/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 23 ms] (6) HASKELL (7) LetRed [EQUIVALENT, 0 ms] (8) HASKELL (9) NumRed [SOUND, 0 ms] (10) HASKELL (11) Narrow [SOUND, 0 ms] (12) AND (13) QDP (14) DependencyGraphProof [EQUIVALENT, 0 ms] (15) AND (16) QDP (17) MNOCProof [EQUIVALENT, 20 ms] (18) QDP (19) NonTerminationLoopProof [COMPLETE, 0 ms] (20) NO (21) QDP (22) QDPOrderProof [EQUIVALENT, 75 ms] (23) QDP (24) DependencyGraphProof [EQUIVALENT, 0 ms] (25) AND (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES (29) QDP (30) QDPSizeChangeProof [EQUIVALENT, 0 ms] (31) YES (32) QDP (33) QDPSizeChangeProof [EQUIVALENT, 0 ms] (34) YES (35) QDP (36) QDPSizeChangeProof [EQUIVALENT, 0 ms] (37) YES (38) QDP (39) QDPSizeChangeProof [EQUIVALENT, 0 ms] (40) YES (41) QDP (42) QDPSizeChangeProof [EQUIVALENT, 0 ms] (43) YES (44) Narrow [COMPLETE, 0 ms] (45) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) IFR (EQUIVALENT) If Reductions: The following If expression "if n >= 0 then x ^ n else recip (x ^ (`negate` n))" is transformed to "prPr0 x n True = x ^ n; prPr0 x n False = recip (x ^ (`negate` n)); " 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; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " The following Function with conditions "g x n|even ng (x * x) (n `quot` 2)|otherwisef x (n - 1) (x * y); " is transformed to "g x n = g2 x n; " "g0 x n True = f x (n - 1) (x * y); " "g1 x n True = g (x * x) (n `quot` 2); g1 x n False = g0 x n otherwise; " "g2 x n = g1 x n (even n); " The following Function with conditions "f vw 0 y = y; f x n y = g x n where { g x n|even ng (x * x) (n `quot` 2)|otherwisef x (n - 1) (x * y); } ; " is transformed to "f vw yu y = f4 vw yu y; f x n y = f0 x n y; " "f0 x n y = g x n where { g x n = g2 x n; ; g0 x n True = f x (n - 1) (x * y); ; g1 x n True = g (x * x) (n `quot` 2); g1 x n False = g0 x n otherwise; ; g2 x n = g1 x n (even n); } ; " "f3 True vw yu y = y; f3 yv yw yx yy = f0 yw yx yy; " "f4 vw yu y = f3 (yu == 0) vw yu y; f4 yz zu zv = f0 yz zu zv; " The following Function with conditions "^ x 0 = 1; ^ x n|n > 0f x (n - 1) x where { f vw 0 y = y; f x n y = g x n where { g x n|even ng (x * x) (n `quot` 2)|otherwisef x (n - 1) (x * y); } ; } ; ^ vx vy = error []; " is transformed to "^ x zy = pr4 x zy; ^ x n = pr2 x n; ^ vx vy = pr0 vx vy; " "pr0 vx vy = error []; " "pr2 x n = pr1 x n (n > 0) where { f vw yu y = f4 vw yu y; f x n y = f0 x n y; ; f0 x n y = g x n where { g x n = g2 x n; ; g0 x n True = f x (n - 1) (x * y); ; g1 x n True = g (x * x) (n `quot` 2); g1 x n False = g0 x n otherwise; ; g2 x n = g1 x n (even n); } ; ; f3 True vw yu y = y; f3 yv yw yx yy = f0 yw yx yy; ; f4 vw yu y = f3 (yu == 0) vw yu y; f4 yz zu zv = f0 yz zu zv; ; pr1 x n True = f x (n - 1) x; pr1 x n False = pr0 x n; } ; pr2 zw zx = pr0 zw zx; " "pr3 True x zy = 1; pr3 zz vuu vuv = pr2 vuu vuv; " "pr4 x zy = pr3 (zy == 0) x zy; pr4 vuw vux = pr2 vuw vux; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "pr1 x n (n > 0) where { f vw yu y = f4 vw yu y; f x n y = f0 x n y; ; f0 x n y = g x n where { g x n = g2 x n; ; g0 x n True = f x (n - 1) (x * y); ; g1 x n True = g (x * x) (n `quot` 2); g1 x n False = g0 x n otherwise; ; g2 x n = g1 x n (even n); } ; ; f3 True vw yu y = y; f3 yv yw yx yy = f0 yw yx yy; ; f4 vw yu y = f3 (yu == 0) vw yu y; f4 yz zu zv = f0 yz zu zv; ; pr1 x n True = f x (n - 1) x; pr1 x n False = pr0 x n; } " are unpacked to the following functions on top level "pr2F vw yu y = pr2F4 vw yu y; pr2F x n y = pr2F0 x n y; " "pr2F0 x n y = pr2F0G y x n; " "pr2F4 vw yu y = pr2F3 (yu == 0) vw yu y; pr2F4 yz zu zv = pr2F0 yz zu zv; " "pr2Pr1 x n True = pr2F x (n - 1) x; pr2Pr1 x n False = pr0 x n; " "pr2F3 True vw yu y = y; pr2F3 yv yw yx yy = pr2F0 yw yx yy; " The bindings of the following Let/Where expression "g x n where { g x n = g2 x n; ; g0 x n True = f x (n - 1) (x * y); ; g1 x n True = g (x * x) (n `quot` 2); g1 x n False = g0 x n otherwise; ; g2 x n = g1 x n (even n); } " are unpacked to the following functions on top level "pr2F0G0 vuy x n True = pr2F x (n - 1) (x * vuy); " "pr2F0G2 vuy x n = pr2F0G1 vuy x n (even n); " "pr2F0G vuy x n = pr2F0G2 vuy x n; " "pr2F0G1 vuy x n True = pr2F0G vuy (x * x) (n `quot` 2); pr2F0G1 vuy x n False = pr2F0G0 vuy x n otherwise; " ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (10) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (11) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="(^^)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="(^^) vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="(^^) vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="prPr0 vuz3 vuz4 (vuz4 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="prPr0 vuz3 vuz4 (compare vuz4 (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="prPr0 vuz3 vuz4 (not (compare vuz4 (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="prPr0 vuz3 vuz4 (not (primCmpInt vuz4 (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];2093[label="vuz4/Pos vuz40",fontsize=10,color="white",style="solid",shape="box"];8 -> 2093[label="",style="solid", color="burlywood", weight=9]; 2093 -> 9[label="",style="solid", color="burlywood", weight=3]; 2094[label="vuz4/Neg vuz40",fontsize=10,color="white",style="solid",shape="box"];8 -> 2094[label="",style="solid", color="burlywood", weight=9]; 2094 -> 10[label="",style="solid", color="burlywood", weight=3]; 9[label="prPr0 vuz3 (Pos vuz40) (not (primCmpInt (Pos vuz40) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];2095[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 2095[label="",style="solid", color="burlywood", weight=9]; 2095 -> 11[label="",style="solid", color="burlywood", weight=3]; 2096[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 2096[label="",style="solid", color="burlywood", weight=9]; 2096 -> 12[label="",style="solid", color="burlywood", weight=3]; 10[label="prPr0 vuz3 (Neg vuz40) (not (primCmpInt (Neg vuz40) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];2097[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];10 -> 2097[label="",style="solid", color="burlywood", weight=9]; 2097 -> 13[label="",style="solid", color="burlywood", weight=3]; 2098[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 2098[label="",style="solid", color="burlywood", weight=9]; 2098 -> 14[label="",style="solid", color="burlywood", weight=3]; 11[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (primCmpInt (Pos (Succ vuz400)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 12[label="prPr0 vuz3 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 13[label="prPr0 vuz3 (Neg (Succ vuz400)) (not (primCmpInt (Neg (Succ vuz400)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 14[label="prPr0 vuz3 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 15[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (primCmpInt (Pos (Succ vuz400)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 16[label="prPr0 vuz3 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 17[label="prPr0 vuz3 (Neg (Succ vuz400)) (not (primCmpInt (Neg (Succ vuz400)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 18[label="prPr0 vuz3 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 19[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (primCmpNat (Succ vuz400) Zero == LT))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="prPr0 vuz3 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="prPr0 vuz3 (Neg (Succ vuz400)) (not (LT == LT))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22[label="prPr0 vuz3 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3]; 23[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (GT == LT))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 24[label="prPr0 vuz3 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 25[label="prPr0 vuz3 (Neg (Succ vuz400)) (not True)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 26[label="prPr0 vuz3 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 27[label="prPr0 vuz3 (Pos (Succ vuz400)) (not False)",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3]; 28[label="prPr0 vuz3 (Pos Zero) True",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3]; 29[label="prPr0 vuz3 (Neg (Succ vuz400)) False",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 30[label="prPr0 vuz3 (Neg Zero) True",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3]; 31[label="prPr0 vuz3 (Pos (Succ vuz400)) True",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3]; 32[label="vuz3 ^ Pos Zero",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3]; 33[label="recip (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3]; 34[label="vuz3 ^ Neg Zero",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3]; 35[label="vuz3 ^ Pos (Succ vuz400)",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 36[label="pr4 vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 37[label="fromInt (Pos (Succ Zero)) / vuz3 ^ (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3]; 38[label="pr4 vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];38 -> 42[label="",style="solid", color="black", weight=3]; 39[label="pr4 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];39 -> 43[label="",style="solid", color="black", weight=3]; 40[label="pr3 (Pos Zero == fromInt (Pos Zero)) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3]; 41[label="primDivFloat (fromInt (Pos (Succ Zero))) (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3]; 42[label="pr3 (Neg Zero == fromInt (Pos Zero)) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3]; 43[label="pr3 (Pos (Succ vuz400) == fromInt (Pos Zero)) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3]; 44[label="pr3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];44 -> 48[label="",style="solid", color="black", weight=3]; 45[label="primDivFloat (primIntToFloat (Pos (Succ Zero))) (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3]; 46[label="pr3 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3]; 47[label="pr3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="triangle"];47 -> 51[label="",style="solid", color="black", weight=3]; 48[label="pr3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3]; 49 -> 68[label="",style="dashed", color="red", weight=0]; 49[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="magenta"];49 -> 69[label="",style="dashed", color="magenta", weight=3]; 50[label="pr3 (primEqInt (Neg Zero) (Pos Zero)) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3]; 51[label="pr3 (primEqInt (Pos (Succ vuz400)) (Pos Zero)) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3]; 52[label="pr3 True vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 69[label="vuz3 ^ (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];69 -> 75[label="",style="solid", color="black", weight=3]; 68[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) vuz5",fontsize=16,color="burlywood",shape="triangle"];2099[label="vuz5/Float vuz50 vuz51",fontsize=10,color="white",style="solid",shape="box"];68 -> 2099[label="",style="solid", color="burlywood", weight=9]; 2099 -> 76[label="",style="solid", color="burlywood", weight=3]; 54[label="pr3 True vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 55[label="pr3 False vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 56[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];56 -> 60[label="",style="solid", color="black", weight=3]; 75[label="pr4 vuz3 (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];75 -> 78[label="",style="solid", color="black", weight=3]; 76[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float vuz50 vuz51)",fontsize=16,color="black",shape="box"];76 -> 79[label="",style="solid", color="black", weight=3]; 58 -> 56[label="",style="dashed", color="red", weight=0]; 58[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];59[label="pr2 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];59 -> 62[label="",style="solid", color="black", weight=3]; 60[label="primIntToFloat (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];60 -> 63[label="",style="solid", color="black", weight=3]; 78[label="pr3 (`negate` Neg (Succ vuz400) == fromInt (Pos Zero)) vuz3 (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];78 -> 81[label="",style="solid", color="black", weight=3]; 79[label="Float (Pos (Succ Zero) * vuz51) (Pos (Succ Zero) * vuz50)",fontsize=16,color="green",shape="box"];79 -> 82[label="",style="dashed", color="green", weight=3]; 79 -> 83[label="",style="dashed", color="green", weight=3]; 62[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (Pos (Succ vuz400) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];62 -> 65[label="",style="solid", color="black", weight=3]; 63[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];81[label="pr3 (primEqInt (`negate` Neg (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];81 -> 85[label="",style="solid", color="black", weight=3]; 82 -> 894[label="",style="dashed", color="red", weight=0]; 82[label="Pos (Succ Zero) * vuz51",fontsize=16,color="magenta"];82 -> 895[label="",style="dashed", color="magenta", weight=3]; 82 -> 896[label="",style="dashed", color="magenta", weight=3]; 83 -> 894[label="",style="dashed", color="red", weight=0]; 83[label="Pos (Succ Zero) * vuz50",fontsize=16,color="magenta"];83 -> 897[label="",style="dashed", color="magenta", weight=3]; 83 -> 898[label="",style="dashed", color="magenta", weight=3]; 65[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (compare (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3]; 85[label="pr3 (primEqInt (primNegInt (Neg (Succ vuz400))) (fromInt (Pos Zero))) vuz3 (primNegInt (Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];85 -> 89[label="",style="solid", color="black", weight=3]; 895[label="vuz51",fontsize=16,color="green",shape="box"];896[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];894[label="vuz15 * vuz50",fontsize=16,color="black",shape="triangle"];894 -> 906[label="",style="solid", color="black", weight=3]; 897[label="vuz50",fontsize=16,color="green",shape="box"];898[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];67[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];67 -> 77[label="",style="solid", color="black", weight=3]; 89 -> 47[label="",style="dashed", color="red", weight=0]; 89[label="pr3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400))",fontsize=16,color="magenta"];89 -> 93[label="",style="dashed", color="magenta", weight=3]; 906[label="primMulInt vuz15 vuz50",fontsize=16,color="burlywood",shape="box"];2100[label="vuz15/Pos vuz150",fontsize=10,color="white",style="solid",shape="box"];906 -> 2100[label="",style="solid", color="burlywood", weight=9]; 2100 -> 918[label="",style="solid", color="burlywood", weight=3]; 2101[label="vuz15/Neg vuz150",fontsize=10,color="white",style="solid",shape="box"];906 -> 2101[label="",style="solid", color="burlywood", weight=9]; 2101 -> 919[label="",style="solid", color="burlywood", weight=3]; 77[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];77 -> 80[label="",style="solid", color="black", weight=3]; 93[label="vuz400",fontsize=16,color="green",shape="box"];918[label="primMulInt (Pos vuz150) vuz50",fontsize=16,color="burlywood",shape="box"];2102[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];918 -> 2102[label="",style="solid", color="burlywood", weight=9]; 2102 -> 932[label="",style="solid", color="burlywood", weight=3]; 2103[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];918 -> 2103[label="",style="solid", color="burlywood", weight=9]; 2103 -> 933[label="",style="solid", color="burlywood", weight=3]; 919[label="primMulInt (Neg vuz150) vuz50",fontsize=16,color="burlywood",shape="box"];2104[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];919 -> 2104[label="",style="solid", color="burlywood", weight=9]; 2104 -> 934[label="",style="solid", color="burlywood", weight=3]; 2105[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];919 -> 2105[label="",style="solid", color="burlywood", weight=9]; 2105 -> 935[label="",style="solid", color="burlywood", weight=3]; 80[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpNat (Succ vuz400) Zero == GT)",fontsize=16,color="black",shape="box"];80 -> 84[label="",style="solid", color="black", weight=3]; 932[label="primMulInt (Pos vuz150) (Pos vuz500)",fontsize=16,color="black",shape="box"];932 -> 945[label="",style="solid", color="black", weight=3]; 933[label="primMulInt (Pos vuz150) (Neg vuz500)",fontsize=16,color="black",shape="box"];933 -> 946[label="",style="solid", color="black", weight=3]; 934[label="primMulInt (Neg vuz150) (Pos vuz500)",fontsize=16,color="black",shape="box"];934 -> 947[label="",style="solid", color="black", weight=3]; 935[label="primMulInt (Neg vuz150) (Neg vuz500)",fontsize=16,color="black",shape="box"];935 -> 948[label="",style="solid", color="black", weight=3]; 84[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (GT == GT)",fontsize=16,color="black",shape="box"];84 -> 88[label="",style="solid", color="black", weight=3]; 945[label="Pos (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];945 -> 974[label="",style="dashed", color="green", weight=3]; 946[label="Neg (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];946 -> 975[label="",style="dashed", color="green", weight=3]; 947[label="Neg (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];947 -> 976[label="",style="dashed", color="green", weight=3]; 948[label="Pos (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];948 -> 977[label="",style="dashed", color="green", weight=3]; 88[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) True",fontsize=16,color="black",shape="box"];88 -> 92[label="",style="solid", color="black", weight=3]; 974[label="primMulNat vuz150 vuz500",fontsize=16,color="burlywood",shape="triangle"];2106[label="vuz150/Succ vuz1500",fontsize=10,color="white",style="solid",shape="box"];974 -> 2106[label="",style="solid", color="burlywood", weight=9]; 2106 -> 1013[label="",style="solid", color="burlywood", weight=3]; 2107[label="vuz150/Zero",fontsize=10,color="white",style="solid",shape="box"];974 -> 2107[label="",style="solid", color="burlywood", weight=9]; 2107 -> 1014[label="",style="solid", color="burlywood", weight=3]; 975 -> 974[label="",style="dashed", color="red", weight=0]; 975[label="primMulNat vuz150 vuz500",fontsize=16,color="magenta"];975 -> 1015[label="",style="dashed", color="magenta", weight=3]; 976 -> 974[label="",style="dashed", color="red", weight=0]; 976[label="primMulNat vuz150 vuz500",fontsize=16,color="magenta"];976 -> 1016[label="",style="dashed", color="magenta", weight=3]; 977 -> 974[label="",style="dashed", color="red", weight=0]; 977[label="primMulNat vuz150 vuz500",fontsize=16,color="magenta"];977 -> 1017[label="",style="dashed", color="magenta", weight=3]; 977 -> 1018[label="",style="dashed", color="magenta", weight=3]; 92[label="pr2F vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];92 -> 96[label="",style="solid", color="black", weight=3]; 1013[label="primMulNat (Succ vuz1500) vuz500",fontsize=16,color="burlywood",shape="box"];2108[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];1013 -> 