",style="solid", color="blue", weight=9];
84.37/50.03	4896 -> 4604[label="",style="solid", color="blue", weight=3];
84.37/50.03	4897[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4566 -> 4897[label="",style="solid", color="blue", weight=9];
84.37/50.03	4897 -> 4605[label="",style="solid", color="blue", weight=3];
84.37/50.03	4567[label="vuz216",fontsize=16,color="green",shape="box"];4629 -> 1605[label="",style="dashed", color="red", weight=0];
84.37/50.03	4629[label="pr2F0G1 (vuz222 * vuz223) (vuz222 * vuz222) (Pos (primDivNatS (Succ vuz224) (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS (Succ vuz224) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4629 -> 4646[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4629 -> 4647[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4629 -> 4648[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4629 -> 4649[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4666[label="vuz222",fontsize=16,color="green",shape="box"];4667[label="vuz223",fontsize=16,color="green",shape="box"];4668[label="vuz222",fontsize=16,color="green",shape="box"];4669[label="vuz223",fontsize=16,color="green",shape="box"];4670[label="vuz223",fontsize=16,color="green",shape="box"];4671[label="vuz222",fontsize=16,color="green",shape="box"];4672[label="vuz223",fontsize=16,color="green",shape="box"];4673[label="vuz222",fontsize=16,color="green",shape="box"];4674[label="vuz222",fontsize=16,color="green",shape="box"];4675[label="vuz223",fontsize=16,color="green",shape="box"];4664 -> 23[label="",style="dashed", color="red", weight=0];
84.37/50.03	4664[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4676[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (primQuotInt (Neg (Succ vuz230)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Neg (Succ vuz230)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];4676 -> 4685[label="",style="solid", color="black", weight=3];
84.37/50.03	4698[label="vuz230",fontsize=16,color="green",shape="box"];4699[label="vuz228",fontsize=16,color="green",shape="box"];4700[label="vuz228 * vuz229",fontsize=16,color="blue",shape="box"];4898[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4898[label="",style="solid", color="blue", weight=9];
84.37/50.03	4898 -> 4706[label="",style="solid", color="blue", weight=3];
84.37/50.03	4899[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4899[label="",style="solid", color="blue", weight=9];
84.37/50.03	4899 -> 4707[label="",style="solid", color="blue", weight=3];
84.37/50.03	4900[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4900[label="",style="solid", color="blue", weight=9];
84.37/50.03	4900 -> 4708[label="",style="solid", color="blue", weight=3];
84.37/50.03	4901[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4901[label="",style="solid", color="blue", weight=9];
84.37/50.03	4901 -> 4709[label="",style="solid", color="blue", weight=3];
84.37/50.03	4902[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4700 -> 4902[label="",style="solid", color="blue", weight=9];
84.37/50.03	4902 -> 4710[label="",style="solid", color="blue", weight=3];
84.37/50.03	4701[label="vuz233",fontsize=16,color="green",shape="box"];4599[label="Zero",fontsize=16,color="green",shape="box"];4600[label="Zero",fontsize=16,color="green",shape="box"];4601 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4601[label="vuz216 * vuz217",fontsize=16,color="magenta"];4601 -> 4616[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4601 -> 4617[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4602 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4602[label="vuz216 * vuz217",fontsize=16,color="magenta"];4602 -> 4618[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4602 -> 4619[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4603 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4603[label="vuz216 * vuz217",fontsize=16,color="magenta"];4603 -> 4620[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4603 -> 4621[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4604 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4604[label="vuz216 * vuz217",fontsize=16,color="magenta"];4604 -> 4622[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4604 -> 4623[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4605 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4605[label="vuz216 * vuz217",fontsize=16,color="magenta"];4605 -> 4624[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4605 -> 4625[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4646[label="vuz222",fontsize=16,color="green",shape="box"];4647 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4647[label="primDivNatS (Succ vuz224) (Succ (Succ Zero))",fontsize=16,color="magenta"];4647 -> 4677[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4648[label="vuz222 * vuz223",fontsize=16,color="blue",shape="box"];4903[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4903[label="",style="solid", color="blue", weight=9];
