10.55/4.21 YES 12.76/4.84 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 12.76/4.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.76/4.84 12.76/4.84 12.76/4.84 H-Termination with start terms of the given HASKELL could be proven: 12.76/4.84 12.76/4.84 (0) HASKELL 12.76/4.84 (1) LR [EQUIVALENT, 0 ms] 12.76/4.84 (2) HASKELL 12.76/4.84 (3) IFR [EQUIVALENT, 0 ms] 12.76/4.84 (4) HASKELL 12.76/4.84 (5) BR [EQUIVALENT, 0 ms] 12.76/4.84 (6) HASKELL 12.76/4.84 (7) COR [EQUIVALENT, 0 ms] 12.76/4.84 (8) HASKELL 12.76/4.84 (9) LetRed [EQUIVALENT, 1 ms] 12.76/4.84 (10) HASKELL 12.76/4.84 (11) NumRed [SOUND, 0 ms] 12.76/4.84 (12) HASKELL 12.76/4.84 (13) Narrow [SOUND, 0 ms] 12.76/4.84 (14) AND 12.76/4.84 (15) QDP 12.76/4.84 (16) DependencyGraphProof [EQUIVALENT, 0 ms] 12.76/4.84 (17) AND 12.76/4.84 (18) QDP 12.76/4.84 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (20) YES 12.76/4.84 (21) QDP 12.76/4.84 (22) QDPOrderProof [EQUIVALENT, 0 ms] 12.76/4.84 (23) QDP 12.76/4.84 (24) DependencyGraphProof [EQUIVALENT, 0 ms] 12.76/4.84 (25) QDP 12.76/4.84 (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (27) YES 12.76/4.84 (28) QDP 12.76/4.84 (29) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (30) YES 12.76/4.84 (31) QDP 12.76/4.84 (32) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (33) YES 12.76/4.84 (34) QDP 12.76/4.84 (35) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (36) YES 12.76/4.84 (37) QDP 12.76/4.84 (38) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (39) YES 12.76/4.84 (40) QDP 12.76/4.84 (41) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (42) YES 12.76/4.84 (43) QDP 12.76/4.84 (44) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/4.84 (45) YES 12.76/4.84 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (0) 12.76/4.84 Obligation: 12.76/4.84 mainModule Main 12.76/4.84 module Main where { 12.76/4.84 import qualified Prelude; 12.76/4.84 } 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (1) LR (EQUIVALENT) 12.76/4.84 Lambda Reductions: 12.76/4.84 The following Lambda expression 12.76/4.84 "\(m,_)->m" 12.76/4.84 is transformed to 12.76/4.84 "m0 (m,_) = m; 12.76/4.84 " 12.76/4.84 The following Lambda expression 12.76/4.84 "\(q,_)->q" 12.76/4.84 is transformed to 12.76/4.84 "q1 (q,_) = q; 12.76/4.84 " 12.76/4.84 The following Lambda expression 12.76/4.84 "\(_,r)->r" 12.76/4.84 is transformed to 12.76/4.84 "r0 (_,r) = r; 12.76/4.84 " 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (2) 12.76/4.84 Obligation: 12.76/4.84 mainModule Main 12.76/4.84 module Main where { 12.76/4.84 import qualified Prelude; 12.76/4.84 } 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (3) IFR (EQUIVALENT) 12.76/4.84 If Reductions: 12.76/4.84 The following If expression 12.76/4.84 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 12.76/4.84 is transformed to 12.76/4.84 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 12.76/4.84 primDivNatS0 x y False = Zero; 12.76/4.84 " 12.76/4.84 The following If expression 12.76/4.84 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 12.76/4.84 is transformed to 12.76/4.84 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 12.76/4.84 primModNatS0 x y False = Succ x; 12.76/4.84 " 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (4) 12.76/4.84 Obligation: 12.76/4.84 mainModule Main 12.76/4.84 module Main where { 12.76/4.84 import qualified Prelude; 12.76/4.84 } 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (5) BR (EQUIVALENT) 12.76/4.84 Replaced joker patterns by fresh variables and removed binding patterns. 12.76/4.84 12.76/4.84 Binding Reductions: 12.76/4.84 The bind variable of the following binding Pattern 12.76/4.84 "frac@(Float vz wu)" 12.76/4.84 is replaced by the following term 12.76/4.84 "Float vz wu" 12.76/4.84 The bind variable of the following binding Pattern 12.76/4.84 "frac@(Double xu xv)" 12.76/4.84 is replaced by the following term 12.76/4.84 "Double xu xv" 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (6) 12.76/4.84 Obligation: 12.76/4.84 mainModule Main 12.76/4.84 module Main where { 12.76/4.84 import qualified Prelude; 12.76/4.84 } 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (7) COR (EQUIVALENT) 12.76/4.84 Cond Reductions: 12.76/4.84 The following Function with conditions 12.76/4.84 "undefined |Falseundefined; 12.76/4.84 " 12.76/4.84 is transformed to 12.76/4.84 "undefined = undefined1; 12.76/4.84 " 12.76/4.84 "undefined0 True = undefined; 12.76/4.84 " 12.76/4.84 "undefined1 = undefined0 False; 12.76/4.84 " 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (8) 12.76/4.84 Obligation: 12.76/4.84 mainModule Main 12.76/4.84 module Main where { 12.76/4.84 import qualified Prelude; 12.76/4.84 } 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (9) LetRed (EQUIVALENT) 12.76/4.84 Let/Where Reductions: 12.76/4.84 The bindings of the following Let/Where expression 12.76/4.84 "m where { 12.76/4.84 m = m0 vu6; 12.76/4.84 ; 12.76/4.84 m0 (m,vv) = m; 12.76/4.84 ; 12.76/4.84 vu6 = properFraction x; 12.76/4.84 } 12.76/4.84 " 12.76/4.84 are unpacked to the following functions on top level 12.76/4.84 "truncateVu6 xw = properFraction xw; 12.76/4.84 " 12.76/4.84 "truncateM xw = truncateM0 xw (truncateVu6 xw); 12.76/4.84 " 12.76/4.84 "truncateM0 xw (m,vv) = m; 12.76/4.84 " 12.76/4.84 The bindings of the following Let/Where expression 12.76/4.84 "(fromIntegral q,r :% y) where { 12.76/4.84 q = q1 vu30; 12.76/4.84 ; 12.76/4.84 q1 (q,vw) = q; 12.76/4.84 ; 12.76/4.84 r = r0 vu30; 12.76/4.84 ; 12.76/4.84 r0 (vx,r) = r; 12.76/4.84 ; 12.76/4.84 vu30 = quotRem x y; 12.76/4.84 } 12.76/4.84 " 12.76/4.84 are unpacked to the following functions on top level 12.76/4.84 "properFractionQ1 xx xy (q,vw) = q; 12.76/4.84 " 12.76/4.84 "properFractionR xx xy = properFractionR0 xx xy (properFractionVu30 xx xy); 12.76/4.84 " 12.76/4.84 "properFractionR0 xx xy (vx,r) = r; 12.76/4.84 " 12.76/4.84 "properFractionQ xx xy = properFractionQ1 xx xy (properFractionVu30 xx xy); 12.76/4.84 " 12.76/4.84 "properFractionVu30 xx xy = quotRem xx xy; 12.76/4.84 " 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (10) 12.76/4.84 Obligation: 12.76/4.84 mainModule Main 12.76/4.84 module Main where { 12.76/4.84 import qualified Prelude; 12.76/4.84 } 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (11) NumRed (SOUND) 12.76/4.84 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (12) 12.76/4.84 Obligation: 12.76/4.84 mainModule Main 12.76/4.84 module Main where { 12.76/4.84 import qualified Prelude; 12.76/4.84 } 12.76/4.84 12.76/4.84 ---------------------------------------- 12.76/4.84 12.76/4.84 (13) Narrow (SOUND) 12.76/4.84 Haskell To QDPs 12.76/4.84 12.76/4.84 digraph dp_graph { 12.76/4.84 node [outthreshold=100, inthreshold=100];1[label="succ",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 12.76/4.84 3[label="succ xz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 12.76/4.84 4[label="toEnum . (Pos (Succ Zero) +) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 12.76/4.84 5[label="toEnum ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 12.76/4.84 6[label="fromInt ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 12.76/4.84 7[label="intToRatio ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 12.76/4.84 8[label="fromInt ((Pos (Succ Zero) +) . fromEnum) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3]; 12.76/4.84 8 -> 10[label="",style="dashed", color="green", weight=3]; 12.76/4.84 9[label="fromInt ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 12.76/4.84 10[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 12.76/4.84 11[label="(Pos (Succ Zero) +) . fromEnum",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12.76/4.84 12[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];13[label="Pos (Succ Zero) + fromEnum xz3",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 12.76/4.84 14[label="primPlusInt (Pos (Succ Zero)) (fromEnum xz3)",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 12.76/4.84 15[label="primPlusInt (Pos (Succ Zero)) (truncate xz3)",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 12.76/4.84 16[label="primPlusInt (Pos (Succ Zero)) (truncateM xz3)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 12.76/4.84 17[label="primPlusInt (Pos (Succ Zero)) (truncateM0 xz3 (truncateVu6 xz3))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 12.76/4.84 18[label="primPlusInt (Pos (Succ Zero)) (truncateM0 xz3 (properFraction xz3))",fontsize=16,color="burlywood",shape="box"];2391[label="xz3/xz30 :% xz31",fontsize=10,color="white",style="solid",shape="box"];18 -> 2391[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2391 -> 19[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 19[label="primPlusInt (Pos (Succ Zero)) (truncateM0 (xz30 :% xz31) (properFraction (xz30 :% xz31)))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3]; 12.76/4.84 20[label="primPlusInt (Pos (Succ Zero)) (truncateM0 (xz30 :% xz31) (fromIntegral (properFractionQ xz30 xz31),properFractionR xz30 xz31 :% xz31))",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3]; 12.76/4.84 21[label="primPlusInt (Pos (Succ Zero)) (fromIntegral (properFractionQ xz30 xz31))",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3]; 12.76/4.84 22[label="primPlusInt (Pos (Succ Zero)) (fromInteger . toInteger)",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3]; 12.76/4.84 23[label="primPlusInt (Pos (Succ Zero)) (fromInteger (toInteger (properFractionQ xz30 xz31)))",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3]; 12.76/4.84 24[label="primPlusInt (Pos (Succ Zero)) (fromInteger (Integer (properFractionQ xz30 xz31)))",fontsize=16,color="black",shape="box"];24 -> 25[label="",style="solid", color="black", weight=3]; 12.76/4.84 25[label="primPlusInt (Pos (Succ Zero)) (properFractionQ xz30 xz31)",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3]; 12.76/4.84 26[label="primPlusInt (Pos (Succ Zero)) (properFractionQ1 xz30 xz31 (properFractionVu30 xz30 xz31))",fontsize=16,color="black",shape="box"];26 -> 27[label="",style="solid", color="black", weight=3]; 12.76/4.84 27[label="primPlusInt (Pos (Succ Zero)) (properFractionQ1 xz30 xz31 (quotRem xz30 xz31))",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3]; 12.76/4.84 28[label="primPlusInt (Pos (Succ Zero)) (properFractionQ1 xz30 xz31 (primQrmInt xz30 xz31))",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3]; 12.76/4.84 29[label="primPlusInt (Pos (Succ Zero)) (properFractionQ1 xz30 xz31 (primQuotInt xz30 xz31,primRemInt xz30 xz31))",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3]; 12.76/4.84 30[label="primPlusInt (Pos (Succ Zero)) (primQuotInt xz30 xz31)",fontsize=16,color="burlywood",shape="box"];2392[label="xz30/Pos xz300",fontsize=10,color="white",style="solid",shape="box"];30 -> 2392[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2392 -> 31[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2393[label="xz30/Neg xz300",fontsize=10,color="white",style="solid",shape="box"];30 -> 2393[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2393 -> 32[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 31[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) xz31)",fontsize=16,color="burlywood",shape="box"];2394[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];31 -> 2394[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2394 -> 33[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2395[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];31 -> 2395[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2395 -> 34[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 32[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) xz31)",fontsize=16,color="burlywood",shape="box"];2396[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];32 -> 2396[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2396 -> 35[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2397[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];32 -> 2397[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2397 -> 36[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 33[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Pos xz310))",fontsize=16,color="burlywood",shape="box"];2398[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];33 -> 2398[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2398 -> 37[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2399[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 2399[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2399 -> 38[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 34[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Neg xz310))",fontsize=16,color="burlywood",shape="box"];2400[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];34 -> 2400[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2400 -> 39[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2401[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 2401[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2401 -> 40[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 35[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Pos xz310))",fontsize=16,color="burlywood",shape="box"];2402[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];35 -> 2402[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2402 -> 41[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2403[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 2403[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2403 -> 42[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 36[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Neg xz310))",fontsize=16,color="burlywood",shape="box"];2404[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];36 -> 2404[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2404 -> 43[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2405[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 2405[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2405 -> 44[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 37[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Pos (Succ xz3100)))",fontsize=16,color="black",shape="box"];37 -> 45[label="",style="solid", color="black", weight=3]; 12.76/4.84 38[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Pos Zero))",fontsize=16,color="black",shape="box"];38 -> 46[label="",style="solid", color="black", weight=3]; 12.76/4.84 39[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Neg (Succ xz3100)))",fontsize=16,color="black",shape="box"];39 -> 47[label="",style="solid", color="black", weight=3]; 12.76/4.84 40[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Neg Zero))",fontsize=16,color="black",shape="box"];40 -> 48[label="",style="solid", color="black", weight=3]; 12.76/4.84 41[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Pos (Succ xz3100)))",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3]; 12.76/4.84 42[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Pos Zero))",fontsize=16,color="black",shape="box"];42 -> 50[label="",style="solid", color="black", weight=3]; 12.76/4.84 43[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Neg (Succ xz3100)))",fontsize=16,color="black",shape="box"];43 -> 51[label="",style="solid", color="black", weight=3]; 12.76/4.84 44[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Neg Zero))",fontsize=16,color="black",shape="box"];44 -> 52[label="",style="solid", color="black", weight=3]; 12.76/4.84 45[label="primPlusInt (Pos (Succ Zero)) (Pos (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="black",shape="triangle"];45 -> 53[label="",style="solid", color="black", weight=3]; 12.76/4.84 46[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="black",shape="triangle"];46 -> 54[label="",style="solid", color="black", weight=3]; 12.76/4.84 47[label="primPlusInt (Pos (Succ Zero)) (Neg (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="black",shape="triangle"];47 -> 55[label="",style="solid", color="black", weight=3]; 12.76/4.84 48 -> 46[label="",style="dashed", color="red", weight=0]; 12.76/4.84 48[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="magenta"];49 -> 47[label="",style="dashed", color="red", weight=0]; 12.76/4.84 49[label="primPlusInt (Pos (Succ Zero)) (Neg (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="magenta"];49 -> 56[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 49 -> 57[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 50 -> 46[label="",style="dashed", color="red", weight=0]; 12.76/4.84 50[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="magenta"];51 -> 45[label="",style="dashed", color="red", weight=0]; 12.76/4.84 51[label="primPlusInt (Pos (Succ Zero)) (Pos (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="magenta"];51 -> 58[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 51 -> 59[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 52 -> 46[label="",style="dashed", color="red", weight=0]; 12.76/4.84 52[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="magenta"];53[label="Pos (primPlusNat (Succ Zero) (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="green",shape="box"];53 -> 60[label="",style="dashed", color="green", weight=3]; 12.76/4.84 54[label="error []",fontsize=16,color="red",shape="box"];55[label="primMinusNat (Succ Zero) (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="burlywood",shape="box"];2406[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];55 -> 2406[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2406 -> 61[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2407[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 2407[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2407 -> 62[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 56[label="xz3100",fontsize=16,color="green",shape="box"];57[label="xz300",fontsize=16,color="green",shape="box"];58[label="xz3100",fontsize=16,color="green",shape="box"];59[label="xz300",fontsize=16,color="green",shape="box"];60[label="primPlusNat (Succ Zero) (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="burlywood",shape="box"];2408[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];60 -> 2408[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2408 -> 63[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2409[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];60 -> 2409[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2409 -> 64[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 61[label="primMinusNat (Succ Zero) (primDivNatS (Succ xz3000) (Succ xz3100))",fontsize=16,color="black",shape="box"];61 -> 65[label="",style="solid", color="black", weight=3]; 12.76/4.84 62[label="primMinusNat (Succ Zero) (primDivNatS Zero (Succ xz3100))",fontsize=16,color="black",shape="box"];62 -> 66[label="",style="solid", color="black", weight=3]; 12.76/4.84 63[label="primPlusNat (Succ Zero) (primDivNatS (Succ xz3000) (Succ xz3100))",fontsize=16,color="black",shape="box"];63 -> 67[label="",style="solid", color="black", weight=3]; 12.76/4.84 64[label="primPlusNat (Succ Zero) (primDivNatS Zero (Succ xz3100))",fontsize=16,color="black",shape="box"];64 -> 68[label="",style="solid", color="black", weight=3]; 12.76/4.84 65[label="primMinusNat (Succ Zero) (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100))",fontsize=16,color="burlywood",shape="box"];2410[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];65 -> 2410[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2410 -> 69[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2411[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 2411[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2411 -> 70[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 66[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="triangle"];66 -> 71[label="",style="solid", color="black", weight=3]; 12.76/4.84 67[label="primPlusNat (Succ Zero) (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100))",fontsize=16,color="burlywood",shape="box"];2412[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];67 -> 2412[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2412 -> 72[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2413[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];67 -> 2413[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2413 -> 73[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 68[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="black",shape="triangle"];68 -> 74[label="",style="solid", color="black", weight=3]; 12.76/4.84 69[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100))",fontsize=16,color="burlywood",shape="box"];2414[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];69 -> 2414[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2414 -> 75[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2415[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 2415[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2415 -> 76[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 70[label="primMinusNat (Succ Zero) (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100))",fontsize=16,color="burlywood",shape="box"];2416[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];70 -> 2416[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2416 -> 77[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2417[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 2417[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2417 -> 78[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 71[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];72[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100))",fontsize=16,color="burlywood",shape="box"];2418[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];72 -> 2418[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2418 -> 79[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2419[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 2419[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2419 -> 80[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 73[label="primPlusNat (Succ Zero) (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100))",fontsize=16,color="burlywood",shape="box"];2420[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];73 -> 2420[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2420 -> 81[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2421[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];73 -> 2421[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2421 -> 82[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 74[label="Succ Zero",fontsize=16,color="green",shape="box"];75[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000)))",fontsize=16,color="black",shape="box"];75 -> 83[label="",style="solid", color="black", weight=3]; 12.76/4.84 76[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero))",fontsize=16,color="black",shape="box"];76 -> 84[label="",style="solid", color="black", weight=3]; 12.76/4.84 77[label="primMinusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000)))",fontsize=16,color="black",shape="box"];77 -> 85[label="",style="solid", color="black", weight=3]; 12.76/4.84 78[label="primMinusNat (Succ Zero) (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];78 -> 86[label="",style="solid", color="black", weight=3]; 12.76/4.84 79[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000)))",fontsize=16,color="black",shape="box"];79 -> 87[label="",style="solid", color="black", weight=3]; 12.76/4.84 80[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero))",fontsize=16,color="black",shape="box"];80 -> 88[label="",style="solid", color="black", weight=3]; 12.76/4.84 81[label="primPlusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000)))",fontsize=16,color="black",shape="box"];81 -> 89[label="",style="solid", color="black", weight=3]; 12.76/4.84 82[label="primPlusNat (Succ Zero) (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];82 -> 90[label="",style="solid", color="black", weight=3]; 12.76/4.84 83 -> 694[label="",style="dashed", color="red", weight=0]; 12.76/4.84 83[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000))",fontsize=16,color="magenta"];83 -> 695[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 83 -> 696[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 83 -> 697[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 83 -> 698[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 84[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero True)",fontsize=16,color="black",shape="box"];84 -> 93[label="",style="solid", color="black", weight=3]; 12.76/4.84 85[label="primMinusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) False)",fontsize=16,color="black",shape="box"];85 -> 94[label="",style="solid", color="black", weight=3]; 12.76/4.84 86[label="primMinusNat (Succ Zero) (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];86 -> 95[label="",style="solid", color="black", weight=3]; 12.76/4.84 87 -> 737[label="",style="dashed", color="red", weight=0]; 12.76/4.84 87[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000))",fontsize=16,color="magenta"];87 -> 738[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 87 -> 739[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 87 -> 740[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 87 -> 741[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 88[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero True)",fontsize=16,color="black",shape="box"];88 -> 98[label="",style="solid", color="black", weight=3]; 12.76/4.84 89[label="primPlusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) False)",fontsize=16,color="black",shape="box"];89 -> 99[label="",style="solid", color="black", weight=3]; 12.76/4.84 90[label="primPlusNat (Succ Zero) (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];90 -> 100[label="",style="solid", color="black", weight=3]; 12.76/4.84 695[label="xz30000",fontsize=16,color="green",shape="box"];696[label="xz31000",fontsize=16,color="green",shape="box"];697[label="xz30000",fontsize=16,color="green",shape="box"];698[label="xz31000",fontsize=16,color="green",shape="box"];694[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS xz47 xz48))",fontsize=16,color="burlywood",shape="triangle"];2422[label="xz47/Succ xz470",fontsize=10,color="white",style="solid",shape="box"];694 -> 2422[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2422 -> 735[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2423[label="xz47/Zero",fontsize=10,color="white",style="solid",shape="box"];694 -> 2423[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2423 -> 736[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 93[label="primMinusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];93 -> 105[label="",style="solid", color="black", weight=3]; 12.76/4.84 94 -> 66[label="",style="dashed", color="red", weight=0]; 12.76/4.84 94[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="magenta"];95[label="primMinusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];95 -> 106[label="",style="solid", color="black", weight=3]; 12.76/4.84 738[label="xz30000",fontsize=16,color="green",shape="box"];739[label="xz31000",fontsize=16,color="green",shape="box"];740[label="xz31000",fontsize=16,color="green",shape="box"];741[label="xz30000",fontsize=16,color="green",shape="box"];737[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS xz52 xz53))",fontsize=16,color="burlywood",shape="triangle"];2424[label="xz52/Succ xz520",fontsize=10,color="white",style="solid",shape="box"];737 -> 2424[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2424 -> 778[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2425[label="xz52/Zero",fontsize=10,color="white",style="solid",shape="box"];737 -> 2425[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2425 -> 779[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 98[label="primPlusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];98 -> 111[label="",style="solid", color="black", weight=3]; 12.76/4.84 99 -> 68[label="",style="dashed", color="red", weight=0]; 12.76/4.84 99[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="magenta"];100[label="primPlusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];100 -> 112[label="",style="solid", color="black", weight=3]; 12.76/4.84 735[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS (Succ xz470) xz48))",fontsize=16,color="burlywood",shape="box"];2426[label="xz48/Succ xz480",fontsize=10,color="white",style="solid",shape="box"];735 -> 2426[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2426 -> 780[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2427[label="xz48/Zero",fontsize=10,color="white",style="solid",shape="box"];735 -> 2427[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2427 -> 781[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 736[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS Zero xz48))",fontsize=16,color="burlywood",shape="box"];2428[label="xz48/Succ xz480",fontsize=10,color="white",style="solid",shape="box"];736 -> 2428[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2428 -> 782[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2429[label="xz48/Zero",fontsize=10,color="white",style="solid",shape="box"];736 -> 2429[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2429 -> 783[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 105 -> 1197[label="",style="dashed", color="red", weight=0]; 12.76/4.84 105[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))",fontsize=16,color="magenta"];105 -> 1198[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 105 -> 1199[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 105 -> 1200[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 106 -> 1197[label="",style="dashed", color="red", weight=0]; 12.76/4.84 106[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="magenta"];106 -> 1201[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 106 -> 1202[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 106 -> 1203[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 778[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS (Succ xz520) xz53))",fontsize=16,color="burlywood",shape="box"];2430[label="xz53/Succ xz530",fontsize=10,color="white",style="solid",shape="box"];778 -> 2430[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2430 -> 784[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2431[label="xz53/Zero",fontsize=10,color="white",style="solid",shape="box"];778 -> 2431[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2431 -> 785[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 779[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS Zero xz53))",fontsize=16,color="burlywood",shape="box"];2432[label="xz53/Succ xz530",fontsize=10,color="white",style="solid",shape="box"];779 -> 2432[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2432 -> 786[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2433[label="xz53/Zero",fontsize=10,color="white",style="solid",shape="box"];779 -> 2433[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2433 -> 787[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 111[label="Succ (Succ (primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))))",fontsize=16,color="green",shape="box"];111 -> 123[label="",style="dashed", color="green", weight=3]; 12.76/4.84 112[label="Succ (Succ (primPlusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))))",fontsize=16,color="green",shape="box"];112 -> 124[label="",style="dashed", color="green", weight=3]; 12.76/4.84 780[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS (Succ xz470) (Succ xz480)))",fontsize=16,color="black",shape="box"];780 -> 788[label="",style="solid", color="black", weight=3]; 12.76/4.84 781[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS (Succ xz470) Zero))",fontsize=16,color="black",shape="box"];781 -> 789[label="",style="solid", color="black", weight=3]; 12.76/4.84 782[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS Zero (Succ xz480)))",fontsize=16,color="black",shape="box"];782 -> 790[label="",style="solid", color="black", weight=3]; 12.76/4.84 783[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];783 -> 791[label="",style="solid", color="black", weight=3]; 12.76/4.84 1198[label="Succ xz30000",fontsize=16,color="green",shape="box"];1199[label="Zero",fontsize=16,color="green",shape="box"];1200[label="Zero",fontsize=16,color="green",shape="box"];1197[label="primMinusNat Zero (primDivNatS (primMinusNatS xz57 xz58) (Succ xz59))",fontsize=16,color="burlywood",shape="triangle"];2434[label="xz57/Succ xz570",fontsize=10,color="white",style="solid",shape="box"];1197 -> 2434[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2434 -> 1231[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2435[label="xz57/Zero",fontsize=10,color="white",style="solid",shape="box"];1197 -> 2435[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2435 -> 1232[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 1201[label="Zero",fontsize=16,color="green",shape="box"];1202[label="Zero",fontsize=16,color="green",shape="box"];1203[label="Zero",fontsize=16,color="green",shape="box"];784[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS (Succ xz520) (Succ xz530)))",fontsize=16,color="black",shape="box"];784 -> 792[label="",style="solid", color="black", weight=3]; 12.76/4.84 785[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS (Succ xz520) Zero))",fontsize=16,color="black",shape="box"];785 -> 793[label="",style="solid", color="black", weight=3]; 12.76/4.84 786[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS Zero (Succ xz530)))",fontsize=16,color="black",shape="box"];786 -> 794[label="",style="solid", color="black", weight=3]; 12.76/4.84 787[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];787 -> 795[label="",style="solid", color="black", weight=3]; 12.76/4.84 123 -> 1252[label="",style="dashed", color="red", weight=0]; 12.76/4.84 123[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))",fontsize=16,color="magenta"];123 -> 1253[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 123 -> 1254[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 123 -> 1255[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 124 -> 1252[label="",style="dashed", color="red", weight=0]; 12.76/4.84 124[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="magenta"];124 -> 1256[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 124 -> 1257[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 124 -> 1258[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 788 -> 694[label="",style="dashed", color="red", weight=0]; 12.76/4.84 788[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS xz470 xz480))",fontsize=16,color="magenta"];788 -> 796[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 788 -> 797[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 789[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) True)",fontsize=16,color="black",shape="triangle"];789 -> 798[label="",style="solid", color="black", weight=3]; 12.76/4.84 790[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) False)",fontsize=16,color="black",shape="box"];790 -> 799[label="",style="solid", color="black", weight=3]; 12.76/4.84 791 -> 789[label="",style="dashed", color="red", weight=0]; 12.76/4.84 791[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) True)",fontsize=16,color="magenta"];1231[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz570) xz58) (Succ xz59))",fontsize=16,color="burlywood",shape="box"];2436[label="xz58/Succ xz580",fontsize=10,color="white",style="solid",shape="box"];1231 -> 2436[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2436 -> 1248[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2437[label="xz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1231 -> 2437[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2437 -> 1249[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 1232[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero xz58) (Succ xz59))",fontsize=16,color="burlywood",shape="box"];2438[label="xz58/Succ xz580",fontsize=10,color="white",style="solid",shape="box"];1232 -> 2438[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2438 -> 1250[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2439[label="xz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1232 -> 2439[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2439 -> 1251[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 792 -> 737[label="",style="dashed", color="red", weight=0]; 12.76/4.84 792[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS xz520 xz530))",fontsize=16,color="magenta"];792 -> 800[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 792 -> 801[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 793[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) True)",fontsize=16,color="black",shape="triangle"];793 -> 802[label="",style="solid", color="black", weight=3]; 12.76/4.84 794[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) False)",fontsize=16,color="black",shape="box"];794 -> 803[label="",style="solid", color="black", weight=3]; 12.76/4.84 795 -> 793[label="",style="dashed", color="red", weight=0]; 12.76/4.84 795[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) True)",fontsize=16,color="magenta"];1253[label="Zero",fontsize=16,color="green",shape="box"];1254[label="Succ xz30000",fontsize=16,color="green",shape="box"];1255[label="Zero",fontsize=16,color="green",shape="box"];1252[label="primPlusNat Zero (primDivNatS (primMinusNatS xz61 xz62) (Succ xz63))",fontsize=16,color="burlywood",shape="triangle"];2440[label="xz61/Succ xz610",fontsize=10,color="white",style="solid",shape="box"];1252 -> 2440[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2440 -> 1286[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2441[label="xz61/Zero",fontsize=10,color="white",style="solid",shape="box"];1252 -> 2441[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2441 -> 1287[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 1256[label="Zero",fontsize=16,color="green",shape="box"];1257[label="Zero",fontsize=16,color="green",shape="box"];1258[label="Zero",fontsize=16,color="green",shape="box"];796[label="xz470",fontsize=16,color="green",shape="box"];797[label="xz480",fontsize=16,color="green",shape="box"];798[label="primMinusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz45) (Succ xz46)) (Succ (Succ xz46))))",fontsize=16,color="black",shape="box"];798 -> 804[label="",style="solid", color="black", weight=3]; 12.76/4.84 799 -> 66[label="",style="dashed", color="red", weight=0]; 12.76/4.84 799[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="magenta"];1248[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz570) (Succ xz580)) (Succ xz59))",fontsize=16,color="black",shape="box"];1248 -> 1288[label="",style="solid", color="black", weight=3]; 12.76/4.84 1249[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz570) Zero) (Succ xz59))",fontsize=16,color="black",shape="box"];1249 -> 1289[label="",style="solid", color="black", weight=3]; 12.76/4.84 1250[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero (Succ xz580)) (Succ xz59))",fontsize=16,color="black",shape="box"];1250 -> 1290[label="",style="solid", color="black", weight=3]; 12.76/4.84 1251[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ xz59))",fontsize=16,color="black",shape="box"];1251 -> 1291[label="",style="solid", color="black", weight=3]; 12.76/4.84 800[label="xz530",fontsize=16,color="green",shape="box"];801[label="xz520",fontsize=16,color="green",shape="box"];802[label="primPlusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz50) (Succ xz51)) (Succ (Succ xz51))))",fontsize=16,color="black",shape="box"];802 -> 805[label="",style="solid", color="black", weight=3]; 12.76/4.84 803 -> 68[label="",style="dashed", color="red", weight=0]; 12.76/4.84 803[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="magenta"];1286[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz610) xz62) (Succ xz63))",fontsize=16,color="burlywood",shape="box"];2442[label="xz62/Succ xz620",fontsize=10,color="white",style="solid",shape="box"];1286 -> 2442[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2442 -> 1292[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2443[label="xz62/Zero",fontsize=10,color="white",style="solid",shape="box"];1286 -> 2443[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2443 -> 1293[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 1287[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero xz62) (Succ xz63))",fontsize=16,color="burlywood",shape="box"];2444[label="xz62/Succ xz620",fontsize=10,color="white",style="solid",shape="box"];1287 -> 2444[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2444 -> 1294[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2445[label="xz62/Zero",fontsize=10,color="white",style="solid",shape="box"];1287 -> 2445[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2445 -> 1295[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 804 -> 1197[label="",style="dashed", color="red", weight=0]; 12.76/4.84 804[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz45) (Succ xz46)) (Succ (Succ xz46)))",fontsize=16,color="magenta"];804 -> 1204[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 804 -> 1205[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 804 -> 1206[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 1288 -> 1197[label="",style="dashed", color="red", weight=0]; 12.76/4.84 1288[label="primMinusNat Zero (primDivNatS (primMinusNatS xz570 xz580) (Succ xz59))",fontsize=16,color="magenta"];1288 -> 1296[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 1288 -> 1297[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 1289[label="primMinusNat Zero (primDivNatS (Succ xz570) (Succ xz59))",fontsize=16,color="black",shape="box"];1289 -> 1298[label="",style="solid", color="black", weight=3]; 12.76/4.84 1290[label="primMinusNat Zero (primDivNatS Zero (Succ xz59))",fontsize=16,color="black",shape="triangle"];1290 -> 1299[label="",style="solid", color="black", weight=3]; 12.76/4.84 1291 -> 1290[label="",style="dashed", color="red", weight=0]; 12.76/4.84 1291[label="primMinusNat Zero (primDivNatS Zero (Succ xz59))",fontsize=16,color="magenta"];805[label="Succ (Succ (primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz50) (Succ xz51)) (Succ (Succ xz51)))))",fontsize=16,color="green",shape="box"];805 -> 807[label="",style="dashed", color="green", weight=3]; 12.76/4.84 1292[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz610) (Succ xz620)) (Succ xz63))",fontsize=16,color="black",shape="box"];1292 -> 1300[label="",style="solid", color="black", weight=3]; 12.76/4.84 1293[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz610) Zero) (Succ xz63))",fontsize=16,color="black",shape="box"];1293 -> 1301[label="",style="solid", color="black", weight=3]; 12.76/4.84 1294[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero (Succ xz620)) (Succ xz63))",fontsize=16,color="black",shape="box"];1294 -> 1302[label="",style="solid", color="black", weight=3]; 12.76/4.84 1295[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ xz63))",fontsize=16,color="black",shape="box"];1295 -> 1303[label="",style="solid", color="black", weight=3]; 12.76/4.84 1204[label="Succ xz45",fontsize=16,color="green",shape="box"];1205[label="Succ xz46",fontsize=16,color="green",shape="box"];1206[label="Succ xz46",fontsize=16,color="green",shape="box"];1296[label="xz570",fontsize=16,color="green",shape="box"];1297[label="xz580",fontsize=16,color="green",shape="box"];1298[label="primMinusNat Zero (primDivNatS0 xz570 xz59 (primGEqNatS xz570 xz59))",fontsize=16,color="burlywood",shape="box"];2446[label="xz570/Succ xz5700",fontsize=10,color="white",style="solid",shape="box"];1298 -> 2446[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2446 -> 1304[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 2447[label="xz570/Zero",fontsize=10,color="white",style="solid",shape="box"];1298 -> 2447[label="",style="solid", color="burlywood", weight=9]; 12.76/4.84 2447 -> 1305[label="",style="solid", color="burlywood", weight=3]; 12.76/4.84 1299[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1299 -> 1306[label="",style="solid", color="black", weight=3]; 12.76/4.84 807 -> 1252[label="",style="dashed", color="red", weight=0]; 12.76/4.84 807[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz50) (Succ xz51)) (Succ (Succ xz51)))",fontsize=16,color="magenta"];807 -> 1259[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 807 -> 1260[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 807 -> 1261[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 1300 -> 1252[label="",style="dashed", color="red", weight=0]; 12.76/4.84 1300[label="primPlusNat Zero (primDivNatS (primMinusNatS xz610 xz620) (Succ xz63))",fontsize=16,color="magenta"];1300 -> 1307[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 1300 -> 1308[label="",style="dashed", color="magenta", weight=3]; 12.76/4.84 1301[label="primPlusNat Zero (primDivNatS (Succ xz610) (Succ xz63))",fontsize=16,color="black",shape="box"];1301 -> 1309[label="",style="solid", color="black", weight=3]; 12.76/4.85 1302[label="primPlusNat Zero (primDivNatS Zero (Succ xz63))",fontsize=16,color="black",shape="triangle"];1302 -> 1310[label="",style="solid", color="black", weight=3]; 12.76/4.85 1303 -> 1302[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1303[label="primPlusNat Zero (primDivNatS Zero (Succ xz63))",fontsize=16,color="magenta"];1304[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) xz59 (primGEqNatS (Succ xz5700) xz59))",fontsize=16,color="burlywood",shape="box"];2448[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1304 -> 2448[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2448 -> 1311[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2449[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1304 -> 2449[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2449 -> 1312[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1305[label="primMinusNat Zero (primDivNatS0 Zero xz59 (primGEqNatS Zero xz59))",fontsize=16,color="burlywood",shape="box"];2450[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1305 -> 2450[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2450 -> 1313[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2451[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1305 -> 2451[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2451 -> 1314[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1306[label="Pos Zero",fontsize=16,color="green",shape="box"];1259[label="Succ xz51",fontsize=16,color="green",shape="box"];1260[label="Succ xz50",fontsize=16,color="green",shape="box"];1261[label="Succ xz51",fontsize=16,color="green",shape="box"];1307[label="xz620",fontsize=16,color="green",shape="box"];1308[label="xz610",fontsize=16,color="green",shape="box"];1309[label="primPlusNat Zero (primDivNatS0 xz610 xz63 (primGEqNatS xz610 xz63))",fontsize=16,color="burlywood",shape="box"];2452[label="xz610/Succ xz6100",fontsize=10,color="white",style="solid",shape="box"];1309 -> 2452[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2452 -> 1315[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2453[label="xz610/Zero",fontsize=10,color="white",style="solid",shape="box"];1309 -> 2453[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2453 -> 1316[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1310[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1310 -> 1317[label="",style="solid", color="black", weight=3]; 12.76/4.85 1311[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) (Succ xz590) (primGEqNatS (Succ xz5700) (Succ xz590)))",fontsize=16,color="black",shape="box"];1311 -> 1318[label="",style="solid", color="black", weight=3]; 12.76/4.85 1312[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) Zero (primGEqNatS (Succ xz5700) Zero))",fontsize=16,color="black",shape="box"];1312 -> 1319[label="",style="solid", color="black", weight=3]; 12.76/4.85 1313[label="primMinusNat Zero (primDivNatS0 Zero (Succ xz590) (primGEqNatS Zero (Succ xz590)))",fontsize=16,color="black",shape="box"];1313 -> 1320[label="",style="solid", color="black", weight=3]; 12.76/4.85 1314[label="primMinusNat Zero (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];1314 -> 1321[label="",style="solid", color="black", weight=3]; 12.76/4.85 1315[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) xz63 (primGEqNatS (Succ xz6100) xz63))",fontsize=16,color="burlywood",shape="box"];2454[label="xz63/Succ xz630",fontsize=10,color="white",style="solid",shape="box"];1315 -> 2454[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2454 -> 1322[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2455[label="xz63/Zero",fontsize=10,color="white",style="solid",shape="box"];1315 -> 2455[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2455 -> 1323[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1316[label="primPlusNat Zero (primDivNatS0 Zero xz63 (primGEqNatS Zero xz63))",fontsize=16,color="burlywood",shape="box"];2456[label="xz63/Succ xz630",fontsize=10,color="white",style="solid",shape="box"];1316 -> 2456[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2456 -> 1324[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2457[label="xz63/Zero",fontsize=10,color="white",style="solid",shape="box"];1316 -> 2457[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2457 -> 1325[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1317[label="Zero",fontsize=16,color="green",shape="box"];1318 -> 1881[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1318[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) (Succ xz590) (primGEqNatS xz5700 xz590))",fontsize=16,color="magenta"];1318 -> 1882[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1318 -> 1883[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1318 -> 1884[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1318 -> 1885[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1319[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) Zero True)",fontsize=16,color="black",shape="box"];1319 -> 1328[label="",style="solid", color="black", weight=3]; 12.76/4.85 1320[label="primMinusNat Zero (primDivNatS0 Zero (Succ xz590) False)",fontsize=16,color="black",shape="box"];1320 -> 1329[label="",style="solid", color="black", weight=3]; 12.76/4.85 1321[label="primMinusNat Zero (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];1321 -> 1330[label="",style="solid", color="black", weight=3]; 12.76/4.85 1322[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) (Succ xz630) (primGEqNatS (Succ xz6100) (Succ xz630)))",fontsize=16,color="black",shape="box"];1322 -> 1331[label="",style="solid", color="black", weight=3]; 12.76/4.85 1323[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) Zero (primGEqNatS (Succ xz6100) Zero))",fontsize=16,color="black",shape="box"];1323 -> 1332[label="",style="solid", color="black", weight=3]; 12.76/4.85 1324[label="primPlusNat Zero (primDivNatS0 Zero (Succ xz630) (primGEqNatS Zero (Succ xz630)))",fontsize=16,color="black",shape="box"];1324 -> 1333[label="",style="solid", color="black", weight=3]; 12.76/4.85 1325[label="primPlusNat Zero (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];1325 -> 1334[label="",style="solid", color="black", weight=3]; 12.76/4.85 1882[label="xz5700",fontsize=16,color="green",shape="box"];1883[label="xz590",fontsize=16,color="green",shape="box"];1884[label="xz5700",fontsize=16,color="green",shape="box"];1885[label="xz590",fontsize=16,color="green",shape="box"];1881[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS xz96 xz97))",fontsize=16,color="burlywood",shape="triangle"];2458[label="xz96/Succ xz960",fontsize=10,color="white",style="solid",shape="box"];1881 -> 2458[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2458 -> 1922[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2459[label="xz96/Zero",fontsize=10,color="white",style="solid",shape="box"];1881 -> 2459[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2459 -> 1923[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1328 -> 1687[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1328[label="primMinusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz5700) Zero) (Succ Zero)))",fontsize=16,color="magenta"];1328 -> 1688[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1329 -> 1299[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1329[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];1330 -> 1687[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1330[label="primMinusNat Zero (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];1330 -> 1689[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1331 -> 1986[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1331[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) (Succ xz630) (primGEqNatS xz6100 xz630))",fontsize=16,color="magenta"];1331 -> 1987[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1331 -> 1988[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1331 -> 1989[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1331 -> 1990[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1332[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) Zero True)",fontsize=16,color="black",shape="box"];1332 -> 1343[label="",style="solid", color="black", weight=3]; 12.76/4.85 1333[label="primPlusNat Zero (primDivNatS0 Zero (Succ xz630) False)",fontsize=16,color="black",shape="box"];1333 -> 1344[label="",style="solid", color="black", weight=3]; 12.76/4.85 1334[label="primPlusNat Zero (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];1334 -> 1345[label="",style="solid", color="black", weight=3]; 12.76/4.85 1922[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS (Succ xz960) xz97))",fontsize=16,color="burlywood",shape="box"];2460[label="xz97/Succ xz970",fontsize=10,color="white",style="solid",shape="box"];1922 -> 2460[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2460 -> 1936[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2461[label="xz97/Zero",fontsize=10,color="white",style="solid",shape="box"];1922 -> 2461[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2461 -> 1937[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1923[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS Zero xz97))",fontsize=16,color="burlywood",shape="box"];2462[label="xz97/Succ xz970",fontsize=10,color="white",style="solid",shape="box"];1923 -> 2462[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2462 -> 1938[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2463[label="xz97/Zero",fontsize=10,color="white",style="solid",shape="box"];1923 -> 2463[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2463 -> 1939[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1688 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1688[label="primDivNatS (primMinusNatS (Succ xz5700) Zero) (Succ Zero)",fontsize=16,color="magenta"];1688 -> 2107[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1688 -> 2108[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1688 -> 2109[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1687[label="primMinusNat Zero (Succ xz79)",fontsize=16,color="black",shape="triangle"];1687 -> 1703[label="",style="solid", color="black", weight=3]; 12.76/4.85 1689 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1689[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1689 -> 2110[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1689 -> 2111[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1689 -> 2112[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1987[label="xz630",fontsize=16,color="green",shape="box"];1988[label="xz630",fontsize=16,color="green",shape="box"];1989[label="xz6100",fontsize=16,color="green",shape="box"];1990[label="xz6100",fontsize=16,color="green",shape="box"];1986[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS xz109 xz110))",fontsize=16,color="burlywood",shape="triangle"];2464[label="xz109/Succ xz1090",fontsize=10,color="white",style="solid",shape="box"];1986 -> 2464[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2464 -> 2027[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2465[label="xz109/Zero",fontsize=10,color="white",style="solid",shape="box"];1986 -> 2465[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2465 -> 2028[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1343 -> 1751[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1343[label="primPlusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz6100) Zero) (Succ Zero)))",fontsize=16,color="magenta"];1343 -> 1752[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1344 -> 1310[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1344[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];1345 -> 1751[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1345[label="primPlusNat Zero (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];1345 -> 1753[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1936[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS (Succ xz960) (Succ xz970)))",fontsize=16,color="black",shape="box"];1936 -> 1953[label="",style="solid", color="black", weight=3]; 12.76/4.85 1937[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS (Succ xz960) Zero))",fontsize=16,color="black",shape="box"];1937 -> 1954[label="",style="solid", color="black", weight=3]; 12.76/4.85 1938[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS Zero (Succ xz970)))",fontsize=16,color="black",shape="box"];1938 -> 1955[label="",style="solid", color="black", weight=3]; 12.76/4.85 1939[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];1939 -> 1956[label="",style="solid", color="black", weight=3]; 12.76/4.85 2107[label="Succ xz5700",fontsize=16,color="green",shape="box"];2108[label="Zero",fontsize=16,color="green",shape="box"];2109[label="Zero",fontsize=16,color="green",shape="box"];2106[label="primDivNatS (primMinusNatS xz115 xz116) (Succ xz117)",fontsize=16,color="burlywood",shape="triangle"];2466[label="xz115/Succ xz1150",fontsize=10,color="white",style="solid",shape="box"];2106 -> 2466[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2466 -> 2158[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2467[label="xz115/Zero",fontsize=10,color="white",style="solid",shape="box"];2106 -> 2467[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2467 -> 2159[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1703[label="Neg (Succ xz79)",fontsize=16,color="green",shape="box"];2110[label="Zero",fontsize=16,color="green",shape="box"];2111[label="Zero",fontsize=16,color="green",shape="box"];2112[label="Zero",fontsize=16,color="green",shape="box"];2027[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS (Succ xz1090) xz110))",fontsize=16,color="burlywood",shape="box"];2468[label="xz110/Succ xz1100",fontsize=10,color="white",style="solid",shape="box"];2027 -> 2468[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2468 -> 2043[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2469[label="xz110/Zero",fontsize=10,color="white",style="solid",shape="box"];2027 -> 2469[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2469 -> 2044[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2028[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS Zero xz110))",fontsize=16,color="burlywood",shape="box"];2470[label="xz110/Succ xz1100",fontsize=10,color="white",style="solid",shape="box"];2028 -> 2470[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2470 -> 2045[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2471[label="xz110/Zero",fontsize=10,color="white",style="solid",shape="box"];2028 -> 2471[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2471 -> 2046[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 1752 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1752[label="primDivNatS (primMinusNatS (Succ xz6100) Zero) (Succ Zero)",fontsize=16,color="magenta"];1752 -> 2119[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1752 -> 2120[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1752 -> 2121[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1751[label="primPlusNat Zero (Succ xz82)",fontsize=16,color="black",shape="triangle"];1751 -> 1767[label="",style="solid", color="black", weight=3]; 12.76/4.85 1753 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1753[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1753 -> 2122[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1753 -> 2123[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1753 -> 2124[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1953 -> 1881[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1953[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS xz960 xz970))",fontsize=16,color="magenta"];1953 -> 1971[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1953 -> 1972[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1954[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) True)",fontsize=16,color="black",shape="triangle"];1954 -> 1973[label="",style="solid", color="black", weight=3]; 12.76/4.85 1955[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) False)",fontsize=16,color="black",shape="box"];1955 -> 1974[label="",style="solid", color="black", weight=3]; 12.76/4.85 1956 -> 1954[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1956[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) True)",fontsize=16,color="magenta"];2158[label="primDivNatS (primMinusNatS (Succ xz1150) xz116) (Succ xz117)",fontsize=16,color="burlywood",shape="box"];2472[label="xz116/Succ xz1160",fontsize=10,color="white",style="solid",shape="box"];2158 -> 2472[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2472 -> 2160[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2473[label="xz116/Zero",fontsize=10,color="white",style="solid",shape="box"];2158 -> 2473[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2473 -> 2161[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2159[label="primDivNatS (primMinusNatS Zero xz116) (Succ xz117)",fontsize=16,color="burlywood",shape="box"];2474[label="xz116/Succ xz1160",fontsize=10,color="white",style="solid",shape="box"];2159 -> 2474[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2474 -> 2162[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2475[label="xz116/Zero",fontsize=10,color="white",style="solid",shape="box"];2159 -> 2475[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2475 -> 2163[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2043[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS (Succ xz1090) (Succ xz1100)))",fontsize=16,color="black",shape="box"];2043 -> 2056[label="",style="solid", color="black", weight=3]; 12.76/4.85 2044[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS (Succ xz1090) Zero))",fontsize=16,color="black",shape="box"];2044 -> 2057[label="",style="solid", color="black", weight=3]; 12.76/4.85 2045[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS Zero (Succ xz1100)))",fontsize=16,color="black",shape="box"];2045 -> 2058[label="",style="solid", color="black", weight=3]; 12.76/4.85 2046[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];2046 -> 2059[label="",style="solid", color="black", weight=3]; 12.76/4.85 2119[label="Succ xz6100",fontsize=16,color="green",shape="box"];2120[label="Zero",fontsize=16,color="green",shape="box"];2121[label="Zero",fontsize=16,color="green",shape="box"];1767[label="Succ xz82",fontsize=16,color="green",shape="box"];2122[label="Zero",fontsize=16,color="green",shape="box"];2123[label="Zero",fontsize=16,color="green",shape="box"];2124[label="Zero",fontsize=16,color="green",shape="box"];1971[label="xz960",fontsize=16,color="green",shape="box"];1972[label="xz970",fontsize=16,color="green",shape="box"];1973 -> 1687[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1973[label="primMinusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz94) (Succ xz95)) (Succ (Succ xz95))))",fontsize=16,color="magenta"];1973 -> 2029[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 1974 -> 1299[label="",style="dashed", color="red", weight=0]; 12.76/4.85 1974[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];2160[label="primDivNatS (primMinusNatS (Succ xz1150) (Succ xz1160)) (Succ xz117)",fontsize=16,color="black",shape="box"];2160 -> 2164[label="",style="solid", color="black", weight=3]; 12.76/4.85 2161[label="primDivNatS (primMinusNatS (Succ xz1150) Zero) (Succ xz117)",fontsize=16,color="black",shape="box"];2161 -> 2165[label="",style="solid", color="black", weight=3]; 12.76/4.85 2162[label="primDivNatS (primMinusNatS Zero (Succ xz1160)) (Succ xz117)",fontsize=16,color="black",shape="box"];2162 -> 2166[label="",style="solid", color="black", weight=3]; 12.76/4.85 2163[label="primDivNatS (primMinusNatS Zero Zero) (Succ xz117)",fontsize=16,color="black",shape="box"];2163 -> 2167[label="",style="solid", color="black", weight=3]; 12.76/4.85 2056 -> 1986[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2056[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS xz1090 xz1100))",fontsize=16,color="magenta"];2056 -> 2066[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2056 -> 2067[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2057[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) True)",fontsize=16,color="black",shape="triangle"];2057 -> 2068[label="",style="solid", color="black", weight=3]; 12.76/4.85 2058[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) False)",fontsize=16,color="black",shape="box"];2058 -> 2069[label="",style="solid", color="black", weight=3]; 12.76/4.85 2059 -> 2057[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2059[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) True)",fontsize=16,color="magenta"];2029 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2029[label="primDivNatS (primMinusNatS (Succ xz94) (Succ xz95)) (Succ (Succ xz95))",fontsize=16,color="magenta"];2029 -> 2128[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2029 -> 2129[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2029 -> 2130[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2164 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2164[label="primDivNatS (primMinusNatS xz1150 xz1160) (Succ xz117)",fontsize=16,color="magenta"];2164 -> 2168[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2164 -> 2169[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2165[label="primDivNatS (Succ xz1150) (Succ xz117)",fontsize=16,color="black",shape="box"];2165 -> 2170[label="",style="solid", color="black", weight=3]; 12.76/4.85 2166[label="primDivNatS Zero (Succ xz117)",fontsize=16,color="black",shape="triangle"];2166 -> 2171[label="",style="solid", color="black", weight=3]; 12.76/4.85 2167 -> 2166[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2167[label="primDivNatS Zero (Succ xz117)",fontsize=16,color="magenta"];2066[label="xz1100",fontsize=16,color="green",shape="box"];2067[label="xz1090",fontsize=16,color="green",shape="box"];2068 -> 1751[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2068[label="primPlusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz107) (Succ xz108)) (Succ (Succ xz108))))",fontsize=16,color="magenta"];2068 -> 2080[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2069 -> 1310[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2069[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];2128[label="Succ xz94",fontsize=16,color="green",shape="box"];2129[label="Succ xz95",fontsize=16,color="green",shape="box"];2130[label="Succ xz95",fontsize=16,color="green",shape="box"];2168[label="xz1150",fontsize=16,color="green",shape="box"];2169[label="xz1160",fontsize=16,color="green",shape="box"];2170[label="primDivNatS0 xz1150 xz117 (primGEqNatS xz1150 xz117)",fontsize=16,color="burlywood",shape="box"];2476[label="xz1150/Succ xz11500",fontsize=10,color="white",style="solid",shape="box"];2170 -> 2476[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2476 -> 2172[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2477[label="xz1150/Zero",fontsize=10,color="white",style="solid",shape="box"];2170 -> 2477[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2477 -> 2173[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2171[label="Zero",fontsize=16,color="green",shape="box"];2080 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2080[label="primDivNatS (primMinusNatS (Succ xz107) (Succ xz108)) (Succ (Succ xz108))",fontsize=16,color="magenta"];2080 -> 2131[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2080 -> 2132[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2080 -> 2133[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2172[label="primDivNatS0 (Succ xz11500) xz117 (primGEqNatS (Succ xz11500) xz117)",fontsize=16,color="burlywood",shape="box"];2478[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2172 -> 2478[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2478 -> 2174[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2479[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2172 -> 2479[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2479 -> 2175[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2173[label="primDivNatS0 Zero xz117 (primGEqNatS Zero xz117)",fontsize=16,color="burlywood",shape="box"];2480[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2173 -> 2480[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2480 -> 2176[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2481[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2173 -> 2481[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2481 -> 2177[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2131[label="Succ xz107",fontsize=16,color="green",shape="box"];2132[label="Succ xz108",fontsize=16,color="green",shape="box"];2133[label="Succ xz108",fontsize=16,color="green",shape="box"];2174[label="primDivNatS0 (Succ xz11500) (Succ xz1170) (primGEqNatS (Succ xz11500) (Succ xz1170))",fontsize=16,color="black",shape="box"];2174 -> 2178[label="",style="solid", color="black", weight=3]; 12.76/4.85 2175[label="primDivNatS0 (Succ xz11500) Zero (primGEqNatS (Succ xz11500) Zero)",fontsize=16,color="black",shape="box"];2175 -> 2179[label="",style="solid", color="black", weight=3]; 12.76/4.85 2176[label="primDivNatS0 Zero (Succ xz1170) (primGEqNatS Zero (Succ xz1170))",fontsize=16,color="black",shape="box"];2176 -> 2180[label="",style="solid", color="black", weight=3]; 12.76/4.85 2177[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2177 -> 2181[label="",style="solid", color="black", weight=3]; 12.76/4.85 2178 -> 2340[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2178[label="primDivNatS0 (Succ xz11500) (Succ xz1170) (primGEqNatS xz11500 xz1170)",fontsize=16,color="magenta"];2178 -> 2341[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2178 -> 2342[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2178 -> 2343[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2178 -> 2344[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2179[label="primDivNatS0 (Succ xz11500) Zero True",fontsize=16,color="black",shape="box"];2179 -> 2184[label="",style="solid", color="black", weight=3]; 12.76/4.85 2180[label="primDivNatS0 Zero (Succ xz1170) False",fontsize=16,color="black",shape="box"];2180 -> 2185[label="",style="solid", color="black", weight=3]; 12.76/4.85 2181[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2181 -> 2186[label="",style="solid", color="black", weight=3]; 12.76/4.85 2341[label="xz11500",fontsize=16,color="green",shape="box"];2342[label="xz1170",fontsize=16,color="green",shape="box"];2343[label="xz11500",fontsize=16,color="green",shape="box"];2344[label="xz1170",fontsize=16,color="green",shape="box"];2340[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS xz136 xz137)",fontsize=16,color="burlywood",shape="triangle"];2482[label="xz136/Succ xz1360",fontsize=10,color="white",style="solid",shape="box"];2340 -> 2482[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2482 -> 2373[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2483[label="xz136/Zero",fontsize=10,color="white",style="solid",shape="box"];2340 -> 2483[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2483 -> 2374[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2184[label="Succ (primDivNatS (primMinusNatS (Succ xz11500) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2184 -> 2191[label="",style="dashed", color="green", weight=3]; 12.76/4.85 2185[label="Zero",fontsize=16,color="green",shape="box"];2186[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2186 -> 2192[label="",style="dashed", color="green", weight=3]; 12.76/4.85 2373[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS (Succ xz1360) xz137)",fontsize=16,color="burlywood",shape="box"];2484[label="xz137/Succ xz1370",fontsize=10,color="white",style="solid",shape="box"];2373 -> 2484[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2484 -> 2375[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2485[label="xz137/Zero",fontsize=10,color="white",style="solid",shape="box"];2373 -> 2485[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2485 -> 2376[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2374[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS Zero xz137)",fontsize=16,color="burlywood",shape="box"];2486[label="xz137/Succ xz1370",fontsize=10,color="white",style="solid",shape="box"];2374 -> 2486[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2486 -> 2377[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2487[label="xz137/Zero",fontsize=10,color="white",style="solid",shape="box"];2374 -> 2487[label="",style="solid", color="burlywood", weight=9]; 12.76/4.85 2487 -> 2378[label="",style="solid", color="burlywood", weight=3]; 12.76/4.85 2191 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2191[label="primDivNatS (primMinusNatS (Succ xz11500) Zero) (Succ Zero)",fontsize=16,color="magenta"];2191 -> 2197[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2191 -> 2198[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2191 -> 2199[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2192 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2192[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2192 -> 2200[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2192 -> 2201[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2192 -> 2202[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2375[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS (Succ xz1360) (Succ xz1370))",fontsize=16,color="black",shape="box"];2375 -> 2379[label="",style="solid", color="black", weight=3]; 12.76/4.85 2376[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS (Succ xz1360) Zero)",fontsize=16,color="black",shape="box"];2376 -> 2380[label="",style="solid", color="black", weight=3]; 12.76/4.85 2377[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS Zero (Succ xz1370))",fontsize=16,color="black",shape="box"];2377 -> 2381[label="",style="solid", color="black", weight=3]; 12.76/4.85 2378[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2378 -> 2382[label="",style="solid", color="black", weight=3]; 12.76/4.85 2197[label="Succ xz11500",fontsize=16,color="green",shape="box"];2198[label="Zero",fontsize=16,color="green",shape="box"];2199[label="Zero",fontsize=16,color="green",shape="box"];2200[label="Zero",fontsize=16,color="green",shape="box"];2201[label="Zero",fontsize=16,color="green",shape="box"];2202[label="Zero",fontsize=16,color="green",shape="box"];2379 -> 2340[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2379[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS xz1360 xz1370)",fontsize=16,color="magenta"];2379 -> 2383[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2379 -> 2384[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2380[label="primDivNatS0 (Succ xz134) (Succ xz135) True",fontsize=16,color="black",shape="triangle"];2380 -> 2385[label="",style="solid", color="black", weight=3]; 12.76/4.85 2381[label="primDivNatS0 (Succ xz134) (Succ xz135) False",fontsize=16,color="black",shape="box"];2381 -> 2386[label="",style="solid", color="black", weight=3]; 12.76/4.85 2382 -> 2380[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2382[label="primDivNatS0 (Succ xz134) (Succ xz135) True",fontsize=16,color="magenta"];2383[label="xz1360",fontsize=16,color="green",shape="box"];2384[label="xz1370",fontsize=16,color="green",shape="box"];2385[label="Succ (primDivNatS (primMinusNatS (Succ xz134) (Succ xz135)) (Succ (Succ xz135)))",fontsize=16,color="green",shape="box"];2385 -> 2387[label="",style="dashed", color="green", weight=3]; 12.76/4.85 2386[label="Zero",fontsize=16,color="green",shape="box"];2387 -> 2106[label="",style="dashed", color="red", weight=0]; 12.76/4.85 2387[label="primDivNatS (primMinusNatS (Succ xz134) (Succ xz135)) (Succ (Succ xz135))",fontsize=16,color="magenta"];2387 -> 2388[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2387 -> 2389[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2387 -> 2390[label="",style="dashed", color="magenta", weight=3]; 12.76/4.85 2388[label="Succ xz134",fontsize=16,color="green",shape="box"];2389[label="Succ xz135",fontsize=16,color="green",shape="box"];2390[label="Succ xz135",fontsize=16,color="green",shape="box"];} 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (14) 12.76/4.85 Complex Obligation (AND) 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (15) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primDivNatS0(xz134, xz135, Zero, Zero) -> new_primDivNatS00(xz134, xz135) 12.76/4.85 new_primDivNatS(Succ(Zero), Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) 12.76/4.85 new_primDivNatS00(xz134, xz135) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) 12.76/4.85 new_primDivNatS(Succ(xz1150), Succ(xz1160), xz117) -> new_primDivNatS(xz1150, xz1160, xz117) 12.76/4.85 new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) 12.76/4.85 new_primDivNatS(Succ(Succ(xz11500)), Zero, Succ(xz1170)) -> new_primDivNatS0(xz11500, xz1170, xz11500, xz1170) 12.76/4.85 new_primDivNatS0(xz134, xz135, Succ(xz1360), Zero) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) 12.76/4.85 new_primDivNatS(Succ(Succ(xz11500)), Zero, Zero) -> new_primDivNatS(Succ(xz11500), Zero, Zero) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (16) DependencyGraphProof (EQUIVALENT) 12.76/4.85 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (17) 12.76/4.85 Complex Obligation (AND) 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (18) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primDivNatS(Succ(Succ(xz11500)), Zero, Zero) -> new_primDivNatS(Succ(xz11500), Zero, Zero) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (19) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primDivNatS(Succ(Succ(xz11500)), Zero, Zero) -> new_primDivNatS(Succ(xz11500), Zero, Zero) 12.76/4.85 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 2, 2 >= 3, 3 >= 3 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (20) 12.76/4.85 YES 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (21) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primDivNatS00(xz134, xz135) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) 12.76/4.85 new_primDivNatS(Succ(xz1150), Succ(xz1160), xz117) -> new_primDivNatS(xz1150, xz1160, xz117) 12.76/4.85 new_primDivNatS(Succ(Succ(xz11500)), Zero, Succ(xz1170)) -> new_primDivNatS0(xz11500, xz1170, xz11500, xz1170) 12.76/4.85 new_primDivNatS0(xz134, xz135, Zero, Zero) -> new_primDivNatS00(xz134, xz135) 12.76/4.85 new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) 12.76/4.85 new_primDivNatS0(xz134, xz135, Succ(xz1360), Zero) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (22) QDPOrderProof (EQUIVALENT) 12.76/4.85 We use the reduction pair processor [LPAR04,JAR06]. 12.76/4.85 12.76/4.85 12.76/4.85 The following pairs can be oriented strictly and are deleted. 12.76/4.85 12.76/4.85 new_primDivNatS(Succ(xz1150), Succ(xz1160), xz117) -> new_primDivNatS(xz1150, xz1160, xz117) 12.76/4.85 new_primDivNatS(Succ(Succ(xz11500)), Zero, Succ(xz1170)) -> new_primDivNatS0(xz11500, xz1170, xz11500, xz1170) 12.76/4.85 The remaining pairs can at least be oriented weakly. 12.76/4.85 Used ordering: Polynomial interpretation [POLO]: 12.76/4.85 12.76/4.85 POL(Succ(x_1)) = 1 + x_1 12.76/4.85 POL(Zero) = 1 12.76/4.85 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 12.76/4.85 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 12.76/4.85 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 12.76/4.85 12.76/4.85 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 12.76/4.85 none 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (23) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primDivNatS00(xz134, xz135) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) 12.76/4.85 new_primDivNatS0(xz134, xz135, Zero, Zero) -> new_primDivNatS00(xz134, xz135) 12.76/4.85 new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) 12.76/4.85 new_primDivNatS0(xz134, xz135, Succ(xz1360), Zero) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (24) DependencyGraphProof (EQUIVALENT) 12.76/4.85 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (25) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (26) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) 12.76/4.85 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (27) 12.76/4.85 YES 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (28) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primMinusNat0(Succ(xz570), Succ(xz580), xz59) -> new_primMinusNat0(xz570, xz580, xz59) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (29) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primMinusNat0(Succ(xz570), Succ(xz580), xz59) -> new_primMinusNat0(xz570, xz580, xz59) 12.76/4.85 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (30) 12.76/4.85 YES 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (31) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primPlusNat0(Succ(xz610), Succ(xz620), xz63) -> new_primPlusNat0(xz610, xz620, xz63) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (32) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primPlusNat0(Succ(xz610), Succ(xz620), xz63) -> new_primPlusNat0(xz610, xz620, xz63) 12.76/4.85 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (33) 12.76/4.85 YES 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (34) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primPlusNat1(xz50, xz51, Succ(xz520), Succ(xz530)) -> new_primPlusNat1(xz50, xz51, xz520, xz530) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (35) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primPlusNat1(xz50, xz51, Succ(xz520), Succ(xz530)) -> new_primPlusNat1(xz50, xz51, xz520, xz530) 12.76/4.85 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (36) 12.76/4.85 YES 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (37) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primMinusNat(xz94, xz95, Succ(xz960), Succ(xz970)) -> new_primMinusNat(xz94, xz95, xz960, xz970) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (38) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primMinusNat(xz94, xz95, Succ(xz960), Succ(xz970)) -> new_primMinusNat(xz94, xz95, xz960, xz970) 12.76/4.85 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (39) 12.76/4.85 YES 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (40) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primPlusNat(xz107, xz108, Succ(xz1090), Succ(xz1100)) -> new_primPlusNat(xz107, xz108, xz1090, xz1100) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (41) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primPlusNat(xz107, xz108, Succ(xz1090), Succ(xz1100)) -> new_primPlusNat(xz107, xz108, xz1090, xz1100) 12.76/4.85 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (42) 12.76/4.85 YES 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (43) 12.76/4.85 Obligation: 12.76/4.85 Q DP problem: 12.76/4.85 The TRS P consists of the following rules: 12.76/4.85 12.76/4.85 new_primMinusNat1(xz45, xz46, Succ(xz470), Succ(xz480)) -> new_primMinusNat1(xz45, xz46, xz470, xz480) 12.76/4.85 12.76/4.85 R is empty. 12.76/4.85 Q is empty. 12.76/4.85 We have to consider all minimal (P,Q,R)-chains. 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (44) QDPSizeChangeProof (EQUIVALENT) 12.76/4.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 12.76/4.85 12.76/4.85 From the DPs we obtained the following set of size-change graphs: 12.76/4.85 *new_primMinusNat1(xz45, xz46, Succ(xz470), Succ(xz480)) -> new_primMinusNat1(xz45, xz46, xz470, xz480) 12.76/4.85 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 12.76/4.85 12.76/4.85 12.76/4.85 ---------------------------------------- 12.76/4.85 12.76/4.85 (45) 12.76/4.85 YES 12.90/4.88 EOF