28.25/15.34	MAYBE
30.41/15.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
30.41/15.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
30.41/15.89	
30.41/15.89	
30.41/15.89	H-Termination with start terms of the given HASKELL could not be shown:
30.41/15.89	
30.41/15.89	(0) HASKELL
30.41/15.89	(1) IFR [EQUIVALENT, 0 ms]
30.41/15.89	(2) HASKELL
30.41/15.89	(3) BR [EQUIVALENT, 0 ms]
30.41/15.89	(4) HASKELL
30.41/15.89	(5) COR [EQUIVALENT, 0 ms]
30.41/15.89	(6) HASKELL
30.41/15.89	(7) NumRed [SOUND, 0 ms]
30.41/15.89	(8) HASKELL
30.41/15.89	(9) Narrow [SOUND, 0 ms]
30.41/15.89	(10) AND
30.41/15.89	    (11) QDP
30.41/15.89	        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	        (13) QDP
30.41/15.89	        (14) QDPOrderProof [EQUIVALENT, 0 ms]
30.41/15.89	        (15) QDP
30.41/15.89	        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	        (17) QDP
30.41/15.89	        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
30.41/15.89	        (19) YES
30.41/15.89	    (20) QDP
30.41/15.89	        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
30.41/15.89	        (22) YES
30.41/15.89	    (23) QDP
30.41/15.89	        (24) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	        (25) QDP
30.41/15.89	        (26) QDPOrderProof [EQUIVALENT, 0 ms]
30.41/15.89	        (27) QDP
30.41/15.89	        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	        (29) QDP
30.41/15.89	        (30) QDPSizeChangeProof [EQUIVALENT, 0 ms]
30.41/15.89	        (31) YES
30.41/15.89	    (32) QDP
30.41/15.89	        (33) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	        (34) QDP
30.41/15.89	        (35) TransformationProof [EQUIVALENT, 0 ms]
30.41/15.89	        (36) QDP
30.41/15.89	        (37) UsableRulesProof [EQUIVALENT, 0 ms]
30.41/15.89	        (38) QDP
30.41/15.89	        (39) QReductionProof [EQUIVALENT, 0 ms]
30.41/15.89	        (40) QDP
30.41/15.89	        (41) MNOCProof [EQUIVALENT, 0 ms]
30.41/15.89	        (42) QDP
30.41/15.89	        (43) InductionCalculusProof [EQUIVALENT, 0 ms]
30.41/15.89	        (44) QDP
30.41/15.89	        (45) TransformationProof [EQUIVALENT, 0 ms]
30.41/15.89	        (46) QDP
30.41/15.89	            (47) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	            (48) QDP
30.41/15.89	            (49) TransformationProof [EQUIVALENT, 0 ms]
30.41/15.89	            (50) QDP
30.41/15.89	            (51) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	            (52) QDP
30.41/15.89	            (53) TransformationProof [EQUIVALENT, 0 ms]
30.41/15.89	            (54) QDP
30.41/15.89	            (55) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	            (56) QDP
30.41/15.89	            (57) TransformationProof [EQUIVALENT, 0 ms]
30.41/15.89	            (58) QDP
30.41/15.89	            (59) DependencyGraphProof [EQUIVALENT, 0 ms]
30.41/15.89	            (60) QDP
30.41/15.89	            (61) MNOCProof [EQUIVALENT, 0 ms]
30.41/15.89	            (62) QDP
30.41/15.89	            (63) InductionCalculusProof [EQUIVALENT, 0 ms]
30.41/15.89	            (64) QDP
30.41/15.89	(65) Narrow [COMPLETE, 0 ms]
30.41/15.89	(66) TRUE
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(0)
30.41/15.89	Obligation:
30.41/15.89	mainModule Main 
30.41/15.89	module Main where {
30.41/15.89	import qualified Prelude;
30.41/15.89	}
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(1) IFR (EQUIVALENT)
30.41/15.89	If Reductions:
30.41/15.89	The following If expression
30.41/15.89	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
30.41/15.89	is transformed to
30.41/15.89	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
30.41/15.89	primModNatS0 x y False = Succ x;
30.41/15.89	"
30.41/15.89	The following If expression
30.41/15.89	"if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x"
30.41/15.89	is transformed to
30.41/15.89	"primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y);
30.41/15.89	primModNatP0 x y False = primMinusNatS y x;
30.41/15.89	"
30.41/15.89	The following If expression
30.41/15.89	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
30.41/15.89	is transformed to
30.41/15.89	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
30.41/15.89	primDivNatS0 x y False = Zero;
30.41/15.89	"
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(2)
30.41/15.89	Obligation:
30.41/15.89	mainModule Main 
30.41/15.89	module Main where {
30.41/15.89	import qualified Prelude;
30.41/15.89	}
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(3) BR (EQUIVALENT)
30.41/15.89	Replaced joker patterns by fresh variables and removed binding patterns.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(4)
30.41/15.89	Obligation:
30.41/15.89	mainModule Main 
30.41/15.89	module Main where {
30.41/15.89	import qualified Prelude;
30.41/15.89	}
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(5) COR (EQUIVALENT)
30.41/15.89	Cond Reductions:
30.41/15.89	The following Function with conditions
30.41/15.89	"undefined |Falseundefined;
30.41/15.89	"
30.41/15.89	is transformed to
30.41/15.89	"undefined  = undefined1;
30.41/15.89	"
30.41/15.89	"undefined0 True = undefined;
30.41/15.89	"
30.41/15.89	"undefined1  = undefined0 False;
30.41/15.89	"
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(6)
30.41/15.89	Obligation:
30.41/15.89	mainModule Main 
30.41/15.89	module Main where {
30.41/15.89	import qualified Prelude;
30.41/15.89	}
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(7) NumRed (SOUND)
30.41/15.89	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(8)
30.41/15.89	Obligation:
30.41/15.89	mainModule Main 
30.41/15.89	module Main where {
30.41/15.89	import qualified Prelude;
30.41/15.89	}
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(9) Narrow (SOUND)
30.41/15.89	Haskell To QDPs
30.41/15.89	
30.41/15.89	digraph dp_graph {
30.41/15.89	node [outthreshold=100, inthreshold=100];1[label="shows",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
30.41/15.89	3[label="shows ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
30.41/15.89	4[label="shows ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
30.41/15.89	5[label="showsPrec (Pos Zero) ww3 ww4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
30.41/15.89	6 -> 36[label="",style="dashed", color="red", weight=0];
30.41/15.89	6[label="show ww3 ++ ww4",fontsize=16,color="magenta"];6 -> 37[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	6 -> 38[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	37[label="ww4",fontsize=16,color="green",shape="box"];38[label="show ww3",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
30.41/15.89	36[label="ww21 ++ ww20",fontsize=16,color="burlywood",shape="triangle"];924[label="ww21/ww210 : ww211",fontsize=10,color="white",style="solid",shape="box"];36 -> 924[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	924 -> 53[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	925[label="ww21/[]",fontsize=10,color="white",style="solid",shape="box"];36 -> 925[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	925 -> 54[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	52[label="primShowInt ww3",fontsize=16,color="burlywood",shape="triangle"];926[label="ww3/Pos ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 926[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	926 -> 55[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	927[label="ww3/Neg ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 927[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	927 -> 56[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	53[label="(ww210 : ww211) ++ ww20",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
30.41/15.89	54[label="[] ++ ww20",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
30.41/15.89	55[label="primShowInt (Pos ww30)",fontsize=16,color="burlywood",shape="box"];928[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];55 -> 928[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	928 -> 59[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	929[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 929[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	929 -> 60[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	56[label="primShowInt (Neg ww30)",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3];
30.41/15.89	57[label="ww210 : ww211 ++ ww20",fontsize=16,color="green",shape="box"];57 -> 62[label="",style="dashed", color="green", weight=3];
30.41/15.89	58[label="ww20",fontsize=16,color="green",shape="box"];59[label="primShowInt (Pos (Succ ww300))",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
30.41/15.89	60[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
30.41/15.89	61[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos ww30)",fontsize=16,color="green",shape="box"];61 -> 65[label="",style="dashed", color="green", weight=3];
30.41/15.89	62 -> 36[label="",style="dashed", color="red", weight=0];
30.41/15.89	62[label="ww211 ++ ww20",fontsize=16,color="magenta"];62 -> 66[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	63 -> 36[label="",style="dashed", color="red", weight=0];
30.41/15.89	63[label="primShowInt (div Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];63 -> 67[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	63 -> 68[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	64[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))) : []",fontsize=16,color="green",shape="box"];65 -> 52[label="",style="dashed", color="red", weight=0];
30.41/15.89	65[label="primShowInt (Pos ww30)",fontsize=16,color="magenta"];65 -> 69[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	66[label="ww211",fontsize=16,color="green",shape="box"];67[label="toEnum (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];67 -> 70[label="",style="dashed", color="green", weight=3];
30.41/15.89	68 -> 52[label="",style="dashed", color="red", weight=0];
30.41/15.89	68[label="primShowInt (div Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];68 -> 71[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	69[label="Pos ww30",fontsize=16,color="green",shape="box"];70[label="toEnum (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];70 -> 88[label="",style="solid", color="black", weight=3];
30.41/15.89	71 -> 75[label="",style="dashed", color="red", weight=0];
30.41/15.89	71[label="div Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];71 -> 76[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	71 -> 77[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	88 -> 99[label="",style="dashed", color="red", weight=0];
30.41/15.89	88[label="primIntToChar (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];88 -> 100[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	88 -> 101[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	76[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];77[label="ww300",fontsize=16,color="green",shape="box"];75[label="div Pos (Succ ww26) Pos (Succ ww27)",fontsize=16,color="black",shape="triangle"];75 -> 87[label="",style="solid", color="black", weight=3];
30.41/15.89	100[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];101[label="ww300",fontsize=16,color="green",shape="box"];99[label="primIntToChar (mod Pos (Succ ww29) Pos (Succ ww30))",fontsize=16,color="black",shape="triangle"];99 -> 102[label="",style="solid", color="black", weight=3];
30.41/15.89	87[label="primDivInt (Pos (Succ ww26)) (Pos (Succ ww27))",fontsize=16,color="black",shape="box"];87 -> 98[label="",style="solid", color="black", weight=3];
30.41/15.89	102[label="primIntToChar (primModInt (Pos (Succ ww29)) (Pos (Succ ww30)))",fontsize=16,color="black",shape="box"];102 -> 104[label="",style="solid", color="black", weight=3];
30.41/15.89	98[label="Pos (primDivNatS (Succ ww26) (Succ ww27))",fontsize=16,color="green",shape="box"];98 -> 103[label="",style="dashed", color="green", weight=3];
30.41/15.89	104[label="primIntToChar (Pos (primModNatS (Succ ww29) (Succ ww30)))",fontsize=16,color="black",shape="box"];104 -> 106[label="",style="solid", color="black", weight=3];
30.41/15.89	103[label="primDivNatS (Succ ww26) (Succ ww27)",fontsize=16,color="black",shape="triangle"];103 -> 105[label="",style="solid", color="black", weight=3];
30.41/15.89	106[label="Char (primModNatS (Succ ww29) (Succ ww30))",fontsize=16,color="green",shape="box"];106 -> 109[label="",style="dashed", color="green", weight=3];