2108[label="",style="solid", color="burlywood", weight=9]; 2108 -> 1027[label="",style="solid", color="burlywood", weight=3]; 2109[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];1013 -> 2109[label="",style="solid", color="burlywood", weight=9]; 2109 -> 1028[label="",style="solid", color="burlywood", weight=3]; 1014[label="primMulNat Zero vuz500",fontsize=16,color="burlywood",shape="box"];2110[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];1014 -> 2110[label="",style="solid", color="burlywood", weight=9]; 2110 -> 1029[label="",style="solid", color="burlywood", weight=3]; 2111[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];1014 -> 2111[label="",style="solid", color="burlywood", weight=9]; 2111 -> 1030[label="",style="solid", color="burlywood", weight=3]; 1015[label="vuz500",fontsize=16,color="green",shape="box"];1016[label="vuz150",fontsize=16,color="green",shape="box"];1017[label="vuz500",fontsize=16,color="green",shape="box"];1018[label="vuz150",fontsize=16,color="green",shape="box"];96[label="pr2F4 vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];96 -> 99[label="",style="solid", color="black", weight=3]; 1027[label="primMulNat (Succ vuz1500) (Succ vuz5000)",fontsize=16,color="black",shape="box"];1027 -> 1040[label="",style="solid", color="black", weight=3]; 1028[label="primMulNat (Succ vuz1500) Zero",fontsize=16,color="black",shape="box"];1028 -> 1041[label="",style="solid", color="black", weight=3]; 1029[label="primMulNat Zero (Succ vuz5000)",fontsize=16,color="black",shape="box"];1029 -> 1042[label="",style="solid", color="black", weight=3]; 1030[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1030 -> 1043[label="",style="solid", color="black", weight=3]; 99[label="pr2F3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];99 -> 103[label="",style="solid", color="black", weight=3]; 1040 -> 1052[label="",style="dashed", color="red", weight=0]; 1040[label="primPlusNat (primMulNat vuz1500 (Succ vuz5000)) (Succ vuz5000)",fontsize=16,color="magenta"];1040 -> 1053[label="",style="dashed", color="magenta", weight=3]; 1041[label="Zero",fontsize=16,color="green",shape="box"];1042[label="Zero",fontsize=16,color="green",shape="box"];1043[label="Zero",fontsize=16,color="green",shape="box"];103[label="pr2F3 (primEqInt (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];103 -> 106[label="",style="solid", color="black", weight=3]; 1053 -> 974[label="",style="dashed", color="red", weight=0]; 1053[label="primMulNat vuz1500 (Succ vuz5000)",fontsize=16,color="magenta"];1053 -> 1054[label="",style="dashed", color="magenta", weight=3]; 1053 -> 1055[label="",style="dashed", color="magenta", weight=3]; 1052[label="primPlusNat vuz58 (Succ vuz5000)",fontsize=16,color="burlywood",shape="triangle"];2112[label="vuz58/Succ vuz580",fontsize=10,color="white",style="solid",shape="box"];1052 -> 2112[label="",style="solid", color="burlywood", weight=9]; 2112 -> 1056[label="",style="solid", color="burlywood", weight=3]; 2113[label="vuz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1052 -> 2113[label="",style="solid", color="burlywood", weight=9]; 2113 -> 1057[label="",style="solid", color="burlywood", weight=3]; 106[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (fromInt (Pos (Succ Zero)))) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (fromInt (Pos (Succ Zero)))) vuz3",fontsize=16,color="black",shape="box"];106 -> 108[label="",style="solid", color="black", weight=3]; 1054[label="Succ vuz5000",fontsize=16,color="green",shape="box"];1055[label="vuz1500",fontsize=16,color="green",shape="box"];1056[label="primPlusNat (Succ vuz580) (Succ vuz5000)",fontsize=16,color="black",shape="box"];1056 -> 1062[label="",style="solid", color="black", weight=3]; 1057[label="primPlusNat Zero (Succ vuz5000)",fontsize=16,color="black",shape="box"];1057 -> 1063[label="",style="solid", color="black", weight=3]; 108[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];108 -> 110[label="",style="solid", color="black", weight=3]; 1062[label="Succ (Succ (primPlusNat vuz580 vuz5000))",fontsize=16,color="green",shape="box"];1062 -> 1070[label="",style="dashed", color="green", weight=3]; 1063[label="Succ vuz5000",fontsize=16,color="green",shape="box"];110[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) (Succ Zero)) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) (Succ Zero)) vuz3",fontsize=16,color="black",shape="box"];110 -> 111[label="",style="solid", color="black", weight=3]; 1070[label="primPlusNat vuz580 vuz5000",fontsize=16,color="burlywood",shape="triangle"];2114[label="vuz580/Succ vuz5800",fontsize=10,color="white",style="solid",shape="box"];1070 -> 2114[label="",style="solid", color="burlywood", weight=9]; 2114 -> 1078[label="",style="solid", color="burlywood", weight=3]; 2115[label="vuz580/Zero",fontsize=10,color="white",style="solid",shape="box"];1070 -> 2115[label="",style="solid", color="burlywood", weight=9]; 2115 -> 1079[label="",style="solid", color="burlywood", weight=3]; 111[label="pr2F3 (primEqInt (primMinusNat vuz400 Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat vuz400 Zero) vuz3",fontsize=16,color="burlywood",shape="box"];2116[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];111 -> 2116[label="",style="solid", color="burlywood", weight=9]; 2116 -> 112[label="",style="solid", color="burlywood", weight=3]; 2117[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];111 -> 2117[label="",style="solid", color="burlywood", weight=9]; 2117 -> 113[label="",style="solid", color="burlywood", weight=3]; 1078[label="primPlusNat (Succ vuz5800) vuz5000",fontsize=16,color="burlywood",shape="box"];2118[label="vuz5000/Succ vuz50000",fontsize=10,color="white",style="solid",shape="box"];1078 -> 2118[label="",style="solid", color="burlywood", weight=9]; 2118 -> 1088[label="",style="solid", color="burlywood", weight=3]; 2119[label="vuz5000/Zero",fontsize=10,color="white",style="solid",shape="box"];1078 -> 2119[label="",style="solid", color="burlywood", weight=9]; 2119 -> 1089[label="",style="solid", color="burlywood", weight=3]; 1079[label="primPlusNat Zero vuz5000",fontsize=16,color="burlywood",shape="box"];2120[label="vuz5000/Succ vuz50000",fontsize=10,color="white",style="solid",shape="box"];1079 -> 2120[label="",style="solid", color="burlywood", weight=9]; 2120 -> 1090[label="",style="solid", color="burlywood", weight=3]; 2121[label="vuz5000/Zero",fontsize=10,color="white",style="solid",shape="box"];1079 -> 2121[label="",style="solid", color="burlywood", weight=9]; 2121 -> 1091[label="",style="solid", color="burlywood", weight=3]; 112[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) Zero) vuz3",fontsize=16,color="black",shape="box"];112 -> 114[label="",style="solid", color="black", weight=3]; 113[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero Zero) vuz3",fontsize=16,color="black",shape="box"];113 -> 115[label="",style="solid", color="black", weight=3]; 1088[label="primPlusNat (Succ vuz5800) (Succ vuz50000)",fontsize=16,color="black",shape="box"];1088 -> 1100[label="",style="solid", color="black", weight=3]; 1089[label="primPlusNat (Succ vuz5800) Zero",fontsize=16,color="black",shape="box"];1089 -> 1101[label="",style="solid", color="black", weight=3]; 1090[label="primPlusNat Zero (Succ vuz50000)",fontsize=16,color="black",shape="box"];1090 -> 1102[label="",style="solid", color="black", weight=3]; 1091[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1091 -> 1103[label="",style="solid", color="black", weight=3]; 114[label="pr2F3 (primEqInt (Pos (Succ vuz4000)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];114 -> 116[label="",style="solid", color="black", weight=3]; 115[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];115 -> 117[label="",style="solid", color="black", weight=3]; 1100[label="Succ (Succ (primPlusNat vuz5800 vuz50000))",fontsize=16,color="green",shape="box"];1100 -> 1113[label="",style="dashed", color="green", weight=3]; 1101[label="Succ vuz5800",fontsize=16,color="green",shape="box"];1102[label="Succ vuz50000",fontsize=16,color="green",shape="box"];1103[label="Zero",fontsize=16,color="green",shape="box"];116[label="pr2F3 (primEqInt (Pos (Succ vuz4000)) (Pos Zero)) vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];116 -> 118[label="",style="solid", color="black", weight=3]; 117[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];117 -> 119[label="",style="solid", color="black", weight=3]; 1113 -> 1070[label="",style="dashed", color="red", weight=0]; 1113[label="primPlusNat vuz5800 vuz50000",fontsize=16,color="magenta"];1113 -> 1123[label="",style="dashed", color="magenta", weight=3]; 1113 -> 1124[label="",style="dashed", color="magenta", weight=3]; 118[label="pr2F3 False vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];118 -> 120[label="",style="solid", color="black", weight=3]; 119[label="pr2F3 True vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];119 -> 121[label="",style="solid", color="black", weight=3]; 1123[label="vuz5800",fontsize=16,color="green",shape="box"];1124[label="vuz50000",fontsize=16,color="green",shape="box"];120[label="pr2F0 vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];120 -> 122[label="",style="solid", color="black", weight=3]; 121[label="vuz3",fontsize=16,color="green",shape="box"];122[label="pr2F0G vuz3 vuz3 (Pos (Succ vuz4000))",fontsize=16,color="black",shape="box"];122 -> 123[label="",style="solid", color="black", weight=3]; 123[label="pr2F0G2 vuz3 vuz3 (Pos (Succ vuz4000))",fontsize=16,color="black",shape="box"];123 -> 124[label="",style="solid", color="black", weight=3]; 124[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz4000)) (even (Pos (Succ vuz4000)))",fontsize=16,color="black",shape="box"];124 -> 125[label="",style="solid", color="black", weight=3]; 125[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz4000)) (primEvenInt (Pos (Succ vuz4000)))",fontsize=16,color="black",shape="box"];125 -> 126[label="",style="solid", color="black", weight=3]; 126 -> 159[label="",style="dashed", color="red", weight=0]; 126[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz4000)) (primEvenNat (Succ vuz4000))",fontsize=16,color="magenta"];126 -> 160[label="",style="dashed", color="magenta", weight=3]; 126 -> 161[label="",style="dashed", color="magenta", weight=3]; 126 -> 162[label="",style="dashed", color="magenta", weight=3]; 160[label="Succ vuz4000",fontsize=16,color="green",shape="box"];161[label="vuz4000",fontsize=16,color="green",shape="box"];162[label="vuz3",fontsize=16,color="green",shape="box"];159[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat vuz9)",fontsize=16,color="burlywood",shape="triangle"];2122[label="vuz9/Succ vuz90",fontsize=10,color="white",style="solid",shape="box"];159 -> 2122[label="",style="solid", color="burlywood", weight=9]; 2122 -> 172[label="",style="solid", color="burlywood", weight=3]; 2123[label="vuz9/Zero",fontsize=10,color="white",style="solid",shape="box"];159 -> 2123[label="",style="solid", color="burlywood", weight=9]; 2123 -> 173[label="",style="solid", color="burlywood", weight=3]; 172[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat (Succ vuz90))",fontsize=16,color="burlywood",shape="box"];2124[label="vuz90/Succ vuz900",fontsize=10,color="white",style="solid",shape="box"];172 -> 2124[label="",style="solid", color="burlywood", weight=9]; 2124 -> 174[label="",style="solid", color="burlywood", weight=3]; 2125[label="vuz90/Zero",fontsize=10,color="white",style="solid",shape="box"];172 -> 2125[label="",style="solid", color="burlywood", weight=9]; 2125 -> 175[label="",style="solid", color="burlywood", weight=3]; 173[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];173 -> 176[label="",style="solid", color="black", weight=3]; 174[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat (Succ (Succ vuz900)))",fontsize=16,color="black",shape="box"];174 -> 177[label="",style="solid", color="black", weight=3]; 175[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];175 -> 178[label="",style="solid", color="black", weight=3]; 176[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) True",fontsize=16,color="black",shape="box"];176 -> 179[label="",style="solid", color="black", weight=3]; 177 -> 159[label="",style="dashed", color="red", weight=0]; 177[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat vuz900)",fontsize=16,color="magenta"];177 -> 180[label="",style="dashed", color="magenta", weight=3]; 178[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) False",fontsize=16,color="black",shape="box"];178 -> 181[label="",style="solid", color="black", weight=3]; 179[label="pr2F0G vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];179 -> 182[label="",style="solid", color="black", weight=3]; 180[label="vuz900",fontsize=16,color="green",shape="box"];181[label="pr2F0G0 vuz7 vuz7 (Pos (Succ vuz8)) otherwise",fontsize=16,color="black",shape="box"];181 -> 183[label="",style="solid", color="black", weight=3]; 182[label="pr2F0G2 vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];182 -> 184[label="",style="solid", color="black", weight=3]; 183[label="pr2F0G0 vuz7 vuz7 (Pos (Succ vuz8)) True",fontsize=16,color="black",shape="box"];183 -> 185[label="",style="solid", color="black", weight=3]; 184[label="pr2F0G1 vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];184 -> 186[label="",style="solid", color="black", weight=3]; 185[label="pr2F vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="black",shape="box"];185 -> 187[label="",style="solid", color="black", weight=3]; 186[label="pr2F0G1 vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];186 -> 188[label="",style="solid", color="black", weight=3]; 187[label="pr2F4 vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="black",shape="box"];187 -> 189[label="",style="solid", color="black", weight=3]; 188[label="pr2F0G1 vuz7 (vuz7 * vuz7) (primQuotInt (Pos (Succ vuz8)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz8)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];188 -> 190[label="",style="solid", color="black", weight=3]; 189[label="pr2F3 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="black",shape="box"];189 -> 191[label="",style="solid", color="black", weight=3]; 190 -> 991[label="",style="dashed", color="red", weight=0]; 190[label="pr2F0G1 vuz7 (vuz7 * vuz7) (primQuotInt (Pos (Succ vuz8)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz8)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];190 -> 992[label="",style="dashed", color="magenta", weight=3]; 190 -> 993[label="",style="dashed", color="magenta", weight=3]; 190 -> 994[label="",style="dashed", color="magenta", weight=3]; 191 -> 1922[label="",style="dashed", color="red", weight=0]; 191[label="pr2F3 (primEqInt (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="magenta"];191 -> 1923[label="",style="dashed", color="magenta", weight=3]; 191 -> 1924[label="",style="dashed", color="magenta", weight=3]; 191 -> 1925[label="",style="dashed", color="magenta", weight=3]; 992[label="Succ vuz8",fontsize=16,color="green",shape="box"];993[label="vuz7",fontsize=16,color="green",shape="box"];994[label="vuz7",fontsize=16,color="green",shape="box"];991[label="pr2F0G1 vuz55 (vuz56 * vuz56) (primQuotInt (Pos vuz57) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos vuz57) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];991 -> 1019[label="",style="solid", color="black", weight=3]; 1923[label="vuz8",fontsize=16,color="green",shape="box"];1924[label="vuz7",fontsize=16,color="green",shape="box"];1925[label="vuz7",fontsize=16,color="green",shape="box"];1922[label="pr2F3 (primEqInt (Pos (Succ vuz88) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz89 (Pos (Succ vuz88) - fromInt (Pos (Succ Zero))) (vuz89 * vuz90)",fontsize=16,color="black",shape="triangle"];1922 -> 1944[label="",style="solid", color="black", weight=3]; 1019[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS vuz57 (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS vuz57 (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1019 -> 1031[label="",style="solid", color="black", weight=3]; 1944[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz88)) (fromInt (Pos (Succ Zero)))) (fromInt (Pos Zero))) vuz89 (primMinusInt (Pos (Succ vuz88)) (fromInt (Pos (Succ Zero)))) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1944 -> 1950[label="",style="solid", color="black", weight=3]; 1031[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS vuz57 (Succ (Succ Zero)))) (primEvenNat (primDivNatS vuz57 (Succ (Succ Zero))))",fontsize=16,color="burlywood",shape="box"];2126[label="vuz57/Succ vuz570",fontsize=10,color="white",style="solid",shape="box"];1031 -> 2126[label="",style="solid", color="burlywood", weight=9]; 2126 -> 1044[label="",style="solid", color="burlywood", weight=3]; 2127[label="vuz57/Zero",fontsize=10,color="white",style="solid",shape="box"];1031 -> 2127[label="",style="solid", color="burlywood", weight=9]; 2127 -> 1045[label="",style="solid", color="burlywood", weight=3]; 1950[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz88)) (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz89 (primMinusInt (Pos (Succ vuz88)) (Pos (Succ Zero))) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1950 -> 1956[label="",style="solid", color="black", weight=3]; 1044[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS (Succ vuz570) (Succ (Succ Zero)))) (primEvenNat (primDivNatS (Succ vuz570) (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1044 -> 1058[label="",style="solid", color="black", weight=3]; 1045[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS Zero (Succ (Succ Zero)))) (primEvenNat (primDivNatS Zero (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1045 -> 1059[label="",style="solid", color="black", weight=3]; 1956[label="pr2F3 (primEqInt (primMinusNat (Succ vuz88) (Succ Zero)) (fromInt (Pos Zero))) vuz89 (primMinusNat (Succ vuz88) (Succ Zero)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1956 -> 1957[label="",style="solid", color="black", weight=3]; 1058[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 vuz570 (Succ Zero) (primGEqNatS vuz570 (Succ Zero)))) (primEvenNat (primDivNatS0 vuz570 (Succ Zero) (primGEqNatS vuz570 (Succ Zero))))",fontsize=16,color="burlywood",shape="box"];2128[label="vuz570/Succ vuz5700",fontsize=10,color="white",style="solid",shape="box"];1058 -> 2128[label="",style="solid", color="burlywood", weight=9]; 2128 -> 1064[label="",style="solid", color="burlywood", weight=3]; 2129[label="vuz570/Zero",fontsize=10,color="white",style="solid",shape="box"];1058 -> 2129[label="",style="solid", color="burlywood", weight=9]; 2129 -> 1065[label="",style="solid", color="burlywood", weight=3]; 1059[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos Zero) (primEvenNat Zero)",fontsize=16,color="black",shape="triangle"];1059 -> 1066[label="",style="solid", color="black", weight=3]; 1957[label="pr2F3 (primEqInt (primMinusNat vuz88 Zero) (fromInt (Pos Zero))) vuz89 (primMinusNat vuz88 Zero) (vuz89 * vuz90)",fontsize=16,color="burlywood",shape="box"];2130[label="vuz88/Succ vuz880",fontsize=10,color="white",style="solid",shape="box"];1957 -> 2130[label="",style="solid", color="burlywood", weight=9]; 