/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) IFR [EQUIVALENT, 0 ms] (4)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, 0 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 "properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx); " "properFractionR xw xx = properFractionR0 xw xx (properFractionVu30 xw xx); " "properFractionR0 xw xx (wz,r) = r; " "properFractionVu30 xw xx = quotRem xw xx; " "properFractionQ1 xw xx (q,wy) = q; " 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; " "truncateM xy = truncateM0 xy (truncateVu6 xy); " "truncateM0 xy (m,xv) = m; " ---------------------------------------- (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="pred",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="pred xz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="toEnum . (subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="toEnum ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="fromInt ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="intToRatio ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="fromInt ((subtract (Pos (Succ Zero))) . fromEnum) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3]; 8 -> 10[label="",style="dashed", color="green", weight=3]; 9[label="fromInt ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="(subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];13[label="subtract (Pos (Succ Zero)) (fromEnum xz3)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 14[label="flip (-) (Pos (Succ Zero)) (fromEnum xz3)",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 15[label="(-) fromEnum xz3 Pos (Succ Zero)",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 16[label="primMinusInt (fromEnum xz3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 17[label="primMinusInt (truncate xz3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 18[label="primMinusInt (truncateM xz3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 19[label="primMinusInt (truncateM0 xz3 (truncateVu6 xz3)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3]; 20[label="primMinusInt (truncateM0 xz3 (properFraction xz3)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2343[label="xz3/xz30 :% xz31",fontsize=10,color="white",style="solid",shape="box"];20 -> 2343[label="",style="solid", color="burlywood", weight=9]; 2343 -> 21[label="",style="solid", color="burlywood", weight=3]; 21[label="primMinusInt (truncateM0 (xz30 :% xz31) (properFraction (xz30 :% xz31))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3]; 22[label="primMinusInt (truncateM0 (xz30 :% xz31) (fromIntegral (properFractionQ xz30 xz31),properFractionR xz30 xz31 :% xz31)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3]; 23[label="primMinusInt (fromIntegral (properFractionQ xz30 xz31)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3]; 24[label="primMinusInt (fromInteger . toInteger) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];24 -> 25[label="",style="solid", color="black", weight=3]; 25[label="primMinusInt (fromInteger (toInteger (properFractionQ xz30 xz31))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3]; 26[label="primMinusInt (fromInteger (Integer (properFractionQ xz30 xz31))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];26 -> 27[label="",style="solid", color="black", weight=3]; 27[label="primMinusInt (properFractionQ xz30 xz31) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3]; 28[label="primMinusInt (properFractionQ1 xz30 xz31 (properFractionVu30 xz30 xz31)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3]; 29[label="primMinusInt (properFractionQ1 xz30 xz31 (quotRem xz30 xz31)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3]; 30[label="primMinusInt (properFractionQ1 xz30 xz31 (primQrmInt xz30 xz31)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];30 -> 31[label="",style="solid", color="black", weight=3]; 31[label="primMinusInt (properFractionQ1 xz30 xz31 (primQuotInt xz30 xz31,primRemInt xz30 xz31)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];31 -> 32[label="",style="solid", color="black", weight=3]; 32[label="primMinusInt (primQuotInt xz30 xz31) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2344[label="xz30/Pos xz300",fontsize=10,color="white",style="solid",shape="box"];32 -> 2344[label="",style="solid", color="burlywood", weight=9]; 2344 -> 33[label="",style="solid", color="burlywood", weight=3]; 2345[label="xz30/Neg xz300",fontsize=10,color="white",style="solid",shape="box"];32 -> 2345[label="",style="solid", color="burlywood", weight=9]; 2345 -> 34[label="",style="solid", color="burlywood", weight=3]; 33[label="primMinusInt (primQuotInt (Pos xz300) xz31) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2346[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];33 -> 2346[label="",style="solid", color="burlywood", weight=9]; 2346 -> 35[label="",style="solid", color="burlywood", weight=3]; 2347[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];33 -> 2347[label="",style="solid", color="burlywood", weight=9]; 2347 -> 36[label="",style="solid", color="burlywood", weight=3]; 34[label="primMinusInt (primQuotInt (Neg xz300) xz31) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2348[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];34 -> 2348[label="",style="solid", color="burlywood", weight=9]; 2348 -> 37[label="",style="solid", color="burlywood", weight=3]; 2349[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];34 -> 2349[label="",style="solid", color="burlywood", weight=9]; 2349 -> 38[label="",style="solid", color="burlywood", weight=3]; 35[label="primMinusInt (primQuotInt (Pos xz300) (Pos xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2350[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];35 -> 2350[label="",style="solid", color="burlywood", weight=9]; 2350 -> 39[label="",style="solid", color="burlywood", weight=3]; 2351[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 2351[label="",style="solid", color="burlywood", weight=9]; 2351 -> 40[label="",style="solid", color="burlywood", weight=3]; 36[label="primMinusInt (primQuotInt (Pos xz300) (Neg xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2352[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];36 -> 2352[label="",style="solid", color="burlywood", weight=9]; 2352 -> 41[label="",style="solid", color="burlywood", weight=3]; 2353[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 2353[label="",style="solid", color="burlywood", weight=9]; 2353 -> 42[label="",style="solid", color="burlywood", weight=3]; 37[label="primMinusInt (primQuotInt (Neg xz300) (Pos xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2354[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];37 -> 2354[label="",style="solid", color="burlywood", weight=9]; 2354 -> 43[label="",style="solid", color="burlywood", weight=3]; 2355[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 2355[label="",style="solid", color="burlywood", weight=9]; 2355 -> 44[label="",style="solid", color="burlywood", weight=3]; 38[label="primMinusInt (primQuotInt (Neg xz300) (Neg xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2356[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];38 -> 2356[label="",style="solid", color="burlywood", weight=9]; 2356 -> 45[label="",style="solid", color="burlywood", weight=3]; 2357[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];38 -> 2357[label="",style="solid", color="burlywood", weight=9]; 2357 -> 46[label="",style="solid", color="burlywood", weight=3]; 39[label="primMinusInt (primQuotInt (Pos xz300) (Pos (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];39 -> 47[label="",style="solid", color="black", weight=3]; 40[label="primMinusInt (primQuotInt (Pos xz300) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];40 -> 48[label="",style="solid", color="black", weight=3]; 41[label="primMinusInt (primQuotInt (Pos xz300) (Neg (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3]; 42[label="primMinusInt (primQuotInt (Pos xz300) (Neg Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];42 -> 50[label="",style="solid", color="black", weight=3]; 43[label="primMinusInt (primQuotInt (Neg xz300) (Pos (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];43 -> 51[label="",style="solid", color="black", weight=3]; 44[label="primMinusInt (primQuotInt (Neg xz300) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];44 -> 52[label="",style="solid", color="black", weight=3]; 45[label="primMinusInt (primQuotInt (Neg xz300) (Neg (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];45 -> 53[label="",style="solid", color="black", weight=3]; 46[label="primMinusInt (primQuotInt (Neg xz300) (Neg Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];46 -> 54[label="",style="solid", color="black", weight=3]; 47[label="primMinusInt (Pos (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];47 -> 55[label="",style="solid", color="black", weight=3]; 48[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];48 -> 56[label="",style="solid", color="black", weight=3]; 49[label="primMinusInt (Neg (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];49 -> 57[label="",style="solid", color="black", weight=3]; 50 -> 48[label="",style="dashed", color="red", weight=0]; 50[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="magenta"];51 -> 49[label="",style="dashed", color="red", weight=0]; 51[label="primMinusInt (Neg (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="magenta"];51 -> 58[label="",style="dashed", color="magenta", weight=3]; 51 -> 59[label="",style="dashed", color="magenta", weight=3]; 52 -> 48[label="",style="dashed", color="red", weight=0]; 52[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="magenta"];53 -> 47[label="",style="dashed", color="red", weight=0]; 53[label="primMinusInt (Pos (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="magenta"];53 -> 60[label="",style="dashed", color="magenta", weight=3]; 53 -> 61[label="",style="dashed", color="magenta", weight=3]; 54 -> 48[label="",style="dashed", color="red", weight=0]; 54[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="magenta"];55[label="primMinusNat (primDivNatS xz300 (Succ xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2358[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];55 -> 2358[label="",style="solid", color="burlywood", weight=9]; 2358 -> 62[label="",style="solid", color="burlywood", weight=3]; 2359[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 2359[label="",style="solid", color="burlywood", weight=9]; 2359 -> 63[label="",style="solid", color="burlywood", weight=3]; 56[label="error []",fontsize=16,color="red",shape="box"];57[label="Neg (primPlusNat (primDivNatS xz300 (Succ xz3100)) (Succ Zero))",fontsize=16,color="green",shape="box"];57 -> 64[label="",style="dashed", color="green", weight=3]; 58[label="xz3100",fontsize=16,color="green",shape="box"];59[label="xz300",fontsize=16,color="green",shape="box"];60[label="xz300",fontsize=16,color="green",shape="box"];61[label="xz3100",fontsize=16,color="green",shape="box"];62[label="primMinusNat (primDivNatS (Succ xz3000) (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];62 -> 65[label="",style="solid", color="black", weight=3]; 63[label="primMinusNat (primDivNatS Zero (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];63 -> 66[label="",style="solid", color="black", weight=3]; 64[label="primPlusNat (primDivNatS xz300 (Succ xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2360[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];64 -> 2360[label="",style="solid", color="burlywood", weight=9]; 2360 -> 67[label="",style="solid", color="burlywood", weight=3]; 2361[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 2361[label="",style="solid", color="burlywood", weight=9]; 2361 -> 68[label="",style="solid", color="burlywood", weight=3]; 65[label="primMinusNat (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2362[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];65 -> 2362[label="",style="solid", color="burlywood", weight=9]; 2362 -> 69[label="",style="solid", color="burlywood", weight=3]; 2363[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 2363[label="",style="solid", color="burlywood", weight=9]; 2363 -> 70[label="",style="solid", color="burlywood", weight=3]; 66[label="primMinusNat Zero (Succ Zero)",fontsize=16,color="black",shape="triangle"];66 -> 71[label="",style="solid", color="black", weight=3]; 67[label="primPlusNat (primDivNatS (Succ xz3000) (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];67 -> 72[label="",style="solid", color="black", weight=3]; 68[label="primPlusNat (primDivNatS Zero (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];68 -> 73[label="",style="solid", color="black", weight=3]; 69[label="primMinusNat (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2364[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];69 -> 2364[label="",style="solid", color="burlywood", weight=9]; 2364 -> 74[label="",style="solid", color="burlywood", weight=3]; 2365[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 2365[label="",style="solid", color="burlywood", weight=9]; 2365 -> 75[label="",style="solid", color="burlywood", weight=3]; 70[label="primMinusNat (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2366[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];70 -> 2366[label="",style="solid", color="burlywood", weight=9]; 2366 -> 76[label="",style="solid", color="burlywood", weight=3]; 2367[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 2367[label="",style="solid", color="burlywood", weight=9]; 2367 -> 77[label="",style="solid", color="burlywood", weight=3]; 71[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];72[label="primPlusNat (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2368[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];72 -> 2368[label="",style="solid", color="burlywood", weight=9]; 2368 -> 78[label="",style="solid", color="burlywood", weight=3]; 2369[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 2369[label="",style="solid", color="burlywood", weight=9]; 2369 -> 79[label="",style="solid", color="burlywood", weight=3]; 73[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="triangle"];73 -> 80[label="",style="solid", color="black", weight=3]; 74[label="primMinusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];74 -> 81[label="",style="solid", color="black", weight=3]; 75[label="primMinusNat (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];75 -> 82[label="",style="solid", color="black", weight=3]; 76[label="primMinusNat (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];76 -> 83[label="",style="solid", color="black", weight=3]; 77[label="primMinusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];77 -> 84[label="",style="solid", color="black", weight=3]; 78[label="primPlusNat (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2370[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];78 -> 2370[label="",style="solid", color="burlywood", weight=9]; 2370 -> 85[label="",style="solid", color="burlywood", weight=3]; 2371[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];78 -> 2371[label="",style="solid", color="burlywood", weight=9]; 2371 -> 86[label="",style="solid", color="burlywood", weight=3]; 79[label="primPlusNat (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2372[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];79 -> 2372[label="",style="solid", color="burlywood", weight=9]; 2372 -> 87[label="",style="solid", color="burlywood", weight=3]; 2373[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 2373[label="",style="solid", color="burlywood", weight=9]; 2373 -> 88[label="",style="solid", color="burlywood", weight=3]; 80[label="Succ Zero",fontsize=16,color="green",shape="box"];81 -> 674[label="",style="dashed", color="red", weight=0]; 81[label="primMinusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000)) (Succ Zero)",fontsize=16,color="magenta"];81 -> 675[label="",style="dashed", color="magenta", weight=3]; 81 -> 676[label="",style="dashed", color="magenta", weight=3]; 81 -> 677[label="",style="dashed", color="magenta", weight=3]; 81 -> 678[label="",style="dashed", color="magenta", weight=3]; 82[label="primMinusNat (primDivNatS0 (Succ xz30000) Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];82 -> 91[label="",style="solid", color="black", weight=3]; 83[label="primMinusNat (primDivNatS0 Zero (Succ xz31000) False) (Succ Zero)",fontsize=16,color="black",shape="box"];83 -> 92[label="",style="solid", color="black", weight=3]; 84[label="primMinusNat (primDivNatS0 Zero Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];84 -> 93[label="",style="solid", color="black", weight=3]; 85[label="primPlusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];85 -> 94[label="",style="solid", color="black", weight=3]; 86[label="primPlusNat (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];86 -> 95[label="",style="solid", color="black", weight=3]; 87[label="primPlusNat (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];87 -> 96[label="",style="solid", color="black", weight=3]; 88[label="primPlusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];88 -> 97[label="",style="solid", color="black", weight=3]; 675[label="xz31000",fontsize=16,color="green",shape="box"];676[label="xz31000",fontsize=16,color="green",shape="box"];677[label="xz30000",fontsize=16,color="green",shape="box"];678[label="xz30000",fontsize=16,color="green",shape="box"];674[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS xz40 xz41)) (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];2374[label="xz40/Succ xz400",fontsize=10,color="white",style="solid",shape="box"];674 -> 2374[label="",style="solid", color="burlywood", weight=9]; 2374 -> 715[label="",style="solid", color="burlywood", weight=3]; 2375[label="xz40/Zero",fontsize=10,color="white",style="solid",shape="box"];674 -> 2375[label="",style="solid", color="burlywood", weight=9]; 2375 -> 716[label="",style="solid", color="burlywood", weight=3]; 91[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];91 -> 102[label="",style="solid", color="black", weight=3]; 