/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) IFR [EQUIVALENT, 0 ms] (4) HASKELL (5) BR [EQUIVALENT, 0 ms] (6) HASKELL (7) COR [EQUIVALENT, 0 ms] (8) HASKELL (9) LetRed [EQUIVALENT, 0 ms] (10) HASKELL (11) NumRed [SOUND, 0 ms] (12) HASKELL (13) Narrow [SOUND, 0 ms] (14) AND (15) QDP (16) DependencyGraphProof [EQUIVALENT, 0 ms] (17) AND (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) QDPOrderProof [EQUIVALENT, 12 ms] (23) QDP (24) DependencyGraphProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) QDP (29) QDPSizeChangeProof [EQUIVALENT, 0 ms] (30) YES (31) QDP (32) QDPSizeChangeProof [EQUIVALENT, 0 ms] (33) YES (34) QDP (35) QDPSizeChangeProof [EQUIVALENT, 0 ms] (36) YES (37) QDP (38) QDPSizeChangeProof [EQUIVALENT, 0 ms] (39) YES (40) QDP (41) QDPSizeChangeProof [EQUIVALENT, 0 ms] (42) YES (43) QDP (44) QDPSizeChangeProof [EQUIVALENT, 0 ms] (45) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\(q,_)->q" is transformed to "q1 (q,_) = q; " The following Lambda expression "\(_,r)->r" is transformed to "r0 (_,r) = r; " The following Lambda expression "\(m,_)->m" is transformed to "m0 (m,_) = m; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) IFR (EQUIVALENT) If Reductions: The following If expression "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" is transformed to "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); primDivNatS0 x y False = Zero; " The following If expression "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" is transformed to "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); primModNatS0 x y False = Succ x; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. Binding Reductions: The bind variable of the following binding Pattern "frac@(Float vv vw)" is replaced by the following term "Float vv vw" The bind variable of the following binding Pattern "frac@(Double ww wx)" is replaced by the following term "Double ww wx" ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "(fromIntegral q,r :% y) where { q = q1 vu30; ; q1 (q,wy) = q; ; r = r0 vu30; ; r0 (wz,r) = r; ; vu30 = quotRem x y; } " are unpacked to the following functions on top level "properFractionR0 xw xx (wz,r) = r; " "properFractionQ1 xw xx (q,wy) = q; " "properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx); " "properFractionVu30 xw xx = quotRem xw xx; " "properFractionR xw xx = properFractionR0 xw xx (properFractionVu30 xw xx); " The bindings of the following Let/Where expression "m where { m = m0 vu6; ; m0 (m,xv) = m; ; vu6 = properFraction x; } " are unpacked to the following functions on top level "truncateVu6 xy = properFraction xy; " "truncateM0 xy (m,xv) = m; " "truncateM xy = truncateM0 xy (truncateVu6 xy); " ---------------------------------------- (10) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (11) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (12) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (13) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="succ",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="succ xz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="toEnum . (Pos (Succ Zero) +) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="toEnum ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="primIntToFloat ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="Float ((Pos (Succ Zero) +) . fromEnum) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3]; 8[label="(Pos (Succ Zero) +) . fromEnum",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9[label="Pos (Succ Zero) + fromEnum xz3",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 10[label="primPlusInt (Pos (Succ Zero)) (fromEnum xz3)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11[label="primPlusInt (Pos (Succ Zero)) (truncate xz3)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 12[label="primPlusInt (Pos (Succ Zero)) (truncateM xz3)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 13[label="primPlusInt (Pos (Succ Zero)) (truncateM0 xz3 (truncateVu6 xz3))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 14[label="primPlusInt (Pos (Succ Zero)) (truncateM0 xz3 (properFraction xz3))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 15[label="primPlusInt (Pos (Succ Zero)) (truncateM0 xz3 (floatProperFractionFloat xz3))",fontsize=16,color="burlywood",shape="box"];2381[label="xz3/Float xz30 xz31",fontsize=10,color="white",style="solid",shape="box"];15 -> 2381[label="",style="solid", color="burlywood", weight=9]; 2381 -> 16[label="",style="solid", color="burlywood", weight=3]; 16[label="primPlusInt (Pos (Succ Zero)) (truncateM0 (Float xz30 xz31) (floatProperFractionFloat (Float xz30 xz31)))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 17[label="primPlusInt (Pos (Succ Zero)) (truncateM0 (Float xz30 xz31) (fromInt (xz30 `quot` xz31),Float xz30 xz31 - fromInt (xz30 `quot` xz31)))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 18[label="primPlusInt (Pos (Succ Zero)) (fromInt (xz30 `quot` xz31))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 19[label="primPlusInt (Pos (Succ Zero)) (xz30 `quot` xz31)",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3]; 20[label="primPlusInt (Pos (Succ Zero)) (primQuotInt xz30 xz31)",fontsize=16,color="burlywood",shape="box"];2382[label="xz30/Pos xz300",fontsize=10,color="white",style="solid",shape="box"];20 -> 2382[label="",style="solid", color="burlywood", weight=9]; 2382 -> 21[label="",style="solid", color="burlywood", weight=3]; 2383[label="xz30/Neg xz300",fontsize=10,color="white",style="solid",shape="box"];20 -> 2383[label="",style="solid", color="burlywood", weight=9]; 2383 -> 22[label="",style="solid", color="burlywood", weight=3]; 21[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) xz31)",fontsize=16,color="burlywood",shape="box"];2384[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];21 -> 2384[label="",style="solid", color="burlywood", weight=9]; 2384 -> 23[label="",style="solid", color="burlywood", weight=3]; 2385[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];21 -> 2385[label="",style="solid", color="burlywood", weight=9]; 2385 -> 24[label="",style="solid", color="burlywood", weight=3]; 22[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) xz31)",fontsize=16,color="burlywood",shape="box"];2386[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];22 -> 2386[label="",style="solid", color="burlywood", weight=9]; 2386 -> 25[label="",style="solid", color="burlywood", weight=3]; 2387[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];22 -> 2387[label="",style="solid", color="burlywood", weight=9]; 2387 -> 26[label="",style="solid", color="burlywood", weight=3]; 23[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Pos xz310))",fontsize=16,color="burlywood",shape="box"];2388[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];23 -> 2388[label="",style="solid", color="burlywood", weight=9]; 2388 -> 27[label="",style="solid", color="burlywood", weight=3]; 2389[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 2389[label="",style="solid", color="burlywood", weight=9]; 2389 -> 28[label="",style="solid", color="burlywood", weight=3]; 24[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Neg xz310))",fontsize=16,color="burlywood",shape="box"];2390[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];24 -> 2390[label="",style="solid", color="burlywood", weight=9]; 2390 -> 29[label="",style="solid", color="burlywood", weight=3]; 2391[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 2391[label="",style="solid", color="burlywood", weight=9]; 2391 -> 30[label="",style="solid", color="burlywood", weight=3]; 25[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Pos xz310))",fontsize=16,color="burlywood",shape="box"];2392[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];25 -> 2392[label="",style="solid", color="burlywood", weight=9]; 2392 -> 31[label="",style="solid", color="burlywood", weight=3]; 2393[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 2393[label="",style="solid", color="burlywood", weight=9]; 2393 -> 32[label="",style="solid", color="burlywood", weight=3]; 26[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Neg xz310))",fontsize=16,color="burlywood",shape="box"];2394[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];26 -> 2394[label="",style="solid", color="burlywood", weight=9]; 2394 -> 33[label="",style="solid", color="burlywood", weight=3]; 2395[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 2395[label="",style="solid", color="burlywood", weight=9]; 2395 -> 34[label="",style="solid", color="burlywood", weight=3]; 27[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Pos (Succ xz3100)))",fontsize=16,color="black",shape="box"];27 -> 35[label="",style="solid", color="black", weight=3]; 28[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Pos Zero))",fontsize=16,color="black",shape="box"];28 -> 36[label="",style="solid", color="black", weight=3]; 29[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Neg (Succ xz3100)))",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3]; 30[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Pos xz300) (Neg Zero))",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3]; 31[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Pos (Succ xz3100)))",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3]; 32[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Pos Zero))",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3]; 