2130 -> 1958[label="",style="solid", color="burlywood", weight=3]; 2131[label="vuz88/Zero",fontsize=10,color="white",style="solid",shape="box"];1957 -> 2131[label="",style="solid", color="burlywood", weight=9]; 2131 -> 1959[label="",style="solid", color="burlywood", weight=3]; 1064[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS (Succ vuz5700) (Succ Zero)))) (primEvenNat (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS (Succ vuz5700) (Succ Zero))))",fontsize=16,color="black",shape="box"];1064 -> 1071[label="",style="solid", color="black", weight=3]; 1065[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero)))) (primEvenNat (primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero))))",fontsize=16,color="black",shape="box"];1065 -> 1072[label="",style="solid", color="black", weight=3]; 1066[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos Zero) True",fontsize=16,color="black",shape="box"];1066 -> 1073[label="",style="solid", color="black", weight=3]; 1958[label="pr2F3 (primEqInt (primMinusNat (Succ vuz880) Zero) (fromInt (Pos Zero))) vuz89 (primMinusNat (Succ vuz880) Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1958 -> 1960[label="",style="solid", color="black", weight=3]; 1959[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz89 (primMinusNat Zero Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1959 -> 1961[label="",style="solid", color="black", weight=3]; 1071[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS vuz5700 Zero))) (primEvenNat (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS vuz5700 Zero)))",fontsize=16,color="burlywood",shape="box"];2132[label="vuz5700/Succ vuz57000",fontsize=10,color="white",style="solid",shape="box"];1071 -> 2132[label="",style="solid", color="burlywood", weight=9]; 2132 -> 1080[label="",style="solid", color="burlywood", weight=3]; 2133[label="vuz5700/Zero",fontsize=10,color="white",style="solid",shape="box"];1071 -> 2133[label="",style="solid", color="burlywood", weight=9]; 2133 -> 1081[label="",style="solid", color="burlywood", weight=3]; 1072[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 Zero (Succ Zero) False)) (primEvenNat (primDivNatS0 Zero (Succ Zero) False))",fontsize=16,color="black",shape="box"];1072 -> 1082[label="",style="solid", color="black", weight=3]; 1073[label="pr2F0G vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1073 -> 1083[label="",style="solid", color="black", weight=3]; 1960[label="pr2F3 (primEqInt (Pos (Succ vuz880)) (fromInt (Pos Zero))) vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1960 -> 1962[label="",style="solid", color="black", weight=3]; 1961[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz89 (Pos Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1961 -> 1963[label="",style="solid", color="black", weight=3]; 1080[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) (primGEqNatS (Succ vuz57000) Zero))) (primEvenNat (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) (primGEqNatS (Succ vuz57000) Zero)))",fontsize=16,color="black",shape="box"];1080 -> 1092[label="",style="solid", color="black", weight=3]; 1081[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero))) (primEvenNat (primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];1081 -> 1093[label="",style="solid", color="black", weight=3]; 1082 -> 1059[label="",style="dashed", color="red", weight=0]; 1082[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos Zero) (primEvenNat Zero)",fontsize=16,color="magenta"];1083[label="pr2F0G2 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1083 -> 1094[label="",style="solid", color="black", weight=3]; 1962[label="pr2F3 (primEqInt (Pos (Succ vuz880)) (Pos Zero)) vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1962 -> 1964[label="",style="solid", color="black", weight=3]; 1963[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz89 (Pos Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1963 -> 1965[label="",style="solid", color="black", weight=3]; 1092[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) True)) (primEvenNat (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) True))",fontsize=16,color="black",shape="box"];1092 -> 1104[label="",style="solid", color="black", weight=3]; 1093[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ Zero) (Succ Zero) True)) (primEvenNat (primDivNatS0 (Succ Zero) (Succ Zero) True))",fontsize=16,color="black",shape="box"];1093 -> 1105[label="",style="solid", color="black", weight=3]; 1094[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1094 -> 1106[label="",style="solid", color="black", weight=3]; 1964[label="pr2F3 False vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1964 -> 1966[label="",style="solid", color="black", weight=3]; 1965[label="pr2F3 True vuz89 (Pos Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1965 -> 1967[label="",style="solid", color="black", weight=3]; 1104 -> 1318[label="",style="dashed", color="red", weight=0]; 1104[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (Succ (primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero))))) (primEvenNat (Succ (primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1104 -> 1319[label="",style="dashed", color="magenta", weight=3]; 1104 -> 1320[label="",style="dashed", color="magenta", weight=3]; 1104 -> 1321[label="",style="dashed", color="magenta", weight=3]; 1104 -> 1322[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1318[label="",style="dashed", color="red", weight=0]; 1105[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))))) (primEvenNat (Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1105 -> 1323[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1324[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1325[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1326[label="",style="dashed", color="magenta", weight=3]; 1106[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1106 -> 1116[label="",style="solid", color="black", weight=3]; 1966[label="pr2F0 vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1966 -> 1968[label="",style="solid", color="black", weight=3]; 1967[label="vuz89 * vuz90",fontsize=16,color="blue",shape="box"];2134[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2134[label="",style="solid", color="blue", weight=9]; 2134 -> 1969[label="",style="solid", color="blue", weight=3]; 2135[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2135[label="",style="solid", color="blue", weight=9]; 2135 -> 1970[label="",style="solid", color="blue", weight=3]; 2136[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2136[label="",style="solid", color="blue", weight=9]; 2136 -> 1971[label="",style="solid", color="blue", weight=3]; 2137[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2137[label="",style="solid", color="blue", weight=9]; 2137 -> 1972[label="",style="solid", color="blue", weight=3]; 2138[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2138[label="",style="solid", color="blue", weight=9]; 2138 -> 1973[label="",style="solid", color="blue", weight=3]; 1319[label="Succ (primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1319 -> 1343[label="",style="dashed", color="green", weight=3]; 1320[label="primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];1320 -> 1344[label="",style="solid", color="black", weight=3]; 1321[label="vuz55",fontsize=16,color="green",shape="box"];1322[label="vuz56",fontsize=16,color="green",shape="box"];1318[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat vuz71)",fontsize=16,color="burlywood",shape="triangle"];2139[label="vuz71/Succ vuz710",fontsize=10,color="white",style="solid",shape="box"];1318 -> 2139[label="",style="solid", color="burlywood", weight=9]; 2139 -> 1345[label="",style="solid", color="burlywood", weight=3]; 2140[label="vuz71/Zero",fontsize=10,color="white",style="solid",shape="box"];1318 -> 2140[label="",style="solid", color="burlywood", weight=9]; 2140 -> 1346[label="",style="solid", color="burlywood", weight=3]; 1323[label="Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1323 -> 1347[label="",style="dashed", color="green", weight=3]; 1324[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];1324 -> 1348[label="",style="solid", color="black", weight=3]; 1325[label="vuz55",fontsize=16,color="green",shape="box"];1326[label="vuz56",fontsize=16,color="green",shape="box"];1116[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1116 -> 1127[label="",style="solid", color="black", weight=3]; 1968[label="pr2F0G (vuz89 * vuz90) vuz89 (Pos (Succ vuz880))",fontsize=16,color="black",shape="box"];1968 -> 1974[label="",style="solid", color="black", weight=3]; 1969 -> 878[label="",style="dashed", color="red", weight=0]; 1969[label="vuz89 * vuz90",fontsize=16,color="magenta"];1969 -> 1975[label="",style="dashed", color="magenta", weight=3]; 1969 -> 1976[label="",style="dashed", color="magenta", weight=3]; 1970 -> 894[label="",style="dashed", color="red", weight=0]; 1970[label="vuz89 * vuz90",fontsize=16,color="magenta"];1970 -> 1977[label="",style="dashed", color="magenta", weight=3]; 1970 -> 1978[label="",style="dashed", color="magenta", weight=3]; 1971 -> 914[label="",style="dashed", color="red", weight=0]; 1971[label="vuz89 * vuz90",fontsize=16,color="magenta"];1971 -> 1979[label="",style="dashed", color="magenta", weight=3]; 1971 -> 1980[label="",style="dashed", color="magenta", weight=3]; 1972 -> 928[label="",style="dashed", color="red", weight=0]; 1972[label="vuz89 * vuz90",fontsize=16,color="magenta"];1972 -> 1981[label="",style="dashed", color="magenta", weight=3]; 1972 -> 1982[label="",style="dashed", color="magenta", weight=3]; 1973 -> 941[label="",style="dashed", color="red", weight=0]; 1973[label="vuz89 * vuz90",fontsize=16,color="magenta"];1973 -> 1983[label="",style="dashed", color="magenta", weight=3]; 1973 -> 1984[label="",style="dashed", color="magenta", weight=3]; 1343 -> 1320[label="",style="dashed", color="red", weight=0]; 1343[label="primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1344[label="primDivNatS (primMinusNatS (Succ vuz57000) Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1344 -> 1351[label="",style="solid", color="black", weight=3]; 1345[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat (Succ vuz710))",fontsize=16,color="burlywood",shape="box"];2141[label="vuz710/Succ vuz7100",fontsize=10,color="white",style="solid",shape="box"];1345 -> 2141[label="",style="solid", color="burlywood", weight=9]; 2141 -> 1352[label="",style="solid", color="burlywood", weight=3]; 2142[label="vuz710/Zero",fontsize=10,color="white",style="solid",shape="box"];1345 -> 2142[label="",style="solid", color="burlywood", weight=9]; 2142 -> 1353[label="",style="solid", color="burlywood", weight=3]; 1346[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];1346 -> 1354[label="",style="solid", color="black", weight=3]; 1347 -> 1324[label="",style="dashed", color="red", weight=0]; 1347[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1348[label="primDivNatS (primMinusNatS Zero Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1348 -> 1355[label="",style="solid", color="black", weight=3]; 1127 -> 991[label="",style="dashed", color="red", weight=0]; 1127[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1127 -> 1143[label="",style="dashed", color="magenta", weight=3]; 1127 -> 1144[label="",style="dashed", color="magenta", weight=3]; 1974[label="pr2F0G2 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880))",fontsize=16,color="black",shape="box"];1974 -> 1985[label="",style="solid", color="black", weight=3]; 1975[label="vuz89",fontsize=16,color="green",shape="box"];1976[label="vuz90",fontsize=16,color="green",shape="box"];878[label="vuz15 * vuz49",fontsize=16,color="black",shape="triangle"];878 -> 883[label="",style="solid", color="black", weight=3]; 1977[label="vuz90",fontsize=16,color="green",shape="box"];1978[label="vuz89",fontsize=16,color="green",shape="box"];1979[label="vuz90",fontsize=16,color="green",shape="box"];1980[label="vuz89",fontsize=16,color="green",shape="box"];914[label="vuz15 * vuz51",fontsize=16,color="black",shape="triangle"];914 -> 920[label="",style="solid", color="black", weight=3]; 1981[label="vuz89",fontsize=16,color="green",shape="box"];1982[label="vuz90",fontsize=16,color="green",shape="box"];928[label="vuz15 * vuz52",fontsize=16,color="black",shape="triangle"];928 -> 936[label="",style="solid", color="black", weight=3]; 1983[label="vuz90",fontsize=16,color="green",shape="box"];1984[label="vuz89",fontsize=16,color="green",shape="box"];941[label="vuz15 * vuz53",fontsize=16,color="black",shape="triangle"];941 -> 949[label="",style="solid", color="black", weight=3]; 1351[label="primDivNatS (Succ vuz57000) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1351 -> 1358[label="",style="solid", color="black", weight=3]; 1352[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat (Succ (Succ vuz7100)))",fontsize=16,color="black",shape="box"];1352 -> 1359[label="",style="solid", color="black", weight=3]; 1353[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];1353 -> 1360[label="",style="solid", color="black", weight=3]; 1354[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) True",fontsize=16,color="black",shape="box"];1354 -> 1361[label="",style="solid", color="black", weight=3]; 1355[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1355 -> 1362[label="",style="solid", color="black", weight=3]; 1143[label="Zero",fontsize=16,color="green",shape="box"];1144[label="vuz56 * vuz56",fontsize=16,color="blue",shape="box"];2143[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2143[label="",style="solid", color="blue", weight=9]; 2143 -> 1150[label="",style="solid", color="blue", weight=3]; 2144[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2144[label="",style="solid", color="blue", weight=9]; 2144 -> 1151[label="",style="solid", color="blue", weight=3]; 2145[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2145[label="",style="solid", color="blue", weight=9]; 2145 -> 1152[label="",style="solid", color="blue", weight=3]; 2146[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2146[label="",style="solid", color="blue", weight=9]; 2146 -> 1153[label="",style="solid", color="blue", weight=3]; 2147[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2147[label="",style="solid", color="blue", weight=9]; 2147 -> 1154[label="",style="solid", color="blue", weight=3]; 1985[label="pr2F0G1 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880)) (even (Pos (Succ vuz880)))",fontsize=16,color="black",shape="box"];1985 -> 1986[label="",style="solid", color="black", weight=3]; 883[label="error []",fontsize=16,color="red",shape="box"];920[label="error []",fontsize=16,color="red",shape="box"];936[label="primMulFloat vuz15 vuz52",fontsize=16,color="burlywood",shape="box"];2148[label="vuz15/Float vuz150 vuz151",fontsize=10,color="white",style="solid",shape="box"];936 -> 2148[label="",style="solid", color="burlywood", weight=9]; 2148 -> 950[label="",style="solid", color="burlywood", weight=3]; 949[label="error []",fontsize=16,color="red",shape="box"];1358[label="primDivNatS0 vuz57000 (Succ Zero) (primGEqNatS vuz57000 (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2149[label="vuz57000/Succ vuz570000",fontsize=10,color="white",style="solid",shape="box"];1358 -> 2149[label="",style="solid", color="burlywood", weight=9]; 2149 -> 1365[label="",style="solid", color="burlywood", weight=3]; 2150[label="vuz57000/Zero",fontsize=10,color="white",style="solid",shape="box"];1358 -> 2150[label="",style="solid", color="burlywood", weight=9]; 2150 -> 1366[label="",style="solid", color="burlywood", weight=3]; 1359 -> 1318[label="",style="dashed", color="red", weight=0]; 1359[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat vuz7100)",fontsize=16,color="magenta"];1359 -> 1367[label="",style="dashed", color="magenta", weight=3]; 1360[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) False",fontsize=16,color="black",shape="box"];1360 -> 1368[label="",style="solid", color="black", weight=3]; 1361[label="pr2F0G vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1361 -> 1369[label="",style="solid", color="black", weight=3]; 1362[label="Zero",fontsize=16,color="green",shape="box"];1150 -> 229[label="",style="dashed", color="red", weight=0]; 1150[label="vuz56 * vuz56",fontsize=16,color="magenta"];1150 -> 1161[label="",style="dashed", color="magenta", weight=3]; 1151 -> 230[label="",style="dashed", color="red", weight=0]; 1151[label="vuz56 * vuz56",fontsize=16,color="magenta"];1151 -> 1162[label="",style="dashed", color="magenta", weight=3]; 1152 -> 231[label="",style="dashed", color="red", weight=0]; 1152[label="vuz56 * vuz56",fontsize=16,color="magenta"];1152 -> 1163[label="",style="dashed", color="magenta", weight=3]; 1153 -> 232[label="",style="dashed", color="red", weight=0]; 1153[label="vuz56 * vuz56",fontsize=16,color="magenta"];1153 -> 1164[label="",style="dashed", color="magenta", weight=3]; 1154 -> 233[label="",style="dashed", color="red", weight=0]; 1154[label="vuz56 * vuz56",fontsize=16,color="magenta"];1154 -> 1165[label="",style="dashed", color="magenta", weight=3]; 1986[label="pr2F0G1 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880)) (primEvenInt (Pos (Succ vuz880)))",fontsize=16,color="black",shape="box"];1986 -> 1987[label="",style="solid", color="black", weight=3]; 950[label="primMulFloat (Float vuz150 vuz151) vuz52",fontsize=16,color="burlywood",shape="box"];2151[label="vuz52/Float vuz520 vuz521",fontsize=10,color="white",style="solid",shape="box"];950 -> 2151[label="",style="solid", color="burlywood", weight=9]; 2151 -> 978[label="",style="solid", color="burlywood", weight=3]; 1365[label="primDivNatS0 (Succ vuz570000) (Succ Zero) (primGEqNatS (Succ vuz570000) (Succ Zero))",fontsize=16,color="black",shape="box"];1365 -> 1372[label="",style="solid", color="black", weight=3]; 1366[label="primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero))",fontsize=16,color="black",shape="box"];1366 -> 1373[label="",style="solid", color="black", weight=3]; 1367[label="vuz7100",fontsize=16,color="green",shape="box"];1368[label="pr2F0G0 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) otherwise",fontsize=16,color="black",shape="box"];1368 -> 1374[label="",style="solid", color="black", weight=3]; 1369[label="pr2F0G2 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1369 -> 1375[label="",style="solid", color="black", weight=3]; 1161[label="vuz56",fontsize=16,color="green",shape="box"];229 -> 878[label="",style="dashed", color="red", weight=0]; 229[label="vuz7 * vuz7",fontsize=16,color="magenta"];229 -> 879[label="",style="dashed", color="magenta", weight=3]; 229 -> 880[label="",style="dashed", color="magenta", weight=3]; 1162[label="vuz56",fontsize=16,color="green",shape="box"];230 -> 894[label="",style="dashed", color="red", weight=0]; 230[label="vuz7 * vuz7",fontsize=16,color="magenta"];230 -> 899[label="",style="dashed", color="magenta", weight=3]; 230 -> 900[label="",style="dashed", color="magenta", weight=3]; 1163[label="vuz56",fontsize=16,color="green",shape="box"];231 -> 