92 -> 66[label="",style="dashed", color="red", weight=0]; 92[label="primMinusNat Zero (Succ Zero)",fontsize=16,color="magenta"];93[label="primMinusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];93 -> 103[label="",style="solid", color="black", weight=3]; 94 -> 747[label="",style="dashed", color="red", weight=0]; 94[label="primPlusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000)) (Succ Zero)",fontsize=16,color="magenta"];94 -> 748[label="",style="dashed", color="magenta", weight=3]; 94 -> 749[label="",style="dashed", color="magenta", weight=3]; 94 -> 750[label="",style="dashed", color="magenta", weight=3]; 94 -> 751[label="",style="dashed", color="magenta", weight=3]; 95[label="primPlusNat (primDivNatS0 (Succ xz30000) Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];95 -> 106[label="",style="solid", color="black", weight=3]; 96[label="primPlusNat (primDivNatS0 Zero (Succ xz31000) False) (Succ Zero)",fontsize=16,color="black",shape="box"];96 -> 107[label="",style="solid", color="black", weight=3]; 97[label="primPlusNat (primDivNatS0 Zero Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];97 -> 108[label="",style="solid", color="black", weight=3]; 715[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS (Succ xz400) xz41)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2376[label="xz41/Succ xz410",fontsize=10,color="white",style="solid",shape="box"];715 -> 2376[label="",style="solid", color="burlywood", weight=9]; 2376 -> 721[label="",style="solid", color="burlywood", weight=3]; 2377[label="xz41/Zero",fontsize=10,color="white",style="solid",shape="box"];715 -> 2377[label="",style="solid", color="burlywood", weight=9]; 2377 -> 722[label="",style="solid", color="burlywood", weight=3]; 716[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS Zero xz41)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2378[label="xz41/Succ xz410",fontsize=10,color="white",style="solid",shape="box"];716 -> 2378[label="",style="solid", color="burlywood", weight=9]; 2378 -> 723[label="",style="solid", color="burlywood", weight=3]; 2379[label="xz41/Zero",fontsize=10,color="white",style="solid",shape="box"];716 -> 2379[label="",style="solid", color="burlywood", weight=9]; 2379 -> 724[label="",style="solid", color="burlywood", weight=3]; 102 -> 1155[label="",style="dashed", color="red", weight=0]; 102[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];102 -> 1156[label="",style="dashed", color="magenta", weight=3]; 102 -> 1157[label="",style="dashed", color="magenta", weight=3]; 102 -> 1158[label="",style="dashed", color="magenta", weight=3]; 103 -> 1155[label="",style="dashed", color="red", weight=0]; 103[label="primMinusNat (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];103 -> 1159[label="",style="dashed", color="magenta", weight=3]; 103 -> 1160[label="",style="dashed", color="magenta", weight=3]; 103 -> 1161[label="",style="dashed", color="magenta", weight=3]; 748[label="xz31000",fontsize=16,color="green",shape="box"];749[label="xz30000",fontsize=16,color="green",shape="box"];750[label="xz31000",fontsize=16,color="green",shape="box"];751[label="xz30000",fontsize=16,color="green",shape="box"];747[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS xz53 xz54)) (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];2380[label="xz53/Succ xz530",fontsize=10,color="white",style="solid",shape="box"];747 -> 2380[label="",style="solid", color="burlywood", weight=9]; 2380 -> 788[label="",style="solid", color="burlywood", weight=3]; 2381[label="xz53/Zero",fontsize=10,color="white",style="solid",shape="box"];747 -> 2381[label="",style="solid", color="burlywood", weight=9]; 2381 -> 789[label="",style="solid", color="burlywood", weight=3]; 106[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];106 -> 119[label="",style="solid", color="black", weight=3]; 107 -> 73[label="",style="dashed", color="red", weight=0]; 107[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="magenta"];108[label="primPlusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];108 -> 120[label="",style="solid", color="black", weight=3]; 721[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS (Succ xz400) (Succ xz410))) (Succ Zero)",fontsize=16,color="black",shape="box"];721 -> 728[label="",style="solid", color="black", weight=3]; 722[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS (Succ xz400) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];722 -> 729[label="",style="solid", color="black", weight=3]; 723[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS Zero (Succ xz410))) (Succ Zero)",fontsize=16,color="black",shape="box"];723 -> 730[label="",style="solid", color="black", weight=3]; 724[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];724 -> 731[label="",style="solid", color="black", weight=3]; 1156[label="Succ xz30000",fontsize=16,color="green",shape="box"];1157[label="Zero",fontsize=16,color="green",shape="box"];1158[label="Zero",fontsize=16,color="green",shape="box"];1155[label="primMinusNat (primDivNatS (primMinusNatS xz58 xz59) (Succ xz60)) Zero",fontsize=16,color="burlywood",shape="triangle"];2382[label="xz58/Succ xz580",fontsize=10,color="white",style="solid",shape="box"];1155 -> 2382[label="",style="solid", color="burlywood", weight=9]; 2382 -> 1189[label="",style="solid", color="burlywood", weight=3]; 2383[label="xz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1155 -> 2383[label="",style="solid", color="burlywood", weight=9]; 2383 -> 1190[label="",style="solid", color="burlywood", weight=3]; 1159[label="Zero",fontsize=16,color="green",shape="box"];1160[label="Zero",fontsize=16,color="green",shape="box"];1161[label="Zero",fontsize=16,color="green",shape="box"];788[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS (Succ xz530) xz54)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2384[label="xz54/Succ xz540",fontsize=10,color="white",style="solid",shape="box"];788 -> 2384[label="",style="solid", color="burlywood", weight=9]; 2384 -> 791[label="",style="solid", color="burlywood", weight=3]; 2385[label="xz54/Zero",fontsize=10,color="white",style="solid",shape="box"];788 -> 2385[label="",style="solid", color="burlywood", weight=9]; 2385 -> 792[label="",style="solid", color="burlywood", weight=3]; 789[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS Zero xz54)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2386[label="xz54/Succ xz540",fontsize=10,color="white",style="solid",shape="box"];789 -> 2386[label="",style="solid", color="burlywood", weight=9]; 2386 -> 793[label="",style="solid", color="burlywood", weight=3]; 2387[label="xz54/Zero",fontsize=10,color="white",style="solid",shape="box"];789 -> 2387[label="",style="solid", color="burlywood", weight=9]; 2387 -> 794[label="",style="solid", color="burlywood", weight=3]; 119[label="Succ (Succ (primPlusNat (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)) Zero))",fontsize=16,color="green",shape="box"];119 -> 132[label="",style="dashed", color="green", weight=3]; 120[label="Succ (Succ (primPlusNat (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)) Zero))",fontsize=16,color="green",shape="box"];120 -> 133[label="",style="dashed", color="green", weight=3]; 728 -> 674[label="",style="dashed", color="red", weight=0]; 728[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS xz400 xz410)) (Succ Zero)",fontsize=16,color="magenta"];728 -> 734[label="",style="dashed", color="magenta", weight=3]; 728 -> 735[label="",style="dashed", color="magenta", weight=3]; 729[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) True) (Succ Zero)",fontsize=16,color="black",shape="triangle"];729 -> 736[label="",style="solid", color="black", weight=3]; 730[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) False) (Succ Zero)",fontsize=16,color="black",shape="box"];730 -> 737[label="",style="solid", color="black", weight=3]; 731 -> 729[label="",style="dashed", color="red", weight=0]; 731[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) True) (Succ Zero)",fontsize=16,color="magenta"];1189[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz580) xz59) (Succ xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2388[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1189 -> 2388[label="",style="solid", color="burlywood", weight=9]; 2388 -> 1204[label="",style="solid", color="burlywood", weight=3]; 2389[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1189 -> 2389[label="",style="solid", color="burlywood", weight=9]; 2389 -> 1205[label="",style="solid", color="burlywood", weight=3]; 1190[label="primMinusNat (primDivNatS (primMinusNatS Zero xz59) (Succ xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2390[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1190 -> 2390[label="",style="solid", color="burlywood", weight=9]; 2390 -> 1206[label="",style="solid", color="burlywood", weight=3]; 2391[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1190 -> 2391[label="",style="solid", color="burlywood", weight=9]; 2391 -> 1207[label="",style="solid", color="burlywood", weight=3]; 