33[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Neg (Succ xz3100)))",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3]; 34[label="primPlusInt (Pos (Succ Zero)) (primQuotInt (Neg xz300) (Neg Zero))",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3]; 35[label="primPlusInt (Pos (Succ Zero)) (Pos (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="black",shape="triangle"];35 -> 43[label="",style="solid", color="black", weight=3]; 36[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="black",shape="triangle"];36 -> 44[label="",style="solid", color="black", weight=3]; 37[label="primPlusInt (Pos (Succ Zero)) (Neg (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="black",shape="triangle"];37 -> 45[label="",style="solid", color="black", weight=3]; 38 -> 36[label="",style="dashed", color="red", weight=0]; 38[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="magenta"];39 -> 37[label="",style="dashed", color="red", weight=0]; 39[label="primPlusInt (Pos (Succ Zero)) (Neg (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="magenta"];39 -> 46[label="",style="dashed", color="magenta", weight=3]; 39 -> 47[label="",style="dashed", color="magenta", weight=3]; 40 -> 36[label="",style="dashed", color="red", weight=0]; 40[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="magenta"];41 -> 35[label="",style="dashed", color="red", weight=0]; 41[label="primPlusInt (Pos (Succ Zero)) (Pos (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="magenta"];41 -> 48[label="",style="dashed", color="magenta", weight=3]; 41 -> 49[label="",style="dashed", color="magenta", weight=3]; 42 -> 36[label="",style="dashed", color="red", weight=0]; 42[label="primPlusInt (Pos (Succ Zero)) (error [])",fontsize=16,color="magenta"];43[label="Pos (primPlusNat (Succ Zero) (primDivNatS xz300 (Succ xz3100)))",fontsize=16,color="green",shape="box"];43 -> 50[label="",style="dashed", color="green", weight=3]; 44[label="error []",fontsize=16,color="red",shape="box"];45[label="primMinusNat (Succ Zero) (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="burlywood",shape="box"];2396[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];45 -> 2396[label="",style="solid", color="burlywood", weight=9]; 2396 -> 51[label="",style="solid", color="burlywood", weight=3]; 2397[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 2397[label="",style="solid", color="burlywood", weight=9]; 2397 -> 52[label="",style="solid", color="burlywood", weight=3]; 46[label="xz3100",fontsize=16,color="green",shape="box"];47[label="xz300",fontsize=16,color="green",shape="box"];48[label="xz3100",fontsize=16,color="green",shape="box"];49[label="xz300",fontsize=16,color="green",shape="box"];50[label="primPlusNat (Succ Zero) (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="burlywood",shape="box"];2398[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];50 -> 2398[label="",style="solid", color="burlywood", weight=9]; 2398 -> 53[label="",style="solid", color="burlywood", weight=3]; 2399[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 2399[label="",style="solid", color="burlywood", weight=9]; 2399 -> 54[label="",style="solid", color="burlywood", weight=3]; 51[label="primMinusNat (Succ Zero) (primDivNatS (Succ xz3000) (Succ xz3100))",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3]; 52[label="primMinusNat (Succ Zero) (primDivNatS Zero (Succ xz3100))",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 53[label="primPlusNat (Succ Zero) (primDivNatS (Succ xz3000) (Succ xz3100))",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3]; 54[label="primPlusNat (Succ Zero) (primDivNatS Zero (Succ xz3100))",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 55[label="primMinusNat (Succ Zero) (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100))",fontsize=16,color="burlywood",shape="box"];2400[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];55 -> 2400[label="",style="solid", color="burlywood", weight=9]; 2400 -> 59[label="",style="solid", color="burlywood", weight=3]; 2401[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 2401[label="",style="solid", color="burlywood", weight=9]; 2401 -> 60[label="",style="solid", color="burlywood", weight=3]; 56[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="triangle"];56 -> 61[label="",style="solid", color="black", weight=3]; 57[label="primPlusNat (Succ Zero) (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100))",fontsize=16,color="burlywood",shape="box"];2402[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];57 -> 2402[label="",style="solid", color="burlywood", weight=9]; 2402 -> 62[label="",style="solid", color="burlywood", weight=3]; 2403[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 2403[label="",style="solid", color="burlywood", weight=9]; 2403 -> 63[label="",style="solid", color="burlywood", weight=3]; 58[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="black",shape="triangle"];58 -> 64[label="",style="solid", color="black", weight=3]; 59[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100))",fontsize=16,color="burlywood",shape="box"];2404[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];59 -> 2404[label="",style="solid", color="burlywood", weight=9]; 2404 -> 65[label="",style="solid", color="burlywood", weight=3]; 2405[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 2405[label="",style="solid", color="burlywood", weight=9]; 2405 -> 66[label="",style="solid", color="burlywood", weight=3]; 60[label="primMinusNat (Succ Zero) (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100))",fontsize=16,color="burlywood",shape="box"];2406[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];60 -> 2406[label="",style="solid", color="burlywood", weight=9]; 2406 -> 67[label="",style="solid", color="burlywood", weight=3]; 2407[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];60 -> 2407[label="",style="solid", color="burlywood", weight=9]; 2407 -> 68[label="",style="solid", color="burlywood", weight=3]; 61[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];62[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100))",fontsize=16,color="burlywood",shape="box"];2408[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];62 -> 2408[label="",style="solid", color="burlywood", weight=9]; 2408 -> 69[label="",style="solid", color="burlywood", weight=3]; 2409[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];62 -> 2409[label="",style="solid", color="burlywood", weight=9]; 2409 -> 70[label="",style="solid", color="burlywood", weight=3]; 63[label="primPlusNat (Succ Zero) (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100))",fontsize=16,color="burlywood",shape="box"];2410[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];63 -> 2410[label="",style="solid", color="burlywood", weight=9]; 2410 -> 71[label="",style="solid", color="burlywood", weight=3]; 2411[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];63 -> 2411[label="",style="solid", color="burlywood", weight=9]; 2411 -> 72[label="",style="solid", color="burlywood", weight=3]; 64[label="Succ Zero",fontsize=16,color="green",shape="box"];65[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000)))",fontsize=16,color="black",shape="box"];65 -> 73[label="",style="solid", color="black", weight=3]; 66[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero))",fontsize=16,color="black",shape="box"];66 -> 74[label="",style="solid", color="black", weight=3]; 67[label="primMinusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000)))",fontsize=16,color="black",shape="box"];67 -> 75[label="",style="solid", color="black", weight=3]; 68[label="primMinusNat (Succ Zero) (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];68 -> 76[label="",style="solid", color="black", weight=3]; 69[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000)))",fontsize=16,color="black",shape="box"];69 -> 77[label="",style="solid", color="black", weight=3]; 70[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero))",fontsize=16,color="black",shape="box"];70 -> 78[label="",style="solid", color="black", weight=3]; 71[label="primPlusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000)))",fontsize=16,color="black",shape="box"];71 -> 79[label="",style="solid", color="black", weight=3]; 72[label="primPlusNat (Succ Zero) (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];72 -> 80[label="",style="solid", color="black", weight=3]; 73 -> 684[label="",style="dashed", color="red", weight=0]; 73[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000))",fontsize=16,color="magenta"];73 -> 685[label="",style="dashed", color="magenta", weight=3]; 73 -> 686[label="",style="dashed", color="magenta", weight=3]; 73 -> 687[label="",style="dashed", color="magenta", weight=3]; 73 -> 688[label="",style="dashed", color="magenta", weight=3]; 74[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero True)",fontsize=16,color="black",shape="box"];74 -> 83[label="",style="solid", color="black", weight=3]; 75[label="primMinusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) False)",fontsize=16,color="black",shape="box"];75 -> 84[label="",style="solid", color="black", weight=3]; 76[label="primMinusNat (Succ Zero) (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];76 -> 85[label="",style="solid", color="black", weight=3]; 77 -> 727[label="",style="dashed", color="red", weight=0]; 77[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000))",fontsize=16,color="magenta"];77 -> 