84.37/50.03	4903 -> 4678[label="",style="solid", color="blue", weight=3];
84.37/50.03	4904[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4904[label="",style="solid", color="blue", weight=9];
84.37/50.03	4904 -> 4679[label="",style="solid", color="blue", weight=3];
84.37/50.03	4905[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4905[label="",style="solid", color="blue", weight=9];
84.37/50.03	4905 -> 4680[label="",style="solid", color="blue", weight=3];
84.37/50.03	4906[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4906[label="",style="solid", color="blue", weight=9];
84.37/50.03	4906 -> 4681[label="",style="solid", color="blue", weight=3];
84.37/50.03	4907[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4648 -> 4907[label="",style="solid", color="blue", weight=9];
84.37/50.03	4907 -> 4682[label="",style="solid", color="blue", weight=3];
84.37/50.03	4649 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4649[label="primDivNatS (Succ vuz224) (Succ (Succ Zero))",fontsize=16,color="magenta"];4649 -> 4683[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4685[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (primQuotInt (Neg (Succ vuz230)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Neg (Succ vuz230)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];4685 -> 4697[label="",style="solid", color="black", weight=3];
84.37/50.03	4706 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4706[label="vuz228 * vuz229",fontsize=16,color="magenta"];4706 -> 4718[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4706 -> 4719[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4707 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4707[label="vuz228 * vuz229",fontsize=16,color="magenta"];4707 -> 4720[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4707 -> 4721[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4708 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4708[label="vuz228 * vuz229",fontsize=16,color="magenta"];4708 -> 4722[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4708 -> 4723[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4709 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4709[label="vuz228 * vuz229",fontsize=16,color="magenta"];4709 -> 4724[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4709 -> 4725[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4710 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4710[label="vuz228 * vuz229",fontsize=16,color="magenta"];4710 -> 4726[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4710 -> 4727[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4616[label="vuz216",fontsize=16,color="green",shape="box"];4617[label="vuz217",fontsize=16,color="green",shape="box"];4618[label="vuz216",fontsize=16,color="green",shape="box"];4619[label="vuz217",fontsize=16,color="green",shape="box"];4620[label="vuz217",fontsize=16,color="green",shape="box"];4621[label="vuz216",fontsize=16,color="green",shape="box"];4622[label="vuz217",fontsize=16,color="green",shape="box"];4623[label="vuz216",fontsize=16,color="green",shape="box"];4624[label="vuz216",fontsize=16,color="green",shape="box"];4625[label="vuz217",fontsize=16,color="green",shape="box"];4677[label="Succ vuz224",fontsize=16,color="green",shape="box"];4678 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4678[label="vuz222 * vuz223",fontsize=16,color="magenta"];4678 -> 4686[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4678 -> 4687[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4679 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4679[label="vuz222 * vuz223",fontsize=16,color="magenta"];4679 -> 4688[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4679 -> 4689[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4680 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4680[label="vuz222 * vuz223",fontsize=16,color="magenta"];4680 -> 4690[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4680 -> 4691[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4681 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4681[label="vuz222 * vuz223",fontsize=16,color="magenta"];4681 -> 4692[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4681 -> 4693[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4682 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4682[label="vuz222 * vuz223",fontsize=16,color="magenta"];4682 -> 4694[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4682 -> 4695[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4683[label="Succ vuz224",fontsize=16,color="green",shape="box"];4697 -> 1755[label="",style="dashed", color="red", weight=0];