791[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS (Succ xz530) (Succ xz540))) (Succ Zero)",fontsize=16,color="black",shape="box"];791 -> 796[label="",style="solid", color="black", weight=3]; 792[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS (Succ xz530) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];792 -> 797[label="",style="solid", color="black", weight=3]; 793[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS Zero (Succ xz540))) (Succ Zero)",fontsize=16,color="black",shape="box"];793 -> 798[label="",style="solid", color="black", weight=3]; 794[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];794 -> 799[label="",style="solid", color="black", weight=3]; 132 -> 1267[label="",style="dashed", color="red", weight=0]; 132[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];132 -> 1268[label="",style="dashed", color="magenta", weight=3]; 132 -> 1269[label="",style="dashed", color="magenta", weight=3]; 132 -> 1270[label="",style="dashed", color="magenta", weight=3]; 133 -> 1267[label="",style="dashed", color="red", weight=0]; 133[label="primPlusNat (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];133 -> 1271[label="",style="dashed", color="magenta", weight=3]; 133 -> 1272[label="",style="dashed", color="magenta", weight=3]; 133 -> 1273[label="",style="dashed", color="magenta", weight=3]; 734[label="xz410",fontsize=16,color="green",shape="box"];735[label="xz400",fontsize=16,color="green",shape="box"];736[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz38) (Succ xz39)) (Succ (Succ xz39)))) (Succ Zero)",fontsize=16,color="black",shape="box"];736 -> 790[label="",style="solid", color="black", weight=3]; 737 -> 66[label="",style="dashed", color="red", weight=0]; 737[label="primMinusNat Zero (Succ Zero)",fontsize=16,color="magenta"];1204[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz580) (Succ xz590)) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1204 -> 1223[label="",style="solid", color="black", weight=3]; 1205[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz580) Zero) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1205 -> 1224[label="",style="solid", color="black", weight=3]; 1206[label="primMinusNat (primDivNatS (primMinusNatS Zero (Succ xz590)) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1206 -> 1225[label="",style="solid", color="black", weight=3]; 1207[label="primMinusNat (primDivNatS (primMinusNatS Zero Zero) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1207 -> 1226[label="",style="solid", color="black", weight=3]; 796 -> 747[label="",style="dashed", color="red", weight=0]; 796[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS xz530 xz540)) (Succ Zero)",fontsize=16,color="magenta"];796 -> 802[label="",style="dashed", color="magenta", weight=3]; 796 -> 803[label="",style="dashed", color="magenta", weight=3]; 797[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) True) (Succ Zero)",fontsize=16,color="black",shape="triangle"];797 -> 804[label="",style="solid", color="black", weight=3]; 798[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) False) (Succ Zero)",fontsize=16,color="black",shape="box"];798 -> 805[label="",style="solid", color="black", weight=3]; 799 -> 797[label="",style="dashed", color="red", weight=0]; 799[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) True) (Succ Zero)",fontsize=16,color="magenta"];1268[label="Succ xz30000",fontsize=16,color="green",shape="box"];1269[label="Zero",fontsize=16,color="green",shape="box"];1270[label="Zero",fontsize=16,color="green",shape="box"];1267[label="primPlusNat (primDivNatS (primMinusNatS xz64 xz65) (Succ xz66)) Zero",fontsize=16,color="burlywood",shape="triangle"];2392[label="xz64/Succ xz640",fontsize=10,color="white",style="solid",shape="box"];1267 -> 2392[label="",style="solid", color="burlywood", weight=9]; 2392 -> 1301[label="",style="solid", color="burlywood", weight=3]; 2393[label="xz64/Zero",fontsize=10,color="white",style="solid",shape="box"];1267 -> 2393[label="",style="solid", color="burlywood", weight=9]; 2393 -> 1302[label="",style="solid", color="burlywood", weight=3]; 1271[label="Zero",fontsize=16,color="green",shape="box"];1272[label="Zero",fontsize=16,color="green",shape="box"];1273[label="Zero",fontsize=16,color="green",shape="box"];790 -> 1155[label="",style="dashed", color="red", weight=0]; 790[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz38) (Succ xz39)) (Succ (Succ xz39))) Zero",fontsize=16,color="magenta"];790 -> 1162[label="",style="dashed", color="magenta", weight=3]; 790 -> 1163[label="",style="dashed", color="magenta", weight=3]; 790 -> 1164[label="",style="dashed", color="magenta", weight=3]; 1223 -> 1155[label="",style="dashed", color="red", weight=0]; 1223[label="primMinusNat (primDivNatS (primMinusNatS xz580 xz590) (Succ xz60)) Zero",fontsize=16,color="magenta"];1223 -> 1242[label="",style="dashed", color="magenta", weight=3]; 1223 -> 1243[label="",style="dashed", color="magenta", weight=3]; 1224[label="primMinusNat (primDivNatS (Succ xz580) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1224 -> 1244[label="",style="solid", color="black", weight=3]; 1225[label="primMinusNat (primDivNatS Zero (Succ xz60)) Zero",fontsize=16,color="black",shape="triangle"];1225 -> 1245[label="",style="solid", color="black", weight=3]; 1226 -> 1225[label="",style="dashed", color="red", weight=0]; 1226[label="primMinusNat (primDivNatS Zero (Succ xz60)) Zero",fontsize=16,color="magenta"];802[label="xz540",fontsize=16,color="green",shape="box"];803[label="xz530",fontsize=16,color="green",shape="box"];804[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz51) (Succ xz52)) (Succ (Succ xz52)))) (Succ Zero)",fontsize=16,color="black",shape="box"];804 -> 810[label="",style="solid", color="black", weight=3]; 805 -> 73[label="",style="dashed", color="red", weight=0]; 805[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="magenta"];1301[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz640) xz65) (Succ xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2394[label="xz65/Succ xz650",fontsize=10,color="white",style="solid",shape="box"];1301 -> 2394[label="",style="solid", color="burlywood", weight=9]; 2394 -> 1307[label="",style="solid", color="burlywood", weight=3]; 2395[label="xz65/Zero",fontsize=10,color="white",style="solid",shape="box"];1301 -> 2395[label="",style="solid", color="burlywood", weight=9]; 2395 -> 1308[label="",style="solid", color="burlywood", weight=3]; 1302[label="primPlusNat (primDivNatS (primMinusNatS Zero xz65) (Succ xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2396[label="xz65/Succ xz650",fontsize=10,color="white",style="solid",shape="box"];1302 -> 2396[label="",style="solid", color="burlywood", weight=9]; 2396 -> 1309[label="",style="solid", color="burlywood", weight=3]; 2397[label="xz65/Zero",fontsize=10,color="white",style="solid",shape="box"];1302 -> 2397[label="",style="solid", color="burlywood", weight=9]; 2397 -> 1310[label="",style="solid", color="burlywood", weight=3]; 1162[label="Succ xz38",fontsize=16,color="green",shape="box"];1163[label="Succ xz39",fontsize=16,color="green",shape="box"];1164[label="Succ xz39",fontsize=16,color="green",shape="box"];1242[label="xz580",fontsize=16,color="green",shape="box"];1243[label="xz590",fontsize=16,color="green",shape="box"];1244[label="primMinusNat (primDivNatS0 xz580 xz60 (primGEqNatS xz580 xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2398[label="xz580/Succ xz5800",fontsize=10,color="white",style="solid",shape="box"];1244 -> 2398[label="",style="solid", color="burlywood", weight=9]; 2398 -> 1259[label="",style="solid", color="burlywood", weight=3]; 2399[label="xz580/Zero",fontsize=10,color="white",style="solid",shape="box"];1244 -> 2399[label="",style="solid", color="burlywood", weight=9]; 2399 -> 1260[label="",style="solid", color="burlywood", weight=3]; 1245[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1245 -> 1261[label="",style="solid", color="black", weight=3]; 810[label="Succ (Succ (primPlusNat (primDivNatS (primMinusNatS (Succ xz51) (Succ xz52)) (Succ (Succ xz52))) Zero))",fontsize=16,color="green",shape="box"];810 -> 815[label="",style="dashed", color="green", weight=3]; 1307[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz640) (Succ xz650)) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1307 -> 1315[label="",style="solid", color="black", weight=3]; 1308[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz640) Zero) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1308 -> 1316[label="",style="solid", color="black", weight=3]; 1309[label="primPlusNat (primDivNatS (primMinusNatS Zero (Succ xz650)) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1309 -> 1317[label="",style="solid", color="black", weight=3]; 1310[label="primPlusNat (primDivNatS (primMinusNatS Zero Zero) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1310 -> 1318[label="",style="solid", color="black", weight=3]; 1259[label="primMinusNat (primDivNatS0 (Succ xz5800) xz60 (primGEqNatS (Succ xz5800) xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2400[label="xz60/Succ xz600",fontsize=10,color="white",style="solid",shape="box"];1259 -> 2400[label="",style="solid", color="burlywood", weight=9]; 2400 -> 1303[label="",style="solid", color="burlywood", weight=3]; 2401[label="xz60/Zero",fontsize=10,color="white",style="solid",shape="box"];1259 -> 2401[label="",style="solid", color="burlywood", weight=9]; 2401 -> 1304[label="",style="solid", color="burlywood", weight=3]; 1260[label="primMinusNat (primDivNatS0 Zero xz60 (primGEqNatS Zero xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2402[label="xz60/Succ xz600",fontsize=10,color="white",style="solid",shape="box"];1260 -> 2402[label="",style="solid", color="burlywood", weight=9]; 2402 -> 1305[label="",style="solid", color="burlywood", weight=3]; 2403[label="xz60/Zero",fontsize=10,color="white",style="solid",shape="box"];1260 -> 2403[label="",style="solid", color="burlywood", weight=9]; 2403 -> 1306[label="",style="solid", color="burlywood", weight=3]; 1261[label="Pos Zero",fontsize=16,color="green",shape="box"];815 -> 1267[label="",style="dashed", color="red", weight=0]; 815[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz51) (Succ xz52)) (Succ (Succ xz52))) Zero",fontsize=16,color="magenta"];815 -> 1274[label="",style="dashed", color="magenta", weight=3]; 815 -> 1275[label="",style="dashed", color="magenta", weight=3]; 815 -> 1276[label="",style="dashed", color="magenta", weight=3]; 1315 -> 1267[label="",style="dashed", color="red", weight=0]; 1315[label="primPlusNat (primDivNatS (primMinusNatS xz640 xz650) (Succ xz66)) Zero",fontsize=16,color="magenta"];1315 -> 1324[label="",style="dashed", color="magenta", weight=3]; 1315 -> 1325[label="",style="dashed", color="magenta", weight=3]; 1316[label="primPlusNat (primDivNatS (Succ xz640) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1316 -> 1326[label="",style="solid", color="black", weight=3]; 1317[label="primPlusNat (primDivNatS Zero (Succ xz66)) Zero",fontsize=16,color="black",shape="triangle"];1317 -> 1327[label="",style="solid", color="black", weight=3]; 1318 -> 1317[label="",style="dashed", color="red", weight=0]; 1318[label="primPlusNat (primDivNatS Zero (Succ xz66)) Zero",fontsize=16,color="magenta"];1303[label="primMinusNat (primDivNatS0 (Succ xz5800) (Succ xz600) (primGEqNatS (Succ xz5800) (Succ xz600))) Zero",fontsize=16,color="black",shape="box"];1303 -> 1311[label="",style="solid", color="black", weight=3]; 1304[label="primMinusNat (primDivNatS0 (Succ xz5800) Zero (primGEqNatS (Succ xz5800) Zero)) Zero",fontsize=16,color="black",shape="box"];1304 -> 1312[label="",style="solid", color="black", weight=3]; 1305[label="primMinusNat (primDivNatS0 Zero (Succ xz600) (primGEqNatS Zero (Succ xz600))) Zero",fontsize=16,color="black",shape="box"];1305 -> 1313[label="",style="solid", color="black", weight=3]; 1306[label="primMinusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];1306 -> 1314[label="",style="solid", color="black", weight=3]; 1274[label="Succ xz51",fontsize=16,color="green",shape="box"];1275[label="Succ xz52",fontsize=16,color="green",shape="box"];1276[label="Succ xz52",fontsize=16,color="green",shape="box"];1324[label="xz640",fontsize=16,color="green",shape="box"];1325[label="xz650",fontsize=16,color="green",shape="box"];1326[label="primPlusNat (primDivNatS0 xz640 xz66 (primGEqNatS xz640 xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2404[label="xz640/Succ xz6400",fontsize=10,color="white",style="solid",shape="box"];1326 -> 2404[label="",style="solid", color="burlywood", weight=9]; 2404 -> 1334[label="",style="solid", color="burlywood", weight=3]; 2405[label="xz640/Zero",fontsize=10,color="white",style="solid",shape="box"];1326 -> 2405[label="",style="solid", color="burlywood", weight=9]; 2405 -> 1335[label="",style="solid", color="burlywood", weight=3]; 1327[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1327 -> 1336[label="",style="solid", color="black", weight=3]; 1311 -> 1830[label="",style="dashed", color="red", weight=0]; 1311[label="primMinusNat (primDivNatS0 (Succ xz5800) (Succ xz600) (primGEqNatS xz5800 xz600)) Zero",fontsize=16,color="magenta"];1311 -> 1831[label="",style="dashed", color="magenta", weight=3]; 1311 -> 1832[label="",style="dashed", color="magenta", weight=3]; 1311 -> 1833[label="",style="dashed", color="magenta", weight=3]; 1311 -> 1834[label="",style="dashed", color="magenta", weight=3]; 1312[label="primMinusNat (primDivNatS0 (Succ xz5800) Zero True) Zero",fontsize=16,color="black",shape="box"];1312 -> 1321[label="",style="solid", color="black", weight=3]; 1313[label="primMinusNat (primDivNatS0 Zero (Succ xz600) False) Zero",fontsize=16,color="black",shape="box"];1313 -> 1322[label="",style="solid", color="black", weight=3]; 1314[label="primMinusNat (primDivNatS0 Zero Zero True) Zero",fontsize=16,color="black",shape="box"];1314 -> 1323[label="",style="solid", color="black", weight=3]; 1334[label="primPlusNat (primDivNatS0 (Succ xz6400) xz66 (primGEqNatS (Succ xz6400) xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2406[label="xz66/Succ xz660",fontsize=10,color="white",style="solid",shape="box"];1334 -> 2406[label="",style="solid", color="burlywood", weight=9]; 2406 -> 1343[label="",style="solid", color="burlywood", weight=3]; 2407[label="xz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1334 -> 2407[label="",style="solid", color="burlywood", weight=9]; 2407 -> 1344[label="",style="solid", color="burlywood", weight=3]; 1335[label="primPlusNat (primDivNatS0 Zero xz66 (primGEqNatS Zero xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2408[label="xz66/Succ xz660",fontsize=10,color="white",style="solid",shape="box"];1335 -> 2408[label="",style="solid", color="burlywood", weight=9]; 2408 -> 1345[label="",style="solid", color="burlywood", weight=3]; 2409[label="xz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1335 -> 2409[label="",style="solid", color="burlywood", weight=9]; 2409 -> 1346[label="",style="solid", color="burlywood", weight=3]; 1336[label="Zero",fontsize=16,color="green",shape="box"];1831[label="xz600",fontsize=16,color="green",shape="box"];1832[label="xz5800",fontsize=16,color="green",shape="box"];1833[label="xz5800",fontsize=16,color="green",shape="box"];1834[label="xz600",fontsize=16,color="green",shape="box"];1830[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS xz97 xz98)) Zero",fontsize=16,color="burlywood",shape="triangle"];2410[label="xz97/Succ xz970",fontsize=10,color="white",style="solid",shape="box"];1830 -> 2410[label="",style="solid", color="burlywood", weight=9]; 2410 -> 1871[label="",style="solid", color="burlywood", weight=3]; 2411[label="xz97/Zero",fontsize=10,color="white",style="solid",shape="box"];1830 -> 2411[label="",style="solid", color="burlywood", weight=9]; 2411 -> 1872[label="",style="solid", color="burlywood", weight=3]; 1321 -> 1676[label="",style="dashed", color="red", weight=0]; 1321[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz5800) Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1321 -> 1677[label="",style="dashed", color="magenta", weight=3]; 1322 -> 1245[label="",style="dashed", color="red", weight=0]; 1322[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];1323 -> 1676[label="",style="dashed", color="red", weight=0]; 1323[label="primMinusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1323 -> 1678[label="",style="dashed", color="magenta", weight=3]; 1343[label="primPlusNat (primDivNatS0 (Succ xz6400) (Succ xz660) (primGEqNatS (Succ xz6400) (Succ xz660))) Zero",fontsize=16,color="black",shape="box"];1343 -> 1354[label="",style="solid", color="black", weight=3]; 1344[label="primPlusNat (primDivNatS0 (Succ xz6400) Zero (primGEqNatS (Succ xz6400) Zero)) Zero",fontsize=16,color="black",shape="box"];1344 -> 1355[label="",style="solid", color="black", weight=3]; 1345[label="primPlusNat (primDivNatS0 Zero (Succ xz660) (primGEqNatS Zero (Succ xz660))) Zero",fontsize=16,color="black",shape="box"];1345 -> 1356[label="",style="solid", color="black", weight=3]; 1346[label="primPlusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];1346 -> 1357[label="",style="solid", color="black", weight=3]; 1871[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS (Succ xz970) xz98)) Zero",fontsize=16,color="burlywood",shape="box"];2412[label="xz98/Succ xz980",fontsize=10,color="white",style="solid",shape="box"];1871 -> 2412[label="",style="solid", color="burlywood", weight=9]; 2412 -> 1886[label="",style="solid", color="burlywood", weight=3]; 2413[label="xz98/Zero",fontsize=10,color="white",style="solid",shape="box"];1871 -> 2413[label="",style="solid", color="burlywood", weight=9]; 2413 -> 1887[label="",style="solid", color="burlywood", weight=3]; 1872[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS Zero xz98)) Zero",fontsize=16,color="burlywood",shape="box"];2414[label="xz98/Succ xz980",fontsize=10,color="white",style="solid",shape="box"];1872 -> 2414[label="",style="solid", color="burlywood", weight=9]; 2414 -> 1888[label="",style="solid", color="burlywood", weight=3]; 