728[label="",style="dashed", color="magenta", weight=3]; 77 -> 729[label="",style="dashed", color="magenta", weight=3]; 77 -> 730[label="",style="dashed", color="magenta", weight=3]; 77 -> 731[label="",style="dashed", color="magenta", weight=3]; 78[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz30000) Zero True)",fontsize=16,color="black",shape="box"];78 -> 88[label="",style="solid", color="black", weight=3]; 79[label="primPlusNat (Succ Zero) (primDivNatS0 Zero (Succ xz31000) False)",fontsize=16,color="black",shape="box"];79 -> 89[label="",style="solid", color="black", weight=3]; 80[label="primPlusNat (Succ Zero) (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];80 -> 90[label="",style="solid", color="black", weight=3]; 685[label="xz31000",fontsize=16,color="green",shape="box"];686[label="xz31000",fontsize=16,color="green",shape="box"];687[label="xz30000",fontsize=16,color="green",shape="box"];688[label="xz30000",fontsize=16,color="green",shape="box"];684[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS xz47 xz48))",fontsize=16,color="burlywood",shape="triangle"];2412[label="xz47/Succ xz470",fontsize=10,color="white",style="solid",shape="box"];684 -> 2412[label="",style="solid", color="burlywood", weight=9]; 2412 -> 725[label="",style="solid", color="burlywood", weight=3]; 2413[label="xz47/Zero",fontsize=10,color="white",style="solid",shape="box"];684 -> 2413[label="",style="solid", color="burlywood", weight=9]; 2413 -> 726[label="",style="solid", color="burlywood", weight=3]; 83[label="primMinusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];83 -> 95[label="",style="solid", color="black", weight=3]; 84 -> 56[label="",style="dashed", color="red", weight=0]; 84[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="magenta"];85[label="primMinusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];85 -> 96[label="",style="solid", color="black", weight=3]; 728[label="xz31000",fontsize=16,color="green",shape="box"];729[label="xz30000",fontsize=16,color="green",shape="box"];730[label="xz31000",fontsize=16,color="green",shape="box"];731[label="xz30000",fontsize=16,color="green",shape="box"];727[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS xz52 xz53))",fontsize=16,color="burlywood",shape="triangle"];2414[label="xz52/Succ xz520",fontsize=10,color="white",style="solid",shape="box"];727 -> 2414[label="",style="solid", color="burlywood", weight=9]; 2414 -> 768[label="",style="solid", color="burlywood", weight=3]; 2415[label="xz52/Zero",fontsize=10,color="white",style="solid",shape="box"];727 -> 2415[label="",style="solid", color="burlywood", weight=9]; 2415 -> 769[label="",style="solid", color="burlywood", weight=3]; 88[label="primPlusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];88 -> 101[label="",style="solid", color="black", weight=3]; 89 -> 58[label="",style="dashed", color="red", weight=0]; 89[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="magenta"];90[label="primPlusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];90 -> 102[label="",style="solid", color="black", weight=3]; 725[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS (Succ xz470) xz48))",fontsize=16,color="burlywood",shape="box"];2416[label="xz48/Succ xz480",fontsize=10,color="white",style="solid",shape="box"];725 -> 2416[label="",style="solid", color="burlywood", weight=9]; 2416 -> 770[label="",style="solid", color="burlywood", weight=3]; 2417[label="xz48/Zero",fontsize=10,color="white",style="solid",shape="box"];725 -> 2417[label="",style="solid", color="burlywood", weight=9]; 2417 -> 771[label="",style="solid", color="burlywood", weight=3]; 726[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS Zero xz48))",fontsize=16,color="burlywood",shape="box"];2418[label="xz48/Succ xz480",fontsize=10,color="white",style="solid",shape="box"];726 -> 2418[label="",style="solid", color="burlywood", weight=9]; 2418 -> 772[label="",style="solid", color="burlywood", weight=3]; 2419[label="xz48/Zero",fontsize=10,color="white",style="solid",shape="box"];726 -> 2419[label="",style="solid", color="burlywood", weight=9]; 2419 -> 773[label="",style="solid", color="burlywood", weight=3]; 95 -> 1187[label="",style="dashed", color="red", weight=0]; 95[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))",fontsize=16,color="magenta"];95 -> 1188[label="",style="dashed", color="magenta", weight=3]; 95 -> 1189[label="",style="dashed", color="magenta", weight=3]; 95 -> 1190[label="",style="dashed", color="magenta", weight=3]; 96 -> 1187[label="",style="dashed", color="red", weight=0]; 96[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="magenta"];96 -> 1191[label="",style="dashed", color="magenta", weight=3]; 96 -> 1192[label="",style="dashed", color="magenta", weight=3]; 96 -> 1193[label="",style="dashed", color="magenta", weight=3]; 768[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS (Succ xz520) xz53))",fontsize=16,color="burlywood",shape="box"];2420[label="xz53/Succ xz530",fontsize=10,color="white",style="solid",shape="box"];768 -> 2420[label="",style="solid", color="burlywood", weight=9]; 2420 -> 774[label="",style="solid", color="burlywood", weight=3]; 2421[label="xz53/Zero",fontsize=10,color="white",style="solid",shape="box"];768 -> 2421[label="",style="solid", color="burlywood", weight=9]; 2421 -> 775[label="",style="solid", color="burlywood", weight=3]; 769[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS Zero xz53))",fontsize=16,color="burlywood",shape="box"];2422[label="xz53/Succ xz530",fontsize=10,color="white",style="solid",shape="box"];769 -> 2422[label="",style="solid", color="burlywood", weight=9]; 2422 -> 776[label="",style="solid", color="burlywood", weight=3]; 2423[label="xz53/Zero",fontsize=10,color="white",style="solid",shape="box"];769 -> 2423[label="",style="solid", color="burlywood", weight=9]; 2423 -> 777[label="",style="solid", color="burlywood", weight=3]; 101[label="Succ (Succ (primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))))",fontsize=16,color="green",shape="box"];101 -> 113[label="",style="dashed", color="green", weight=3]; 102[label="Succ (Succ (primPlusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))))",fontsize=16,color="green",shape="box"];102 -> 114[label="",style="dashed", color="green", weight=3]; 770[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS (Succ xz470) (Succ xz480)))",fontsize=16,color="black",shape="box"];770 -> 778[label="",style="solid", color="black", weight=3]; 771[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS (Succ xz470) Zero))",fontsize=16,color="black",shape="box"];771 -> 779[label="",style="solid", color="black", weight=3]; 772[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS Zero (Succ xz480)))",fontsize=16,color="black",shape="box"];772 -> 780[label="",style="solid", color="black", weight=3]; 773[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];773 -> 781[label="",style="solid", color="black", weight=3]; 1188[label="Zero",fontsize=16,color="green",shape="box"];1189[label="Zero",fontsize=16,color="green",shape="box"];1190[label="Succ xz30000",fontsize=16,color="green",shape="box"];1187[label="primMinusNat Zero (primDivNatS (primMinusNatS xz57 xz58) (Succ xz59))",fontsize=16,color="burlywood",shape="triangle"];2424[label="xz57/Succ xz570",fontsize=10,color="white",style="solid",shape="box"];1187 -> 2424[label="",style="solid", color="burlywood", weight=9]; 2424 -> 1221[label="",style="solid", color="burlywood", weight=3]; 2425[label="xz57/Zero",fontsize=10,color="white",style="solid",shape="box"];1187 -> 2425[label="",style="solid", color="burlywood", weight=9]; 2425 -> 1222[label="",style="solid", color="burlywood", weight=3]; 1191[label="Zero",fontsize=16,color="green",shape="box"];1192[label="Zero",fontsize=16,color="green",shape="box"];1193[label="Zero",fontsize=16,color="green",shape="box"];774[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS (Succ xz520) (Succ xz530)))",fontsize=16,color="black",shape="box"];774 -> 782[label="",style="solid", color="black", weight=3]; 775[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS (Succ xz520) Zero))",fontsize=16,color="black",shape="box"];775 -> 783[label="",style="solid", color="black", weight=3]; 776[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS Zero (Succ xz530)))",fontsize=16,color="black",shape="box"];776 -> 784[label="",style="solid", color="black", weight=3]; 777[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];777 -> 785[label="",style="solid", color="black", weight=3]; 113 -> 1242[label="",style="dashed", color="red", weight=0]; 113[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))",fontsize=16,color="magenta"];113 -> 1243[label="",style="dashed", color="magenta", weight=3]; 113 -> 1244[label="",style="dashed", color="magenta", weight=3]; 113 -> 1245[label="",style="dashed", color="magenta", weight=3]; 114 -> 1242[label="",style="dashed", color="red", weight=0]; 114[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="magenta"];114 -> 1246[label="",style="dashed", color="magenta", weight=3]; 114 -> 1247[label="",style="dashed", color="magenta", weight=3]; 114 -> 1248[label="",style="dashed", color="magenta", weight=3]; 778 -> 684[label="",style="dashed", color="red", weight=0]; 778[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) (primGEqNatS xz470 xz480))",fontsize=16,color="magenta"];778 -> 786[label="",style="dashed", color="magenta", weight=3]; 778 -> 