30.41/15.89	105[label="primDivNatS0 ww26 ww27 (primGEqNatS ww26 ww27)",fontsize=16,color="burlywood",shape="box"];930[label="ww26/Succ ww260",fontsize=10,color="white",style="solid",shape="box"];105 -> 930[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	930 -> 107[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	931[label="ww26/Zero",fontsize=10,color="white",style="solid",shape="box"];105 -> 931[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	931 -> 108[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	109[label="primModNatS (Succ ww29) (Succ ww30)",fontsize=16,color="black",shape="triangle"];109 -> 114[label="",style="solid", color="black", weight=3];
30.41/15.89	107[label="primDivNatS0 (Succ ww260) ww27 (primGEqNatS (Succ ww260) ww27)",fontsize=16,color="burlywood",shape="box"];932[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];107 -> 932[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	932 -> 110[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	933[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 933[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	933 -> 111[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	108[label="primDivNatS0 Zero ww27 (primGEqNatS Zero ww27)",fontsize=16,color="burlywood",shape="box"];934[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];108 -> 934[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	934 -> 112[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	935[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];108 -> 935[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	935 -> 113[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	114[label="primModNatS0 ww29 ww30 (primGEqNatS ww29 ww30)",fontsize=16,color="burlywood",shape="box"];936[label="ww29/Succ ww290",fontsize=10,color="white",style="solid",shape="box"];114 -> 936[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	936 -> 119[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	937[label="ww29/Zero",fontsize=10,color="white",style="solid",shape="box"];114 -> 937[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	937 -> 120[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	110[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS (Succ ww260) (Succ ww270))",fontsize=16,color="black",shape="box"];110 -> 115[label="",style="solid", color="black", weight=3];
30.41/15.89	111[label="primDivNatS0 (Succ ww260) Zero (primGEqNatS (Succ ww260) Zero)",fontsize=16,color="black",shape="box"];111 -> 116[label="",style="solid", color="black", weight=3];
30.41/15.89	112[label="primDivNatS0 Zero (Succ ww270) (primGEqNatS Zero (Succ ww270))",fontsize=16,color="black",shape="box"];112 -> 117[label="",style="solid", color="black", weight=3];
30.41/15.89	113[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];113 -> 118[label="",style="solid", color="black", weight=3];
30.41/15.89	119[label="primModNatS0 (Succ ww290) ww30 (primGEqNatS (Succ ww290) ww30)",fontsize=16,color="burlywood",shape="box"];938[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];119 -> 938[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	938 -> 126[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	939[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];119 -> 939[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	939 -> 127[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	120[label="primModNatS0 Zero ww30 (primGEqNatS Zero ww30)",fontsize=16,color="burlywood",shape="box"];940[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];120 -> 940[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	940 -> 128[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	941[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];120 -> 941[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	941 -> 129[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	115 -> 640[label="",style="dashed", color="red", weight=0];
30.41/15.89	115[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS ww260 ww270)",fontsize=16,color="magenta"];115 -> 641[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	115 -> 642[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	115 -> 643[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	115 -> 644[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	116[label="primDivNatS0 (Succ ww260) Zero True",fontsize=16,color="black",shape="box"];116 -> 123[label="",style="solid", color="black", weight=3];
30.41/15.89	117[label="primDivNatS0 Zero (Succ ww270) False",fontsize=16,color="black",shape="box"];117 -> 124[label="",style="solid", color="black", weight=3];
30.41/15.89	118[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];118 -> 125[label="",style="solid", color="black", weight=3];
30.41/15.89	126[label="primModNatS0 (Succ ww290) (Succ ww300) (primGEqNatS (Succ ww290) (Succ ww300))",fontsize=16,color="black",shape="box"];126 -> 136[label="",style="solid", color="black", weight=3];
30.41/15.89	127[label="primModNatS0 (Succ ww290) Zero (primGEqNatS (Succ ww290) Zero)",fontsize=16,color="black",shape="box"];127 -> 137[label="",style="solid", color="black", weight=3];
30.41/15.89	128[label="primModNatS0 Zero (Succ ww300) (primGEqNatS Zero (Succ ww300))",fontsize=16,color="black",shape="box"];128 -> 138[label="",style="solid", color="black", weight=3];
30.41/15.89	129[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];129 -> 139[label="",style="solid", color="black", weight=3];
30.41/15.89	641[label="ww260",fontsize=16,color="green",shape="box"];642[label="ww260",fontsize=16,color="green",shape="box"];643[label="ww270",fontsize=16,color="green",shape="box"];644[label="ww270",fontsize=16,color="green",shape="box"];640[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww75 ww76)",fontsize=16,color="burlywood",shape="triangle"];942[label="ww75/Succ ww750",fontsize=10,color="white",style="solid",shape="box"];640 -> 942[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	942 -> 681[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	943[label="ww75/Zero",fontsize=10,color="white",style="solid",shape="box"];640 -> 943[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	943 -> 682[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	123[label="Succ (primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];123 -> 134[label="",style="dashed", color="green", weight=3];
30.41/15.89	124[label="Zero",fontsize=16,color="green",shape="box"];125[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];125 -> 135[label="",style="dashed", color="green", weight=3];
30.41/15.89	136 -> 701[label="",style="dashed", color="red", weight=0];
30.41/15.89	136[label="primModNatS0 (Succ ww290) (Succ ww300) (primGEqNatS ww290 ww300)",fontsize=16,color="magenta"];136 -> 702[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	136 -> 703[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	136 -> 704[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	136 -> 705[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	137[label="primModNatS0 (Succ ww290) Zero True",fontsize=16,color="black",shape="box"];137 -> 148[label="",style="solid", color="black", weight=3];
30.41/15.89	138[label="primModNatS0 Zero (Succ ww300) False",fontsize=16,color="black",shape="box"];138 -> 149[label="",style="solid", color="black", weight=3];
30.41/15.89	139[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];139 -> 150[label="",style="solid", color="black", weight=3];
30.41/15.89	681[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) ww76)",fontsize=16,color="burlywood",shape="box"];944[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];681 -> 944[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	944 -> 693[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	945[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 945[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	945 -> 694[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	682[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero ww76)",fontsize=16,color="burlywood",shape="box"];946[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];682 -> 946[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	946 -> 695[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	947[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];682 -> 947[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	947 -> 696[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	134 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.89	134[label="primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero)",fontsize=16,color="magenta"];134 -> 885[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	134 -> 886[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	134 -> 887[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	135 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.89	135[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];135 -> 888[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	135 -> 889[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	135 -> 890[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	702[label="ww290",fontsize=16,color="green",shape="box"];703[label="ww290",fontsize=16,color="green",shape="box"];704[label="ww300",fontsize=16,color="green",shape="box"];705[label="ww300",fontsize=16,color="green",shape="box"];701[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS ww80 ww81)",fontsize=16,color="burlywood",shape="triangle"];948[label="ww80/Succ ww800",fontsize=10,color="white",style="solid",shape="box"];701 -> 948[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	948 -> 742[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	949[label="ww80/Zero",fontsize=10,color="white",style="solid",shape="box"];701 -> 949[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	949 -> 743[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	148 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.89	148[label="primModNatS (primMinusNatS (Succ ww290) Zero) (Succ Zero)",fontsize=16,color="magenta"];148 -> 789[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	148 -> 790[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	148 -> 791[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	149[label="Succ Zero",fontsize=16,color="green",shape="box"];150 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.89	150[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];150 -> 792[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	150 -> 793[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	150 -> 794[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	693[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) (Succ ww760))",fontsize=16,color="black",shape="box"];693 -> 744[label="",style="solid", color="black", weight=3];
30.41/15.89	694[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) Zero)",fontsize=16,color="black",shape="box"];694 -> 745[label="",style="solid", color="black", weight=3];
30.41/15.89	695[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero (Succ ww760))",fontsize=16,color="black",shape="box"];695 -> 746[label="",style="solid", color="black", weight=3];
30.41/15.89	696[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];696 -> 747[label="",style="solid", color="black", weight=3];
30.41/15.89	885[label="Zero",fontsize=16,color="green",shape="box"];886[label="Zero",fontsize=16,color="green",shape="box"];887[label="Succ ww260",fontsize=16,color="green",shape="box"];884[label="primDivNatS (primMinusNatS ww87 ww88) (Succ ww89)",fontsize=16,color="burlywood",shape="triangle"];950[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];884 -> 950[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	950 -> 909[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	951[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];884 -> 951[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	951 -> 910[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	888[label="Zero",fontsize=16,color="green",shape="box"];889[label="Zero",fontsize=16,color="green",shape="box"];890[label="Zero",fontsize=16,color="green",shape="box"];742[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS (Succ ww800) ww81)",fontsize=16,color="burlywood",shape="box"];952[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];742 -> 952[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	952 -> 752[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	953[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];742 -> 953[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	953 -> 753[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	743[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS Zero ww81)",fontsize=16,color="burlywood",shape="box"];954[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];743 -> 954[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	954 -> 754[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	955[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];743 -> 955[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	955 -> 755[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	789[label="Succ ww290",fontsize=16,color="green",shape="box"];790[label="Zero",fontsize=16,color="green",shape="box"];791[label="Zero",fontsize=16,color="green",shape="box"];788[label="primModNatS (primMinusNatS ww83 ww84) (Succ ww85)",fontsize=16,color="burlywood",shape="triangle"];956[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];788 -> 956[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	956 -> 819[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	957[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];788 -> 957[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	957 -> 820[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	792[label="Zero",fontsize=16,color="green",shape="box"];793[label="Zero",fontsize=16,color="green",shape="box"];794[label="Zero",fontsize=16,color="green",shape="box"];744 -> 640[label="",style="dashed", color="red", weight=0];