84.37/50.03	4697[label="pr2F0G1 (vuz228 * vuz229) (vuz228 * vuz228) (Neg (primDivNatS (Succ vuz230) (Succ (Succ Zero)))) (primEvenInt (Neg (primDivNatS (Succ vuz230) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];4697 -> 4702[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4697 -> 4703[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4697 -> 4704[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4697 -> 4705[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4718[label="vuz228",fontsize=16,color="green",shape="box"];4719[label="vuz229",fontsize=16,color="green",shape="box"];4720[label="vuz228",fontsize=16,color="green",shape="box"];4721[label="vuz229",fontsize=16,color="green",shape="box"];4722[label="vuz229",fontsize=16,color="green",shape="box"];4723[label="vuz228",fontsize=16,color="green",shape="box"];4724[label="vuz229",fontsize=16,color="green",shape="box"];4725[label="vuz228",fontsize=16,color="green",shape="box"];4726[label="vuz228",fontsize=16,color="green",shape="box"];4727[label="vuz229",fontsize=16,color="green",shape="box"];4686[label="vuz222",fontsize=16,color="green",shape="box"];4687[label="vuz223",fontsize=16,color="green",shape="box"];4688[label="vuz222",fontsize=16,color="green",shape="box"];4689[label="vuz223",fontsize=16,color="green",shape="box"];4690[label="vuz223",fontsize=16,color="green",shape="box"];4691[label="vuz222",fontsize=16,color="green",shape="box"];4692[label="vuz223",fontsize=16,color="green",shape="box"];4693[label="vuz222",fontsize=16,color="green",shape="box"];4694[label="vuz222",fontsize=16,color="green",shape="box"];4695[label="vuz223",fontsize=16,color="green",shape="box"];4702 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4702[label="primDivNatS (Succ vuz230) (Succ (Succ Zero))",fontsize=16,color="magenta"];4702 -> 4711[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4703 -> 1222[label="",style="dashed", color="red", weight=0];
84.37/50.03	4703[label="primDivNatS (Succ vuz230) (Succ (Succ Zero))",fontsize=16,color="magenta"];4703 -> 4712[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4704[label="vuz228 * vuz229",fontsize=16,color="blue",shape="box"];4908[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4908[label="",style="solid", color="blue", weight=9];
84.37/50.03	4908 -> 4713[label="",style="solid", color="blue", weight=3];
84.37/50.03	4909[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4909[label="",style="solid", color="blue", weight=9];
84.37/50.03	4909 -> 4714[label="",style="solid", color="blue", weight=3];
84.37/50.03	4910[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4910[label="",style="solid", color="blue", weight=9];
84.37/50.03	4910 -> 4715[label="",style="solid", color="blue", weight=3];
84.37/50.03	4911[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4911[label="",style="solid", color="blue", weight=9];
84.37/50.03	4911 -> 4716[label="",style="solid", color="blue", weight=3];
84.37/50.03	4912[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4704 -> 4912[label="",style="solid", color="blue", weight=9];
84.37/50.03	4912 -> 4717[label="",style="solid", color="blue", weight=3];
84.37/50.03	4705[label="vuz228",fontsize=16,color="green",shape="box"];4711[label="Succ vuz230",fontsize=16,color="green",shape="box"];4712[label="Succ vuz230",fontsize=16,color="green",shape="box"];4713 -> 1024[label="",style="dashed", color="red", weight=0];
84.37/50.03	4713[label="vuz228 * vuz229",fontsize=16,color="magenta"];4713 -> 4728[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4713 -> 4729[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4714 -> 1041[label="",style="dashed", color="red", weight=0];
84.37/50.03	4714[label="vuz228 * vuz229",fontsize=16,color="magenta"];4714 -> 4730[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4714 -> 4731[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4715 -> 1051[label="",style="dashed", color="red", weight=0];
84.37/50.03	4715[label="vuz228 * vuz229",fontsize=16,color="magenta"];4715 -> 4732[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4715 -> 4733[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4716 -> 1059[label="",style="dashed", color="red", weight=0];
84.37/50.03	4716[label="vuz228 * vuz229",fontsize=16,color="magenta"];4716 -> 4734[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4716 -> 4735[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4717 -> 1069[label="",style="dashed", color="red", weight=0];
84.37/50.03	4717[label="vuz228 * vuz229",fontsize=16,color="magenta"];4717 -> 4736[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4717 -> 4737[label="",style="dashed", color="magenta", weight=3];
84.37/50.03	4728[label="vuz228",fontsize=16,color="green",shape="box"];4729[label="vuz229",fontsize=16,color="green",shape="box"];4730[label="vuz228",fontsize=16,color="green",shape="box"];4731[label="vuz229",fontsize=16,color="green",shape="box"];4732[label="vuz229",fontsize=16,color="green",shape="box"];4733[label="vuz228",fontsize=16,color="green",shape="box"];4734[label="vuz229",fontsize=16,color="green",shape="box"];4735[label="vuz228",fontsize=16,color="green",shape="box"];4736[label="vuz228",fontsize=16,color="green",shape="box"];4737[label="vuz229",fontsize=16,color="green",shape="box"];}
84.37/50.03	
84.37/50.03	----------------------------------------
84.37/50.03	
84.37/50.03	(139)
84.37/50.03	TRUE
84.38/50.07	EOF