787[label="",style="dashed", color="magenta", weight=3]; 779[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) True)",fontsize=16,color="black",shape="triangle"];779 -> 788[label="",style="solid", color="black", weight=3]; 780[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) False)",fontsize=16,color="black",shape="box"];780 -> 789[label="",style="solid", color="black", weight=3]; 781 -> 779[label="",style="dashed", color="red", weight=0]; 781[label="primMinusNat (Succ Zero) (primDivNatS0 (Succ xz45) (Succ xz46) True)",fontsize=16,color="magenta"];1221[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz570) xz58) (Succ xz59))",fontsize=16,color="burlywood",shape="box"];2426[label="xz58/Succ xz580",fontsize=10,color="white",style="solid",shape="box"];1221 -> 2426[label="",style="solid", color="burlywood", weight=9]; 2426 -> 1238[label="",style="solid", color="burlywood", weight=3]; 2427[label="xz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1221 -> 2427[label="",style="solid", color="burlywood", weight=9]; 2427 -> 1239[label="",style="solid", color="burlywood", weight=3]; 1222[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero xz58) (Succ xz59))",fontsize=16,color="burlywood",shape="box"];2428[label="xz58/Succ xz580",fontsize=10,color="white",style="solid",shape="box"];1222 -> 2428[label="",style="solid", color="burlywood", weight=9]; 2428 -> 1240[label="",style="solid", color="burlywood", weight=3]; 2429[label="xz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1222 -> 2429[label="",style="solid", color="burlywood", weight=9]; 2429 -> 1241[label="",style="solid", color="burlywood", weight=3]; 782 -> 727[label="",style="dashed", color="red", weight=0]; 782[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) (primGEqNatS xz520 xz530))",fontsize=16,color="magenta"];782 -> 790[label="",style="dashed", color="magenta", weight=3]; 782 -> 791[label="",style="dashed", color="magenta", weight=3]; 783[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) True)",fontsize=16,color="black",shape="triangle"];783 -> 792[label="",style="solid", color="black", weight=3]; 784[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) False)",fontsize=16,color="black",shape="box"];784 -> 793[label="",style="solid", color="black", weight=3]; 785 -> 783[label="",style="dashed", color="red", weight=0]; 785[label="primPlusNat (Succ Zero) (primDivNatS0 (Succ xz50) (Succ xz51) True)",fontsize=16,color="magenta"];1243[label="Zero",fontsize=16,color="green",shape="box"];1244[label="Zero",fontsize=16,color="green",shape="box"];1245[label="Succ xz30000",fontsize=16,color="green",shape="box"];1242[label="primPlusNat Zero (primDivNatS (primMinusNatS xz61 xz62) (Succ xz63))",fontsize=16,color="burlywood",shape="triangle"];2430[label="xz61/Succ xz610",fontsize=10,color="white",style="solid",shape="box"];1242 -> 2430[label="",style="solid", color="burlywood", weight=9]; 2430 -> 1276[label="",style="solid", color="burlywood", weight=3]; 2431[label="xz61/Zero",fontsize=10,color="white",style="solid",shape="box"];1242 -> 2431[label="",style="solid", color="burlywood", weight=9]; 2431 -> 1277[label="",style="solid", color="burlywood", weight=3]; 1246[label="Zero",fontsize=16,color="green",shape="box"];1247[label="Zero",fontsize=16,color="green",shape="box"];1248[label="Zero",fontsize=16,color="green",shape="box"];786[label="xz480",fontsize=16,color="green",shape="box"];787[label="xz470",fontsize=16,color="green",shape="box"];788[label="primMinusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz45) (Succ xz46)) (Succ (Succ xz46))))",fontsize=16,color="black",shape="box"];788 -> 794[label="",style="solid", color="black", weight=3]; 789 -> 56[label="",style="dashed", color="red", weight=0]; 789[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="magenta"];1238[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz570) (Succ xz580)) (Succ xz59))",fontsize=16,color="black",shape="box"];1238 -> 1278[label="",style="solid", color="black", weight=3]; 1239[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz570) Zero) (Succ xz59))",fontsize=16,color="black",shape="box"];1239 -> 1279[label="",style="solid", color="black", weight=3]; 1240[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero (Succ xz580)) (Succ xz59))",fontsize=16,color="black",shape="box"];1240 -> 1280[label="",style="solid", color="black", weight=3]; 1241[label="primMinusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ xz59))",fontsize=16,color="black",shape="box"];1241 -> 1281[label="",style="solid", color="black", weight=3]; 790[label="xz530",fontsize=16,color="green",shape="box"];791[label="xz520",fontsize=16,color="green",shape="box"];792[label="primPlusNat (Succ Zero) (Succ (primDivNatS (primMinusNatS (Succ xz50) (Succ xz51)) (Succ (Succ xz51))))",fontsize=16,color="black",shape="box"];792 -> 795[label="",style="solid", color="black", weight=3]; 793 -> 58[label="",style="dashed", color="red", weight=0]; 793[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="magenta"];1276[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz610) xz62) (Succ xz63))",fontsize=16,color="burlywood",shape="box"];2432[label="xz62/Succ xz620",fontsize=10,color="white",style="solid",shape="box"];1276 -> 2432[label="",style="solid", color="burlywood", weight=9]; 2432 -> 1282[label="",style="solid", color="burlywood", weight=3]; 2433[label="xz62/Zero",fontsize=10,color="white",style="solid",shape="box"];1276 -> 2433[label="",style="solid", color="burlywood", weight=9]; 2433 -> 1283[label="",style="solid", color="burlywood", weight=3]; 1277[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero xz62) (Succ xz63))",fontsize=16,color="burlywood",shape="box"];2434[label="xz62/Succ xz620",fontsize=10,color="white",style="solid",shape="box"];1277 -> 2434[label="",style="solid", color="burlywood", weight=9]; 2434 -> 1284[label="",style="solid", color="burlywood", weight=3]; 2435[label="xz62/Zero",fontsize=10,color="white",style="solid",shape="box"];1277 -> 2435[label="",style="solid", color="burlywood", weight=9]; 2435 -> 1285[label="",style="solid", color="burlywood", weight=3]; 794 -> 1187[label="",style="dashed", color="red", weight=0]; 794[label="primMinusNat Zero (primDivNatS (primMinusNatS (Succ xz45) (Succ xz46)) (Succ (Succ xz46)))",fontsize=16,color="magenta"];794 -> 1194[label="",style="dashed", color="magenta", weight=3]; 794 -> 1195[label="",style="dashed", color="magenta", weight=3]; 794 -> 1196[label="",style="dashed", color="magenta", weight=3]; 1278 -> 1187[label="",style="dashed", color="red", weight=0]; 1278[label="primMinusNat Zero (primDivNatS (primMinusNatS xz570 xz580) (Succ xz59))",fontsize=16,color="magenta"];1278 -> 1286[label="",style="dashed", color="magenta", weight=3]; 1278 -> 1287[label="",style="dashed", color="magenta", weight=3]; 1279[label="primMinusNat Zero (primDivNatS (Succ xz570) (Succ xz59))",fontsize=16,color="black",shape="box"];1279 -> 1288[label="",style="solid", color="black", weight=3]; 1280[label="primMinusNat Zero (primDivNatS Zero (Succ xz59))",fontsize=16,color="black",shape="triangle"];1280 -> 1289[label="",style="solid", color="black", weight=3]; 1281 -> 1280[label="",style="dashed", color="red", weight=0]; 1281[label="primMinusNat Zero (primDivNatS Zero (Succ xz59))",fontsize=16,color="magenta"];795[label="Succ (Succ (primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz50) (Succ xz51)) (Succ (Succ xz51)))))",fontsize=16,color="green",shape="box"];795 -> 797[label="",style="dashed", color="green", weight=3]; 1282[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz610) (Succ xz620)) (Succ xz63))",fontsize=16,color="black",shape="box"];1282 -> 1290[label="",style="solid", color="black", weight=3]; 1283[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz610) Zero) (Succ xz63))",fontsize=16,color="black",shape="box"];1283 -> 1291[label="",style="solid", color="black", weight=3]; 1284[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero (Succ xz620)) (Succ xz63))",fontsize=16,color="black",shape="box"];1284 -> 1292[label="",style="solid", color="black", weight=3]; 1285[label="primPlusNat Zero (primDivNatS (primMinusNatS Zero Zero) (Succ xz63))",fontsize=16,color="black",shape="box"];1285 -> 1293[label="",style="solid", color="black", weight=3]; 1194[label="Succ xz46",fontsize=16,color="green",shape="box"];1195[label="Succ xz46",fontsize=16,color="green",shape="box"];1196[label="Succ xz45",fontsize=16,color="green",shape="box"];1286[label="xz580",fontsize=16,color="green",shape="box"];1287[label="xz570",fontsize=16,color="green",shape="box"];1288[label="primMinusNat Zero (primDivNatS0 xz570 xz59 (primGEqNatS xz570 xz59))",fontsize=16,color="burlywood",shape="box"];2436[label="xz570/Succ xz5700",fontsize=10,color="white",style="solid",shape="box"];1288 -> 2436[label="",style="solid", color="burlywood", weight=9]; 2436 -> 1294[label="",style="solid", color="burlywood", weight=3]; 2437[label="xz570/Zero",fontsize=10,color="white",style="solid",shape="box"];1288 -> 2437[label="",style="solid", color="burlywood", weight=9]; 2437 -> 1295[label="",style="solid", color="burlywood", weight=3]; 1289[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1289 -> 1296[label="",style="solid", color="black", weight=3]; 797 -> 1242[label="",style="dashed", color="red", weight=0]; 797[label="primPlusNat Zero (primDivNatS (primMinusNatS (Succ xz50) (Succ xz51)) (Succ (Succ xz51)))",fontsize=16,color="magenta"];797 -> 1249[label="",style="dashed", color="magenta", weight=3]; 797 -> 1250[label="",style="dashed", color="magenta", weight=3]; 797 -> 1251[label="",style="dashed", color="magenta", weight=3]; 1290 -> 1242[label="",style="dashed", color="red", weight=0]; 1290[label="primPlusNat Zero (primDivNatS (primMinusNatS xz610 xz620) (Succ xz63))",fontsize=16,color="magenta"];1290 -> 1297[label="",style="dashed", color="magenta", weight=3]; 1290 -> 1298[label="",style="dashed", color="magenta", weight=3]; 1291[label="primPlusNat Zero (primDivNatS (Succ xz610) (Succ xz63))",fontsize=16,color="black",shape="box"];1291 -> 1299[label="",style="solid", color="black", weight=3]; 1292[label="primPlusNat Zero (primDivNatS Zero (Succ xz63))",fontsize=16,color="black",shape="triangle"];1292 -> 1300[label="",style="solid", color="black", weight=3]; 1293 -> 1292[label="",style="dashed", color="red", weight=0]; 1293[label="primPlusNat Zero (primDivNatS Zero (Succ xz63))",fontsize=16,color="magenta"];1294[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) xz59 (primGEqNatS (Succ xz5700) xz59))",fontsize=16,color="burlywood",shape="box"];2438[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1294 -> 2438[label="",style="solid", color="burlywood", weight=9]; 2438 -> 1301[label="",style="solid", color="burlywood", weight=3]; 2439[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1294 -> 2439[label="",style="solid", color="burlywood", weight=9]; 2439 -> 1302[label="",style="solid", color="burlywood", weight=3]; 1295[label="primMinusNat Zero (primDivNatS0 Zero xz59 (primGEqNatS Zero xz59))",fontsize=16,color="burlywood",shape="box"];2440[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1295 -> 2440[label="",style="solid", color="burlywood", weight=9]; 2440 -> 1303[label="",style="solid", color="burlywood", weight=3]; 2441[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1295 -> 2441[label="",style="solid", color="burlywood", weight=9]; 2441 -> 1304[label="",style="solid", color="burlywood", weight=3]; 1296[label="Pos Zero",fontsize=16,color="green",shape="box"];1249[label="Succ xz51",fontsize=16,color="green",shape="box"];1250[label="Succ xz51",fontsize=16,color="green",shape="box"];1251[label="Succ xz50",fontsize=16,color="green",shape="box"];1297[label="xz620",fontsize=16,color="green",shape="box"];1298[label="xz610",fontsize=16,color="green",shape="box"];1299[label="primPlusNat Zero (primDivNatS0 xz610 xz63 (primGEqNatS xz610 xz63))",fontsize=16,color="burlywood",shape="box"];2442[label="xz610/Succ xz6100",fontsize=10,color="white",style="solid",shape="box"];1299 -> 2442[label="",style="solid", color="burlywood", weight=9]; 2442 -> 1305[label="",style="solid", color="burlywood", weight=3]; 2443[label="xz610/Zero",fontsize=10,color="white",style="solid",shape="box"];1299 -> 2443[label="",style="solid", color="burlywood", weight=9]; 2443 -> 1306[label="",style="solid", color="burlywood", weight=3]; 1300[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1300 -> 1307[label="",style="solid", color="black", weight=3]; 1301[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) (Succ xz590) (primGEqNatS (Succ xz5700) (Succ xz590)))",fontsize=16,color="black",shape="box"];1301 -> 1308[label="",style="solid", color="black", weight=3]; 1302[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) Zero (primGEqNatS (Succ xz5700) Zero))",fontsize=16,color="black",shape="box"];1302 -> 1309[label="",style="solid", color="black", weight=3]; 1303[label="primMinusNat Zero (primDivNatS0 Zero (Succ xz590) (primGEqNatS Zero (Succ xz590)))",fontsize=16,color="black",shape="box"];1303 -> 1310[label="",style="solid", color="black", weight=3]; 1304[label="primMinusNat Zero (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];1304 -> 1311[label="",style="solid", color="black", weight=3]; 1305[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) xz63 (primGEqNatS (Succ xz6100) xz63))",fontsize=16,color="burlywood",shape="box"];2444[label="xz63/Succ xz630",fontsize=10,color="white",style="solid",shape="box"];1305 -> 2444[label="",style="solid", color="burlywood", weight=9]; 2444 -> 1312[label="",style="solid", color="burlywood", weight=3]; 2445[label="xz63/Zero",fontsize=10,color="white",style="solid",shape="box"];1305 -> 2445[label="",style="solid", color="burlywood", weight=9]; 2445 -> 1313[label="",style="solid", color="burlywood", weight=3]; 1306[label="primPlusNat Zero (primDivNatS0 Zero xz63 (primGEqNatS Zero xz63))",fontsize=16,color="burlywood",shape="box"];2446[label="xz63/Succ xz630",fontsize=10,color="white",style="solid",shape="box"];1306 -> 2446[label="",style="solid", color="burlywood", weight=9]; 2446 -> 1314[label="",style="solid", color="burlywood", weight=3]; 2447[label="xz63/Zero",fontsize=10,color="white",style="solid",shape="box"];1306 -> 2447[label="",style="solid", color="burlywood", weight=9]; 2447 -> 1315[label="",style="solid", color="burlywood", weight=3]; 1307[label="Zero",fontsize=16,color="green",shape="box"];1308 -> 1871[label="",style="dashed", color="red", weight=0]; 1308[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) (Succ xz590) (primGEqNatS xz5700 xz590))",fontsize=16,color="magenta"];1308 -> 1872[label="",style="dashed", color="magenta", weight=3]; 1308 -> 1873[label="",style="dashed", color="magenta", weight=3]; 1308 -> 1874[label="",style="dashed", color="magenta", weight=3]; 1308 -> 1875[label="",style="dashed", color="magenta", weight=3]; 1309[label="primMinusNat Zero (primDivNatS0 (Succ xz5700) Zero True)",fontsize=16,color="black",shape="box"];1309 -> 1318[label="",style="solid", color="black", weight=3]; 1310[label="primMinusNat Zero (primDivNatS0 Zero (Succ xz590) False)",fontsize=16,color="black",shape="box"];1310 -> 1319[label="",style="solid", color="black", weight=3]; 1311[label="primMinusNat Zero (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];1311 -> 1320[label="",style="solid", color="black", weight=3]; 1312[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) (Succ xz630) (primGEqNatS (Succ xz6100) (Succ xz630)))",fontsize=16,color="black",shape="box"];1312 -> 1321[label="",style="solid", color="black", weight=3]; 1313[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) Zero (primGEqNatS (Succ xz6100) Zero))",fontsize=16,color="black",shape="box"];1313 -> 1322[label="",style="solid", color="black", weight=3]; 1314[label="primPlusNat Zero (primDivNatS0 Zero (Succ xz630) (primGEqNatS Zero (Succ xz630)))",fontsize=16,color="black",shape="box"];1314 -> 1323[label="",style="solid", color="black", weight=3]; 1315[label="primPlusNat Zero (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];1315 -> 1324[label="",style="solid", color="black", weight=3]; 1872[label="xz5700",fontsize=16,color="green",shape="box"];1873[label="xz590",fontsize=16,color="green",shape="box"];1874[label="xz5700",fontsize=16,color="green",shape="box"];1875[label="xz590",fontsize=16,color="green",shape="box"];1871[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS xz96 xz97))",fontsize=16,color="burlywood",shape="triangle"];2448[label="xz96/Succ xz960",fontsize=10,color="white",style="solid",shape="box"];1871 -> 2448[label="",style="solid", color="burlywood", weight=9]; 2448 -> 1912[label="",style="solid", color="burlywood", weight=3]; 2449[label="xz96/Zero",fontsize=10,color="white",style="solid",shape="box"];1871 -> 2449[label="",style="solid", color="burlywood", weight=9]; 2449 -> 1913[label="",style="solid", color="burlywood", weight=3]; 1318 -> 1677[label="",style="dashed", color="red", weight=0]; 1318[label="primMinusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz5700) Zero) (Succ Zero)))",fontsize=16,color="magenta"];1318 -> 1678[label="",style="dashed", color="magenta", weight=3]; 1319 -> 1289[label="",style="dashed", color="red", weight=0]; 1319[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];1320 -> 1677[label="",style="dashed", color="red", weight=0]; 1320[label="primMinusNat Zero (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];1320 -> 1679[label="",style="dashed", color="magenta", weight=3]; 1321 -> 1976[label="",style="dashed", color="red", weight=0]; 1321[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) (Succ xz630) (primGEqNatS xz6100 xz630))",fontsize=16,color="magenta"];1321 -> 1977[label="",style="dashed", color="magenta", weight=3]; 1321 -> 1978[label="",style="dashed", color="magenta", weight=3]; 1321 -> 1979[label="",style="dashed", color="magenta", weight=3]; 1321 -> 1980[label="",style="dashed", color="magenta", weight=3]; 1322[label="primPlusNat Zero (primDivNatS0 (Succ xz6100) Zero True)",fontsize=16,color="black",shape="box"];1322 -> 1333[label="",style="solid", color="black", weight=3]; 1323[label="primPlusNat Zero (primDivNatS0 Zero (Succ xz630) False)",fontsize=16,color="black",shape="box"];1323 -> 1334[label="",style="solid", color="black", weight=3]; 1324[label="primPlusNat Zero (primDivNatS0 Zero Zero True)",fontsize=16,color="black",shape="box"];1324 -> 1335[label="",style="solid", color="black", weight=3]; 1912[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS (Succ xz960) xz97))",fontsize=16,color="burlywood",shape="box"];2450[label="xz97/Succ xz970",fontsize=10,color="white",style="solid",shape="box"];1912 -> 2450[label="",style="solid", color="burlywood", weight=9]; 2450 -> 1926[label="",style="solid", color="burlywood", weight=3]; 2451[label="xz97/Zero",fontsize=10,color="white",style="solid",shape="box"];1912 -> 2451[label="",style="solid", color="burlywood", weight=9]; 2451 -> 1927[label="",style="solid", color="burlywood", weight=3]; 1913[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS Zero xz97))",fontsize=16,color="burlywood",shape="box"];2452[label="xz97/Succ xz970",fontsize=10,color="white",style="solid",shape="box"];1913 -> 2452[label="",style="solid", color="burlywood", weight=9]; 2452 -> 1928[label="",style="solid", color="burlywood", weight=3]; 2453[label="xz97/Zero",fontsize=10,color="white",style="solid",shape="box"];1913 -> 2453[label="",style="solid", color="burlywood", weight=9]; 2453 -> 1929[label="",style="solid", color="burlywood", weight=3]; 1678 -> 2096[label="",style="dashed", color="red", weight=0]; 1678[label="primDivNatS (primMinusNatS (Succ xz5700) Zero) (Succ Zero)",fontsize=16,color="magenta"];1678 -> 2097[label="",style="dashed", color="magenta", weight=3]; 1678 -> 2098[label="",style="dashed", color="magenta", weight=3]; 1678 -> 2099[label="",style="dashed", color="magenta", weight=3]; 1677[label="primMinusNat Zero (Succ xz79)",fontsize=16,color="black",shape="triangle"];1677 -> 1693[label="",style="solid", color="black", weight=3]; 1679 -> 2096[label="",style="dashed", color="red", weight=0]; 1679[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1679 -> 2100[label="",style="dashed", color="magenta", weight=3]; 1679 -> 2101[label="",style="dashed", color="magenta", weight=3]; 1679 -> 2102[label="",style="dashed", color="magenta", weight=3]; 1977[label="xz6100",fontsize=16,color="green",shape="box"];1978[label="xz6100",fontsize=16,color="green",shape="box"];1979[label="xz630",fontsize=16,color="green",shape="box"];1980[label="xz630",fontsize=16,color="green",shape="box"];1976[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS xz109 xz110))",fontsize=16,color="burlywood",shape="triangle"];2454[label="xz109/Succ xz1090",fontsize=10,color="white",style="solid",shape="box"];1976 -> 2454[label="",style="solid", color="burlywood", weight=9]; 2454 -> 2017[label="",style="solid", color="burlywood", weight=3]; 2455[label="xz109/Zero",fontsize=10,color="white",style="solid",shape="box"];1976 -> 2455[label="",style="solid", color="burlywood", weight=9]; 2455 -> 2018[label="",style="solid", color="burlywood", weight=3]; 1333 -> 1741[label="",style="dashed", color="red", weight=0]; 1333[label="primPlusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz6100) Zero) (Succ Zero)))",fontsize=16,color="magenta"];1333 -> 1742[label="",style="dashed", color="magenta", weight=3]; 1334 -> 1300[label="",style="dashed", color="red", weight=0]; 1334[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];1335 -> 1741[label="",style="dashed", color="red", weight=0]; 1335[label="primPlusNat Zero (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];1335 -> 1743[label="",style="dashed", color="magenta", weight=3]; 1926[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS (Succ xz960) (Succ xz970)))",fontsize=16,color="black",shape="box"];1926 -> 1943[label="",style="solid", color="black", weight=3]; 1927[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS (Succ xz960) Zero))",fontsize=16,color="black",shape="box"];1927 -> 1944[label="",style="solid", color="black", weight=3]; 1928[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS Zero (Succ xz970)))",fontsize=16,color="black",shape="box"];1928 -> 1945[label="",style="solid", color="black", weight=3]; 1929[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];1929 -> 1946[label="",style="solid", color="black", weight=3]; 2097[label="Zero",fontsize=16,color="green",shape="box"];2098[label="Succ xz5700",fontsize=16,color="green",shape="box"];2099[label="Zero",fontsize=16,color="green",shape="box"];2096[label="primDivNatS (primMinusNatS xz115 xz116) (Succ xz117)",fontsize=16,color="burlywood",shape="triangle"];2456[label="xz115/Succ xz1150",fontsize=10,color="white",style="solid",shape="box"];2096 -> 2456[label="",style="solid", color="burlywood", weight=9]; 2456 -> 2148[label="",style="solid", color="burlywood", weight=3]; 2457[label="xz115/Zero",fontsize=10,color="white",style="solid",shape="box"];2096 -> 2457[label="",style="solid", color="burlywood", weight=9]; 2457 -> 2149[label="",style="solid", color="burlywood", weight=3]; 1693[label="Neg (Succ xz79)",fontsize=16,color="green",shape="box"];2100[label="Zero",fontsize=16,color="green",shape="box"];2101[label="Zero",fontsize=16,color="green",shape="box"];2102[label="Zero",fontsize=16,color="green",shape="box"];2017[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS (Succ xz1090) xz110))",fontsize=16,color="burlywood",shape="box"];2458[label="xz110/Succ xz1100",fontsize=10,color="white",style="solid",shape="box"];2017 -> 2458[label="",style="solid", color="burlywood", weight=9]; 2458 -> 2033[label="",style="solid", color="burlywood", weight=3]; 2459[label="xz110/Zero",fontsize=10,color="white",style="solid",shape="box"];2017 -> 2459[label="",style="solid", color="burlywood", weight=9]; 2459 -> 2034[label="",style="solid", color="burlywood", weight=3]; 2018[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS Zero xz110))",fontsize=16,color="burlywood",shape="box"];2460[label="xz110/Succ xz1100",fontsize=10,color="white",style="solid",shape="box"];2018 -> 2460[label="",style="solid", color="burlywood", weight=9]; 2460 -> 2035[label="",style="solid", color="burlywood", weight=3]; 2461[label="xz110/Zero",fontsize=10,color="white",style="solid",shape="box"];2018 -> 2461[label="",style="solid", color="burlywood", weight=9]; 2461 -> 2036[label="",style="solid", color="burlywood", weight=3]; 1742 -> 2096[label="",style="dashed", color="red", weight=0]; 1742[label="primDivNatS (primMinusNatS (Succ xz6100) Zero) (Succ Zero)",fontsize=16,color="magenta"];1742 -> 2109[label="",style="dashed", color="magenta", weight=3]; 1742 -> 2110[label="",style="dashed", color="magenta", weight=3]; 1742 -> 2111[label="",style="dashed", color="magenta", weight=3]; 1741[label="primPlusNat Zero (Succ xz82)",fontsize=16,color="black",shape="triangle"];1741 -> 1757[label="",style="solid", color="black", weight=3]; 1743 -> 2096[label="",style="dashed", color="red", weight=0]; 1743[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1743 -> 2112[label="",style="dashed", color="magenta", weight=3]; 1743 -> 2113[label="",style="dashed", color="magenta", weight=3]; 1743 -> 2114[label="",style="dashed", color="magenta", weight=3]; 1943 -> 1871[label="",style="dashed", color="red", weight=0]; 1943[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) (primGEqNatS xz960 xz970))",fontsize=16,color="magenta"];1943 -> 1961[label="",style="dashed", color="magenta", weight=3]; 1943 -> 1962[label="",style="dashed", color="magenta", weight=3]; 1944[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) True)",fontsize=16,color="black",shape="triangle"];1944 -> 1963[label="",style="solid", color="black", weight=3]; 1945[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) False)",fontsize=16,color="black",shape="box"];1945 -> 1964[label="",style="solid", color="black", weight=3]; 1946 -> 1944[label="",style="dashed", color="red", weight=0]; 1946[label="primMinusNat Zero (primDivNatS0 (Succ xz94) (Succ xz95) True)",fontsize=16,color="magenta"];2148[label="primDivNatS (primMinusNatS (Succ xz1150) xz116) (Succ xz117)",fontsize=16,color="burlywood",shape="box"];2462[label="xz116/Succ xz1160",fontsize=10,color="white",style="solid",shape="box"];2148 -> 2462[label="",style="solid", color="burlywood", weight=9]; 2462 -> 2150[label="",style="solid", color="burlywood", weight=3]; 2463[label="xz116/Zero",fontsize=10,color="white",style="solid",shape="box"];2148 -> 2463[label="",style="solid", color="burlywood", weight=9]; 2463 -> 2151[label="",style="solid", color="burlywood", weight=3]; 2149[label="primDivNatS (primMinusNatS Zero xz116) (Succ xz117)",fontsize=16,color="burlywood",shape="box"];2464[label="xz116/Succ xz1160",fontsize=10,color="white",style="solid",shape="box"];2149 -> 2464[label="",style="solid", color="burlywood", weight=9]; 2464 -> 2152[label="",style="solid", color="burlywood", weight=3]; 2465[label="xz116/Zero",fontsize=10,color="white",style="solid",shape="box"];2149 -> 2465[label="",style="solid", color="burlywood", weight=9]; 2465 -> 2153[label="",style="solid", color="burlywood", weight=3]; 2033[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS (Succ xz1090) (Succ xz1100)))",fontsize=16,color="black",shape="box"];2033 -> 2046[label="",style="solid", color="black", weight=3]; 2034[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS (Succ xz1090) Zero))",fontsize=16,color="black",shape="box"];2034 -> 2047[label="",style="solid", color="black", weight=3]; 2035[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS Zero (Succ xz1100)))",fontsize=16,color="black",shape="box"];2035 -> 2048[label="",style="solid", color="black", weight=3]; 2036[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS Zero Zero))",fontsize=16,color="black",shape="box"];2036 -> 2049[label="",style="solid", color="black", weight=3]; 2109[label="Zero",fontsize=16,color="green",shape="box"];2110[label="Succ xz6100",fontsize=16,color="green",shape="box"];2111[label="Zero",fontsize=16,color="green",shape="box"];1757[label="Succ xz82",fontsize=16,color="green",shape="box"];2112[label="Zero",fontsize=16,color="green",shape="box"];2113[label="Zero",fontsize=16,color="green",shape="box"];2114[label="Zero",fontsize=16,color="green",shape="box"];1961[label="xz960",fontsize=16,color="green",shape="box"];1962[label="xz970",fontsize=16,color="green",shape="box"];1963 -> 1677[label="",style="dashed", color="red", weight=0]; 1963[label="primMinusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz94) (Succ xz95)) (Succ (Succ xz95))))",fontsize=16,color="magenta"];1963 -> 2019[label="",style="dashed", color="magenta", weight=3]; 1964 -> 1289[label="",style="dashed", color="red", weight=0]; 1964[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];2150[label="primDivNatS (primMinusNatS (Succ xz1150) (Succ xz1160)) (Succ xz117)",fontsize=16,color="black",shape="box"];2150 -> 2154[label="",style="solid", color="black", weight=3]; 2151[label="primDivNatS (primMinusNatS (Succ xz1150) Zero) (Succ xz117)",fontsize=16,color="black",shape="box"];2151 -> 2155[label="",style="solid", color="black", weight=3]; 2152[label="primDivNatS (primMinusNatS Zero (Succ xz1160)) (Succ xz117)",fontsize=16,color="black",shape="box"];2152 -> 2156[label="",style="solid", color="black", weight=3]; 2153[label="primDivNatS (primMinusNatS Zero Zero) (Succ xz117)",fontsize=16,color="black",shape="box"];2153 -> 2157[label="",style="solid", color="black", weight=3]; 2046 -> 1976[label="",style="dashed", color="red", weight=0]; 2046[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) (primGEqNatS xz1090 xz1100))",fontsize=16,color="magenta"];2046 -> 2056[label="",style="dashed", color="magenta", weight=3]; 2046 -> 2057[label="",style="dashed", color="magenta", weight=3]; 2047[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) True)",fontsize=16,color="black",shape="triangle"];2047 -> 2058[label="",style="solid", color="black", weight=3]; 2048[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) False)",fontsize=16,color="black",shape="box"];2048 -> 2059[label="",style="solid", color="black", weight=3]; 2049 -> 2047[label="",style="dashed", color="red", weight=0]; 2049[label="primPlusNat Zero (primDivNatS0 (Succ xz107) (Succ xz108) True)",fontsize=16,color="magenta"];2019 -> 2096[label="",style="dashed", color="red", weight=0]; 2019[label="primDivNatS (primMinusNatS (Succ xz94) (Succ xz95)) (Succ (Succ xz95))",fontsize=16,color="magenta"];2019 -> 2118[label="",style="dashed", color="magenta", weight=3]; 2019 -> 2119[label="",style="dashed", color="magenta", weight=3]; 2019 -> 2120[label="",style="dashed", color="magenta", weight=3]; 2154 -> 2096[label="",style="dashed", color="red", weight=0]; 2154[label="primDivNatS (primMinusNatS xz1150 xz1160) (Succ xz117)",fontsize=16,color="magenta"];2154 -> 2158[label="",style="dashed", color="magenta", weight=3]; 2154 -> 2159[label="",style="dashed", color="magenta", weight=3]; 2155[label="primDivNatS (Succ xz1150) (Succ xz117)",fontsize=16,color="black",shape="box"];2155 -> 2160[label="",style="solid", color="black", weight=3]; 2156[label="primDivNatS Zero (Succ xz117)",fontsize=16,color="black",shape="triangle"];2156 -> 2161[label="",style="solid", color="black", weight=3]; 2157 -> 2156[label="",style="dashed", color="red", weight=0]; 2157[label="primDivNatS Zero (Succ xz117)",fontsize=16,color="magenta"];2056[label="xz1090",fontsize=16,color="green",shape="box"];2057[label="xz1100",fontsize=16,color="green",shape="box"];2058 -> 1741[label="",style="dashed", color="red", weight=0]; 2058[label="primPlusNat Zero (Succ (primDivNatS (primMinusNatS (Succ xz107) (Succ xz108)) (Succ (Succ xz108))))",fontsize=16,color="magenta"];2058 -> 2070[label="",style="dashed", color="magenta", weight=3]; 2059 -> 1300[label="",style="dashed", color="red", weight=0]; 2059[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];2118[label="Succ xz95",fontsize=16,color="green",shape="box"];2119[label="Succ xz94",fontsize=16,color="green",shape="box"];2120[label="Succ xz95",fontsize=16,color="green",shape="box"];2158[label="xz1150",fontsize=16,color="green",shape="box"];2159[label="xz1160",fontsize=16,color="green",shape="box"];2160[label="primDivNatS0 xz1150 xz117 (primGEqNatS xz1150 xz117)",fontsize=16,color="burlywood",shape="box"];2466[label="xz1150/Succ xz11500",fontsize=10,color="white",style="solid",shape="box"];2160 -> 2466[label="",style="solid", color="burlywood", weight=9]; 2466 -> 2162[label="",style="solid", color="burlywood", weight=3]; 2467[label="xz1150/Zero",fontsize=10,color="white",style="solid",shape="box"];2160 -> 2467[label="",style="solid", color="burlywood", weight=9]; 2467 -> 2163[label="",style="solid", color="burlywood", weight=3]; 2161[label="Zero",fontsize=16,color="green",shape="box"];2070 -> 2096[label="",style="dashed", color="red", weight=0]; 2070[label="primDivNatS (primMinusNatS (Succ xz107) (Succ xz108)) (Succ (Succ xz108))",fontsize=16,color="magenta"];2070 -> 2121[label="",style="dashed", color="magenta", weight=3]; 2070 -> 2122[label="",style="dashed", color="magenta", weight=3]; 2070 -> 2123[label="",style="dashed", color="magenta", weight=3]; 2162[label="primDivNatS0 (Succ xz11500) xz117 (primGEqNatS (Succ xz11500) xz117)",fontsize=16,color="burlywood",shape="box"];2468[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2162 -> 2468[label="",style="solid", color="burlywood", weight=9]; 2468 -> 2164[label="",style="solid", color="burlywood", weight=3]; 2469[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2162 -> 2469[label="",style="solid", color="burlywood", weight=9]; 2469 -> 2165[label="",style="solid", color="burlywood", weight=3]; 2163[label="primDivNatS0 Zero xz117 (primGEqNatS Zero xz117)",fontsize=16,color="burlywood",shape="box"];2470[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2163 -> 2470[label="",style="solid", color="burlywood", weight=9]; 2470 -> 2166[label="",style="solid", color="burlywood", weight=3]; 2471[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2163 -> 2471[label="",style="solid", color="burlywood", weight=9]; 2471 -> 2167[label="",style="solid", color="burlywood", weight=3]; 2121[label="Succ xz108",fontsize=16,color="green",shape="box"];2122[label="Succ xz107",fontsize=16,color="green",shape="box"];2123[label="Succ xz108",fontsize=16,color="green",shape="box"];2164[label="primDivNatS0 (Succ xz11500) (Succ xz1170) (primGEqNatS (Succ xz11500) (Succ xz1170))",fontsize=16,color="black",shape="box"];2164 -> 2168[label="",style="solid", color="black", weight=3]; 2165[label="primDivNatS0 (Succ xz11500) Zero (primGEqNatS (Succ xz11500) Zero)",fontsize=16,color="black",shape="box"];2165 -> 2169[label="",style="solid", color="black", weight=3]; 2166[label="primDivNatS0 Zero (Succ xz1170) (primGEqNatS Zero (Succ xz1170))",fontsize=16,color="black",shape="box"];2166 -> 2170[label="",style="solid", color="black", weight=3]; 2167[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2167 -> 2171[label="",style="solid", color="black", weight=3]; 2168 -> 2330[label="",style="dashed", color="red", weight=0]; 2168[label="primDivNatS0 (Succ xz11500) (Succ xz1170) (primGEqNatS xz11500 xz1170)",fontsize=16,color="magenta"];2168 -> 2331[label="",style="dashed", color="magenta", weight=3]; 2168 -> 2332[label="",style="dashed", color="magenta", weight=3]; 2168 -> 2333[label="",style="dashed", color="magenta", weight=3]; 2168 -> 2334[label="",style="dashed", color="magenta", weight=3]; 2169[label="primDivNatS0 (Succ xz11500) Zero True",fontsize=16,color="black",shape="box"];2169 -> 2174[label="",style="solid", color="black", weight=3]; 2170[label="primDivNatS0 Zero (Succ xz1170) False",fontsize=16,color="black",shape="box"];2170 -> 2175[label="",style="solid", color="black", weight=3]; 2171[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2171 -> 2176[label="",style="solid", color="black", weight=3]; 2331[label="xz11500",fontsize=16,color="green",shape="box"];2332[label="xz11500",fontsize=16,color="green",shape="box"];2333[label="xz1170",fontsize=16,color="green",shape="box"];2334[label="xz1170",fontsize=16,color="green",shape="box"];2330[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS xz136 xz137)",fontsize=16,color="burlywood",shape="triangle"];2472[label="xz136/Succ xz1360",fontsize=10,color="white",style="solid",shape="box"];2330 -> 2472[label="",style="solid", color="burlywood", weight=9]; 2472 -> 2363[label="",style="solid", color="burlywood", weight=3]; 2473[label="xz136/Zero",fontsize=10,color="white",style="solid",shape="box"];2330 -> 2473[label="",style="solid", color="burlywood", weight=9]; 2473 -> 2364[label="",style="solid", color="burlywood", weight=3]; 2174[label="Succ (primDivNatS (primMinusNatS (Succ xz11500) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2174 -> 2181[label="",style="dashed", color="green", weight=3]; 2175[label="Zero",fontsize=16,color="green",shape="box"];2176[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2176 -> 2182[label="",style="dashed", color="green", weight=3]; 2363[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS (Succ xz1360) xz137)",fontsize=16,color="burlywood",shape="box"];2474[label="xz137/Succ xz1370",fontsize=10,color="white",style="solid",shape="box"];2363 -> 2474[label="",style="solid", color="burlywood", weight=9]; 2474 -> 2365[label="",style="solid", color="burlywood", weight=3]; 2475[label="xz137/Zero",fontsize=10,color="white",style="solid",shape="box"];2363 -> 2475[label="",style="solid", color="burlywood", weight=9]; 2475 -> 2366[label="",style="solid", color="burlywood", weight=3]; 2364[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS Zero