914[label="",style="dashed", color="red", weight=0]; 231[label="vuz7 * vuz7",fontsize=16,color="magenta"];231 -> 915[label="",style="dashed", color="magenta", weight=3]; 231 -> 916[label="",style="dashed", color="magenta", weight=3]; 1164[label="vuz56",fontsize=16,color="green",shape="box"];232 -> 928[label="",style="dashed", color="red", weight=0]; 232[label="vuz7 * vuz7",fontsize=16,color="magenta"];232 -> 929[label="",style="dashed", color="magenta", weight=3]; 232 -> 930[label="",style="dashed", color="magenta", weight=3]; 1165[label="vuz56",fontsize=16,color="green",shape="box"];233 -> 941[label="",style="dashed", color="red", weight=0]; 233[label="vuz7 * vuz7",fontsize=16,color="magenta"];233 -> 942[label="",style="dashed", color="magenta", weight=3]; 233 -> 943[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2020[label="",style="dashed", color="red", weight=0]; 1987[label="pr2F0G1 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880)) (primEvenNat (Succ vuz880))",fontsize=16,color="magenta"];1987 -> 2021[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2022[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2023[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2024[label="",style="dashed", color="magenta", weight=3]; 978[label="primMulFloat (Float vuz150 vuz151) (Float vuz520 vuz521)",fontsize=16,color="black",shape="box"];978 -> 1020[label="",style="solid", color="black", weight=3]; 1372[label="primDivNatS0 (Succ vuz570000) (Succ Zero) (primGEqNatS vuz570000 Zero)",fontsize=16,color="burlywood",shape="box"];2152[label="vuz570000/Succ vuz5700000",fontsize=10,color="white",style="solid",shape="box"];1372 -> 2152[label="",style="solid", color="burlywood", weight=9]; 2152 -> 1382[label="",style="solid", color="burlywood", weight=3]; 2153[label="vuz570000/Zero",fontsize=10,color="white",style="solid",shape="box"];1372 -> 2153[label="",style="solid", color="burlywood", weight=9]; 2153 -> 1383[label="",style="solid", color="burlywood", weight=3]; 1373[label="primDivNatS0 Zero (Succ Zero) False",fontsize=16,color="black",shape="box"];1373 -> 1384[label="",style="solid", color="black", weight=3]; 1374[label="pr2F0G0 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) True",fontsize=16,color="black",shape="box"];1374 -> 1385[label="",style="solid", color="black", weight=3]; 1375[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1375 -> 1386[label="",style="solid", color="black", weight=3]; 879[label="vuz7",fontsize=16,color="green",shape="box"];880[label="vuz7",fontsize=16,color="green",shape="box"];899[label="vuz7",fontsize=16,color="green",shape="box"];900[label="vuz7",fontsize=16,color="green",shape="box"];915[label="vuz7",fontsize=16,color="green",shape="box"];916[label="vuz7",fontsize=16,color="green",shape="box"];929[label="vuz7",fontsize=16,color="green",shape="box"];930[label="vuz7",fontsize=16,color="green",shape="box"];942[label="vuz7",fontsize=16,color="green",shape="box"];943[label="vuz7",fontsize=16,color="green",shape="box"];2021[label="Succ vuz880",fontsize=16,color="green",shape="box"];2022[label="vuz89",fontsize=16,color="green",shape="box"];2023[label="vuz90",fontsize=16,color="green",shape="box"];2024[label="vuz880",fontsize=16,color="green",shape="box"];2020[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat vuz95)",fontsize=16,color="burlywood",shape="triangle"];2154[label="vuz95/Succ vuz950",fontsize=10,color="white",style="solid",shape="box"];2020 -> 2154[label="",style="solid", color="burlywood", weight=9]; 2154 -> 2037[label="",style="solid", color="burlywood", weight=3]; 2155[label="vuz95/Zero",fontsize=10,color="white",style="solid",shape="box"];2020 -> 2155[label="",style="solid", color="burlywood", weight=9]; 2155 -> 2038[label="",style="solid", color="burlywood", weight=3]; 1020[label="Float (vuz150 * vuz520) (vuz151 * vuz521)",fontsize=16,color="green",shape="box"];1020 -> 1032[label="",style="dashed", color="green", weight=3]; 1020 -> 1033[label="",style="dashed", color="green", weight=3]; 1382[label="primDivNatS0 (Succ (Succ vuz5700000)) (Succ Zero) (primGEqNatS (Succ vuz5700000) Zero)",fontsize=16,color="black",shape="box"];1382 -> 1398[label="",style="solid", color="black", weight=3]; 1383[label="primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1383 -> 1399[label="",style="solid", color="black", weight=3]; 1384[label="Zero",fontsize=16,color="green",shape="box"];1385[label="pr2F (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="black",shape="box"];1385 -> 1400[label="",style="solid", color="black", weight=3]; 1386[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1386 -> 1401[label="",style="solid", color="black", weight=3]; 2037[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat (Succ vuz950))",fontsize=16,color="burlywood",shape="box"];2156[label="vuz950/Succ vuz9500",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2156[label="",style="solid", color="burlywood", weight=9]; 2156 -> 2039[label="",style="solid", color="burlywood", weight=3]; 2157[label="vuz950/Zero",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2157[label="",style="solid", color="burlywood", weight=9]; 2157 -> 2040[label="",style="solid", color="burlywood", weight=3]; 2038[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];2038 -> 2041[label="",style="solid", color="black", weight=3]; 1032 -> 894[label="",style="dashed", color="red", weight=0]; 1032[label="vuz150 * vuz520",fontsize=16,color="magenta"];1032 -> 1046[label="",style="dashed", color="magenta", weight=3]; 1032 -> 1047[label="",style="dashed", color="magenta", weight=3]; 1033 -> 894[label="",style="dashed", color="red", weight=0]; 1033[label="vuz151 * vuz521",fontsize=16,color="magenta"];1033 -> 1048[label="",style="dashed", color="magenta", weight=3]; 1033 -> 1049[label="",style="dashed", color="magenta", weight=3]; 1398[label="primDivNatS0 (Succ (Succ vuz5700000)) (Succ Zero) True",fontsize=16,color="black",shape="box"];1398 -> 1413[label="",style="solid", color="black", weight=3]; 1399[label="primDivNatS0 (Succ Zero) (Succ Zero) True",fontsize=16,color="black",shape="box"];1399 -> 1414[label="",style="solid", color="black", weight=3]; 1400[label="pr2F4 (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="black",shape="box"];1400 -> 1415[label="",style="solid", color="black", weight=3]; 1401[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (primQuotInt (Pos (Succ vuz70)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz70)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1401 -> 1416[label="",style="solid", color="black", weight=3]; 2039[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat (Succ (Succ vuz9500)))",fontsize=16,color="black",shape="box"];2039 -> 2042[label="",style="solid", color="black", weight=3]; 2040[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];2040 -> 2043[label="",style="solid", color="black", weight=3]; 2041[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) True",fontsize=16,color="black",shape="box"];2041 -> 2044[label="",style="solid", color="black", weight=3]; 1046[label="vuz520",fontsize=16,color="green",shape="box"];1047[label="vuz150",fontsize=16,color="green",shape="box"];1048[label="vuz521",fontsize=16,color="green",shape="box"];1049[label="vuz151",fontsize=16,color="green",shape="box"];1413[label="Succ (primDivNatS (primMinusNatS (Succ (Succ vuz5700000)) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1413 -> 1423[label="",style="dashed", color="green", weight=3]; 1414[label="Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1414 -> 1424[label="",style="dashed", color="green", weight=3]; 1415[label="pr2F3 (Pos (Succ vuz70) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="black",shape="box"];1415 -> 1425[label="",style="solid", color="black", weight=3]; 1416 -> 991[label="",style="dashed", color="red", weight=0]; 1416[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (primQuotInt (Pos (Succ vuz70)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz70)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1416 -> 1426[label="",style="dashed", color="magenta", weight=3]; 1416 -> 1427[label="",style="dashed", color="magenta", weight=3]; 1416 -> 1428[label="",style="dashed", color="magenta", weight=3]; 2042 -> 2020[label="",style="dashed", color="red", weight=0]; 2042[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat vuz9500)",fontsize=16,color="magenta"];2042 -> 2045[label="",style="dashed", color="magenta", weight=3]; 2043[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) False",fontsize=16,color="black",shape="box"];2043 -> 2046[label="",style="solid", color="black", weight=3]; 2044[label="pr2F0G (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];2044 -> 2047[label="",style="solid", color="black", weight=3]; 1423 -> 1320[label="",style="dashed", color="red", weight=0]; 1423[label="primDivNatS (primMinusNatS (Succ (Succ vuz5700000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1423 -> 1430[label="",style="dashed", color="magenta", weight=3]; 1424 -> 1324[label="",style="dashed", color="red", weight=0]; 1424[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1425 -> 1922[label="",style="dashed", color="red", weight=0]; 1425[label="pr2F3 (primEqInt (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="magenta"];1425 -> 1926[label="",style="dashed", color="magenta", weight=3]; 1425 -> 1927[label="",style="dashed", color="magenta", weight=3]; 1425 -> 1928[label="",style="dashed", color="magenta", weight=3]; 1426[label="Succ vuz70",fontsize=16,color="green",shape="box"];1427[label="vuz68",fontsize=16,color="green",shape="box"];1428[label="vuz69 * vuz69",fontsize=16,color="blue",shape="box"];2158[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2158[label="",style="solid", color="blue", weight=9]; 2158 -> 1432[label="",style="solid", color="blue", weight=3]; 2159[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2159[label="",style="solid", color="blue", weight=9]; 2159 -> 1433[label="",style="solid", color="blue", weight=3]; 2160[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2160[label="",style="solid", color="blue", weight=9]; 2160 -> 1434[label="",style="solid", color="blue", weight=3]; 2161[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2161[label="",style="solid", color="blue", weight=9]; 2161 -> 1435[label="",style="solid", color="blue", weight=3]; 2162[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2162[label="",style="solid", color="blue", weight=9]; 2162 -> 1436[label="",style="solid", color="blue", weight=3]; 2045[label="vuz9500",fontsize=16,color="green",shape="box"];2046[label="pr2F0G0 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) otherwise",fontsize=16,color="black",shape="box"];2046 -> 2048[label="",style="solid", color="black", weight=3]; 2047[label="pr2F0G2 (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];2047 -> 2049[label="",style="solid", color="black", weight=3]; 1430[label="vuz5700000",fontsize=16,color="green",shape="box"];1926[label="vuz70",fontsize=16,color="green",shape="box"];1927[label="vuz69 * vuz69",fontsize=16,color="blue",shape="box"];2163[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2163[label="",style="solid", color="blue", weight=9]; 2163 -> 1945[label="",style="solid", color="blue", weight=3]; 2164[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2164[label="",style="solid", color="blue", weight=9]; 2164 -> 1946[label="",style="solid", color="blue", weight=3]; 2165[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2165[label="",style="solid", color="blue", weight=9]; 2165 -> 1947[label="",style="solid", color="blue", weight=3]; 2166[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2166[label="",style="solid", color="blue", weight=9]; 2166 -> 1948[label="",style="solid", color="blue", weight=3]; 2167[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2167[label="",style="solid", color="blue", weight=9]; 2167 -> 1949[label="",style="solid", color="blue", weight=3]; 1928[label="vuz68",fontsize=16,color="green",shape="box"];1432 -> 229[label="",style="dashed", color="red", weight=0]; 1432[label="vuz69 * vuz69",fontsize=16,color="magenta"];1432 -> 1440[label="",style="dashed", color="magenta", weight=3]; 1433 -> 230[label="",style="dashed", color="red", weight=0]; 1433[label="vuz69 * vuz69",fontsize=16,color="magenta"];1433 -> 1441[label="",style="dashed", color="magenta", weight=3]; 1434 -> 231[label="",style="dashed", color="red", weight=0]; 1434[label="vuz69 * vuz69",fontsize=16,color="magenta"];1434 -> 1442[label="",style="dashed", color="magenta", weight=3]; 1435 -> 232[label="",style="dashed", color="red", weight=0]; 1435[label="vuz69 * vuz69",fontsize=16,color="magenta"];1435 -> 1443[label="",style="dashed", color="magenta", weight=3]; 1436 -> 233[label="",style="dashed", color="red", weight=0]; 1436[label="vuz69 * vuz69",fontsize=16,color="magenta"];1436 -> 1444[label="",style="dashed", color="magenta", weight=3]; 2048[label="pr2F0G0 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) True",fontsize=16,color="black",shape="box"];2048 -> 2050[label="",style="solid", color="black", weight=3]; 2049[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];2049 -> 2051[label="",style="solid", color="black", weight=3]; 1945 -> 229[label="",style="dashed", color="red", weight=0]; 1945[label="vuz69 * vuz69",fontsize=16,color="magenta"];1945 -> 1951[label="",style="dashed", color="magenta", weight=3]; 1946 -> 230[label="",style="dashed", color="red", weight=0]; 1946[label="vuz69 * vuz69",fontsize=16,color="magenta"];1946 -> 1952[label="",style="dashed", color="magenta", weight=3]; 1947 -> 231[label="",style="dashed", color="red", weight=0]; 1947[label="vuz69 * vuz69",fontsize=16,color="magenta"];1947 -> 1953[label="",style="dashed", color="magenta", weight=3]; 1948 -> 232[label="",style="dashed", color="red", weight=0]; 1948[label="vuz69 * vuz69",fontsize=16,color="magenta"];1948 -> 1954[label="",style="dashed", color="magenta", weight=3]; 1949 -> 233[label="",style="dashed", color="red", weight=0]; 1949[label="vuz69 * vuz69",fontsize=16,color="magenta"];1949 -> 1955[label="",style="dashed", color="magenta", weight=3]; 1440[label="vuz69",fontsize=16,color="green",shape="box"];1441[label="vuz69",fontsize=16,color="green",shape="box"];1442[label="vuz69",fontsize=16,color="green",shape="box"];1443[label="vuz69",fontsize=16,color="green",shape="box"];1444[label="vuz69",fontsize=16,color="green",shape="box"];2050[label="pr2F vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="black",shape="box"];2050 -> 2052[label="",style="solid", color="black", weight=3]; 2051[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];2051 -> 2053[label="",style="solid", color="black", weight=3]; 1951[label="vuz69",fontsize=16,color="green",shape="box"];1952[label="vuz69",fontsize=16,color="green",shape="box"];1953[label="vuz69",fontsize=16,color="green",shape="box"];1954[label="vuz69",fontsize=16,color="green",shape="box"];1955[label="vuz69",fontsize=16,color="green",shape="box"];2052[label="pr2F4 vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="black",shape="box"];2052 -> 2054[label="",style="solid", color="black", weight=3]; 2053[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (primQuotInt (Pos (Succ vuz94)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz94)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];2053 -> 2055[label="",style="solid", color="black", weight=3]; 2054[label="pr2F3 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="black",shape="box"];2054 -> 2056[label="",style="solid", color="black", weight=3]; 2055 -> 991[label="",style="dashed", color="red", weight=0]; 2055[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (primQuotInt (Pos (Succ vuz94)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz94)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];2055 -> 2057[label="",style="dashed", color="magenta", weight=3]; 2055 -> 2058[label="",style="dashed", color="magenta", weight=3]; 2055 -> 2059[label="",style="dashed", color="magenta", weight=3]; 2056 -> 1922[label="",style="dashed", color="red", weight=0]; 2056[label="pr2F3 (primEqInt (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="magenta"];2056 -> 2060[label="",style="dashed", color="magenta", weight=3]; 2056 -> 2061[label="",style="dashed", color="magenta", weight=3]; 2056 -> 2062[label="",style="dashed", color="magenta", weight=3]; 2057[label="Succ vuz94",fontsize=16,color="green",shape="box"];2058[label="vuz92 * vuz93",fontsize=16,color="blue",shape="box"];2168[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2168[label="",style="solid", color="blue", weight=9]; 2168 -> 2063[label="",style="solid", color="blue", weight=3]; 2169[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2169[label="",style="solid", color="blue", weight=9]; 2169 -> 2064[label="",style="solid", color="blue", weight=3]; 2170[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2170[label="",style="solid", color="blue", weight=9]; 2170 -> 2065[label="",style="solid", color="blue", weight=3]; 2171[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2171[label="",style="solid", color="blue", weight=9]; 2171 -> 2066[label="",style="solid", color="blue", weight=3]; 2172[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2172[label="",style="solid", color="blue", weight=9]; 2172 -> 2067[label="",style="solid", color="blue", weight=3]; 2059[label="vuz92",fontsize=16,color="green",shape="box"];2060[label="vuz94",fontsize=16,color="green",shape="box"];2061[label="vuz92",fontsize=16,color="green",shape="box"];2062[label="vuz92 * vuz93",fontsize=16,color="blue",shape="box"];2173[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2173[label="",style="solid", color="blue", weight=9]; 2173 -> 2068[label="",style="solid", color="blue", weight=3]; 2174[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2174[label="",style="solid", color="blue", weight=9]; 2174 -> 2069[label="",style="solid", color="blue", weight=3]; 2175[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2175[label="",style="solid", color="blue", weight=9]; 2175 -> 2070[label="",style="solid", color="blue", weight=3]; 2176[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2176[label="",style="solid", color="blue", weight=9]; 2176 -> 2071[label="",style="solid", color="blue", weight=3]; 2177[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2177[label="",style="solid", color="blue", weight=9]; 2177 -> 2072[label="",style="solid", color="blue", weight=3]; 2063 -> 878[label="",style="dashed", color="red", weight=0]; 2063[label="vuz92 * vuz93",fontsize=16,color="magenta"];2063 -> 2073[label="",style="dashed", color="magenta", weight=3]; 2063 -> 2074[label="",style="dashed", color="magenta", weight=3]; 2064 -> 894[label="",style="dashed", color="red", weight=0]; 2064[label="vuz92 * vuz93",fontsize=16,color="magenta"];2064 -> 2075[label="",style="dashed", color="magenta", weight=3]; 2064 -> 2076[label="",style="dashed", color="magenta", weight=3]; 2065 -> 914[label="",style="dashed", color="red", weight=0]; 2065[label="vuz92 * vuz93",fontsize=16,color="magenta"];2065 -> 