30.41/15.89	744[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww750 ww760)",fontsize=16,color="magenta"];744 -> 756[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	744 -> 757[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	745[label="primDivNatS0 (Succ ww73) (Succ ww74) True",fontsize=16,color="black",shape="triangle"];745 -> 758[label="",style="solid", color="black", weight=3];
30.41/15.89	746[label="primDivNatS0 (Succ ww73) (Succ ww74) False",fontsize=16,color="black",shape="box"];746 -> 759[label="",style="solid", color="black", weight=3];
30.41/15.89	747 -> 745[label="",style="dashed", color="red", weight=0];
30.41/15.89	747[label="primDivNatS0 (Succ ww73) (Succ ww74) True",fontsize=16,color="magenta"];909[label="primDivNatS (primMinusNatS (Succ ww870) ww88) (Succ ww89)",fontsize=16,color="burlywood",shape="box"];958[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];909 -> 958[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	958 -> 911[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	959[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];909 -> 959[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	959 -> 912[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	910[label="primDivNatS (primMinusNatS Zero ww88) (Succ ww89)",fontsize=16,color="burlywood",shape="box"];960[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];910 -> 960[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	960 -> 913[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	961[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];910 -> 961[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	961 -> 914[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	752[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS (Succ ww800) (Succ ww810))",fontsize=16,color="black",shape="box"];752 -> 766[label="",style="solid", color="black", weight=3];
30.41/15.89	753[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS (Succ ww800) Zero)",fontsize=16,color="black",shape="box"];753 -> 767[label="",style="solid", color="black", weight=3];
30.41/15.89	754[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS Zero (Succ ww810))",fontsize=16,color="black",shape="box"];754 -> 768[label="",style="solid", color="black", weight=3];
30.41/15.89	755[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];755 -> 769[label="",style="solid", color="black", weight=3];
30.41/15.89	819[label="primModNatS (primMinusNatS (Succ ww830) ww84) (Succ ww85)",fontsize=16,color="burlywood",shape="box"];962[label="ww84/Succ ww840",fontsize=10,color="white",style="solid",shape="box"];819 -> 962[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	962 -> 825[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	963[label="ww84/Zero",fontsize=10,color="white",style="solid",shape="box"];819 -> 963[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	963 -> 826[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	820[label="primModNatS (primMinusNatS Zero ww84) (Succ ww85)",fontsize=16,color="burlywood",shape="box"];964[label="ww84/Succ ww840",fontsize=10,color="white",style="solid",shape="box"];820 -> 964[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	964 -> 827[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	965[label="ww84/Zero",fontsize=10,color="white",style="solid",shape="box"];820 -> 965[label="",style="solid", color="burlywood", weight=9];
30.41/15.89	965 -> 828[label="",style="solid", color="burlywood", weight=3];
30.41/15.89	756[label="ww750",fontsize=16,color="green",shape="box"];757[label="ww760",fontsize=16,color="green",shape="box"];758[label="Succ (primDivNatS (primMinusNatS (Succ ww73) (Succ ww74)) (Succ (Succ ww74)))",fontsize=16,color="green",shape="box"];758 -> 770[label="",style="dashed", color="green", weight=3];
30.41/15.89	759[label="Zero",fontsize=16,color="green",shape="box"];911[label="primDivNatS (primMinusNatS (Succ ww870) (Succ ww880)) (Succ ww89)",fontsize=16,color="black",shape="box"];911 -> 915[label="",style="solid", color="black", weight=3];
30.41/15.89	912[label="primDivNatS (primMinusNatS (Succ ww870) Zero) (Succ ww89)",fontsize=16,color="black",shape="box"];912 -> 916[label="",style="solid", color="black", weight=3];
30.41/15.89	913[label="primDivNatS (primMinusNatS Zero (Succ ww880)) (Succ ww89)",fontsize=16,color="black",shape="box"];913 -> 917[label="",style="solid", color="black", weight=3];
30.41/15.89	914[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww89)",fontsize=16,color="black",shape="box"];914 -> 918[label="",style="solid", color="black", weight=3];
30.41/15.89	766 -> 701[label="",style="dashed", color="red", weight=0];
30.41/15.89	766[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS ww800 ww810)",fontsize=16,color="magenta"];766 -> 775[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	766 -> 776[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	767[label="primModNatS0 (Succ ww78) (Succ ww79) True",fontsize=16,color="black",shape="triangle"];767 -> 777[label="",style="solid", color="black", weight=3];
30.41/15.89	768[label="primModNatS0 (Succ ww78) (Succ ww79) False",fontsize=16,color="black",shape="box"];768 -> 778[label="",style="solid", color="black", weight=3];
30.41/15.89	769 -> 767[label="",style="dashed", color="red", weight=0];
30.41/15.89	769[label="primModNatS0 (Succ ww78) (Succ ww79) True",fontsize=16,color="magenta"];825[label="primModNatS (primMinusNatS (Succ ww830) (Succ ww840)) (Succ ww85)",fontsize=16,color="black",shape="box"];825 -> 833[label="",style="solid", color="black", weight=3];
30.41/15.89	826[label="primModNatS (primMinusNatS (Succ ww830) Zero) (Succ ww85)",fontsize=16,color="black",shape="box"];826 -> 834[label="",style="solid", color="black", weight=3];
30.41/15.89	827[label="primModNatS (primMinusNatS Zero (Succ ww840)) (Succ ww85)",fontsize=16,color="black",shape="box"];827 -> 835[label="",style="solid", color="black", weight=3];
30.41/15.89	828[label="primModNatS (primMinusNatS Zero Zero) (Succ ww85)",fontsize=16,color="black",shape="box"];828 -> 836[label="",style="solid", color="black", weight=3];
30.41/15.89	770 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.89	770[label="primDivNatS (primMinusNatS (Succ ww73) (Succ ww74)) (Succ (Succ ww74))",fontsize=16,color="magenta"];770 -> 891[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	770 -> 892[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	770 -> 893[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	915 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.89	915[label="primDivNatS (primMinusNatS ww870 ww880) (Succ ww89)",fontsize=16,color="magenta"];915 -> 919[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	915 -> 920[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	916 -> 103[label="",style="dashed", color="red", weight=0];
30.41/15.89	916[label="primDivNatS (Succ ww870) (Succ ww89)",fontsize=16,color="magenta"];916 -> 921[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	916 -> 922[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	917[label="primDivNatS Zero (Succ ww89)",fontsize=16,color="black",shape="triangle"];917 -> 923[label="",style="solid", color="black", weight=3];
30.41/15.89	918 -> 917[label="",style="dashed", color="red", weight=0];
30.41/15.89	918[label="primDivNatS Zero (Succ ww89)",fontsize=16,color="magenta"];775[label="ww800",fontsize=16,color="green",shape="box"];776[label="ww810",fontsize=16,color="green",shape="box"];777 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.89	777[label="primModNatS (primMinusNatS (Succ ww78) (Succ ww79)) (Succ (Succ ww79))",fontsize=16,color="magenta"];777 -> 801[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	777 -> 802[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	777 -> 803[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	778[label="Succ (Succ ww78)",fontsize=16,color="green",shape="box"];833 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.89	833[label="primModNatS (primMinusNatS ww830 ww840) (Succ ww85)",fontsize=16,color="magenta"];833 -> 843[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	833 -> 844[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	834 -> 109[label="",style="dashed", color="red", weight=0];
30.41/15.89	834[label="primModNatS (Succ ww830) (Succ ww85)",fontsize=16,color="magenta"];834 -> 845[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	834 -> 846[label="",style="dashed", color="magenta", weight=3];
30.41/15.89	835[label="primModNatS Zero (Succ ww85)",fontsize=16,color="black",shape="triangle"];835 -> 847[label="",style="solid", color="black", weight=3];
30.41/15.89	836 -> 835[label="",style="dashed", color="red", weight=0];
30.41/15.89	836[label="primModNatS Zero (Succ ww85)",fontsize=16,color="magenta"];891[label="Succ ww74",fontsize=16,color="green",shape="box"];892[label="Succ ww74",fontsize=16,color="green",shape="box"];893[label="Succ ww73",fontsize=16,color="green",shape="box"];919[label="ww880",fontsize=16,color="green",shape="box"];920[label="ww870",fontsize=16,color="green",shape="box"];921[label="ww89",fontsize=16,color="green",shape="box"];922[label="ww870",fontsize=16,color="green",shape="box"];923[label="Zero",fontsize=16,color="green",shape="box"];801[label="Succ ww78",fontsize=16,color="green",shape="box"];802[label="Succ ww79",fontsize=16,color="green",shape="box"];803[label="Succ ww79",fontsize=16,color="green",shape="box"];843[label="ww830",fontsize=16,color="green",shape="box"];844[label="ww840",fontsize=16,color="green",shape="box"];845[label="ww85",fontsize=16,color="green",shape="box"];846[label="ww830",fontsize=16,color="green",shape="box"];847[label="Zero",fontsize=16,color="green",shape="box"];}
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(10)
30.41/15.89	Complex Obligation (AND)
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(11)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS0(ww73, ww74, Zero, Zero) -> new_primDivNatS00(ww73, ww74)
30.41/15.89	   new_primDivNatS00(ww73, ww74) -> new_primDivNatS(Succ(ww73), Succ(ww74), Succ(ww74))
30.41/15.89	   new_primDivNatS(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS1(Succ(ww260), Zero) -> new_primDivNatS(Succ(ww260), Zero, Zero)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS0(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS(Succ(ww73), Succ(ww74), Succ(ww74))
30.41/15.89	   new_primDivNatS1(Succ(ww260), Succ(ww270)) -> new_primDivNatS0(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero)
30.41/15.89	   new_primDivNatS(Succ(ww870), Zero, ww89) -> new_primDivNatS1(ww870, ww89)
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(12) DependencyGraphProof (EQUIVALENT)
30.41/15.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(13)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS00(ww73, ww74) -> new_primDivNatS(Succ(ww73), Succ(ww74), Succ(ww74))
30.41/15.89	   new_primDivNatS(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS(Succ(ww870), Zero, ww89) -> new_primDivNatS1(ww870, ww89)
30.41/15.89	   new_primDivNatS1(Succ(ww260), Zero) -> new_primDivNatS(Succ(ww260), Zero, Zero)
30.41/15.89	   new_primDivNatS1(Succ(ww260), Succ(ww270)) -> new_primDivNatS0(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Zero, Zero) -> new_primDivNatS00(ww73, ww74)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS0(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS(Succ(ww73), Succ(ww74), Succ(ww74))
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(14) QDPOrderProof (EQUIVALENT)
30.41/15.89	We use the reduction pair processor [LPAR04,JAR06].