xz137)",fontsize=16,color="burlywood",shape="box"];2476[label="xz137/Succ xz1370",fontsize=10,color="white",style="solid",shape="box"];2364 -> 2476[label="",style="solid", color="burlywood", weight=9]; 2476 -> 2367[label="",style="solid", color="burlywood", weight=3]; 2477[label="xz137/Zero",fontsize=10,color="white",style="solid",shape="box"];2364 -> 2477[label="",style="solid", color="burlywood", weight=9]; 2477 -> 2368[label="",style="solid", color="burlywood", weight=3]; 2181 -> 2096[label="",style="dashed", color="red", weight=0]; 2181[label="primDivNatS (primMinusNatS (Succ xz11500) Zero) (Succ Zero)",fontsize=16,color="magenta"];2181 -> 2187[label="",style="dashed", color="magenta", weight=3]; 2181 -> 2188[label="",style="dashed", color="magenta", weight=3]; 2181 -> 2189[label="",style="dashed", color="magenta", weight=3]; 2182 -> 2096[label="",style="dashed", color="red", weight=0]; 2182[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2182 -> 2190[label="",style="dashed", color="magenta", weight=3]; 2182 -> 2191[label="",style="dashed", color="magenta", weight=3]; 2182 -> 2192[label="",style="dashed", color="magenta", weight=3]; 2365[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS (Succ xz1360) (Succ xz1370))",fontsize=16,color="black",shape="box"];2365 -> 2369[label="",style="solid", color="black", weight=3]; 2366[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS (Succ xz1360) Zero)",fontsize=16,color="black",shape="box"];2366 -> 2370[label="",style="solid", color="black", weight=3]; 2367[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS Zero (Succ xz1370))",fontsize=16,color="black",shape="box"];2367 -> 2371[label="",style="solid", color="black", weight=3]; 2368[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2368 -> 2372[label="",style="solid", color="black", weight=3]; 2187[label="Zero",fontsize=16,color="green",shape="box"];2188[label="Succ xz11500",fontsize=16,color="green",shape="box"];2189[label="Zero",fontsize=16,color="green",shape="box"];2190[label="Zero",fontsize=16,color="green",shape="box"];2191[label="Zero",fontsize=16,color="green",shape="box"];2192[label="Zero",fontsize=16,color="green",shape="box"];2369 -> 2330[label="",style="dashed", color="red", weight=0]; 2369[label="primDivNatS0 (Succ xz134) (Succ xz135) (primGEqNatS xz1360 xz1370)",fontsize=16,color="magenta"];2369 -> 2373[label="",style="dashed", color="magenta", weight=3]; 2369 -> 2374[label="",style="dashed", color="magenta", weight=3]; 2370[label="primDivNatS0 (Succ xz134) (Succ xz135) True",fontsize=16,color="black",shape="triangle"];2370 -> 2375[label="",style="solid", color="black", weight=3]; 2371[label="primDivNatS0 (Succ xz134) (Succ xz135) False",fontsize=16,color="black",shape="box"];2371 -> 2376[label="",style="solid", color="black", weight=3]; 2372 -> 2370[label="",style="dashed", color="red", weight=0]; 2372[label="primDivNatS0 (Succ xz134) (Succ xz135) True",fontsize=16,color="magenta"];2373[label="xz1360",fontsize=16,color="green",shape="box"];2374[label="xz1370",fontsize=16,color="green",shape="box"];2375[label="Succ (primDivNatS (primMinusNatS (Succ xz134) (Succ xz135)) (Succ (Succ xz135)))",fontsize=16,color="green",shape="box"];2375 -> 2377[label="",style="dashed", color="green", weight=3]; 2376[label="Zero",fontsize=16,color="green",shape="box"];2377 -> 2096[label="",style="dashed", color="red", weight=0]; 2377[label="primDivNatS (primMinusNatS (Succ xz134) (Succ xz135)) (Succ (Succ xz135))",fontsize=16,color="magenta"];2377 -> 2378[label="",style="dashed", color="magenta", weight=3]; 2377 -> 2379[label="",style="dashed", color="magenta", weight=3]; 2377 -> 2380[label="",style="dashed", color="magenta", weight=3]; 2378[label="Succ xz135",fontsize=16,color="green",shape="box"];2379[label="Succ xz134",fontsize=16,color="green",shape="box"];2380[label="Succ xz135",fontsize=16,color="green",shape="box"];} ---------------------------------------- (14) Complex Obligation (AND) ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(xz134, xz135, Zero, Zero) -> new_primDivNatS00(xz134, xz135) new_primDivNatS(Succ(Zero), Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) new_primDivNatS00(xz134, xz135) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) new_primDivNatS(Succ(xz1150), Succ(xz1160), xz117) -> new_primDivNatS(xz1150, xz1160, xz117) new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) new_primDivNatS(Succ(Succ(xz11500)), Zero, Succ(xz1170)) -> new_primDivNatS0(xz11500, xz1170, xz11500, xz1170) new_primDivNatS0(xz134, xz135, Succ(xz1360), Zero) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) new_primDivNatS(Succ(Succ(xz11500)), Zero, Zero) -> new_primDivNatS(Succ(xz11500), Zero, Zero) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (17) Complex Obligation (AND) ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS(Succ(Succ(xz11500)), Zero, Zero) -> new_primDivNatS(Succ(xz11500), Zero, Zero) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (19) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primDivNatS(Succ(Succ(xz11500)), Zero, Zero) -> new_primDivNatS(Succ(xz11500), Zero, Zero) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 2, 2 >= 3, 3 >= 3 ---------------------------------------- (20) YES ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(xz134, xz135) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) new_primDivNatS(Succ(xz1150), Succ(xz1160), xz117) -> new_primDivNatS(xz1150, xz1160, xz117) new_primDivNatS(Succ(Succ(xz11500)), Zero, Succ(xz1170)) -> new_primDivNatS0(xz11500, xz1170, xz11500, xz1170) new_primDivNatS0(xz134, xz135, Zero, Zero) -> new_primDivNatS00(xz134, xz135) new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) new_primDivNatS0(xz134, xz135, Succ(xz1360), Zero) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (22) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primDivNatS(Succ(xz1150), Succ(xz1160), xz117) -> new_primDivNatS(xz1150, xz1160, xz117) new_primDivNatS(Succ(Succ(xz11500)), Zero, Succ(xz1170)) -> new_primDivNatS0(xz11500, xz1170, xz11500, xz1170) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: none ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(xz134, xz135) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) new_primDivNatS0(xz134, xz135, Zero, Zero) -> new_primDivNatS00(xz134, xz135) new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) new_primDivNatS0(xz134, xz135, Succ(xz1360), Zero) -> new_primDivNatS(Succ(xz134), Succ(xz135), Succ(xz135)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (26) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primDivNatS0(xz134, xz135, Succ(xz1360), Succ(xz1370)) -> new_primDivNatS0(xz134, xz135, xz1360, xz1370) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (27) YES ---------------------------------------- (28) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNat0(Succ(xz570), Succ(xz580), xz59) -> new_primMinusNat0(xz570, xz580, xz59) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (29) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primMinusNat0(Succ(xz570), Succ(xz580), xz59) -> new_primMinusNat0(xz570, xz580, xz59) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (30) YES ---------------------------------------- (31) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat0(Succ(xz610), Succ(xz620), xz63) -> new_primPlusNat0(xz610, xz620, xz63) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (32) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primPlusNat0(Succ(xz610), Succ(xz620), xz63) -> new_primPlusNat0(xz610, xz620, xz63) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (33) YES ---------------------------------------- (34) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat1(xz50, xz51, Succ(xz520), Succ(xz530)) -> new_primPlusNat1(xz50, xz51, xz520, xz530) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (35) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primPlusNat1(xz50, xz51, Succ(xz520), Succ(xz530)) -> new_primPlusNat1(xz50, xz51, xz520, xz530) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (36) YES ---------------------------------------- (37) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNat(xz94, xz95, Succ(xz960), Succ(xz970)) -> new_primMinusNat(xz94, xz95, xz960, xz970) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (38) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primMinusNat(xz94, xz95, Succ(xz960), Succ(xz970)) -> new_primMinusNat(xz94, xz95, xz960, xz970) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (39) YES ---------------------------------------- (40) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(xz107, xz108, Succ(xz1090), Succ(xz1100)) -> new_primPlusNat(xz107, xz108, xz1090, xz1100) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (41) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primPlusNat(xz107, xz108, Succ(xz1090), Succ(xz1100)) -> new_primPlusNat(xz107, xz108, xz1090, xz1100) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (42) YES ---------------------------------------- (43) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNat1(xz45, xz46, Succ(xz470), Succ(xz480)) -> new_primMinusNat1(xz45, xz46, xz470, xz480) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (44) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primMinusNat1(xz45, xz46, Succ(xz470), Succ(xz480)) -> new_primMinusNat1(xz45, xz46, xz470, xz480) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (45) YES