2415[label="xz98/Zero",fontsize=10,color="white",style="solid",shape="box"];1872 -> 2415[label="",style="solid", color="burlywood", weight=9]; 2415 -> 1889[label="",style="solid", color="burlywood", weight=3]; 1677 -> 2058[label="",style="dashed", color="red", weight=0]; 1677[label="primDivNatS (primMinusNatS (Succ xz5800) Zero) (Succ Zero)",fontsize=16,color="magenta"];1677 -> 2059[label="",style="dashed", color="magenta", weight=3]; 1677 -> 2060[label="",style="dashed", color="magenta", weight=3]; 1677 -> 2061[label="",style="dashed", color="magenta", weight=3]; 1676[label="primMinusNat (Succ xz79) Zero",fontsize=16,color="black",shape="triangle"];1676 -> 1692[label="",style="solid", color="black", weight=3]; 1678 -> 2058[label="",style="dashed", color="red", weight=0]; 1678[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1678 -> 2062[label="",style="dashed", color="magenta", weight=3]; 1678 -> 2063[label="",style="dashed", color="magenta", weight=3]; 1678 -> 2064[label="",style="dashed", color="magenta", weight=3]; 1354 -> 1963[label="",style="dashed", color="red", weight=0]; 1354[label="primPlusNat (primDivNatS0 (Succ xz6400) (Succ xz660) (primGEqNatS xz6400 xz660)) Zero",fontsize=16,color="magenta"];1354 -> 1964[label="",style="dashed", color="magenta", weight=3]; 1354 -> 1965[label="",style="dashed", color="magenta", weight=3]; 1354 -> 1966[label="",style="dashed", color="magenta", weight=3]; 1354 -> 1967[label="",style="dashed", color="magenta", weight=3]; 1355[label="primPlusNat (primDivNatS0 (Succ xz6400) Zero True) Zero",fontsize=16,color="black",shape="box"];1355 -> 1368[label="",style="solid", color="black", weight=3]; 1356[label="primPlusNat (primDivNatS0 Zero (Succ xz660) False) Zero",fontsize=16,color="black",shape="box"];1356 -> 1369[label="",style="solid", color="black", weight=3]; 1357[label="primPlusNat (primDivNatS0 Zero Zero True) Zero",fontsize=16,color="black",shape="box"];1357 -> 1370[label="",style="solid", color="black", weight=3]; 1886[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS (Succ xz970) (Succ xz980))) Zero",fontsize=16,color="black",shape="box"];1886 -> 1904[label="",style="solid", color="black", weight=3]; 1887[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS (Succ xz970) Zero)) Zero",fontsize=16,color="black",shape="box"];1887 -> 1905[label="",style="solid", color="black", weight=3]; 1888[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS Zero (Succ xz980))) Zero",fontsize=16,color="black",shape="box"];1888 -> 1906[label="",style="solid", color="black", weight=3]; 1889[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];1889 -> 1907[label="",style="solid", color="black", weight=3]; 2059[label="Zero",fontsize=16,color="green",shape="box"];2060[label="Zero",fontsize=16,color="green",shape="box"];2061[label="Succ xz5800",fontsize=16,color="green",shape="box"];2058[label="primDivNatS (primMinusNatS xz116 xz117) (Succ xz118)",fontsize=16,color="burlywood",shape="triangle"];2416[label="xz116/Succ xz1160",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2416[label="",style="solid", color="burlywood", weight=9]; 2416 -> 2110[label="",style="solid", color="burlywood", weight=3]; 2417[label="xz116/Zero",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2417[label="",style="solid", color="burlywood", weight=9]; 2417 -> 2111[label="",style="solid", color="burlywood", weight=3]; 1692[label="Pos (Succ xz79)",fontsize=16,color="green",shape="box"];2062[label="Zero",fontsize=16,color="green",shape="box"];2063[label="Zero",fontsize=16,color="green",shape="box"];2064[label="Zero",fontsize=16,color="green",shape="box"];1964[label="xz6400",fontsize=16,color="green",shape="box"];1965[label="xz660",fontsize=16,color="green",shape="box"];1966[label="xz660",fontsize=16,color="green",shape="box"];1967[label="xz6400",fontsize=16,color="green",shape="box"];1963[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS xz113 xz114)) Zero",fontsize=16,color="burlywood",shape="triangle"];2418[label="xz113/Succ xz1130",fontsize=10,color="white",style="solid",shape="box"];1963 -> 2418[label="",style="solid", color="burlywood", weight=9]; 2418 -> 2004[label="",style="solid", color="burlywood", weight=3]; 2419[label="xz113/Zero",fontsize=10,color="white",style="solid",shape="box"];1963 -> 2419[label="",style="solid", color="burlywood", weight=9]; 2419 -> 2005[label="",style="solid", color="burlywood", weight=3]; 1368 -> 1383[label="",style="dashed", color="red", weight=0]; 1368[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz6400) Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1368 -> 1384[label="",style="dashed", color="magenta", weight=3]; 1369 -> 1327[label="",style="dashed", color="red", weight=0]; 1369[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];1370 -> 1383[label="",style="dashed", color="red", weight=0]; 1370[label="primPlusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1370 -> 1385[label="",style="dashed", color="magenta", weight=3]; 1904 -> 1830[label="",style="dashed", color="red", weight=0]; 1904[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS xz970 xz980)) Zero",fontsize=16,color="magenta"];1904 -> 1923[label="",style="dashed", color="magenta", weight=3]; 1904 -> 1924[label="",style="dashed", color="magenta", weight=3]; 1905[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) True) Zero",fontsize=16,color="black",shape="triangle"];1905 -> 1925[label="",style="solid", color="black", weight=3]; 1906[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) False) Zero",fontsize=16,color="black",shape="box"];1906 -> 1926[label="",style="solid", color="black", weight=3]; 1907 -> 1905[label="",style="dashed", color="red", weight=0]; 1907[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) True) Zero",fontsize=16,color="magenta"];2110[label="primDivNatS (primMinusNatS (Succ xz1160) xz117) (Succ xz118)",fontsize=16,color="burlywood",shape="box"];2420[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2110 -> 2420[label="",style="solid", color="burlywood", weight=9]; 2420 -> 2112[label="",style="solid", color="burlywood", weight=3]; 2421[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2110 -> 2421[label="",style="solid", color="burlywood", weight=9]; 2421 -> 2113[label="",style="solid", color="burlywood", weight=3]; 2111[label="primDivNatS (primMinusNatS Zero xz117) (Succ xz118)",fontsize=16,color="burlywood",shape="box"];2422[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2111 -> 2422[label="",style="solid", color="burlywood", weight=9]; 2422 -> 2114[label="",style="solid", color="burlywood", weight=3]; 2423[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2111 -> 2423[label="",style="solid", color="burlywood", weight=9]; 2423 -> 2115[label="",style="solid", color="burlywood", weight=3]; 2004[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS (Succ xz1130) xz114)) Zero",fontsize=16,color="burlywood",shape="box"];2424[label="xz114/Succ xz1140",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2424[label="",style="solid", color="burlywood", weight=9]; 2424 -> 2012[label="",style="solid", color="burlywood", weight=3]; 2425[label="xz114/Zero",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2425[label="",style="solid", color="burlywood", weight=9]; 2425 -> 2013[label="",style="solid", color="burlywood", weight=3]; 2005[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS Zero xz114)) Zero",fontsize=16,color="burlywood",shape="box"];2426[label="xz114/Succ xz1140",fontsize=10,color="white",style="solid",shape="box"];2005 -> 2426[label="",style="solid", color="burlywood", weight=9]; 2426 -> 2014[label="",style="solid", color="burlywood", weight=3]; 2427[label="xz114/Zero",fontsize=10,color="white",style="solid",shape="box"];2005 -> 2427[label="",style="solid", color="burlywood", weight=9]; 2427 -> 2015[label="",style="solid", color="burlywood", weight=3]; 1384 -> 2058[label="",style="dashed", color="red", weight=0]; 1384[label="primDivNatS (primMinusNatS (Succ xz6400) Zero) (Succ Zero)",fontsize=16,color="magenta"];1384 -> 2071[label="",style="dashed", color="magenta", weight=3]; 1384 -> 2072[label="",style="dashed", color="magenta", weight=3]; 1384 -> 2073[label="",style="dashed", color="magenta", weight=3]; 1383[label="primPlusNat (Succ xz67) Zero",fontsize=16,color="black",shape="triangle"];1383 -> 1391[label="",style="solid", color="black", weight=3]; 1385 -> 2058[label="",style="dashed", color="red", weight=0]; 1385[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1385 -> 2074[label="",style="dashed", color="magenta", weight=3]; 1385 -> 2075[label="",style="dashed", color="magenta", weight=3]; 1385 -> 2076[label="",style="dashed", color="magenta", weight=3]; 1923[label="xz980",fontsize=16,color="green",shape="box"];1924[label="xz970",fontsize=16,color="green",shape="box"];1925 -> 1676[label="",style="dashed", color="red", weight=0]; 1925[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz95) (Succ xz96)) (Succ (Succ xz96)))) Zero",fontsize=16,color="magenta"];1925 -> 