30.41/15.89	
30.41/15.89	
30.41/15.89	The following pairs can be oriented strictly and are deleted.
30.41/15.89	
30.41/15.89	   new_primDivNatS(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS1(Succ(ww260), Zero) -> new_primDivNatS(Succ(ww260), Zero, Zero)
30.41/15.89	   new_primDivNatS1(Succ(ww260), Succ(ww270)) -> new_primDivNatS0(ww260, ww270, ww260, ww270)
30.41/15.89	The remaining pairs can at least be oriented weakly.
30.41/15.89	Used ordering:  Polynomial interpretation [POLO]:
30.41/15.89	
30.41/15.89	   POL(Succ(x_1)) = 1 + x_1
30.41/15.89	   POL(Zero) = 0
30.41/15.89	   POL(new_primDivNatS(x_1, x_2, x_3)) = x_1
30.41/15.89	   POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
30.41/15.89	   POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1
30.41/15.89	   POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1
30.41/15.89	
30.41/15.89	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
30.41/15.89	none
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(15)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS00(ww73, ww74) -> new_primDivNatS(Succ(ww73), Succ(ww74), Succ(ww74))
30.41/15.89	   new_primDivNatS(Succ(ww870), Zero, ww89) -> new_primDivNatS1(ww870, ww89)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Zero, Zero) -> new_primDivNatS00(ww73, ww74)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS0(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS0(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS(Succ(ww73), Succ(ww74), Succ(ww74))
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(16) DependencyGraphProof (EQUIVALENT)
30.41/15.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(17)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS0(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS0(ww73, ww74, ww750, ww760)
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(18) QDPSizeChangeProof (EQUIVALENT)
30.41/15.89	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
30.41/15.89	
30.41/15.89	From the DPs we obtained the following set of size-change graphs:
30.41/15.89	*new_primDivNatS0(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS0(ww73, ww74, ww750, ww760)
30.41/15.89	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(19)
30.41/15.89	YES
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(20)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_psPs(:(ww210, ww211), ww20) -> new_psPs(ww211, ww20)
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(21) QDPSizeChangeProof (EQUIVALENT)
30.41/15.89	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
30.41/15.89	
30.41/15.89	From the DPs we obtained the following set of size-change graphs:
30.41/15.89	*new_psPs(:(ww210, ww211), ww20) -> new_psPs(ww211, ww20)
30.41/15.89	The graph contains the following edges 1 > 1, 2 >= 2
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(22)
30.41/15.89	YES
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(23)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primModNatS(Succ(ww830), Zero, ww85) -> new_primModNatS1(ww830, ww85)
30.41/15.89	   new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero)
30.41/15.89	   new_primModNatS00(ww78, ww79) -> new_primModNatS(Succ(ww78), Succ(ww79), Succ(ww79))
30.41/15.89	   new_primModNatS0(ww78, ww79, Succ(ww800), Zero) -> new_primModNatS(Succ(ww78), Succ(ww79), Succ(ww79))
30.41/15.89	   new_primModNatS(Succ(ww830), Succ(ww840), ww85) -> new_primModNatS(ww830, ww840, ww85)
30.41/15.89	   new_primModNatS0(ww78, ww79, Succ(ww800), Succ(ww810)) -> new_primModNatS0(ww78, ww79, ww800, ww810)
30.41/15.89	   new_primModNatS1(Succ(ww290), Succ(ww300)) -> new_primModNatS0(ww290, ww300, ww290, ww300)
30.41/15.89	   new_primModNatS0(ww78, ww79, Zero, Zero) -> new_primModNatS00(ww78, ww79)
30.41/15.89	   new_primModNatS1(Succ(ww290), Zero) -> new_primModNatS(Succ(ww290), Zero, Zero)
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(24) DependencyGraphProof (EQUIVALENT)
30.41/15.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(25)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primModNatS1(Succ(ww290), Succ(ww300)) -> new_primModNatS0(ww290, ww300, ww290, ww300)
30.41/15.89	   new_primModNatS0(ww78, ww79, Succ(ww800), Zero) -> new_primModNatS(Succ(ww78), Succ(ww79), Succ(ww79))
30.41/15.89	   new_primModNatS(Succ(ww830), Succ(ww840), ww85) -> new_primModNatS(ww830, ww840, ww85)
30.41/15.89	   new_primModNatS(Succ(ww830), Zero, ww85) -> new_primModNatS1(ww830, ww85)
30.41/15.89	   new_primModNatS1(Succ(ww290), Zero) -> new_primModNatS(Succ(ww290), Zero, Zero)
30.41/15.89	   new_primModNatS0(ww78, ww79, Succ(ww800), Succ(ww810)) -> new_primModNatS0(ww78, ww79, ww800, ww810)
30.41/15.89	   new_primModNatS0(ww78, ww79, Zero, Zero) -> new_primModNatS00(ww78, ww79)
30.41/15.89	   new_primModNatS00(ww78, ww79) -> new_primModNatS(Succ(ww78), Succ(ww79), Succ(ww79))
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(26) QDPOrderProof (EQUIVALENT)
30.41/15.89	We use the reduction pair processor [LPAR04,JAR06].
30.41/15.89	
30.41/15.89	
30.41/15.89	The following pairs can be oriented strictly and are deleted.
30.41/15.89	
30.41/15.89	   new_primModNatS1(Succ(ww290), Succ(ww300)) -> new_primModNatS0(ww290, ww300, ww290, ww300)
30.41/15.89	   new_primModNatS(Succ(ww830), Succ(ww840), ww85) -> new_primModNatS(ww830, ww840, ww85)
30.41/15.89	   new_primModNatS1(Succ(ww290), Zero) -> new_primModNatS(Succ(ww290), Zero, Zero)
30.41/15.89	The remaining pairs can at least be oriented weakly.
30.41/15.89	Used ordering:  Polynomial interpretation [POLO]:
30.41/15.89	
30.41/15.89	   POL(Succ(x_1)) = 1 + x_1
30.41/15.89	   POL(Zero) = 0
30.41/15.89	   POL(new_primModNatS(x_1, x_2, x_3)) = x_1
30.41/15.89	   POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
30.41/15.89	   POL(new_primModNatS00(x_1, x_2)) = 1 + x_1
30.41/15.89	   POL(new_primModNatS1(x_1, x_2)) = 1 + x_1
30.41/15.89	
30.41/15.89	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
30.41/15.89	none
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(27)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primModNatS0(ww78, ww79, Succ(ww800), Zero) -> new_primModNatS(Succ(ww78), Succ(ww79), Succ(ww79))
30.41/15.89	   new_primModNatS(Succ(ww830), Zero, ww85) -> new_primModNatS1(ww830, ww85)
30.41/15.89	   new_primModNatS0(ww78, ww79, Succ(ww800), Succ(ww810)) -> new_primModNatS0(ww78, ww79, ww800, ww810)
30.41/15.89	   new_primModNatS0(ww78, ww79, Zero, Zero) -> new_primModNatS00(ww78, ww79)
30.41/15.89	   new_primModNatS00(ww78, ww79) -> new_primModNatS(Succ(ww78), Succ(ww79), Succ(ww79))
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(28) DependencyGraphProof (EQUIVALENT)
30.41/15.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(29)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primModNatS0(ww78, ww79, Succ(ww800), Succ(ww810)) -> new_primModNatS0(ww78, ww79, ww800, ww810)
30.41/15.89	
30.41/15.89	R is empty.
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(30) QDPSizeChangeProof (EQUIVALENT)
30.41/15.89	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
30.41/15.89	
30.41/15.89	From the DPs we obtained the following set of size-change graphs:
30.41/15.89	*new_primModNatS0(ww78, ww79, Succ(ww800), Succ(ww810)) -> new_primModNatS0(ww78, ww79, ww800, ww810)
30.41/15.89	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(31)
30.41/15.89	YES
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(32)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primShowInt(Neg(ww30)) -> new_primShowInt(Pos(ww30))
30.41/15.89	   new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(new_div(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
30.41/15.89	
30.41/15.89	The TRS R consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.89	   new_div(ww26, ww27) -> Pos(new_primDivNatS3(ww26, ww27))
30.41/15.89	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.89	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.89	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS4(ww89) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.89	
30.41/15.89	The set Q consists of the following terms:
30.41/15.89	
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.89	   new_div(x0, x1)
30.41/15.89	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.89	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.89	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.89	   new_primDivNatS4(x0)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.89	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.89	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.89	   new_primDivNatS02(x0, x1)
30.41/15.89	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.89	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.89	   new_primDivNatS3(Zero, Zero)
30.41/15.89	
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(33) DependencyGraphProof (EQUIVALENT)
30.41/15.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(34)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(new_div(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
30.41/15.89	
30.41/15.89	The TRS R consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.89	   new_div(ww26, ww27) -> Pos(new_primDivNatS3(ww26, ww27))
30.41/15.89	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.89	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.89	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS4(ww89) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.89	
30.41/15.89	The set Q consists of the following terms:
30.41/15.89	
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.89	   new_div(x0, x1)
30.41/15.89	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.89	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.89	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.89	   new_primDivNatS4(x0)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.89	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.89	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.89	   new_primDivNatS02(x0, x1)
30.41/15.89	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.89	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.89	   new_primDivNatS3(Zero, Zero)
30.41/15.89	
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(35) TransformationProof (EQUIVALENT)
30.41/15.89	By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(new_div(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]:
30.41/15.89	
30.41/15.89	   (new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(36)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
30.41/15.89	
30.41/15.89	The TRS R consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.89	   new_div(ww26, ww27) -> Pos(new_primDivNatS3(ww26, ww27))
30.41/15.89	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.89	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.89	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS4(ww89) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.89	
30.41/15.89	The set Q consists of the following terms:
30.41/15.89	
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.89	   new_div(x0, x1)
30.41/15.89	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.89	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.89	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.89	   new_primDivNatS4(x0)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.89	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.89	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.89	   new_primDivNatS02(x0, x1)
30.41/15.89	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.89	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.89	   new_primDivNatS3(Zero, Zero)
30.41/15.89	
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(37) UsableRulesProof (EQUIVALENT)
30.41/15.89	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(38)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
30.41/15.89	
30.41/15.89	The TRS R consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.89	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.89	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS4(ww89) -> Zero
30.41/15.89	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.89	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.89	
30.41/15.89	The set Q consists of the following terms:
30.41/15.89	
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.89	   new_div(x0, x1)
30.41/15.89	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.89	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.89	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.89	   new_primDivNatS4(x0)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.89	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.89	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.89	   new_primDivNatS02(x0, x1)
30.41/15.89	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.89	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.89	   new_primDivNatS3(Zero, Zero)
30.41/15.89	
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(39) QReductionProof (EQUIVALENT)
30.41/15.89	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
30.41/15.89	
30.41/15.89	   new_div(x0, x1)
30.41/15.89	
30.41/15.89	
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(40)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
30.41/15.89	
30.41/15.89	The TRS R consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.89	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.89	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS4(ww89) -> Zero
30.41/15.89	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.89	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.89	
30.41/15.89	The set Q consists of the following terms:
30.41/15.89	
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.89	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.89	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.89	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.89	   new_primDivNatS4(x0)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.89	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.89	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.89	   new_primDivNatS02(x0, x1)
30.41/15.89	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.89	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.89	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.89	   new_primDivNatS3(Zero, Zero)
30.41/15.89	
30.41/15.89	We have to consider all minimal (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(41) MNOCProof (EQUIVALENT)
30.41/15.89	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(42)
30.41/15.89	Obligation:
30.41/15.89	Q DP problem:
30.41/15.89	The TRS P consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
30.41/15.89	
30.41/15.89	The TRS R consists of the following rules:
30.41/15.89	
30.41/15.89	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.89	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.89	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.89	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.89	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.89	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.89	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.89	   new_primDivNatS4(ww89) -> Zero
30.41/15.89	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.89	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.89	
30.41/15.89	Q is empty.
30.41/15.89	We have to consider all (P,Q,R)-chains.
30.41/15.89	----------------------------------------
30.41/15.89	
30.41/15.89	(43) InductionCalculusProof (EQUIVALENT)
30.41/15.89	Note that final constraints are written in bold face.
30.41/15.89	
30.41/15.89	
30.41/15.89	
30.41/15.89	For Pair new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) the following chains were created:
30.41/15.89	*We consider the chain new_primShowInt(Pos(Succ(x0))) -> new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), new_primShowInt(Pos(Succ(x1))) -> new_primShowInt(Pos(new_primDivNatS3(x1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) which results in the following constraint:
30.41/15.89	
30.41/15.89	(1)    (new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))=new_primShowInt(Pos(Succ(x1)))  ==>  new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.89	
30.41/15.89	
30.41/15.89	
30.41/15.89	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
30.41/15.89	
30.41/15.89	(2)    (Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=x2 & new_primDivNatS3(x0, x2)=Succ(x1)  ==>  new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.89	
30.41/15.89	
30.41/15.89	
30.41/15.89	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS3(x0, x2)=Succ(x1) which results in the following new constraints:
30.41/15.89	
30.41/15.89	(3)    (new_primDivNatS01(x4, x3, x4, x3)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Succ(x3)  ==>  new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.89	
30.41/15.89	(4)    (Succ(new_primDivNatS2(Succ(x6), Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(x6))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x6), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.89	
30.41/15.89	(5)    (Succ(new_primDivNatS2(Zero, Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero  ==>  new_primShowInt(Pos(Succ(Zero)))_>=_new_primShowInt(Pos(new_primDivNatS3(Zero, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.89	
30.41/15.89	
30.41/15.89	
30.41/15.89	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
30.41/15.89	
30.41/15.89	(6)    (x4=x7 & x3=x8 & new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3  ==>  new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.89	
30.41/15.89	
30.41/15.89	
30.41/15.89	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints:
30.41/15.90	
30.41/15.90	(7)    (new_primDivNatS02(x10, x9)=Succ(x1) & x10=Zero & x9=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x9  ==>  new_primShowInt(Pos(Succ(Succ(x10))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x10), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.90	
30.41/15.90	(8)    (new_primDivNatS02(x16, x15)=Succ(x1) & x16=Succ(x14) & x15=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15  ==>  new_primShowInt(Pos(Succ(Succ(x16))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x16), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.90	
30.41/15.90	(9)    (new_primDivNatS01(x20, x19, x18, x17)=Succ(x1) & x20=Succ(x18) & x19=Succ(x17) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 & (\/x21:new_primDivNatS01(x20, x19, x18, x17)=Succ(x21) & x20=x18 & x19=x17 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19  ==>  new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))  ==>  new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	We solved constraint (7) using rules (I), (II), (III).We solved constraint (8) using rules (I), (II), (III).We simplified constraint (9) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
30.41/15.90	
30.41/15.90	(10)    (new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	To summarize, we get the following constraints P__>=_ for the following pairs.
30.41/15.90	
30.41/15.90	*new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
30.41/15.90	
30.41/15.90	*(new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by  "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(44)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(45) TransformationProof (EQUIVALENT)
30.41/15.90	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww300))) -> new_primShowInt(Pos(new_primDivNatS3(ww300, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
30.41/15.90	
30.41/15.90	   (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))),new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
30.41/15.90	   (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)))
30.41/15.90	
30.41/15.90	
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(46)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
30.41/15.90	   new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(47) DependencyGraphProof (EQUIVALENT)
30.41/15.90	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(48)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(49) TransformationProof (EQUIVALENT)
30.41/15.90	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
30.41/15.90	
30.41/15.90	   (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)))
30.41/15.90	   (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))),new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(50)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(51) DependencyGraphProof (EQUIVALENT)
30.41/15.90	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(52)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(53) TransformationProof (EQUIVALENT)
30.41/15.90	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
30.41/15.90	
30.41/15.90	   (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)))
30.41/15.90	   (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(54)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(55) DependencyGraphProof (EQUIVALENT)
30.41/15.90	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(56)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(57) TransformationProof (EQUIVALENT)
30.41/15.90	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
30.41/15.90	
30.41/15.90	   (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)))
30.41/15.90	   (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(58)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(59) DependencyGraphProof (EQUIVALENT)
30.41/15.90	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(60)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(61) MNOCProof (EQUIVALENT)
30.41/15.90	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(62)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	Q is empty.
30.41/15.90	We have to consider all (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(63) InductionCalculusProof (EQUIVALENT)
30.41/15.90	Note that final constraints are written in bold face.