2077[label="",style="dashed", color="magenta", weight=3]; 2065 -> 2078[label="",style="dashed", color="magenta", weight=3]; 2066 -> 928[label="",style="dashed", color="red", weight=0]; 2066[label="vuz92 * vuz93",fontsize=16,color="magenta"];2066 -> 2079[label="",style="dashed", color="magenta", weight=3]; 2066 -> 2080[label="",style="dashed", color="magenta", weight=3]; 2067 -> 941[label="",style="dashed", color="red", weight=0]; 2067[label="vuz92 * vuz93",fontsize=16,color="magenta"];2067 -> 2081[label="",style="dashed", color="magenta", weight=3]; 2067 -> 2082[label="",style="dashed", color="magenta", weight=3]; 2068 -> 878[label="",style="dashed", color="red", weight=0]; 2068[label="vuz92 * vuz93",fontsize=16,color="magenta"];2068 -> 2083[label="",style="dashed", color="magenta", weight=3]; 2068 -> 2084[label="",style="dashed", color="magenta", weight=3]; 2069 -> 894[label="",style="dashed", color="red", weight=0]; 2069[label="vuz92 * vuz93",fontsize=16,color="magenta"];2069 -> 2085[label="",style="dashed", color="magenta", weight=3]; 2069 -> 2086[label="",style="dashed", color="magenta", weight=3]; 2070 -> 914[label="",style="dashed", color="red", weight=0]; 2070[label="vuz92 * vuz93",fontsize=16,color="magenta"];2070 -> 2087[label="",style="dashed", color="magenta", weight=3]; 2070 -> 2088[label="",style="dashed", color="magenta", weight=3]; 2071 -> 928[label="",style="dashed", color="red", weight=0]; 2071[label="vuz92 * vuz93",fontsize=16,color="magenta"];2071 -> 2089[label="",style="dashed", color="magenta", weight=3]; 2071 -> 2090[label="",style="dashed", color="magenta", weight=3]; 2072 -> 941[label="",style="dashed", color="red", weight=0]; 2072[label="vuz92 * vuz93",fontsize=16,color="magenta"];2072 -> 2091[label="",style="dashed", color="magenta", weight=3]; 2072 -> 2092[label="",style="dashed", color="magenta", weight=3]; 2073[label="vuz92",fontsize=16,color="green",shape="box"];2074[label="vuz93",fontsize=16,color="green",shape="box"];2075[label="vuz93",fontsize=16,color="green",shape="box"];2076[label="vuz92",fontsize=16,color="green",shape="box"];2077[label="vuz93",fontsize=16,color="green",shape="box"];2078[label="vuz92",fontsize=16,color="green",shape="box"];2079[label="vuz92",fontsize=16,color="green",shape="box"];2080[label="vuz93",fontsize=16,color="green",shape="box"];2081[label="vuz93",fontsize=16,color="green",shape="box"];2082[label="vuz92",fontsize=16,color="green",shape="box"];2083[label="vuz92",fontsize=16,color="green",shape="box"];2084[label="vuz93",fontsize=16,color="green",shape="box"];2085[label="vuz93",fontsize=16,color="green",shape="box"];2086[label="vuz92",fontsize=16,color="green",shape="box"];2087[label="vuz93",fontsize=16,color="green",shape="box"];2088[label="vuz92",fontsize=16,color="green",shape="box"];2089[label="vuz92",fontsize=16,color="green",shape="box"];2090[label="vuz93",fontsize=16,color="green",shape="box"];2091[label="vuz93",fontsize=16,color="green",shape="box"];2092[label="vuz92",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F3(Succ(vuz880), vuz89, vuz90, ba) -> new_pr2F0G1(vuz89, vuz90, vuz880, Succ(vuz880), ba) new_pr2F0G11(vuz68, vuz69, vuz70, Succ(Zero), bc) -> new_pr2F3(vuz70, new_sr2(vuz69, bc), vuz68, bc) new_pr2F0G10(vuz55, vuz56, Succ(Succ(Zero)), bb) -> new_pr2F0G11(vuz55, vuz56, new_primDivNatS1, Succ(new_primDivNatS1), bb) new_pr2F0G10(vuz55, vuz56, Succ(Zero), bb) -> new_pr2F0G12(vuz55, vuz56, bb) new_pr2F0G11(vuz68, vuz69, vuz70, Zero, bc) -> new_pr2F0G10(vuz68, new_sr3(vuz69, bc), Succ(vuz70), bc) new_pr2F0G11(vuz68, vuz69, vuz70, Succ(Succ(vuz7100)), bc) -> new_pr2F0G11(vuz68, vuz69, vuz70, vuz7100, bc) new_pr2F0G10(vuz55, vuz56, Zero, bb) -> new_pr2F0G10(vuz55, new_sr1(vuz56, bb), Zero, bb) new_pr2F0G1(vuz92, vuz93, vuz94, Succ(Succ(vuz9500)), h) -> new_pr2F0G1(vuz92, vuz93, vuz94, vuz9500, h) new_pr2F0G1(vuz92, vuz93, vuz94, Succ(Zero), h) -> new_pr2F3(vuz94, vuz92, new_sr(vuz92, vuz93, h), h) new_pr2F0G1(vuz92, vuz93, vuz94, Zero, h) -> new_pr2F0G10(new_sr0(vuz92, vuz93, h), vuz92, Succ(vuz94), h) new_pr2F0G10(vuz55, vuz56, Succ(Succ(Succ(vuz57000))), bb) -> new_pr2F0G11(vuz55, vuz56, new_primDivNatS0(vuz57000), Succ(new_primDivNatS0(vuz57000)), bb) new_pr2F0G12(vuz55, vuz56, bb) -> new_pr2F0G10(vuz55, new_sr1(vuz56, bb), Zero, bb) The TRS R consists of the following rules: new_sr13(Pos(vuz150), Pos(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_primPlusNat0(Succ(vuz5800), Zero) -> Succ(vuz5800) new_primPlusNat0(Zero, Succ(vuz50000)) -> Succ(vuz50000) new_sr(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_primMulNat0(Zero, Zero) -> Zero new_sr1(vuz56, ty_Integer) -> new_sr8(vuz56) new_primPlusNat0(Zero, Zero) -> Zero new_sr2(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_primPlusNat1(Zero, vuz5000) -> Succ(vuz5000) new_sr2(vuz69, ty_Integer) -> new_sr8(vuz69) new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_sr0(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) new_sr1(vuz56, ty_Int) -> new_sr5(vuz56) new_sr13(Neg(vuz150), Neg(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_sr(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr2(vuz69, ty_Int) -> new_sr5(vuz69) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_sr1(vuz56, app(ty_Ratio, bf)) -> new_sr4(vuz56, bf) new_sr0(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_sr(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr1(vuz56, ty_Float) -> new_sr7(vuz56) new_sr4(vuz7, bg) -> new_sr12(vuz7, vuz7, bg) new_sr7(vuz7) -> new_sr11(vuz7, vuz7) new_primDivNatS0(Zero) -> Zero new_sr3(vuz69, ty_Double) -> new_sr6(vuz69) new_sr(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_primPlusNat0(Succ(vuz5800), Succ(vuz50000)) -> Succ(Succ(new_primPlusNat0(vuz5800, vuz50000))) new_primMulNat0(Succ(vuz1500), Succ(vuz5000)) -> new_primPlusNat1(new_primMulNat0(vuz1500, Succ(vuz5000)), vuz5000) new_sr5(vuz7) -> new_sr13(vuz7, vuz7) new_sr1(vuz56, ty_Double) -> new_sr6(vuz56) new_sr0(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr2(vuz69, ty_Float) -> new_sr7(vuz69) new_sr13(Pos(vuz150), Neg(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr13(Neg(vuz150), Pos(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr6(vuz7) -> new_sr10(vuz7, vuz7) new_sr0(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_sr8(vuz7) -> new_sr9(vuz7, vuz7) new_sr11(Float(vuz150, vuz151), Float(vuz520, vuz521)) -> Float(new_sr13(vuz150, vuz520), new_sr13(vuz151, vuz521)) new_sr2(vuz69, ty_Double) -> new_sr6(vuz69) new_primDivNatS1 -> Zero new_sr3(vuz69, ty_Int) -> new_sr5(vuz69) new_sr3(vuz69, ty_Float) -> new_sr7(vuz69) new_sr3(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_sr10(vuz15, vuz51) -> error([]) new_sr9(vuz15, vuz53) -> error([]) new_primMulNat0(Succ(vuz1500), Zero) -> Zero new_primMulNat0(Zero, Succ(vuz5000)) -> Zero new_sr12(vuz15, vuz49, be) -> error([]) new_sr3(vuz69, ty_Integer) -> new_sr8(vuz69) new_primPlusNat1(Succ(vuz580), vuz5000) -> Succ(Succ(new_primPlusNat0(vuz580, vuz5000))) new_sr0(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) The set Q consists of the following terms: new_sr6(x0) new_sr1(x0, ty_Integer) new_primMulNat0(Zero, Succ(x0)) new_sr7(x0) new_sr(x0, x1, ty_Double) new_sr(x0, x1, ty_Float) new_sr0(x0, x1, ty_Double) new_sr3(x0, ty_Float) new_sr5(x0) new_primDivNatS0(Zero) new_sr10(x0, x1) new_sr11(Float(x0, x1), Float(x2, x3)) new_primPlusNat0(Zero, Succ(x0)) new_primMulNat0(Zero, Zero) new_primDivNatS0(Succ(Zero)) new_sr4(x0, x1) new_sr2(x0, ty_Int) new_sr1(x0, ty_Double) new_sr0(x0, x1, ty_Float) new_sr0(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Succ(x1)) new_sr(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Succ(x1)) new_sr1(x0, ty_Float) new_primPlusNat1(Zero, x0) new_sr8(x0) new_primDivNatS0(Succ(Succ(x0))) new_sr3(x0, ty_Double) new_primDivNatS1 new_sr0(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Zero) new_sr13(Neg(x0), Neg(x1)) new_sr1(x0, app(ty_Ratio, x1)) new_sr13(Pos(x0), Neg(x1)) new_sr13(Neg(x0), Pos(x1)) new_sr2(x0, ty_Integer) new_sr13(Pos(x0), Pos(x1)) new_sr9(x0, x1) new_sr2(x0, app(ty_Ratio, x1)) new_sr3(x0, ty_Int) new_primPlusNat1(Succ(x0), x1) new_sr3(x0, app(ty_Ratio, x1)) new_sr(x0, x1, app(ty_Ratio, x2)) new_sr3(x0, ty_Integer) new_sr0(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_sr2(x0, ty_Double) new_sr(x0, x1, ty_Integer) new_sr2(x0, ty_Float) new_sr12(x0, x1, x2) new_primPlusNat0(Zero, Zero) new_sr1(x0, ty_Int) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes. ---------------------------------------- (15) Complex Obligation (AND) ---------------------------------------- (16) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F0G10(vuz55, vuz56, Zero, bb) -> new_pr2F0G10(vuz55, new_sr1(vuz56, bb), Zero, bb) The TRS R consists of the following rules: new_sr13(Pos(vuz150), Pos(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_primPlusNat0(Succ(vuz5800), Zero) -> Succ(vuz5800) new_primPlusNat0(Zero, Succ(vuz50000)) -> Succ(vuz50000) new_sr(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_primMulNat0(Zero, Zero) -> Zero new_sr1(vuz56, ty_Integer) -> new_sr8(vuz56) new_primPlusNat0(Zero, Zero) -> Zero new_sr2(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_primPlusNat1(Zero, vuz5000) -> Succ(vuz5000) new_sr2(vuz69, ty_Integer) -> new_sr8(vuz69) new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_sr0(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) new_sr1(vuz56, ty_Int) -> new_sr5(vuz56) new_sr13(Neg(vuz150), Neg(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_sr(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr2(vuz69, ty_Int) -> new_sr5(vuz69) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_sr1(vuz56, app(ty_Ratio, bf)) -> new_sr4(vuz56, bf) new_sr0(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_sr(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr1(vuz56, ty_Float) -> new_sr7(vuz56) new_sr4(vuz7, bg) -> new_sr12(vuz7, vuz7, bg) new_sr7(vuz7) -> new_sr11(vuz7, vuz7) new_primDivNatS0(Zero) -> Zero new_sr3(vuz69, ty_Double) -> new_sr6(vuz69) new_sr(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_primPlusNat0(Succ(vuz5800), Succ(vuz50000)) -> Succ(Succ(new_primPlusNat0(vuz5800, vuz50000))) new_primMulNat0(Succ(vuz1500), Succ(vuz5000)) -> new_primPlusNat1(new_primMulNat0(vuz1500, Succ(vuz5000)), vuz5000) new_sr5(vuz7) -> new_sr13(vuz7, vuz7) new_sr1(vuz56, ty_Double) -> new_sr6(vuz56) new_sr0(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr2(vuz69, ty_Float) -> new_sr7(vuz69) new_sr13(Pos(vuz150), Neg(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr13(Neg(vuz150), Pos(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr6(vuz7) -> new_sr10(vuz7, vuz7) new_sr0(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_sr8(vuz7) -> new_sr9(vuz7, vuz7) new_sr11(Float(vuz150, vuz151), Float(vuz520, vuz521)) -> Float(new_sr13(vuz150, vuz520), new_sr13(vuz151, vuz521)) new_sr2(vuz69, ty_Double) -> new_sr6(vuz69) new_primDivNatS1 -> Zero new_sr3(vuz69, ty_Int) -> new_sr5(vuz69) new_sr3(vuz69, ty_Float) -> new_sr7(vuz69) new_sr3(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_sr10(vuz15, vuz51) -> error([]) new_sr9(vuz15, vuz53) -> error([]) new_primMulNat0(Succ(vuz1500), Zero) -> Zero new_primMulNat0(Zero, Succ(vuz5000)) -> Zero new_sr12(vuz15, vuz49, be) -> error([]) new_sr3(vuz69, ty_Integer) -> new_sr8(vuz69) new_primPlusNat1(Succ(vuz580), vuz5000) -> Succ(Succ(new_primPlusNat0(vuz580, vuz5000))) new_sr0(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) The set Q consists of the following terms: new_sr6(x0) new_sr1(x0, ty_Integer) new_primMulNat0(Zero, Succ(x0)) new_sr7(x0) new_sr(x0, x1, ty_Double) new_sr(x0, x1, ty_Float) new_sr0(x0, x1, ty_Double) new_sr3(x0, ty_Float) new_sr5(x0) new_primDivNatS0(Zero) new_sr10(x0, x1) new_sr11(Float(x0, x1), Float(x2, x3)) new_primPlusNat0(Zero, Succ(x0)) new_primMulNat0(Zero, Zero) new_primDivNatS0(Succ(Zero)) new_sr4(x0, x1) new_sr2(x0, ty_Int) new_sr1(x0, ty_Double) new_sr0(x0, x1, ty_Float) new_sr0(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Succ(x1)) new_sr(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Succ(x1)) new_sr1(x0, ty_Float) new_primPlusNat1(Zero, x0) new_sr8(x0) new_primDivNatS0(Succ(Succ(x0))) new_sr3(x0, ty_Double) new_primDivNatS1 new_sr0(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Zero) new_sr13(Neg(x0), Neg(x1)) new_sr1(x0, app(ty_Ratio, x1)) new_sr13(Pos(x0), Neg(x1)) new_sr13(Neg(x0), Pos(x1)) new_sr2(x0, ty_Integer) new_sr13(Pos(x0), Pos(x1)) new_sr9(x0, x1) new_sr2(x0, app(ty_Ratio, x1)) new_sr3(x0, ty_Int) new_primPlusNat1(Succ(x0), x1) new_sr3(x0, app(ty_Ratio, x1)) new_sr(x0, x1, app(ty_Ratio, x2)) new_sr3(x0, ty_Integer) new_sr0(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_sr2(x0, ty_Double) new_sr(x0, x1, ty_Integer) new_sr2(x0, ty_Float) new_sr12(x0, x1, x2) new_primPlusNat0(Zero, Zero) new_sr1(x0, ty_Int) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (17) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F0G10(vuz55, vuz56, Zero, bb) -> new_pr2F0G10(vuz55, new_sr1(vuz56, bb), Zero, bb) The TRS R consists of the following rules: new_sr13(Pos(vuz150), Pos(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_primPlusNat0(Succ(vuz5800), Zero) -> Succ(vuz5800) new_primPlusNat0(Zero, Succ(vuz50000)) -> Succ(vuz50000) new_sr(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_primMulNat0(Zero, Zero) -> Zero new_sr1(vuz56, ty_Integer) -> new_sr8(vuz56) new_primPlusNat0(Zero, Zero) -> Zero new_sr2(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_primPlusNat1(Zero, vuz5000) -> Succ(vuz5000) new_sr2(vuz69, ty_Integer) -> new_sr8(vuz69) new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_sr0(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) new_sr1(vuz56, ty_Int) -> new_sr5(vuz56) new_sr13(Neg(vuz150), Neg(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_sr(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr2(vuz69, ty_Int) -> new_sr5(vuz69) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_sr1(vuz56, app(ty_Ratio, bf)) -> new_sr4(vuz56, bf) new_sr0(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_sr(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr1(vuz56, ty_Float) -> new_sr7(vuz56) new_sr4(vuz7, bg) -> new_sr12(vuz7, vuz7, bg) new_sr7(vuz7) -> new_sr11(vuz7, vuz7) new_primDivNatS0(Zero) -> Zero new_sr3(vuz69, ty_Double) -> new_sr6(vuz69) new_sr(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_primPlusNat0(Succ(vuz5800), Succ(vuz50000)) -> Succ(Succ(new_primPlusNat0(vuz5800, vuz50000))) new_primMulNat0(Succ(vuz1500), Succ(vuz5000)) -> new_primPlusNat1(new_primMulNat0(vuz1500, Succ(vuz5000)), vuz5000) new_sr5(vuz7) -> new_sr13(vuz7, vuz7) new_sr1(vuz56, ty_Double) -> new_sr6(vuz56) new_sr0(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr2(vuz69, ty_Float) -> new_sr7(vuz69) new_sr13(Pos(vuz150), Neg(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr13(Neg(vuz150), Pos(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr6(vuz7) -> new_sr10(vuz7, vuz7) new_sr0(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_sr8(vuz7) -> new_sr9(vuz7, vuz7) new_sr11(Float(vuz150, vuz151), Float(vuz520, vuz521)) -> Float(new_sr13(vuz150, vuz520), new_sr13(vuz151, vuz521)) new_sr2(vuz69, ty_Double) -> new_sr6(vuz69) new_primDivNatS1 -> Zero new_sr3(vuz69, ty_Int) -> new_sr5(vuz69) new_sr3(vuz69, ty_Float) -> new_sr7(vuz69) new_sr3(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_sr10(vuz15, vuz51) -> error([]) new_sr9(vuz15, vuz53) -> error([]) new_primMulNat0(Succ(vuz1500), Zero) -> Zero new_primMulNat0(Zero, Succ(vuz5000)) -> Zero new_sr12(vuz15, vuz49, be) -> error([]) new_sr3(vuz69, ty_Integer) -> new_sr8(vuz69) new_primPlusNat1(Succ(vuz580), vuz5000) -> Succ(Succ(new_primPlusNat0(vuz580, vuz5000))) new_sr0(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (19) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_pr2F0G10(vuz55, vuz56, Zero, bb) evaluates to t =new_pr2F0G10(vuz55, new_sr1(vuz56, bb), Zero, bb) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [vuz56 / new_sr1(vuz56, bb)] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_pr2F0G10(vuz55, vuz56, Zero, bb) to new_pr2F0G10(vuz55, new_sr1(vuz56, bb), Zero, bb). ---------------------------------------- (20) NO ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F0G1(vuz92, vuz93, vuz94, Succ(Succ(vuz9500)), h) -> new_pr2F0G1(vuz92, vuz93, vuz94, vuz9500, h) new_pr2F0G1(vuz92, vuz93, vuz94, Succ(Zero), h) -> new_pr2F3(vuz94, vuz92, new_sr(vuz92, vuz93, h), h) new_pr2F3(Succ(vuz880), vuz89, vuz90, ba) -> new_pr2F0G1(vuz89, vuz90, vuz880, Succ(vuz880), ba) new_pr2F0G1(vuz92, vuz93, vuz94, Zero, h) -> new_pr2F0G10(new_sr0(vuz92, vuz93, h), vuz92, Succ(vuz94), h) new_pr2F0G10(vuz55, vuz56, Succ(Succ(Zero)), bb) -> new_pr2F0G11(vuz55, vuz56, new_primDivNatS1, Succ(new_primDivNatS1), bb) new_pr2F0G11(vuz68, vuz69, vuz70, Succ(Zero), bc) -> new_pr2F3(vuz70, new_sr2(vuz69, bc), vuz68, bc) new_pr2F0G10(vuz55, vuz56, Succ(Succ(Succ(vuz57000))), bb) -> new_pr2F0G11(vuz55, vuz56, new_primDivNatS0(vuz57000), Succ(new_primDivNatS0(vuz57000)), bb) new_pr2F0G11(vuz68, vuz69, vuz70, Succ(Succ(vuz7100)), bc) -> new_pr2F0G11(vuz68, vuz69, vuz70, vuz7100, bc) new_pr2F0G11(vuz68, vuz69, vuz70, Zero, bc) -> new_pr2F0G10(vuz68, new_sr3(vuz69, bc), Succ(vuz70), bc) The TRS R consists of the following rules: new_sr13(Pos(vuz150), Pos(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_primPlusNat0(Succ(vuz5800), Zero) -> Succ(vuz5800) new_primPlusNat0(Zero, Succ(vuz50000)) -> Succ(vuz50000) new_sr(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_primMulNat0(Zero, Zero) -> Zero new_sr1(vuz56, ty_Integer) -> new_sr8(vuz56) new_primPlusNat0(Zero, Zero) -> Zero new_sr2(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_primPlusNat1(Zero, vuz5000) -> Succ(vuz5000) new_sr2(vuz69, ty_Integer) -> new_sr8(vuz69) new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_sr0(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) new_sr1(vuz56, ty_Int) -> new_sr5(vuz56) new_sr13(Neg(vuz150), Neg(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_sr(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr2(vuz69, ty_Int) -> new_sr5(vuz69) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_sr1(vuz56, app(ty_Ratio, bf)) -> new_sr4(vuz56, bf) new_sr0(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_sr(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr1(vuz56, ty_Float) -> new_sr7(vuz56) new_sr4(vuz7, bg) -> new_sr12(vuz7, vuz7, bg) new_sr7(vuz7) -> new_sr11(vuz7, vuz7) new_primDivNatS0(Zero) -> Zero new_sr3(vuz69, ty_Double) -> new_sr6(vuz69) new_sr(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_primPlusNat0(Succ(vuz5800), Succ(vuz50000)) -> Succ(Succ(new_primPlusNat0(vuz5800, vuz50000))) new_primMulNat0(Succ(vuz1500), Succ(vuz5000)) -> new_primPlusNat1(new_primMulNat0(vuz1500, Succ(vuz5000)), vuz5000) new_sr5(vuz7) -> new_sr13(vuz7, vuz7) new_sr1(vuz56, ty_Double) -> new_sr6(vuz56) new_sr0(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr2(vuz69, ty_Float) -> new_sr7(vuz69) new_sr13(Pos(vuz150), Neg(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr13(Neg(vuz150), Pos(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr6(vuz7) -> new_sr10(vuz7, vuz7) new_sr0(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_sr8(vuz7) -> new_sr9(vuz7, vuz7) new_sr11(Float(vuz150, vuz151), Float(vuz520, vuz521)) -> Float(new_sr13(vuz150, vuz520), new_sr13(vuz151, vuz521)) new_sr2(vuz69, ty_Double) -> new_sr6(vuz69) new_primDivNatS1 -> Zero new_sr3(vuz69, ty_Int) -> new_sr5(vuz69) new_sr3(vuz69, ty_Float) -> new_sr7(vuz69) new_sr3(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_sr10(vuz15, vuz51) -> error([]) new_sr9(vuz15, vuz53) -> error([]) new_primMulNat0(Succ(vuz1500), Zero) -> Zero new_primMulNat0(Zero, Succ(vuz5000)) -> Zero new_sr12(vuz15, vuz49, be) -> error([]) new_sr3(vuz69, ty_Integer) -> new_sr8(vuz69) new_primPlusNat1(Succ(vuz580), vuz5000) -> Succ(Succ(new_primPlusNat0(vuz580, vuz5000))) new_sr0(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) The set Q consists of the following terms: new_sr6(x0) new_sr1(x0, ty_Integer) new_primMulNat0(Zero, Succ(x0)) new_sr7(x0) new_sr(x0, x1, ty_Double) new_sr(x0, x1, ty_Float) new_sr0(x0, x1, ty_Double) new_sr3(x0, ty_Float) new_sr5(x0) new_primDivNatS0(Zero) new_sr10(x0, x1) new_sr11(Float(x0, x1), Float(x2, x3)) new_primPlusNat0(Zero, Succ(x0)) new_primMulNat0(Zero, Zero) new_primDivNatS0(Succ(Zero)) new_sr4(x0, x1) new_sr2(x0, ty_Int) new_sr1(x0, ty_Double) new_sr0(x0, x1, ty_Float) new_sr0(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Succ(x1)) new_sr(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Succ(x1)) new_sr1(x0, ty_Float) new_primPlusNat1(Zero, x0) new_sr8(x0) new_primDivNatS0(Succ(Succ(x0))) new_sr3(x0, ty_Double) new_primDivNatS1 new_sr0(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Zero) new_sr13(Neg(x0), Neg(x1)) new_sr1(x0, app(ty_Ratio, x1)) new_sr13(Pos(x0), Neg(x1)) new_sr13(Neg(x0), Pos(x1)) new_sr2(x0, ty_Integer) new_sr13(Pos(x0), Pos(x1)) new_sr9(x0, x1) new_sr2(x0, app(ty_Ratio, x1)) new_sr3(x0, ty_Int) new_primPlusNat1(Succ(x0), x1) new_sr3(x0, app(ty_Ratio, x1)) new_sr(x0, x1, app(ty_Ratio, x2)) new_sr3(x0, ty_Integer) new_sr0(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_sr2(x0, ty_Double) new_sr(x0, x1, ty_Integer) new_sr2(x0, ty_Float) new_sr12(x0, x1, x2) new_primPlusNat0(Zero, Zero) new_sr1(x0, ty_Int) 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_pr2F0G1(vuz92, vuz93, vuz94, Succ(Zero), h) -> new_pr2F3(vuz94, vuz92, new_sr(vuz92, vuz93, h), h) new_pr2F0G10(vuz55, vuz56, Succ(Succ(Zero)), bb) -> new_pr2F0G11(vuz55, vuz56, new_primDivNatS1, Succ(new_primDivNatS1), bb) new_pr2F0G11(vuz68, vuz69, vuz70, Succ(Zero), bc) -> new_pr2F3(vuz70, new_sr2(vuz69, bc), vuz68, bc) new_pr2F0G10(vuz55, vuz56, Succ(Succ(Succ(vuz57000))), bb) -> new_pr2F0G11(vuz55, vuz56, new_primDivNatS0(vuz57000), Succ(new_primDivNatS0(vuz57000)), bb) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Float(x_1, x_2)) = 0 POL(Neg(x_1)) = 0 POL(Pos(x_1)) = 0 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL([]) = 1 POL(app(x_1, x_2)) = x_1 + x_2 POL(error(x_1)) = 1 + x_1 POL(new_pr2F0G1(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 + x_5 POL(new_pr2F0G10(x_1, x_2, x_3, x_4)) = x_3 + x_4 POL(new_pr2F0G11(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 + x_5 POL(new_pr2F3(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(new_primDivNatS0(x_1)) = x_1 POL(new_primDivNatS1) = 0 POL(new_primMulNat0(x_1, x_2)) = 0 POL(new_primPlusNat0(x_1, x_2)) = 0 POL(new_primPlusNat1(x_1, x_2)) = x_2 POL(new_sr(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_sr0(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_sr10(x_1, x_2)) = 1 + x_2 POL(new_sr11(x_1, x_2)) = 0 POL(new_sr12(x_1, x_2, x_3)) = 1 + x_2 POL(new_sr13(x_1, x_2)) = 0 POL(new_sr2(x_1, x_2)) = x_1 + x_2 POL(new_sr3(x_1, x_2)) = x_1 + x_2 POL(new_sr4(x_1, x_2)) = 1 + x_1 POL(new_sr5(x_1)) = 1 + x_1 POL(new_sr6(x_1)) = 1 + x_1 POL(new_sr7(x_1)) = 1 + x_1 POL(new_sr8(x_1)) = 1 + x_1 POL(new_sr9(x_1, x_2)) = 1 + x_1 POL(ty_Double) = 1 POL(ty_Float) = 1 POL(ty_Int) = 1 POL(ty_Integer) = 1 POL(ty_Ratio) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primDivNatS1 -> Zero new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_primDivNatS0(Zero) -> Zero ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F0G1(vuz92, vuz93, vuz94, Succ(Succ(vuz9500)), h) -> new_pr2F0G1(vuz92, vuz93, vuz94, vuz9500, h) new_pr2F3(Succ(vuz880), vuz89, vuz90, ba) -> new_pr2F0G1(vuz89, vuz90, vuz880, Succ(vuz880), ba) new_pr2F0G1(vuz92, vuz93, vuz94, Zero, h) -> new_pr2F0G10(new_sr0(vuz92, vuz93, h), vuz92, Succ(vuz94), h) new_pr2F0G11(vuz68, vuz69, vuz70, Succ(Succ(vuz7100)), bc) -> new_pr2F0G11(vuz68, vuz69, vuz70, vuz7100, bc) new_pr2F0G11(vuz68, vuz69, vuz70, Zero, bc) -> new_pr2F0G10(vuz68, new_sr3(vuz69, bc), Succ(vuz70), bc) The TRS R consists of the following rules: new_sr13(Pos(vuz150), Pos(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_primPlusNat0(Succ(vuz5800), Zero) -> Succ(vuz5800) new_primPlusNat0(Zero, Succ(vuz50000)) -> Succ(vuz50000) new_sr(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_primMulNat0(Zero, Zero) -> Zero new_sr1(vuz56, ty_Integer) -> new_sr8(vuz56) new_primPlusNat0(Zero, Zero) -> Zero new_sr2(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_primPlusNat1(Zero, vuz5000) -> Succ(vuz5000) new_sr2(vuz69, ty_Integer) -> new_sr8(vuz69) new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_sr0(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) new_sr1(vuz56, ty_Int) -> new_sr5(vuz56) new_sr13(Neg(vuz150), Neg(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_sr(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr2(vuz69, ty_Int) -> new_sr5(vuz69) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_sr1(vuz56, app(ty_Ratio, bf)) -> new_sr4(vuz56, bf) new_sr0(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_sr(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr1(vuz56, ty_Float) -> new_sr7(vuz56) new_sr4(vuz7, bg) -> new_sr12(vuz7, vuz7, bg) new_sr7(vuz7) -> new_sr11(vuz7, vuz7) new_primDivNatS0(Zero) -> Zero new_sr3(vuz69, ty_Double) -> new_sr6(vuz69) new_sr(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_primPlusNat0(Succ(vuz5800), Succ(vuz50000)) -> Succ(Succ(new_primPlusNat0(vuz5800, vuz50000))) new_primMulNat0(Succ(vuz1500), Succ(vuz5000)) -> new_primPlusNat1(new_primMulNat0(vuz1500, Succ(vuz5000)), vuz5000) new_sr5(vuz7) -> new_sr13(vuz7, vuz7) new_sr1(vuz56, ty_Double) -> new_sr6(vuz56) new_sr0(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr2(vuz69, ty_Float) -> new_sr7(vuz69) new_sr13(Pos(vuz150), Neg(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr13(Neg(vuz150), Pos(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr6(vuz7) -> new_sr10(vuz7, vuz7) new_sr0(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_sr8(vuz7) -> new_sr9(vuz7, vuz7) new_sr11(Float(vuz150, vuz151), Float(vuz520, vuz521)) -> Float(new_sr13(vuz150, vuz520), new_sr13(vuz151, vuz521)) new_sr2(vuz69, ty_Double) -> new_sr6(vuz69) new_primDivNatS1 -> Zero new_sr3(vuz69, ty_Int) -> new_sr5(vuz69) new_sr3(vuz69, ty_Float) -> new_sr7(vuz69) new_sr3(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_sr10(vuz15, vuz51) -> error([]) new_sr9(vuz15, vuz53) -> error([]) new_primMulNat0(Succ(vuz1500), Zero) -> Zero new_primMulNat0(Zero, Succ(vuz5000)) -> Zero new_sr12(vuz15, vuz49, be) -> error([]) new_sr3(vuz69, ty_Integer) -> new_sr8(vuz69) new_primPlusNat1(Succ(vuz580), vuz5000) -> Succ(Succ(new_primPlusNat0(vuz580, vuz5000))) new_sr0(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) The set Q consists of the following terms: new_sr6(x0) new_sr1(x0, ty_Integer) new_primMulNat0(Zero, Succ(x0)) new_sr7(x0) new_sr(x0, x1, ty_Double) new_sr(x0, x1, ty_Float) new_sr0(x0, x1, ty_Double) new_sr3(x0, ty_Float) new_sr5(x0) new_primDivNatS0(Zero) new_sr10(x0, x1) new_sr11(Float(x0, x1), Float(x2, x3)) new_primPlusNat0(Zero, Succ(x0)) new_primMulNat0(Zero, Zero) new_primDivNatS0(Succ(Zero)) new_sr4(x0, x1) new_sr2(x0, ty_Int) new_sr1(x0, ty_Double) new_sr0(x0, x1, ty_Float) new_sr0(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Succ(x1)) new_sr(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Succ(x1)) new_sr1(x0, ty_Float) new_primPlusNat1(Zero, x0) new_sr8(x0) new_primDivNatS0(Succ(Succ(x0))) new_sr3(x0, ty_Double) new_primDivNatS1 new_sr0(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Zero) new_sr13(Neg(x0), Neg(x1)) new_sr1(x0, app(ty_Ratio, x1)) new_sr13(Pos(x0), Neg(x1)) new_sr13(Neg(x0), Pos(x1)) new_sr2(x0, ty_Integer) new_sr13(Pos(x0), Pos(x1)) new_sr9(x0, x1) new_sr2(x0, app(ty_Ratio, x1)) new_sr3(x0, ty_Int) new_primPlusNat1(Succ(x0), x1) new_sr3(x0, app(ty_Ratio, x1)) new_sr(x0, x1, app(ty_Ratio, x2)) new_sr3(x0, ty_Integer) new_sr0(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_sr2(x0, ty_Double) new_sr(x0, x1, ty_Integer) new_sr2(x0, ty_Float) new_sr12(x0, x1, x2) new_primPlusNat0(Zero, Zero) new_sr1(x0, ty_Int) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 3 less nodes. ---------------------------------------- (25) Complex Obligation (AND) ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F0G11(vuz68, vuz69, vuz70, Succ(Succ(vuz7100)), bc) -> new_pr2F0G11(vuz68, vuz69, vuz70, vuz7100, bc) The TRS R consists of the following rules: new_sr13(Pos(vuz150), Pos(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_primPlusNat0(Succ(vuz5800), Zero) -> Succ(vuz5800) new_primPlusNat0(Zero, Succ(vuz50000)) -> Succ(vuz50000) new_sr(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_primMulNat0(Zero, Zero) -> Zero new_sr1(vuz56, ty_Integer) -> new_sr8(vuz56) new_primPlusNat0(Zero, Zero) -> Zero new_sr2(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_primPlusNat1(Zero, vuz5000) -> Succ(vuz5000) new_sr2(vuz69, ty_Integer) -> new_sr8(vuz69) new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_sr0(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) new_sr1(vuz56, ty_Int) -> new_sr5(vuz56) new_sr13(Neg(vuz150), Neg(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_sr(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr2(vuz69, ty_Int) -> new_sr5(vuz69) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_sr1(vuz56, app(ty_Ratio, bf)) -> new_sr4(vuz56, bf) new_sr0(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_sr(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr1(vuz56, ty_Float) -> new_sr7(vuz56) new_sr4(vuz7, bg) -> new_sr12(vuz7, vuz7, bg) new_sr7(vuz7) -> new_sr11(vuz7, vuz7) new_primDivNatS0(Zero) -> Zero new_sr3(vuz69, ty_Double) -> new_sr6(vuz69) new_sr(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_primPlusNat0(Succ(vuz5800), Succ(vuz50000)) -> Succ(Succ(new_primPlusNat0(vuz5800, vuz50000))) new_primMulNat0(Succ(vuz1500), Succ(vuz5000)) -> new_primPlusNat1(new_primMulNat0(vuz1500, Succ(vuz5000)), vuz5000) new_sr5(vuz7) -> new_sr13(vuz7, vuz7) new_sr1(vuz56, ty_Double) -> new_sr6(vuz56) new_sr0(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr2(vuz69, ty_Float) -> new_sr7(vuz69) new_sr13(Pos(vuz150), Neg(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr13(Neg(vuz150), Pos(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr6(vuz7) -> new_sr10(vuz7, vuz7) new_sr0(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_sr8(vuz7) -> new_sr9(vuz7, vuz7) new_sr11(Float(vuz150, vuz151), Float(vuz520, vuz521)) -> Float(new_sr13(vuz150, vuz520), new_sr13(vuz151, vuz521)) new_sr2(vuz69, ty_Double) -> new_sr6(vuz69) new_primDivNatS1 -> Zero new_sr3(vuz69, ty_Int) -> new_sr5(vuz69) new_sr3(vuz69, ty_Float) -> new_sr7(vuz69) new_sr3(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_sr10(vuz15, vuz51) -> error([]) new_sr9(vuz15, vuz53) -> error([]) new_primMulNat0(Succ(vuz1500), Zero) -> Zero new_primMulNat0(Zero, Succ(vuz5000)) -> Zero new_sr12(vuz15, vuz49, be) -> error([]) new_sr3(vuz69, ty_Integer) -> new_sr8(vuz69) new_primPlusNat1(Succ(vuz580), vuz5000) -> Succ(Succ(new_primPlusNat0(vuz580, vuz5000))) new_sr0(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) The set Q consists of the following terms: new_sr6(x0) new_sr1(x0, ty_Integer) new_primMulNat0(Zero, Succ(x0)) new_sr7(x0) new_sr(x0, x1, ty_Double) new_sr(x0, x1, ty_Float) new_sr0(x0, x1, ty_Double) new_sr3(x0, ty_Float) new_sr5(x0) new_primDivNatS0(Zero) new_sr10(x0, x1) new_sr11(Float(x0, x1), Float(x2, x3)) new_primPlusNat0(Zero, Succ(x0)) new_primMulNat0(Zero, Zero) new_primDivNatS0(Succ(Zero)) new_sr4(x0, x1) new_sr2(x0, ty_Int) new_sr1(x0, ty_Double) new_sr0(x0, x1, ty_Float) new_sr0(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Succ(x1)) new_sr(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Succ(x1)) new_sr1(x0, ty_Float) new_primPlusNat1(Zero, x0) new_sr8(x0) new_primDivNatS0(Succ(Succ(x0))) new_sr3(x0, ty_Double) new_primDivNatS1 new_sr0(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Zero) new_sr13(Neg(x0), Neg(x1)) new_sr1(x0, app(ty_Ratio, x1)) new_sr13(Pos(x0), Neg(x1)) new_sr13(Neg(x0), Pos(x1)) new_sr2(x0, ty_Integer) new_sr13(Pos(x0), Pos(x1)) new_sr9(x0, x1) new_sr2(x0, app(ty_Ratio, x1)) new_sr3(x0, ty_Int) new_primPlusNat1(Succ(x0), x1) new_sr3(x0, app(ty_Ratio, x1)) new_sr(x0, x1, app(ty_Ratio, x2)) new_sr3(x0, ty_Integer) new_sr0(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_sr2(x0, ty_Double) new_sr(x0, x1, ty_Integer) new_sr2(x0, ty_Float) new_sr12(x0, x1, x2) new_primPlusNat0(Zero, Zero) new_sr1(x0, ty_Int) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) 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_pr2F0G11(vuz68, vuz69, vuz70, Succ(Succ(vuz7100)), bc) -> new_pr2F0G11(vuz68, vuz69, vuz70, vuz7100, bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 ---------------------------------------- (28) YES ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F0G1(vuz92, vuz93, vuz94, Succ(Succ(vuz9500)), h) -> new_pr2F0G1(vuz92, vuz93, vuz94, vuz9500, h) The TRS R consists of the following rules: new_sr13(Pos(vuz150), Pos(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_primPlusNat0(Succ(vuz5800), Zero) -> Succ(vuz5800) new_primPlusNat0(Zero, Succ(vuz50000)) -> Succ(vuz50000) new_sr(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_primMulNat0(Zero, Zero) -> Zero new_sr1(vuz56, ty_Integer) -> new_sr8(vuz56) new_primPlusNat0(Zero, Zero) -> Zero new_sr2(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_primPlusNat1(Zero, vuz5000) -> Succ(vuz5000) new_sr2(vuz69, ty_Integer) -> new_sr8(vuz69) new_primDivNatS0(Succ(Zero)) -> Succ(new_primDivNatS1) new_sr0(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) new_sr1(vuz56, ty_Int) -> new_sr5(vuz56) new_sr13(Neg(vuz150), Neg(vuz500)) -> Pos(new_primMulNat0(vuz150, vuz500)) new_sr(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr2(vuz69, ty_Int) -> new_sr5(vuz69) new_primDivNatS0(Succ(Succ(vuz5700000))) -> Succ(new_primDivNatS0(vuz5700000)) new_sr1(vuz56, app(ty_Ratio, bf)) -> new_sr4(vuz56, bf) new_sr0(vuz92, vuz93, ty_Double) -> new_sr10(vuz92, vuz93) new_sr(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr1(vuz56, ty_Float) -> new_sr7(vuz56) new_sr4(vuz7, bg) -> new_sr12(vuz7, vuz7, bg) new_sr7(vuz7) -> new_sr11(vuz7, vuz7) new_primDivNatS0(Zero) -> Zero new_sr3(vuz69, ty_Double) -> new_sr6(vuz69) new_sr(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_primPlusNat0(Succ(vuz5800), Succ(vuz50000)) -> Succ(Succ(new_primPlusNat0(vuz5800, vuz50000))) new_primMulNat0(Succ(vuz1500), Succ(vuz5000)) -> new_primPlusNat1(new_primMulNat0(vuz1500, Succ(vuz5000)), vuz5000) new_sr5(vuz7) -> new_sr13(vuz7, vuz7) new_sr1(vuz56, ty_Double) -> new_sr6(vuz56) new_sr0(vuz92, vuz93, ty_Int) -> new_sr13(vuz92, vuz93) new_sr2(vuz69, ty_Float) -> new_sr7(vuz69) new_sr13(Pos(vuz150), Neg(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr13(Neg(vuz150), Pos(vuz500)) -> Neg(new_primMulNat0(vuz150, vuz500)) new_sr6(vuz7) -> new_sr10(vuz7, vuz7) new_sr0(vuz92, vuz93, ty_Float) -> new_sr11(vuz92, vuz93) new_sr8(vuz7) -> new_sr9(vuz7, vuz7) new_sr11(Float(vuz150, vuz151), Float(vuz520, vuz521)) -> Float(new_sr13(vuz150, vuz520), new_sr13(vuz151, vuz521)) new_sr2(vuz69, ty_Double) -> new_sr6(vuz69) new_primDivNatS1 -> Zero new_sr3(vuz69, ty_Int) -> new_sr5(vuz69) new_sr3(vuz69, ty_Float) -> new_sr7(vuz69) new_sr3(vuz69, app(ty_Ratio, bd)) -> new_sr4(vuz69, bd) new_sr10(vuz15, vuz51) -> error([]) new_sr9(vuz15, vuz53) -> error([]) new_primMulNat0(Succ(vuz1500), Zero) -> Zero new_primMulNat0(Zero, Succ(vuz5000)) -> Zero new_sr12(vuz15, vuz49, be) -> error([]) new_sr3(vuz69, ty_Integer) -> new_sr8(vuz69) new_primPlusNat1(Succ(vuz580), vuz5000) -> Succ(Succ(new_primPlusNat0(vuz580, vuz5000))) new_sr0(vuz92, vuz93, ty_Integer) -> new_sr9(vuz92, vuz93) new_sr(vuz92, vuz93, app(ty_Ratio, bh)) -> new_sr12(vuz92, vuz93, bh) The set Q consists of the following terms: new_sr6(x0) new_sr1(x0, ty_Integer) new_primMulNat0(Zero, Succ(x0)) new_sr7(x0) new_sr(x0, x1, ty_Double) new_sr(x0, x1, ty_Float) new_sr0(x0, x1, ty_Double) new_sr3(x0, ty_Float) new_sr5(x0) new_primDivNatS0(Zero) new_sr10(x0, x1) new_sr11(Float(x0, x1), Float(x2, x3)) new_primPlusNat0(Zero, Succ(x0)) new_primMulNat0(Zero, Zero) new_primDivNatS0(Succ(Zero)) new_sr4(x0, x1) new_sr2(x0, ty_Int) new_sr1(x0, ty_Double) new_sr0(x0, x1, ty_Float) new_sr0(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Succ(x1)) new_sr(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Succ(x1)) new_sr1(x0, ty_Float) new_primPlusNat1(Zero, x0) new_sr8(x0) new_primDivNatS0(Succ(Succ(x0))) new_sr3(x0, ty_Double) new_primDivNatS1 new_sr0(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Zero) new_sr13(Neg(x0), Neg(x1)) new_sr1(x0, app(ty_Ratio, x1)) new_sr13(Pos(x0), Neg(x1)) new_sr13(Neg(x0), Pos(x1)) new_sr2(x0, ty_Integer) new_sr13(Pos(x0), Pos(x1)) new_sr9(x0, x1) new_sr2(x0, app(ty_Ratio, x1)) new_sr3(x0, ty_Int) new_primPlusNat1(Succ(x0), x1) new_sr3(x0, app(ty_Ratio, x1)) new_sr(x0, x1, app(ty_Ratio, x2)) new_sr3(x0, ty_Integer) new_sr0(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_sr2(x0, ty_Double) new_sr(x0, x1, ty_Integer) new_sr2(x0, ty_Float) new_sr12(x0, x1, x2) new_primPlusNat0(Zero, Zero) new_sr1(x0, ty_Int) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (30) 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_pr2F0G1(vuz92, vuz93, vuz94, Succ(Succ(vuz9500)), h) -> new_pr2F0G1(vuz92, vuz93, vuz94, vuz9500, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 ---------------------------------------- (31) YES ---------------------------------------- (32) Obligation: Q DP problem: The TRS P consists of the following rules: new_pr2F0G13(vuz7, vuz8, Succ(Succ(vuz900)), h) -> new_pr2F0G13(vuz7, vuz8, vuz900, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (33) 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_pr2F0G13(vuz7, vuz8, Succ(Succ(vuz900)), h) -> new_pr2F0G13(vuz7, vuz8, vuz900, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4 ---------------------------------------- (34) YES ---------------------------------------- (35) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(vuz1500), Succ(vuz5000)) -> new_primMulNat(vuz1500, Succ(vuz5000)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (36) 