1938[label="",style="dashed", color="magenta", weight=3]; 1926 -> 1245[label="",style="dashed", color="red", weight=0]; 1926[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];2112[label="primDivNatS (primMinusNatS (Succ xz1160) (Succ xz1170)) (Succ xz118)",fontsize=16,color="black",shape="box"];2112 -> 2116[label="",style="solid", color="black", weight=3]; 2113[label="primDivNatS (primMinusNatS (Succ xz1160) Zero) (Succ xz118)",fontsize=16,color="black",shape="box"];2113 -> 2117[label="",style="solid", color="black", weight=3]; 2114[label="primDivNatS (primMinusNatS Zero (Succ xz1170)) (Succ xz118)",fontsize=16,color="black",shape="box"];2114 -> 2118[label="",style="solid", color="black", weight=3]; 2115[label="primDivNatS (primMinusNatS Zero Zero) (Succ xz118)",fontsize=16,color="black",shape="box"];2115 -> 2119[label="",style="solid", color="black", weight=3]; 2012[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS (Succ xz1130) (Succ xz1140))) Zero",fontsize=16,color="black",shape="box"];2012 -> 2026[label="",style="solid", color="black", weight=3]; 2013[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS (Succ xz1130) Zero)) Zero",fontsize=16,color="black",shape="box"];2013 -> 2027[label="",style="solid", color="black", weight=3]; 2014[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS Zero (Succ xz1140))) Zero",fontsize=16,color="black",shape="box"];2014 -> 2028[label="",style="solid", color="black", weight=3]; 2015[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];2015 -> 2029[label="",style="solid", color="black", weight=3]; 2071[label="Zero",fontsize=16,color="green",shape="box"];2072[label="Zero",fontsize=16,color="green",shape="box"];2073[label="Succ xz6400",fontsize=16,color="green",shape="box"];1391[label="Succ xz67",fontsize=16,color="green",shape="box"];2074[label="Zero",fontsize=16,color="green",shape="box"];2075[label="Zero",fontsize=16,color="green",shape="box"];2076[label="Zero",fontsize=16,color="green",shape="box"];1938 -> 2058[label="",style="dashed", color="red", weight=0]; 1938[label="primDivNatS (primMinusNatS (Succ xz95) (Succ xz96)) (Succ (Succ xz96))",fontsize=16,color="magenta"];1938 -> 2080[label="",style="dashed", color="magenta", weight=3]; 1938 -> 2081[label="",style="dashed", color="magenta", weight=3]; 1938 -> 2082[label="",style="dashed", color="magenta", weight=3]; 2116 -> 2058[label="",style="dashed", color="red", weight=0]; 2116[label="primDivNatS (primMinusNatS xz1160 xz1170) (Succ xz118)",fontsize=16,color="magenta"];2116 -> 2120[label="",style="dashed", color="magenta", weight=3]; 2116 -> 2121[label="",style="dashed", color="magenta", weight=3]; 2117[label="primDivNatS (Succ xz1160) (Succ xz118)",fontsize=16,color="black",shape="box"];2117 -> 2122[label="",style="solid", color="black", weight=3]; 2118[label="primDivNatS Zero (Succ xz118)",fontsize=16,color="black",shape="triangle"];2118 -> 2123[label="",style="solid", color="black", weight=3]; 2119 -> 2118[label="",style="dashed", color="red", weight=0]; 2119[label="primDivNatS Zero (Succ xz118)",fontsize=16,color="magenta"];2026 -> 1963[label="",style="dashed", color="red", weight=0]; 2026[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS xz1130 xz1140)) Zero",fontsize=16,color="magenta"];2026 -> 2038[label="",style="dashed", color="magenta", weight=3]; 2026 -> 2039[label="",style="dashed", color="magenta", weight=3]; 2027[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) True) Zero",fontsize=16,color="black",shape="triangle"];2027 -> 2040[label="",style="solid", color="black", weight=3]; 2028[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) False) Zero",fontsize=16,color="black",shape="box"];2028 -> 2041[label="",style="solid", color="black", weight=3]; 2029 -> 2027[label="",style="dashed", color="red", weight=0]; 2029[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) True) Zero",fontsize=16,color="magenta"];2080[label="Succ xz96",fontsize=16,color="green",shape="box"];2081[label="Succ xz96",fontsize=16,color="green",shape="box"];2082[label="Succ xz95",fontsize=16,color="green",shape="box"];2120[label="xz1170",fontsize=16,color="green",shape="box"];2121[label="xz1160",fontsize=16,color="green",shape="box"];2122[label="primDivNatS0 xz1160 xz118 (primGEqNatS xz1160 xz118)",fontsize=16,color="burlywood",shape="box"];2428[label="xz1160/Succ xz11600",fontsize=10,color="white",style="solid",shape="box"];2122 -> 2428[label="",style="solid", color="burlywood", weight=9]; 2428 -> 2124[label="",style="solid", color="burlywood", weight=3]; 2429[label="xz1160/Zero",fontsize=10,color="white",style="solid",shape="box"];2122 -> 2429[label="",style="solid", color="burlywood", weight=9]; 2429 -> 2125[label="",style="solid", color="burlywood", weight=3]; 2123[label="Zero",fontsize=16,color="green",shape="box"];2038[label="xz1140",fontsize=16,color="green",shape="box"];2039[label="xz1130",fontsize=16,color="green",shape="box"];2040 -> 1383[label="",style="dashed", color="red", weight=0]; 2040[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz111) (Succ xz112)) (Succ (Succ xz112)))) Zero",fontsize=16,color="magenta"];2040 -> 2051[label="",style="dashed", color="magenta", weight=3]; 2041 -> 1327[label="",style="dashed", color="red", weight=0]; 2041[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];2124[label="primDivNatS0 (Succ xz11600) xz118 (primGEqNatS (Succ xz11600) xz118)",fontsize=16,color="burlywood",shape="box"];2430[label="xz118/Succ xz1180",fontsize=10,color="white",style="solid",shape="box"];2124 -> 2430[label="",style="solid", color="burlywood", weight=9]; 2430 -> 2126[label="",style="solid", color="burlywood", weight=3]; 2431[label="xz118/Zero",fontsize=10,color="white",style="solid",shape="box"];2124 -> 2431[label="",style="solid", color="burlywood", weight=9]; 2431 -> 2127[label="",style="solid", color="burlywood", weight=3]; 2125[label="primDivNatS0 Zero xz118 (primGEqNatS Zero xz118)",fontsize=16,color="burlywood",shape="box"];2432[label="xz118/Succ xz1180",fontsize=10,color="white",style="solid",shape="box"];2125 -> 2432[label="",style="solid", color="burlywood", weight=9]; 2432 -> 2128[label="",style="solid", color="burlywood", weight=3]; 2433[label="xz118/Zero",fontsize=10,color="white",style="solid",shape="box"];2125 -> 2433[label="",style="solid", color="burlywood", weight=9]; 2433 -> 2129[label="",style="solid", color="burlywood", weight=3]; 2051 -> 2058[label="",style="dashed", color="red", weight=0]; 2051[label="primDivNatS (primMinusNatS (Succ xz111) (Succ xz112)) (Succ (Succ xz112))",fontsize=16,color="magenta"];2051 -> 2086[label="",style="dashed", color="magenta", weight=3]; 2051 -> 2087[label="",style="dashed", color="magenta", weight=3]; 2051 -> 2088[label="",style="dashed", color="magenta", weight=3]; 2126[label="primDivNatS0 (Succ xz11600) (Succ xz1180) (primGEqNatS (Succ xz11600) (Succ xz1180))",fontsize=16,color="black",shape="box"];2126 -> 2130[label="",style="solid", color="black", weight=3]; 2127[label="primDivNatS0 (Succ xz11600) Zero (primGEqNatS (Succ xz11600) Zero)",fontsize=16,color="black",shape="box"];2127 -> 2131[label="",style="solid", color="black", weight=3]; 2128[label="primDivNatS0 Zero (Succ xz1180) (primGEqNatS Zero (Succ xz1180))",fontsize=16,color="black",shape="box"];2128 -> 2132[label="",style="solid", color="black", weight=3]; 2129[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2129 -> 2133[label="",style="solid", color="black", weight=3]; 2086[label="Succ xz112",fontsize=16,color="green",shape="box"];2087[label="Succ xz112",fontsize=16,color="green",shape="box"];2088[label="Succ xz111",fontsize=16,color="green",shape="box"];2130 -> 2292[label="",style="dashed", color="red", weight=0]; 2130[label="primDivNatS0 (Succ xz11600) (Succ xz1180) (primGEqNatS xz11600 xz1180)",fontsize=16,color="magenta"];2130 -> 2293[label="",style="dashed", color="magenta", weight=3]; 2130 -> 2294[label="",style="dashed", color="magenta", weight=3]; 2130 -> 2295[label="",style="dashed", color="magenta", weight=3]; 2130 -> 2296[label="",style="dashed", color="magenta", weight=3]; 2131[label="primDivNatS0 (Succ xz11600) Zero True",fontsize=16,color="black",shape="box"];2131 -> 2136[label="",style="solid", color="black", weight=3]; 2132[label="primDivNatS0 Zero (Succ xz1180) False",fontsize=16,color="black",shape="box"];2132 -> 2137[label="",style="solid", color="black", weight=3]; 2133[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2133 -> 2138[label="",style="solid", color="black", weight=3]; 2293[label="xz1180",fontsize=16,color="green",shape="box"];2294[label="xz1180",fontsize=16,color="green",shape="box"];2295[label="xz11600",fontsize=16,color="green",shape="box"];2296[label="xz11600",fontsize=16,color="green",shape="box"];2292[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS xz137 xz138)",fontsize=16,color="burlywood",shape="triangle"];2434[label="xz137/Succ xz1370",fontsize=10,color="white",style="solid",shape="box"];2292 -> 2434[label="",style="solid", color="burlywood", weight=9]; 2434 -> 2325[label="",style="solid", color="burlywood", weight=3]; 