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) the following chains were created:
30.41/15.90	*We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))), new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x1))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x1, Succ(Succ(Succ(Succ(Succ(Zero)))))))) which results in the following constraint:
30.41/15.90	
30.41/15.90	(1)    (new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))=new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1)))))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
30.41/15.90	
30.41/15.90	(2)    (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1)))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints:
30.41/15.90	
30.41/15.90	(3)    (new_primDivNatS02(x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x6 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x5 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	(4)    (new_primDivNatS02(x12, x11)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x10))))=x12 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x10))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	(5)    (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x13) & (\/x17:new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x17))))) & Succ(Succ(Succ(x14)))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x13  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x14)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x14))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x14, Succ(Succ(Succ(Succ(Succ(Zero)))))))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	We solved constraint (3) using rules (I), (II).We solved constraint (4) using rules (I), (II).We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
30.41/15.90	
30.41/15.90	(6)    (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Zero))))=x13  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints:
30.41/15.90	
30.41/15.90	(7)    (new_primDivNatS02(x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x19 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x18 & Succ(Succ(Succ(Succ(Zero))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	(8)    (new_primDivNatS02(x25, x24)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x23)))))=x25 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x24 & Succ(Succ(Succ(Succ(Zero))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x23)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	(9)    (new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x27)))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=Succ(x26) & (\/x30:new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x30))))) & Succ(Succ(Succ(Succ(x27))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=x26  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x27)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x27), Succ(Succ(Succ(Succ(Succ(Zero)))))))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	We solved constraint (7) using rules (I), (II).We solved constraint (8) using rules (I), (II).We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint:
30.41/15.90	
30.41/15.90	(10)    (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	To summarize, we get the following constraints P__>=_ for the following pairs.
30.41/15.90	
30.41/15.90	*new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
30.41/15.90	
30.41/15.90	*(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	
30.41/15.90	The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by  "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(64)
30.41/15.90	Obligation:
30.41/15.90	Q DP problem:
30.41/15.90	The TRS P consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
30.41/15.90	
30.41/15.90	The TRS R consists of the following rules:
30.41/15.90	
30.41/15.90	   new_primDivNatS3(Succ(ww260), Succ(ww270)) -> new_primDivNatS01(ww260, ww270, ww260, ww270)
30.41/15.90	   new_primDivNatS3(Zero, Succ(ww270)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Zero, Succ(ww760)) -> Zero
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Zero) -> new_primDivNatS02(ww73, ww74)
30.41/15.90	   new_primDivNatS01(ww73, ww74, Succ(ww750), Succ(ww760)) -> new_primDivNatS01(ww73, ww74, ww750, ww760)
30.41/15.90	   new_primDivNatS02(ww73, ww74) -> Succ(new_primDivNatS2(Succ(ww73), Succ(ww74), Succ(ww74)))
30.41/15.90	   new_primDivNatS2(Succ(ww870), Succ(ww880), ww89) -> new_primDivNatS2(ww870, ww880, ww89)
30.41/15.90	   new_primDivNatS2(Succ(ww870), Zero, ww89) -> new_primDivNatS3(ww870, ww89)
30.41/15.90	   new_primDivNatS2(Zero, Zero, ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS2(Zero, Succ(ww880), ww89) -> new_primDivNatS4(ww89)
30.41/15.90	   new_primDivNatS4(ww89) -> Zero
30.41/15.90	   new_primDivNatS3(Succ(ww260), Zero) -> Succ(new_primDivNatS2(Succ(ww260), Zero, Zero))
30.41/15.90	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
30.41/15.90	
30.41/15.90	The set Q consists of the following terms:
30.41/15.90	
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
30.41/15.90	   new_primDivNatS3(Zero, Succ(x0))
30.41/15.90	   new_primDivNatS2(Zero, Succ(x0), x1)
30.41/15.90	   new_primDivNatS2(Zero, Zero, x0)
30.41/15.90	   new_primDivNatS4(x0)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
30.41/15.90	   new_primDivNatS3(Succ(x0), Succ(x1))
30.41/15.90	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
30.41/15.90	   new_primDivNatS02(x0, x1)
30.41/15.90	   new_primDivNatS3(Succ(x0), Zero)
30.41/15.90	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
30.41/15.90	   new_primDivNatS2(Succ(x0), Zero, x1)
30.41/15.90	   new_primDivNatS3(Zero, Zero)
30.41/15.90	
30.41/15.90	We have to consider all minimal (P,Q,R)-chains.
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(65) Narrow (COMPLETE)
30.41/15.90	Haskell To QDPs
30.41/15.90	
30.41/15.90	digraph dp_graph {
30.41/15.90	node [outthreshold=100, inthreshold=100];1[label="shows",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
30.41/15.90	3[label="shows ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
30.41/15.90	4[label="shows ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
30.41/15.90	5[label="showsPrec (Pos Zero) ww3 ww4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
30.41/15.90	6 -> 36[label="",style="dashed", color="red", weight=0];
30.41/15.90	6[label="show ww3 ++ ww4",fontsize=16,color="magenta"];6 -> 37[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	6 -> 38[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	37[label="ww4",fontsize=16,color="green",shape="box"];38[label="show ww3",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
30.41/15.90	36[label="ww21 ++ ww20",fontsize=16,color="burlywood",shape="triangle"];924[label="ww21/ww210 : ww211",fontsize=10,color="white",style="solid",shape="box"];36 -> 924[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	924 -> 53[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	925[label="ww21/[]",fontsize=10,color="white",style="solid",shape="box"];36 -> 925[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	925 -> 54[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	52[label="primShowInt ww3",fontsize=16,color="burlywood",shape="triangle"];926[label="ww3/Pos ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 926[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	926 -> 55[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	927[label="ww3/Neg ww30",fontsize=10,color="white",style="solid",shape="box"];52 -> 927[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	927 -> 56[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	53[label="(ww210 : ww211) ++ ww20",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
30.41/15.90	54[label="[] ++ ww20",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
30.41/15.90	55[label="primShowInt (Pos ww30)",fontsize=16,color="burlywood",shape="box"];928[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];55 -> 928[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	928 -> 59[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	929[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 929[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	929 -> 60[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	56[label="primShowInt (Neg ww30)",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3];
30.41/15.90	57[label="ww210 : ww211 ++ ww20",fontsize=16,color="green",shape="box"];57 -> 62[label="",style="dashed", color="green", weight=3];
30.41/15.90	58[label="ww20",fontsize=16,color="green",shape="box"];59[label="primShowInt (Pos (Succ ww300))",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
30.41/15.90	60[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
30.41/15.90	61[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos ww30)",fontsize=16,color="green",shape="box"];61 -> 65[label="",style="dashed", color="green", weight=3];
30.41/15.90	62 -> 36[label="",style="dashed", color="red", weight=0];
30.41/15.90	62[label="ww211 ++ ww20",fontsize=16,color="magenta"];62 -> 66[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	63 -> 36[label="",style="dashed", color="red", weight=0];
30.41/15.90	63[label="primShowInt (div Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];63 -> 67[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	63 -> 68[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	64[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))) : []",fontsize=16,color="green",shape="box"];65 -> 52[label="",style="dashed", color="red", weight=0];
30.41/15.90	65[label="primShowInt (Pos ww30)",fontsize=16,color="magenta"];65 -> 69[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	66[label="ww211",fontsize=16,color="green",shape="box"];67[label="toEnum (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];67 -> 70[label="",style="dashed", color="green", weight=3];
30.41/15.90	68 -> 52[label="",style="dashed", color="red", weight=0];
30.41/15.90	68[label="primShowInt (div Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];68 -> 71[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	69[label="Pos ww30",fontsize=16,color="green",shape="box"];70[label="toEnum (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];70 -> 88[label="",style="solid", color="black", weight=3];
30.41/15.90	71 -> 75[label="",style="dashed", color="red", weight=0];
30.41/15.90	71[label="div Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];71 -> 76[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	71 -> 77[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	88 -> 99[label="",style="dashed", color="red", weight=0];
30.41/15.90	88[label="primIntToChar (mod Pos (Succ ww300) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];88 -> 100[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	88 -> 101[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	76[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];77[label="ww300",fontsize=16,color="green",shape="box"];75[label="div Pos (Succ ww26) Pos (Succ ww27)",fontsize=16,color="black",shape="triangle"];75 -> 87[label="",style="solid", color="black", weight=3];
30.41/15.90	100[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];101[label="ww300",fontsize=16,color="green",shape="box"];99[label="primIntToChar (mod Pos (Succ ww29) Pos (Succ ww30))",fontsize=16,color="black",shape="triangle"];99 -> 102[label="",style="solid", color="black", weight=3];
30.41/15.90	87[label="primDivInt (Pos (Succ ww26)) (Pos (Succ ww27))",fontsize=16,color="black",shape="box"];87 -> 98[label="",style="solid", color="black", weight=3];
30.41/15.90	102[label="primIntToChar (primModInt (Pos (Succ ww29)) (Pos (Succ ww30)))",fontsize=16,color="black",shape="box"];102 -> 104[label="",style="solid", color="black", weight=3];
30.41/15.90	98[label="Pos (primDivNatS (Succ ww26) (Succ ww27))",fontsize=16,color="green",shape="box"];98 -> 103[label="",style="dashed", color="green", weight=3];
30.41/15.90	104[label="primIntToChar (Pos (primModNatS (Succ ww29) (Succ ww30)))",fontsize=16,color="black",shape="box"];104 -> 106[label="",style="solid", color="black", weight=3];