2435[label="xz137/Zero",fontsize=10,color="white",style="solid",shape="box"];2292 -> 2435[label="",style="solid", color="burlywood", weight=9]; 2435 -> 2326[label="",style="solid", color="burlywood", weight=3]; 2136[label="Succ (primDivNatS (primMinusNatS (Succ xz11600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2136 -> 2143[label="",style="dashed", color="green", weight=3]; 2137[label="Zero",fontsize=16,color="green",shape="box"];2138[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2138 -> 2144[label="",style="dashed", color="green", weight=3]; 2325[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS (Succ xz1370) xz138)",fontsize=16,color="burlywood",shape="box"];2436[label="xz138/Succ xz1380",fontsize=10,color="white",style="solid",shape="box"];2325 -> 2436[label="",style="solid", color="burlywood", weight=9]; 2436 -> 2327[label="",style="solid", color="burlywood", weight=3]; 2437[label="xz138/Zero",fontsize=10,color="white",style="solid",shape="box"];2325 -> 2437[label="",style="solid", color="burlywood", weight=9]; 2437 -> 2328[label="",style="solid", color="burlywood", weight=3]; 2326[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS Zero xz138)",fontsize=16,color="burlywood",shape="box"];2438[label="xz138/Succ xz1380",fontsize=10,color="white",style="solid",shape="box"];2326 -> 2438[label="",style="solid", color="burlywood", weight=9]; 2438 -> 2329[label="",style="solid", color="burlywood", weight=3]; 2439[label="xz138/Zero",fontsize=10,color="white",style="solid",shape="box"];2326 -> 2439[label="",style="solid", color="burlywood", weight=9]; 2439 -> 2330[label="",style="solid", color="burlywood", weight=3]; 2143 -> 2058[label="",style="dashed", color="red", weight=0]; 2143[label="primDivNatS (primMinusNatS (Succ xz11600) Zero) (Succ Zero)",fontsize=16,color="magenta"];2143 -> 2149[label="",style="dashed", color="magenta", weight=3]; 2143 -> 2150[label="",style="dashed", color="magenta", weight=3]; 2143 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2144 -> 2058[label="",style="dashed", color="red", weight=0]; 2144[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2144 -> 2152[label="",style="dashed", color="magenta", weight=3]; 2144 -> 2153[label="",style="dashed", color="magenta", weight=3]; 2144 -> 2154[label="",style="dashed", color="magenta", weight=3]; 2327[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS (Succ xz1370) (Succ xz1380))",fontsize=16,color="black",shape="box"];2327 -> 2331[label="",style="solid", color="black", weight=3]; 2328[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS (Succ xz1370) Zero)",fontsize=16,color="black",shape="box"];2328 -> 2332[label="",style="solid", color="black", weight=3]; 2329[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS Zero (Succ xz1380))",fontsize=16,color="black",shape="box"];2329 -> 2333[label="",style="solid", color="black", weight=3]; 2330[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2330 -> 2334[label="",style="solid", color="black", weight=3]; 2149[label="Zero",fontsize=16,color="green",shape="box"];2150[label="Zero",fontsize=16,color="green",shape="box"];2151[label="Succ xz11600",fontsize=16,color="green",shape="box"];2152[label="Zero",fontsize=16,color="green",shape="box"];2153[label="Zero",fontsize=16,color="green",shape="box"];2154[label="Zero",fontsize=16,color="green",shape="box"];2331 -> 2292[label="",style="dashed", color="red", weight=0]; 2331[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS xz1370 xz1380)",fontsize=16,color="magenta"];2331 -> 2335[label="",style="dashed", color="magenta", weight=3]; 2331 -> 2336[label="",style="dashed", color="magenta", weight=3]; 2332[label="primDivNatS0 (Succ xz135) (Succ xz136) True",fontsize=16,color="black",shape="triangle"];2332 -> 2337[label="",style="solid", color="black", weight=3]; 2333[label="primDivNatS0 (Succ xz135) (Succ xz136) False",fontsize=16,color="black",shape="box"];2333 -> 2338[label="",style="solid", color="black", weight=3]; 2334 -> 2332[label="",style="dashed", color="red", weight=0]; 2334[label="primDivNatS0 (Succ xz135) (Succ xz136) True",fontsize=16,color="magenta"];2335[label="xz1380",fontsize=16,color="green",shape="box"];2336[label="xz1370",fontsize=16,color="green",shape="box"];2337[label="Succ (primDivNatS (primMinusNatS (Succ xz135) (Succ xz136)) (Succ (Succ xz136)))",fontsize=16,color="green",shape="box"];2337 -> 2339[label="",style="dashed", color="green", weight=3]; 2338[label="Zero",fontsize=16,color="green",shape="box"];2339 -> 2058[label="",style="dashed", color="red", weight=0]; 2339[label="primDivNatS (primMinusNatS (Succ xz135) (Succ xz136)) (Succ (Succ xz136))",fontsize=16,color="magenta"];2339 -> 2340[label="",style="dashed", color="magenta", weight=3]; 2339 -> 2341[label="",style="dashed", color="magenta", weight=3]; 2339 -> 2342[label="",style="dashed", color="magenta", weight=3]; 2340[label="Succ xz136",fontsize=16,color="green",shape="box"];2341[label="Succ xz136",fontsize=16,color="green",shape="box"];2342[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(xz135, xz136, Zero, Zero) -> new_primDivNatS00(xz135, xz136) new_primDivNatS(Succ(Zero), Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) new_primDivNatS00(xz135, xz136) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136)) new_primDivNatS(Succ(xz1160), Succ(xz1170), xz118) -> new_primDivNatS(xz1160, xz1170, xz118) new_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380) new_primDivNatS(Succ(Succ(xz11600)), Zero, Succ(xz1180)) -> new_primDivNatS0(xz11600, xz1180, xz11600, xz1180) new_primDivNatS0(xz135, xz136, Succ(xz1370), Zero) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136)) new_primDivNatS(Succ(Succ(xz11600)), Zero, Zero) -> new_primDivNatS(Succ(xz11600), 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(xz11600)), Zero, Zero) -> new_primDivNatS(Succ(xz11600), 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(xz11600)), Zero, Zero) -> new_primDivNatS(Succ(xz11600), 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(xz135, xz136) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136)) new_primDivNatS(Succ(xz1160), Succ(xz1170), xz118) -> new_primDivNatS(xz1160, xz1170, xz118) new_primDivNatS(Succ(Succ(xz11600)), Zero, Succ(xz1180)) -> new_primDivNatS0(xz11600, xz1180, xz11600, xz1180) new_primDivNatS0(xz135, xz136, Zero, Zero) -> new_primDivNatS00(xz135, xz136) new_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380) new_primDivNatS0(xz135, xz136, Succ(xz1370), Zero) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136)) 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(xz1160), Succ(xz1170), xz118) -> new_primDivNatS(xz1160, xz1170, xz118) new_primDivNatS(Succ(Succ(xz11600)), Zero, Succ(xz1180)) -> new_primDivNatS0(xz11600, xz1180, xz11600, xz1180) 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(xz135, xz136) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136)) new_primDivNatS0(xz135, xz136, Zero, Zero) -> new_primDivNatS00(xz135, xz136) new_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380) new_primDivNatS0(xz135, xz136, Succ(xz1370), Zero) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136)) 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(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380) 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(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380) 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(xz580), Succ(xz590), xz60) -> new_primMinusNat0(xz580, xz590, xz60) 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(xz580), Succ(xz590), xz60) -> new_primMinusNat0(xz580, xz590, xz60) 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(xz640), Succ(xz650), xz66) -> new_primPlusNat0(xz640, xz650, xz66) 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(xz640), Succ(xz650), xz66) -> new_primPlusNat0(xz640, xz650, xz66) 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(xz51, xz52, Succ(xz530), Succ(xz540)) -> new_primPlusNat1(xz51, xz52, xz530, xz540) 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(xz51, xz52, Succ(xz530), Succ(xz540)) -> new_primPlusNat1(xz51, xz52, xz530, xz540) 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(xz95, xz96, Succ(xz970), Succ(xz980)) -> new_primMinusNat(xz95, xz96, xz970, xz980) 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(xz95, xz96, Succ(xz970), Succ(xz980)) -> new_primMinusNat(xz95, xz96, xz970, xz980) 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(xz111, xz112, Succ(xz1130), Succ(xz1140)) -> new_primPlusNat(xz111, xz112, xz1130, xz1140) 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(xz111, xz112, Succ(xz1130), Succ(xz1140)) -> new_primPlusNat(xz111, xz112, xz1130, xz1140) 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(xz38, xz39, Succ(xz400), Succ(xz410)) -> new_primMinusNat1(xz38, xz39, xz400, xz410) 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(xz38, xz39, Succ(xz400), Succ(xz410)) -> new_primMinusNat1(xz38, xz39, xz400, xz410) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (45) YES