30.41/15.90	103[label="primDivNatS (Succ ww26) (Succ ww27)",fontsize=16,color="black",shape="triangle"];103 -> 105[label="",style="solid", color="black", weight=3];
30.41/15.90	106[label="Char (primModNatS (Succ ww29) (Succ ww30))",fontsize=16,color="green",shape="box"];106 -> 109[label="",style="dashed", color="green", weight=3];
30.41/15.90	105[label="primDivNatS0 ww26 ww27 (primGEqNatS ww26 ww27)",fontsize=16,color="burlywood",shape="box"];930[label="ww26/Succ ww260",fontsize=10,color="white",style="solid",shape="box"];105 -> 930[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	930 -> 107[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	931[label="ww26/Zero",fontsize=10,color="white",style="solid",shape="box"];105 -> 931[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	931 -> 108[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	109[label="primModNatS (Succ ww29) (Succ ww30)",fontsize=16,color="black",shape="triangle"];109 -> 114[label="",style="solid", color="black", weight=3];
30.41/15.90	107[label="primDivNatS0 (Succ ww260) ww27 (primGEqNatS (Succ ww260) ww27)",fontsize=16,color="burlywood",shape="box"];932[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];107 -> 932[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	932 -> 110[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	933[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 933[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	933 -> 111[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	108[label="primDivNatS0 Zero ww27 (primGEqNatS Zero ww27)",fontsize=16,color="burlywood",shape="box"];934[label="ww27/Succ ww270",fontsize=10,color="white",style="solid",shape="box"];108 -> 934[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	934 -> 112[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	935[label="ww27/Zero",fontsize=10,color="white",style="solid",shape="box"];108 -> 935[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	935 -> 113[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	114[label="primModNatS0 ww29 ww30 (primGEqNatS ww29 ww30)",fontsize=16,color="burlywood",shape="box"];936[label="ww29/Succ ww290",fontsize=10,color="white",style="solid",shape="box"];114 -> 936[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	936 -> 119[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	937[label="ww29/Zero",fontsize=10,color="white",style="solid",shape="box"];114 -> 937[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	937 -> 120[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	110[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS (Succ ww260) (Succ ww270))",fontsize=16,color="black",shape="box"];110 -> 115[label="",style="solid", color="black", weight=3];
30.41/15.90	111[label="primDivNatS0 (Succ ww260) Zero (primGEqNatS (Succ ww260) Zero)",fontsize=16,color="black",shape="box"];111 -> 116[label="",style="solid", color="black", weight=3];
30.41/15.90	112[label="primDivNatS0 Zero (Succ ww270) (primGEqNatS Zero (Succ ww270))",fontsize=16,color="black",shape="box"];112 -> 117[label="",style="solid", color="black", weight=3];
30.41/15.90	113[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];113 -> 118[label="",style="solid", color="black", weight=3];
30.41/15.90	119[label="primModNatS0 (Succ ww290) ww30 (primGEqNatS (Succ ww290) ww30)",fontsize=16,color="burlywood",shape="box"];938[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];119 -> 938[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	938 -> 126[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	939[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];119 -> 939[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	939 -> 127[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	120[label="primModNatS0 Zero ww30 (primGEqNatS Zero ww30)",fontsize=16,color="burlywood",shape="box"];940[label="ww30/Succ ww300",fontsize=10,color="white",style="solid",shape="box"];120 -> 940[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	940 -> 128[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	941[label="ww30/Zero",fontsize=10,color="white",style="solid",shape="box"];120 -> 941[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	941 -> 129[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	115 -> 640[label="",style="dashed", color="red", weight=0];
30.41/15.90	115[label="primDivNatS0 (Succ ww260) (Succ ww270) (primGEqNatS ww260 ww270)",fontsize=16,color="magenta"];115 -> 641[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	115 -> 642[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	115 -> 643[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	115 -> 644[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	116[label="primDivNatS0 (Succ ww260) Zero True",fontsize=16,color="black",shape="box"];116 -> 123[label="",style="solid", color="black", weight=3];
30.41/15.90	117[label="primDivNatS0 Zero (Succ ww270) False",fontsize=16,color="black",shape="box"];117 -> 124[label="",style="solid", color="black", weight=3];
30.41/15.90	118[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];118 -> 125[label="",style="solid", color="black", weight=3];
30.41/15.90	126[label="primModNatS0 (Succ ww290) (Succ ww300) (primGEqNatS (Succ ww290) (Succ ww300))",fontsize=16,color="black",shape="box"];126 -> 136[label="",style="solid", color="black", weight=3];
30.41/15.90	127[label="primModNatS0 (Succ ww290) Zero (primGEqNatS (Succ ww290) Zero)",fontsize=16,color="black",shape="box"];127 -> 137[label="",style="solid", color="black", weight=3];
30.41/15.90	128[label="primModNatS0 Zero (Succ ww300) (primGEqNatS Zero (Succ ww300))",fontsize=16,color="black",shape="box"];128 -> 138[label="",style="solid", color="black", weight=3];
30.41/15.90	129[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];129 -> 139[label="",style="solid", color="black", weight=3];
30.41/15.90	641[label="ww260",fontsize=16,color="green",shape="box"];642[label="ww260",fontsize=16,color="green",shape="box"];643[label="ww270",fontsize=16,color="green",shape="box"];644[label="ww270",fontsize=16,color="green",shape="box"];640[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww75 ww76)",fontsize=16,color="burlywood",shape="triangle"];942[label="ww75/Succ ww750",fontsize=10,color="white",style="solid",shape="box"];640 -> 942[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	942 -> 681[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	943[label="ww75/Zero",fontsize=10,color="white",style="solid",shape="box"];640 -> 943[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	943 -> 682[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	123[label="Succ (primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];123 -> 134[label="",style="dashed", color="green", weight=3];
30.41/15.90	124[label="Zero",fontsize=16,color="green",shape="box"];125[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];125 -> 135[label="",style="dashed", color="green", weight=3];
30.41/15.90	136 -> 701[label="",style="dashed", color="red", weight=0];
30.41/15.90	136[label="primModNatS0 (Succ ww290) (Succ ww300) (primGEqNatS ww290 ww300)",fontsize=16,color="magenta"];136 -> 702[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	136 -> 703[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	136 -> 704[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	136 -> 705[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	137[label="primModNatS0 (Succ ww290) Zero True",fontsize=16,color="black",shape="box"];137 -> 148[label="",style="solid", color="black", weight=3];
30.41/15.90	138[label="primModNatS0 Zero (Succ ww300) False",fontsize=16,color="black",shape="box"];138 -> 149[label="",style="solid", color="black", weight=3];
30.41/15.90	139[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];139 -> 150[label="",style="solid", color="black", weight=3];
30.41/15.90	681[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) ww76)",fontsize=16,color="burlywood",shape="box"];944[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];681 -> 944[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	944 -> 693[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	945[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 945[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	945 -> 694[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	682[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero ww76)",fontsize=16,color="burlywood",shape="box"];946[label="ww76/Succ ww760",fontsize=10,color="white",style="solid",shape="box"];682 -> 946[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	946 -> 695[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	947[label="ww76/Zero",fontsize=10,color="white",style="solid",shape="box"];682 -> 947[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	947 -> 696[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	134 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.90	134[label="primDivNatS (primMinusNatS (Succ ww260) Zero) (Succ Zero)",fontsize=16,color="magenta"];134 -> 885[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	134 -> 886[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	134 -> 887[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	135 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.90	135[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];135 -> 888[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	135 -> 889[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	135 -> 890[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	702[label="ww290",fontsize=16,color="green",shape="box"];703[label="ww290",fontsize=16,color="green",shape="box"];704[label="ww300",fontsize=16,color="green",shape="box"];705[label="ww300",fontsize=16,color="green",shape="box"];701[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS ww80 ww81)",fontsize=16,color="burlywood",shape="triangle"];948[label="ww80/Succ ww800",fontsize=10,color="white",style="solid",shape="box"];701 -> 948[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	948 -> 742[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	949[label="ww80/Zero",fontsize=10,color="white",style="solid",shape="box"];701 -> 949[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	949 -> 743[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	148 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.90	148[label="primModNatS (primMinusNatS (Succ ww290) Zero) (Succ Zero)",fontsize=16,color="magenta"];148 -> 789[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	148 -> 790[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	148 -> 791[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	149[label="Succ Zero",fontsize=16,color="green",shape="box"];150 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.90	150[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];150 -> 792[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	150 -> 793[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	150 -> 794[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	693[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) (Succ ww760))",fontsize=16,color="black",shape="box"];693 -> 744[label="",style="solid", color="black", weight=3];
30.41/15.90	694[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS (Succ ww750) Zero)",fontsize=16,color="black",shape="box"];694 -> 745[label="",style="solid", color="black", weight=3];
30.41/15.90	695[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero (Succ ww760))",fontsize=16,color="black",shape="box"];695 -> 746[label="",style="solid", color="black", weight=3];
30.41/15.90	696[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];696 -> 747[label="",style="solid", color="black", weight=3];
30.41/15.90	885[label="Zero",fontsize=16,color="green",shape="box"];886[label="Zero",fontsize=16,color="green",shape="box"];887[label="Succ ww260",fontsize=16,color="green",shape="box"];884[label="primDivNatS (primMinusNatS ww87 ww88) (Succ ww89)",fontsize=16,color="burlywood",shape="triangle"];950[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];884 -> 950[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	950 -> 909[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	951[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];884 -> 951[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	951 -> 910[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	888[label="Zero",fontsize=16,color="green",shape="box"];889[label="Zero",fontsize=16,color="green",shape="box"];890[label="Zero",fontsize=16,color="green",shape="box"];742[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS (Succ ww800) ww81)",fontsize=16,color="burlywood",shape="box"];952[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];742 -> 952[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	952 -> 752[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	953[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];742 -> 953[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	953 -> 753[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	743[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS Zero ww81)",fontsize=16,color="burlywood",shape="box"];954[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];743 -> 954[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	954 -> 754[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	955[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];743 -> 955[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	955 -> 755[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	789[label="Succ ww290",fontsize=16,color="green",shape="box"];790[label="Zero",fontsize=16,color="green",shape="box"];791[label="Zero",fontsize=16,color="green",shape="box"];788[label="primModNatS (primMinusNatS ww83 ww84) (Succ ww85)",fontsize=16,color="burlywood",shape="triangle"];956[label="ww83/Succ ww830",fontsize=10,color="white",style="solid",shape="box"];788 -> 956[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	956 -> 819[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	957[label="ww83/Zero",fontsize=10,color="white",style="solid",shape="box"];788 -> 957[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	957 -> 820[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	792[label="Zero",fontsize=16,color="green",shape="box"];793[label="Zero",fontsize=16,color="green",shape="box"];794[label="Zero",fontsize=16,color="green",shape="box"];744 -> 640[label="",style="dashed", color="red", weight=0];
30.41/15.90	744[label="primDivNatS0 (Succ ww73) (Succ ww74) (primGEqNatS ww750 ww760)",fontsize=16,color="magenta"];744 -> 756[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	744 -> 757[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	745[label="primDivNatS0 (Succ ww73) (Succ ww74) True",fontsize=16,color="black",shape="triangle"];745 -> 758[label="",style="solid", color="black", weight=3];
30.41/15.90	746[label="primDivNatS0 (Succ ww73) (Succ ww74) False",fontsize=16,color="black",shape="box"];746 -> 759[label="",style="solid", color="black", weight=3];
30.41/15.90	747 -> 745[label="",style="dashed", color="red", weight=0];
30.41/15.90	747[label="primDivNatS0 (Succ ww73) (Succ ww74) True",fontsize=16,color="magenta"];909[label="primDivNatS (primMinusNatS (Succ ww870) ww88) (Succ ww89)",fontsize=16,color="burlywood",shape="box"];958[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];909 -> 958[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	958 -> 911[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	959[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];909 -> 959[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	959 -> 912[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	910[label="primDivNatS (primMinusNatS Zero ww88) (Succ ww89)",fontsize=16,color="burlywood",shape="box"];960[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];910 -> 960[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	960 -> 913[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	961[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];910 -> 961[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	961 -> 914[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	752[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS (Succ ww800) (Succ ww810))",fontsize=16,color="black",shape="box"];752 -> 766[label="",style="solid", color="black", weight=3];
30.41/15.90	753[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS (Succ ww800) Zero)",fontsize=16,color="black",shape="box"];753 -> 767[label="",style="solid", color="black", weight=3];
30.41/15.90	754[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS Zero (Succ ww810))",fontsize=16,color="black",shape="box"];754 -> 768[label="",style="solid", color="black", weight=3];
30.41/15.90	755[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];755 -> 769[label="",style="solid", color="black", weight=3];
30.41/15.90	819[label="primModNatS (primMinusNatS (Succ ww830) ww84) (Succ ww85)",fontsize=16,color="burlywood",shape="box"];962[label="ww84/Succ ww840",fontsize=10,color="white",style="solid",shape="box"];819 -> 962[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	962 -> 825[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	963[label="ww84/Zero",fontsize=10,color="white",style="solid",shape="box"];819 -> 963[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	963 -> 826[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	820[label="primModNatS (primMinusNatS Zero ww84) (Succ ww85)",fontsize=16,color="burlywood",shape="box"];964[label="ww84/Succ ww840",fontsize=10,color="white",style="solid",shape="box"];820 -> 964[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	964 -> 827[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	965[label="ww84/Zero",fontsize=10,color="white",style="solid",shape="box"];820 -> 965[label="",style="solid", color="burlywood", weight=9];
30.41/15.90	965 -> 828[label="",style="solid", color="burlywood", weight=3];
30.41/15.90	756[label="ww750",fontsize=16,color="green",shape="box"];757[label="ww760",fontsize=16,color="green",shape="box"];758[label="Succ (primDivNatS (primMinusNatS (Succ ww73) (Succ ww74)) (Succ (Succ ww74)))",fontsize=16,color="green",shape="box"];758 -> 770[label="",style="dashed", color="green", weight=3];
30.41/15.90	759[label="Zero",fontsize=16,color="green",shape="box"];911[label="primDivNatS (primMinusNatS (Succ ww870) (Succ ww880)) (Succ ww89)",fontsize=16,color="black",shape="box"];911 -> 915[label="",style="solid", color="black", weight=3];
30.41/15.90	912[label="primDivNatS (primMinusNatS (Succ ww870) Zero) (Succ ww89)",fontsize=16,color="black",shape="box"];912 -> 916[label="",style="solid", color="black", weight=3];
30.41/15.90	913[label="primDivNatS (primMinusNatS Zero (Succ ww880)) (Succ ww89)",fontsize=16,color="black",shape="box"];913 -> 917[label="",style="solid", color="black", weight=3];
30.41/15.90	914[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww89)",fontsize=16,color="black",shape="box"];914 -> 918[label="",style="solid", color="black", weight=3];
30.41/15.90	766 -> 701[label="",style="dashed", color="red", weight=0];
30.41/15.90	766[label="primModNatS0 (Succ ww78) (Succ ww79) (primGEqNatS ww800 ww810)",fontsize=16,color="magenta"];766 -> 775[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	766 -> 776[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	767[label="primModNatS0 (Succ ww78) (Succ ww79) True",fontsize=16,color="black",shape="triangle"];767 -> 777[label="",style="solid", color="black", weight=3];
30.41/15.90	768[label="primModNatS0 (Succ ww78) (Succ ww79) False",fontsize=16,color="black",shape="box"];768 -> 778[label="",style="solid", color="black", weight=3];
30.41/15.90	769 -> 767[label="",style="dashed", color="red", weight=0];
30.41/15.90	769[label="primModNatS0 (Succ ww78) (Succ ww79) True",fontsize=16,color="magenta"];825[label="primModNatS (primMinusNatS (Succ ww830) (Succ ww840)) (Succ ww85)",fontsize=16,color="black",shape="box"];825 -> 833[label="",style="solid", color="black", weight=3];
30.41/15.90	826[label="primModNatS (primMinusNatS (Succ ww830) Zero) (Succ ww85)",fontsize=16,color="black",shape="box"];826 -> 834[label="",style="solid", color="black", weight=3];
30.41/15.90	827[label="primModNatS (primMinusNatS Zero (Succ ww840)) (Succ ww85)",fontsize=16,color="black",shape="box"];827 -> 835[label="",style="solid", color="black", weight=3];
30.41/15.90	828[label="primModNatS (primMinusNatS Zero Zero) (Succ ww85)",fontsize=16,color="black",shape="box"];828 -> 836[label="",style="solid", color="black", weight=3];
30.41/15.90	770 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.90	770[label="primDivNatS (primMinusNatS (Succ ww73) (Succ ww74)) (Succ (Succ ww74))",fontsize=16,color="magenta"];770 -> 891[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	770 -> 892[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	770 -> 893[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	915 -> 884[label="",style="dashed", color="red", weight=0];
30.41/15.90	915[label="primDivNatS (primMinusNatS ww870 ww880) (Succ ww89)",fontsize=16,color="magenta"];915 -> 919[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	915 -> 920[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	916 -> 103[label="",style="dashed", color="red", weight=0];
30.41/15.90	916[label="primDivNatS (Succ ww870) (Succ ww89)",fontsize=16,color="magenta"];916 -> 921[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	916 -> 922[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	917[label="primDivNatS Zero (Succ ww89)",fontsize=16,color="black",shape="triangle"];917 -> 923[label="",style="solid", color="black", weight=3];
30.41/15.90	918 -> 917[label="",style="dashed", color="red", weight=0];
30.41/15.90	918[label="primDivNatS Zero (Succ ww89)",fontsize=16,color="magenta"];775[label="ww800",fontsize=16,color="green",shape="box"];776[label="ww810",fontsize=16,color="green",shape="box"];777 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.90	777[label="primModNatS (primMinusNatS (Succ ww78) (Succ ww79)) (Succ (Succ ww79))",fontsize=16,color="magenta"];777 -> 801[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	777 -> 802[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	777 -> 803[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	778[label="Succ (Succ ww78)",fontsize=16,color="green",shape="box"];833 -> 788[label="",style="dashed", color="red", weight=0];
30.41/15.90	833[label="primModNatS (primMinusNatS ww830 ww840) (Succ ww85)",fontsize=16,color="magenta"];833 -> 843[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	833 -> 844[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	834 -> 109[label="",style="dashed", color="red", weight=0];
30.41/15.90	834[label="primModNatS (Succ ww830) (Succ ww85)",fontsize=16,color="magenta"];834 -> 845[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	834 -> 846[label="",style="dashed", color="magenta", weight=3];
30.41/15.90	835[label="primModNatS Zero (Succ ww85)",fontsize=16,color="black",shape="triangle"];835 -> 847[label="",style="solid", color="black", weight=3];
30.41/15.90	836 -> 835[label="",style="dashed", color="red", weight=0];
30.41/15.90	836[label="primModNatS Zero (Succ ww85)",fontsize=16,color="magenta"];891[label="Succ ww74",fontsize=16,color="green",shape="box"];892[label="Succ ww74",fontsize=16,color="green",shape="box"];893[label="Succ ww73",fontsize=16,color="green",shape="box"];919[label="ww880",fontsize=16,color="green",shape="box"];920[label="ww870",fontsize=16,color="green",shape="box"];921[label="ww89",fontsize=16,color="green",shape="box"];922[label="ww870",fontsize=16,color="green",shape="box"];923[label="Zero",fontsize=16,color="green",shape="box"];801[label="Succ ww78",fontsize=16,color="green",shape="box"];802[label="Succ ww79",fontsize=16,color="green",shape="box"];803[label="Succ ww79",fontsize=16,color="green",shape="box"];843[label="ww830",fontsize=16,color="green",shape="box"];844[label="ww840",fontsize=16,color="green",shape="box"];845[label="ww85",fontsize=16,color="green",shape="box"];846[label="ww830",fontsize=16,color="green",shape="box"];847[label="Zero",fontsize=16,color="green",shape="box"];}
30.41/15.90	
30.41/15.90	----------------------------------------
30.41/15.90	
30.41/15.90	(66)
30.41/15.90	TRUE
30.55/15.96	EOF