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_primMulNat(Succ(vuz1500), Succ(vuz5000)) -> new_primMulNat(vuz1500, Succ(vuz5000)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (37) YES ---------------------------------------- (38) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS(Succ(Succ(vuz5700000))) -> new_primDivNatS(vuz5700000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (39) 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(vuz5700000))) -> new_primDivNatS(vuz5700000) The graph contains the following edges 1 > 1 ---------------------------------------- (40) YES ---------------------------------------- (41) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vuz5800), Succ(vuz50000)) -> new_primPlusNat(vuz5800, vuz50000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (42) 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(Succ(vuz5800), Succ(vuz50000)) -> new_primPlusNat(vuz5800, vuz50000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (43) YES ---------------------------------------- (44) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="(^^)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="(^^) vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="(^^) vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="prPr0 vuz3 vuz4 (vuz4 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="prPr0 vuz3 vuz4 (compare vuz4 (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="prPr0 vuz3 vuz4 (not (compare vuz4 (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="prPr0 vuz3 vuz4 (not (primCmpInt vuz4 (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];2093[label="vuz4/Pos vuz40",fontsize=10,color="white",style="solid",shape="box"];8 -> 2093[label="",style="solid", color="burlywood", weight=9]; 2093 -> 9[label="",style="solid", color="burlywood", weight=3]; 2094[label="vuz4/Neg vuz40",fontsize=10,color="white",style="solid",shape="box"];8 -> 2094[label="",style="solid", color="burlywood", weight=9]; 2094 -> 10[label="",style="solid", color="burlywood", weight=3]; 9[label="prPr0 vuz3 (Pos vuz40) (not (primCmpInt (Pos vuz40) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];2095[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 2095[label="",style="solid", color="burlywood", weight=9]; 2095 -> 11[label="",style="solid", color="burlywood", weight=3]; 2096[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 2096[label="",style="solid", color="burlywood", weight=9]; 2096 -> 12[label="",style="solid", color="burlywood", weight=3]; 10[label="prPr0 vuz3 (Neg vuz40) (not (primCmpInt (Neg vuz40) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];2097[label="vuz40/Succ vuz400",fontsize=10,color="white",style="solid",shape="box"];10 -> 2097[label="",style="solid", color="burlywood", weight=9]; 2097 -> 13[label="",style="solid", color="burlywood", weight=3]; 2098[label="vuz40/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 2098[label="",style="solid", color="burlywood", weight=9]; 2098 -> 14[label="",style="solid", color="burlywood", weight=3]; 11[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (primCmpInt (Pos (Succ vuz400)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 12[label="prPr0 vuz3 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 13[label="prPr0 vuz3 (Neg (Succ vuz400)) (not (primCmpInt (Neg (Succ vuz400)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 14[label="prPr0 vuz3 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 15[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (primCmpInt (Pos (Succ vuz400)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 16[label="prPr0 vuz3 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 17[label="prPr0 vuz3 (Neg (Succ vuz400)) (not (primCmpInt (Neg (Succ vuz400)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 18[label="prPr0 vuz3 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 19[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (primCmpNat (Succ vuz400) Zero == LT))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="prPr0 vuz3 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="prPr0 vuz3 (Neg (Succ vuz400)) (not (LT == LT))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22[label="prPr0 vuz3 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3]; 23[label="prPr0 vuz3 (Pos (Succ vuz400)) (not (GT == LT))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 24[label="prPr0 vuz3 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 25[label="prPr0 vuz3 (Neg (Succ vuz400)) (not True)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 26[label="prPr0 vuz3 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 27[label="prPr0 vuz3 (Pos (Succ vuz400)) (not False)",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3]; 28[label="prPr0 vuz3 (Pos Zero) True",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3]; 29[label="prPr0 vuz3 (Neg (Succ vuz400)) False",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 30[label="prPr0 vuz3 (Neg Zero) True",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3]; 31[label="prPr0 vuz3 (Pos (Succ vuz400)) True",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3]; 32[label="vuz3 ^ Pos Zero",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3]; 33[label="recip (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3]; 34[label="vuz3 ^ Neg Zero",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3]; 35[label="vuz3 ^ Pos (Succ vuz400)",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 36[label="pr4 vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 37[label="fromInt (Pos (Succ Zero)) / vuz3 ^ (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3]; 38[label="pr4 vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];38 -> 42[label="",style="solid", color="black", weight=3]; 39[label="pr4 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];39 -> 43[label="",style="solid", color="black", weight=3]; 40[label="pr3 (Pos Zero == fromInt (Pos Zero)) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3]; 41[label="primDivFloat (fromInt (Pos (Succ Zero))) (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3]; 42[label="pr3 (Neg Zero == fromInt (Pos Zero)) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3]; 43[label="pr3 (Pos (Succ vuz400) == fromInt (Pos Zero)) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3]; 44[label="pr3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];44 -> 48[label="",style="solid", color="black", weight=3]; 45[label="primDivFloat (primIntToFloat (Pos (Succ Zero))) (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3]; 46[label="pr3 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3]; 47[label="pr3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="triangle"];47 -> 51[label="",style="solid", color="black", weight=3]; 48[label="pr3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3]; 49 -> 68[label="",style="dashed", color="red", weight=0]; 49[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (vuz3 ^ (`negate` Neg (Succ vuz400)))",fontsize=16,color="magenta"];49 -> 69[label="",style="dashed", color="magenta", weight=3]; 50[label="pr3 (primEqInt (Neg Zero) (Pos Zero)) vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3]; 51[label="pr3 (primEqInt (Pos (Succ vuz400)) (Pos Zero)) vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3]; 52[label="pr3 True vuz3 (Pos Zero)",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 69[label="vuz3 ^ (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];69 -> 75[label="",style="solid", color="black", weight=3]; 68[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) vuz5",fontsize=16,color="burlywood",shape="triangle"];2099[label="vuz5/Float vuz50 vuz51",fontsize=10,color="white",style="solid",shape="box"];68 -> 2099[label="",style="solid", color="burlywood", weight=9]; 2099 -> 76[label="",style="solid", color="burlywood", weight=3]; 54[label="pr3 True vuz3 (Neg Zero)",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 55[label="pr3 False vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 56[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];56 -> 60[label="",style="solid", color="black", weight=3]; 75[label="pr4 vuz3 (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];75 -> 78[label="",style="solid", color="black", weight=3]; 76[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float vuz50 vuz51)",fontsize=16,color="black",shape="box"];76 -> 79[label="",style="solid", color="black", weight=3]; 58 -> 56[label="",style="dashed", color="red", weight=0]; 58[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];59[label="pr2 vuz3 (Pos (Succ vuz400))",fontsize=16,color="black",shape="box"];59 -> 62[label="",style="solid", color="black", weight=3]; 60[label="primIntToFloat (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];60 -> 63[label="",style="solid", color="black", weight=3]; 78[label="pr3 (`negate` Neg (Succ vuz400) == fromInt (Pos Zero)) vuz3 (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];78 -> 81[label="",style="solid", color="black", weight=3]; 79[label="Float (Pos (Succ Zero) * vuz51) (Pos (Succ Zero) * vuz50)",fontsize=16,color="green",shape="box"];79 -> 82[label="",style="dashed", color="green", weight=3]; 79 -> 83[label="",style="dashed", color="green", weight=3]; 62[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (Pos (Succ vuz400) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];62 -> 65[label="",style="solid", color="black", weight=3]; 63[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];81[label="pr3 (primEqInt (`negate` Neg (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (`negate` Neg (Succ vuz400))",fontsize=16,color="black",shape="box"];81 -> 85[label="",style="solid", color="black", weight=3]; 82 -> 894[label="",style="dashed", color="red", weight=0]; 82[label="Pos (Succ Zero) * vuz51",fontsize=16,color="magenta"];82 -> 895[label="",style="dashed", color="magenta", weight=3]; 82 -> 896[label="",style="dashed", color="magenta", weight=3]; 83 -> 894[label="",style="dashed", color="red", weight=0]; 83[label="Pos (Succ Zero) * vuz50",fontsize=16,color="magenta"];83 -> 897[label="",style="dashed", color="magenta", weight=3]; 83 -> 898[label="",style="dashed", color="magenta", weight=3]; 65[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (compare (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3]; 85[label="pr3 (primEqInt (primNegInt (Neg (Succ vuz400))) (fromInt (Pos Zero))) vuz3 (primNegInt (Neg (Succ vuz400)))",fontsize=16,color="black",shape="box"];85 -> 89[label="",style="solid", color="black", weight=3]; 895[label="vuz51",fontsize=16,color="green",shape="box"];896[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];894[label="vuz15 * vuz50",fontsize=16,color="black",shape="triangle"];894 -> 906[label="",style="solid", color="black", weight=3]; 897[label="vuz50",fontsize=16,color="green",shape="box"];898[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];67[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];67 -> 77[label="",style="solid", color="black", weight=3]; 89 -> 47[label="",style="dashed", color="red", weight=0]; 89[label="pr3 (primEqInt (Pos (Succ vuz400)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400))",fontsize=16,color="magenta"];89 -> 93[label="",style="dashed", color="magenta", weight=3]; 906[label="primMulInt vuz15 vuz50",fontsize=16,color="burlywood",shape="box"];2100[label="vuz15/Pos vuz150",fontsize=10,color="white",style="solid",shape="box"];906 -> 2100[label="",style="solid", color="burlywood", weight=9]; 2100 -> 918[label="",style="solid", color="burlywood", weight=3]; 2101[label="vuz15/Neg vuz150",fontsize=10,color="white",style="solid",shape="box"];906 -> 2101[label="",style="solid", color="burlywood", weight=9]; 2101 -> 919[label="",style="solid", color="burlywood", weight=3]; 77[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpInt (Pos (Succ vuz400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];77 -> 80[label="",style="solid", color="black", weight=3]; 93[label="vuz400",fontsize=16,color="green",shape="box"];918[label="primMulInt (Pos vuz150) vuz50",fontsize=16,color="burlywood",shape="box"];2102[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];918 -> 2102[label="",style="solid", color="burlywood", weight=9]; 2102 -> 932[label="",style="solid", color="burlywood", weight=3]; 2103[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];918 -> 2103[label="",style="solid", color="burlywood", weight=9]; 2103 -> 933[label="",style="solid", color="burlywood", weight=3]; 919[label="primMulInt (Neg vuz150) vuz50",fontsize=16,color="burlywood",shape="box"];2104[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];919 -> 2104[label="",style="solid", color="burlywood", weight=9]; 2104 -> 934[label="",style="solid", color="burlywood", weight=3]; 2105[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];919 -> 2105[label="",style="solid", color="burlywood", weight=9]; 2105 -> 935[label="",style="solid", color="burlywood", weight=3]; 80[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (primCmpNat (Succ vuz400) Zero == GT)",fontsize=16,color="black",shape="box"];80 -> 84[label="",style="solid", color="black", weight=3]; 932[label="primMulInt (Pos vuz150) (Pos vuz500)",fontsize=16,color="black",shape="box"];932 -> 945[label="",style="solid", color="black", weight=3]; 933[label="primMulInt (Pos vuz150) (Neg vuz500)",fontsize=16,color="black",shape="box"];933 -> 946[label="",style="solid", color="black", weight=3]; 934[label="primMulInt (Neg vuz150) (Pos vuz500)",fontsize=16,color="black",shape="box"];934 -> 947[label="",style="solid", color="black", weight=3]; 935[label="primMulInt (Neg vuz150) (Neg vuz500)",fontsize=16,color="black",shape="box"];935 -> 948[label="",style="solid", color="black", weight=3]; 84[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) (GT == GT)",fontsize=16,color="black",shape="box"];84 -> 88[label="",style="solid", color="black", weight=3]; 945[label="Pos (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];945 -> 974[label="",style="dashed", color="green", weight=3]; 946[label="Neg (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];946 -> 975[label="",style="dashed", color="green", weight=3]; 947[label="Neg (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];947 -> 976[label="",style="dashed", color="green", weight=3]; 948[label="Pos (primMulNat vuz150 vuz500)",fontsize=16,color="green",shape="box"];948 -> 977[label="",style="dashed", color="green", weight=3]; 88[label="pr2Pr1 vuz3 (Pos (Succ vuz400)) True",fontsize=16,color="black",shape="box"];88 -> 92[label="",style="solid", color="black", weight=3]; 974[label="primMulNat vuz150 vuz500",fontsize=16,color="burlywood",shape="triangle"];2106[label="vuz150/Succ vuz1500",fontsize=10,color="white",style="solid",shape="box"];974 -> 2106[label="",style="solid", color="burlywood", weight=9]; 2106 -> 1013[label="",style="solid", color="burlywood", weight=3]; 2107[label="vuz150/Zero",fontsize=10,color="white",style="solid",shape="box"];974 -> 2107[label="",style="solid", color="burlywood", weight=9]; 2107 -> 1014[label="",style="solid", color="burlywood", weight=3]; 975 -> 974[label="",style="dashed", color="red", weight=0]; 975[label="primMulNat vuz150 vuz500",fontsize=16,color="magenta"];975 -> 1015[label="",style="dashed", color="magenta", weight=3]; 976 -> 974[label="",style="dashed", color="red", weight=0]; 976[label="primMulNat vuz150 vuz500",fontsize=16,color="magenta"];976 -> 1016[label="",style="dashed", color="magenta", weight=3]; 977 -> 974[label="",style="dashed", color="red", weight=0]; 977[label="primMulNat vuz150 vuz500",fontsize=16,color="magenta"];977 -> 1017[label="",style="dashed", color="magenta", weight=3]; 977 -> 1018[label="",style="dashed", color="magenta", weight=3]; 92[label="pr2F vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];92 -> 96[label="",style="solid", color="black", weight=3]; 1013[label="primMulNat (Succ vuz1500) vuz500",fontsize=16,color="burlywood",shape="box"];2108[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];1013 -> 2108[label="",style="solid", color="burlywood", weight=9]; 2108 -> 1027[label="",style="solid", color="burlywood", weight=3]; 2109[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];1013 -> 2109[label="",style="solid", color="burlywood", weight=9]; 2109 -> 1028[label="",style="solid", color="burlywood", weight=3]; 1014[label="primMulNat Zero vuz500",fontsize=16,color="burlywood",shape="box"];2110[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];1014 -> 2110[label="",style="solid", color="burlywood", weight=9]; 2110 -> 1029[label="",style="solid", color="burlywood", weight=3]; 2111[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];1014 -> 2111[label="",style="solid", color="burlywood", weight=9]; 2111 -> 1030[label="",style="solid", color="burlywood", weight=3]; 1015[label="vuz500",fontsize=16,color="green",shape="box"];1016[label="vuz150",fontsize=16,color="green",shape="box"];1017[label="vuz500",fontsize=16,color="green",shape="box"];1018[label="vuz150",fontsize=16,color="green",shape="box"];96[label="pr2F4 vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];96 -> 99[label="",style="solid", color="black", weight=3]; 1027[label="primMulNat (Succ vuz1500) (Succ vuz5000)",fontsize=16,color="black",shape="box"];1027 -> 1040[label="",style="solid", color="black", weight=3]; 1028[label="primMulNat (Succ vuz1500) Zero",fontsize=16,color="black",shape="box"];1028 -> 1041[label="",style="solid", color="black", weight=3]; 1029[label="primMulNat Zero (Succ vuz5000)",fontsize=16,color="black",shape="box"];1029 -> 1042[label="",style="solid", color="black", weight=3]; 1030[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1030 -> 1043[label="",style="solid", color="black", weight=3]; 99[label="pr2F3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];99 -> 103[label="",style="solid", color="black", weight=3]; 1040 -> 1052[label="",style="dashed", color="red", weight=0]; 1040[label="primPlusNat (primMulNat vuz1500 (Succ vuz5000)) (Succ vuz5000)",fontsize=16,color="magenta"];1040 -> 1053[label="",style="dashed", color="magenta", weight=3]; 1041[label="Zero",fontsize=16,color="green",shape="box"];1042[label="Zero",fontsize=16,color="green",shape="box"];1043[label="Zero",fontsize=16,color="green",shape="box"];103[label="pr2F3 (primEqInt (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz400) - fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];103 -> 106[label="",style="solid", color="black", weight=3]; 1053 -> 974[label="",style="dashed", color="red", weight=0]; 1053[label="primMulNat vuz1500 (Succ vuz5000)",fontsize=16,color="magenta"];1053 -> 1054[label="",style="dashed", color="magenta", weight=3]; 1053 -> 1055[label="",style="dashed", color="magenta", weight=3]; 1052[label="primPlusNat vuz58 (Succ vuz5000)",fontsize=16,color="burlywood",shape="triangle"];2112[label="vuz58/Succ vuz580",fontsize=10,color="white",style="solid",shape="box"];1052 -> 2112[label="",style="solid", color="burlywood", weight=9]; 2112 -> 1056[label="",style="solid", color="burlywood", weight=3]; 2113[label="vuz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1052 -> 2113[label="",style="solid", color="burlywood", weight=9]; 2113 -> 1057[label="",style="solid", color="burlywood", weight=3]; 106[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (fromInt (Pos (Succ Zero)))) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (fromInt (Pos (Succ Zero)))) vuz3",fontsize=16,color="black",shape="box"];106 -> 108[label="",style="solid", color="black", weight=3]; 1054[label="Succ vuz5000",fontsize=16,color="green",shape="box"];1055[label="vuz1500",fontsize=16,color="green",shape="box"];1056[label="primPlusNat (Succ vuz580) (Succ vuz5000)",fontsize=16,color="black",shape="box"];1056 -> 1062[label="",style="solid", color="black", weight=3]; 1057[label="primPlusNat Zero (Succ vuz5000)",fontsize=16,color="black",shape="box"];1057 -> 1063[label="",style="solid", color="black", weight=3]; 108[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz400)) (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz3 (primMinusInt (Pos (Succ vuz400)) (Pos (Succ Zero))) vuz3",fontsize=16,color="black",shape="box"];108 -> 110[label="",style="solid", color="black", weight=3]; 1062[label="Succ (Succ (primPlusNat vuz580 vuz5000))",fontsize=16,color="green",shape="box"];1062 -> 1070[label="",style="dashed", color="green", weight=3]; 1063[label="Succ vuz5000",fontsize=16,color="green",shape="box"];110[label="pr2F3 (primEqInt (primMinusNat (Succ vuz400) (Succ Zero)) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz400) (Succ Zero)) vuz3",fontsize=16,color="black",shape="box"];110 -> 111[label="",style="solid", color="black", weight=3]; 1070[label="primPlusNat vuz580 vuz5000",fontsize=16,color="burlywood",shape="triangle"];2114[label="vuz580/Succ vuz5800",fontsize=10,color="white",style="solid",shape="box"];1070 -> 2114[label="",style="solid", color="burlywood", weight=9]; 2114 -> 1078[label="",style="solid", color="burlywood", weight=3]; 2115[label="vuz580/Zero",fontsize=10,color="white",style="solid",shape="box"];1070 -> 2115[label="",style="solid", color="burlywood", weight=9]; 2115 -> 1079[label="",style="solid", color="burlywood", weight=3]; 111[label="pr2F3 (primEqInt (primMinusNat vuz400 Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat vuz400 Zero) vuz3",fontsize=16,color="burlywood",shape="box"];2116[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];111 -> 2116[label="",style="solid", color="burlywood", weight=9]; 2116 -> 112[label="",style="solid", color="burlywood", weight=3]; 2117[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];111 -> 2117[label="",style="solid", color="burlywood", weight=9]; 2117 -> 113[label="",style="solid", color="burlywood", weight=3]; 1078[label="primPlusNat (Succ vuz5800) vuz5000",fontsize=16,color="burlywood",shape="box"];2118[label="vuz5000/Succ vuz50000",fontsize=10,color="white",style="solid",shape="box"];1078 -> 2118[label="",style="solid", color="burlywood", weight=9]; 2118 -> 1088[label="",style="solid", color="burlywood", weight=3]; 2119[label="vuz5000/Zero",fontsize=10,color="white",style="solid",shape="box"];1078 -> 2119[label="",style="solid", color="burlywood", weight=9]; 2119 -> 1089[label="",style="solid", color="burlywood", weight=3]; 1079[label="primPlusNat Zero vuz5000",fontsize=16,color="burlywood",shape="box"];2120[label="vuz5000/Succ vuz50000",fontsize=10,color="white",style="solid",shape="box"];1079 -> 2120[label="",style="solid", color="burlywood", weight=9]; 2120 -> 1090[label="",style="solid", color="burlywood", weight=3]; 2121[label="vuz5000/Zero",fontsize=10,color="white",style="solid",shape="box"];1079 -> 2121[label="",style="solid", color="burlywood", weight=9]; 2121 -> 1091[label="",style="solid", color="burlywood", weight=3]; 112[label="pr2F3 (primEqInt (primMinusNat (Succ vuz4000) Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat (Succ vuz4000) Zero) vuz3",fontsize=16,color="black",shape="box"];112 -> 114[label="",style="solid", color="black", weight=3]; 113[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz3 (primMinusNat Zero Zero) vuz3",fontsize=16,color="black",shape="box"];113 -> 115[label="",style="solid", color="black", weight=3]; 1088[label="primPlusNat (Succ vuz5800) (Succ vuz50000)",fontsize=16,color="black",shape="box"];1088 -> 1100[label="",style="solid", color="black", weight=3]; 1089[label="primPlusNat (Succ vuz5800) Zero",fontsize=16,color="black",shape="box"];1089 -> 1101[label="",style="solid", color="black", weight=3]; 1090[label="primPlusNat Zero (Succ vuz50000)",fontsize=16,color="black",shape="box"];1090 -> 1102[label="",style="solid", color="black", weight=3]; 1091[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1091 -> 1103[label="",style="solid", color="black", weight=3]; 114[label="pr2F3 (primEqInt (Pos (Succ vuz4000)) (fromInt (Pos Zero))) vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];114 -> 116[label="",style="solid", color="black", weight=3]; 115[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];115 -> 117[label="",style="solid", color="black", weight=3]; 1100[label="Succ (Succ (primPlusNat vuz5800 vuz50000))",fontsize=16,color="green",shape="box"];1100 -> 1113[label="",style="dashed", color="green", weight=3]; 1101[label="Succ vuz5800",fontsize=16,color="green",shape="box"];1102[label="Succ vuz50000",fontsize=16,color="green",shape="box"];1103[label="Zero",fontsize=16,color="green",shape="box"];116[label="pr2F3 (primEqInt (Pos (Succ vuz4000)) (Pos Zero)) vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];116 -> 118[label="",style="solid", color="black", weight=3]; 117[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];117 -> 119[label="",style="solid", color="black", weight=3]; 1113 -> 1070[label="",style="dashed", color="red", weight=0]; 1113[label="primPlusNat vuz5800 vuz50000",fontsize=16,color="magenta"];1113 -> 1123[label="",style="dashed", color="magenta", weight=3]; 1113 -> 1124[label="",style="dashed", color="magenta", weight=3]; 118[label="pr2F3 False vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];118 -> 120[label="",style="solid", color="black", weight=3]; 119[label="pr2F3 True vuz3 (Pos Zero) vuz3",fontsize=16,color="black",shape="box"];119 -> 121[label="",style="solid", color="black", weight=3]; 1123[label="vuz5800",fontsize=16,color="green",shape="box"];1124[label="vuz50000",fontsize=16,color="green",shape="box"];120[label="pr2F0 vuz3 (Pos (Succ vuz4000)) vuz3",fontsize=16,color="black",shape="box"];120 -> 122[label="",style="solid", color="black", weight=3]; 121[label="vuz3",fontsize=16,color="green",shape="box"];122[label="pr2F0G vuz3 vuz3 (Pos (Succ vuz4000))",fontsize=16,color="black",shape="box"];122 -> 123[label="",style="solid", color="black", weight=3]; 123[label="pr2F0G2 vuz3 vuz3 (Pos (Succ vuz4000))",fontsize=16,color="black",shape="box"];123 -> 124[label="",style="solid", color="black", weight=3]; 124[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz4000)) (even (Pos (Succ vuz4000)))",fontsize=16,color="black",shape="box"];124 -> 125[label="",style="solid", color="black", weight=3]; 125[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz4000)) (primEvenInt (Pos (Succ vuz4000)))",fontsize=16,color="black",shape="box"];125 -> 126[label="",style="solid", color="black", weight=3]; 126 -> 159[label="",style="dashed", color="red", weight=0]; 126[label="pr2F0G1 vuz3 vuz3 (Pos (Succ vuz4000)) (primEvenNat (Succ vuz4000))",fontsize=16,color="magenta"];126 -> 160[label="",style="dashed", color="magenta", weight=3]; 126 -> 161[label="",style="dashed", color="magenta", weight=3]; 126 -> 162[label="",style="dashed", color="magenta", weight=3]; 160[label="Succ vuz4000",fontsize=16,color="green",shape="box"];161[label="vuz4000",fontsize=16,color="green",shape="box"];162[label="vuz3",fontsize=16,color="green",shape="box"];159[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat vuz9)",fontsize=16,color="burlywood",shape="triangle"];2122[label="vuz9/Succ vuz90",fontsize=10,color="white",style="solid",shape="box"];159 -> 2122[label="",style="solid", color="burlywood", weight=9]; 2122 -> 172[label="",style="solid", color="burlywood", weight=3]; 2123[label="vuz9/Zero",fontsize=10,color="white",style="solid",shape="box"];159 -> 2123[label="",style="solid", color="burlywood", weight=9]; 2123 -> 173[label="",style="solid", color="burlywood", weight=3]; 172[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat (Succ vuz90))",fontsize=16,color="burlywood",shape="box"];2124[label="vuz90/Succ vuz900",fontsize=10,color="white",style="solid",shape="box"];172 -> 2124[label="",style="solid", color="burlywood", weight=9]; 2124 -> 174[label="",style="solid", color="burlywood", weight=3]; 2125[label="vuz90/Zero",fontsize=10,color="white",style="solid",shape="box"];172 -> 2125[label="",style="solid", color="burlywood", weight=9]; 2125 -> 175[label="",style="solid", color="burlywood", weight=3]; 173[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];173 -> 176[label="",style="solid", color="black", weight=3]; 174[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat (Succ (Succ vuz900)))",fontsize=16,color="black",shape="box"];174 -> 177[label="",style="solid", color="black", weight=3]; 175[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];175 -> 178[label="",style="solid", color="black", weight=3]; 176[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) True",fontsize=16,color="black",shape="box"];176 -> 179[label="",style="solid", color="black", weight=3]; 177 -> 159[label="",style="dashed", color="red", weight=0]; 177[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) (primEvenNat vuz900)",fontsize=16,color="magenta"];177 -> 180[label="",style="dashed", color="magenta", weight=3]; 178[label="pr2F0G1 vuz7 vuz7 (Pos (Succ vuz8)) False",fontsize=16,color="black",shape="box"];178 -> 181[label="",style="solid", color="black", weight=3]; 179[label="pr2F0G vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];179 -> 182[label="",style="solid", color="black", weight=3]; 180[label="vuz900",fontsize=16,color="green",shape="box"];181[label="pr2F0G0 vuz7 vuz7 (Pos (Succ vuz8)) otherwise",fontsize=16,color="black",shape="box"];181 -> 183[label="",style="solid", color="black", weight=3]; 182[label="pr2F0G2 vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];182 -> 184[label="",style="solid", color="black", weight=3]; 183[label="pr2F0G0 vuz7 vuz7 (Pos (Succ vuz8)) True",fontsize=16,color="black",shape="box"];183 -> 185[label="",style="solid", color="black", weight=3]; 184[label="pr2F0G1 vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];184 -> 186[label="",style="solid", color="black", weight=3]; 185[label="pr2F vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="black",shape="box"];185 -> 187[label="",style="solid", color="black", weight=3]; 186[label="pr2F0G1 vuz7 (vuz7 * vuz7) (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz8) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];186 -> 188[label="",style="solid", color="black", weight=3]; 187[label="pr2F4 vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="black",shape="box"];187 -> 189[label="",style="solid", color="black", weight=3]; 188[label="pr2F0G1 vuz7 (vuz7 * vuz7) (primQuotInt (Pos (Succ vuz8)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz8)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];188 -> 190[label="",style="solid", color="black", weight=3]; 189[label="pr2F3 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="black",shape="box"];189 -> 191[label="",style="solid", color="black", weight=3]; 190 -> 991[label="",style="dashed", color="red", weight=0]; 190[label="pr2F0G1 vuz7 (vuz7 * vuz7) (primQuotInt (Pos (Succ vuz8)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz8)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];190 -> 992[label="",style="dashed", color="magenta", weight=3]; 190 -> 993[label="",style="dashed", color="magenta", weight=3]; 190 -> 994[label="",style="dashed", color="magenta", weight=3]; 191 -> 1922[label="",style="dashed", color="red", weight=0]; 191[label="pr2F3 (primEqInt (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz7 (Pos (Succ vuz8) - fromInt (Pos (Succ Zero))) (vuz7 * vuz7)",fontsize=16,color="magenta"];191 -> 1923[label="",style="dashed", color="magenta", weight=3]; 191 -> 1924[label="",style="dashed", color="magenta", weight=3]; 191 -> 1925[label="",style="dashed", color="magenta", weight=3]; 992[label="Succ vuz8",fontsize=16,color="green",shape="box"];993[label="vuz7",fontsize=16,color="green",shape="box"];994[label="vuz7",fontsize=16,color="green",shape="box"];991[label="pr2F0G1 vuz55 (vuz56 * vuz56) (primQuotInt (Pos vuz57) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos vuz57) (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];991 -> 1019[label="",style="solid", color="black", weight=3]; 1923[label="vuz8",fontsize=16,color="green",shape="box"];1924[label="vuz7",fontsize=16,color="green",shape="box"];1925[label="vuz7",fontsize=16,color="green",shape="box"];1922[label="pr2F3 (primEqInt (Pos (Succ vuz88) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz89 (Pos (Succ vuz88) - fromInt (Pos (Succ Zero))) (vuz89 * vuz90)",fontsize=16,color="black",shape="triangle"];1922 -> 1944[label="",style="solid", color="black", weight=3]; 1019[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS vuz57 (Succ (Succ Zero)))) (primEvenInt (Pos (primDivNatS vuz57 (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1019 -> 1031[label="",style="solid", color="black", weight=3]; 1944[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz88)) (fromInt (Pos (Succ Zero)))) (fromInt (Pos Zero))) vuz89 (primMinusInt (Pos (Succ vuz88)) (fromInt (Pos (Succ Zero)))) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1944 -> 1950[label="",style="solid", color="black", weight=3]; 1031[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS vuz57 (Succ (Succ Zero)))) (primEvenNat (primDivNatS vuz57 (Succ (Succ Zero))))",fontsize=16,color="burlywood",shape="box"];2126[label="vuz57/Succ vuz570",fontsize=10,color="white",style="solid",shape="box"];1031 -> 2126[label="",style="solid", color="burlywood", weight=9]; 2126 -> 1044[label="",style="solid", color="burlywood", weight=3]; 2127[label="vuz57/Zero",fontsize=10,color="white",style="solid",shape="box"];1031 -> 2127[label="",style="solid", color="burlywood", weight=9]; 2127 -> 1045[label="",style="solid", color="burlywood", weight=3]; 1950[label="pr2F3 (primEqInt (primMinusInt (Pos (Succ vuz88)) (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz89 (primMinusInt (Pos (Succ vuz88)) (Pos (Succ Zero))) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1950 -> 1956[label="",style="solid", color="black", weight=3]; 1044[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS (Succ vuz570) (Succ (Succ Zero)))) (primEvenNat (primDivNatS (Succ vuz570) (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1044 -> 1058[label="",style="solid", color="black", weight=3]; 1045[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS Zero (Succ (Succ Zero)))) (primEvenNat (primDivNatS Zero (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1045 -> 1059[label="",style="solid", color="black", weight=3]; 1956[label="pr2F3 (primEqInt (primMinusNat (Succ vuz88) (Succ Zero)) (fromInt (Pos Zero))) vuz89 (primMinusNat (Succ vuz88) (Succ Zero)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1956 -> 1957[label="",style="solid", color="black", weight=3]; 1058[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 vuz570 (Succ Zero) (primGEqNatS vuz570 (Succ Zero)))) (primEvenNat (primDivNatS0 vuz570 (Succ Zero) (primGEqNatS vuz570 (Succ Zero))))",fontsize=16,color="burlywood",shape="box"];2128[label="vuz570/Succ vuz5700",fontsize=10,color="white",style="solid",shape="box"];1058 -> 2128[label="",style="solid", color="burlywood", weight=9]; 2128 -> 1064[label="",style="solid", color="burlywood", weight=3]; 2129[label="vuz570/Zero",fontsize=10,color="white",style="solid",shape="box"];1058 -> 2129[label="",style="solid", color="burlywood", weight=9]; 2129 -> 1065[label="",style="solid", color="burlywood", weight=3]; 1059[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos Zero) (primEvenNat Zero)",fontsize=16,color="black",shape="triangle"];1059 -> 1066[label="",style="solid", color="black", weight=3]; 1957[label="pr2F3 (primEqInt (primMinusNat vuz88 Zero) (fromInt (Pos Zero))) vuz89 (primMinusNat vuz88 Zero) (vuz89 * vuz90)",fontsize=16,color="burlywood",shape="box"];2130[label="vuz88/Succ vuz880",fontsize=10,color="white",style="solid",shape="box"];1957 -> 2130[label="",style="solid", color="burlywood", weight=9]; 2130 -> 1958[label="",style="solid", color="burlywood", weight=3]; 2131[label="vuz88/Zero",fontsize=10,color="white",style="solid",shape="box"];1957 -> 2131[label="",style="solid", color="burlywood", weight=9]; 2131 -> 1959[label="",style="solid", color="burlywood", weight=3]; 1064[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS (Succ vuz5700) (Succ Zero)))) (primEvenNat (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS (Succ vuz5700) (Succ Zero))))",fontsize=16,color="black",shape="box"];1064 -> 1071[label="",style="solid", color="black", weight=3]; 1065[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero)))) (primEvenNat (primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero))))",fontsize=16,color="black",shape="box"];1065 -> 1072[label="",style="solid", color="black", weight=3]; 1066[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos Zero) True",fontsize=16,color="black",shape="box"];1066 -> 1073[label="",style="solid", color="black", weight=3]; 1958[label="pr2F3 (primEqInt (primMinusNat (Succ vuz880) Zero) (fromInt (Pos Zero))) vuz89 (primMinusNat (Succ vuz880) Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1958 -> 1960[label="",style="solid", color="black", weight=3]; 1959[label="pr2F3 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) vuz89 (primMinusNat Zero Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1959 -> 1961[label="",style="solid", color="black", weight=3]; 1071[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS vuz5700 Zero))) (primEvenNat (primDivNatS0 (Succ vuz5700) (Succ Zero) (primGEqNatS vuz5700 Zero)))",fontsize=16,color="burlywood",shape="box"];2132[label="vuz5700/Succ vuz57000",fontsize=10,color="white",style="solid",shape="box"];1071 -> 2132[label="",style="solid", color="burlywood", weight=9]; 2132 -> 1080[label="",style="solid", color="burlywood", weight=3]; 2133[label="vuz5700/Zero",fontsize=10,color="white",style="solid",shape="box"];1071 -> 2133[label="",style="solid", color="burlywood", weight=9]; 2133 -> 1081[label="",style="solid", color="burlywood", weight=3]; 1072[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 Zero (Succ Zero) False)) (primEvenNat (primDivNatS0 Zero (Succ Zero) False))",fontsize=16,color="black",shape="box"];1072 -> 1082[label="",style="solid", color="black", weight=3]; 1073[label="pr2F0G vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1073 -> 1083[label="",style="solid", color="black", weight=3]; 1960[label="pr2F3 (primEqInt (Pos (Succ vuz880)) (fromInt (Pos Zero))) vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1960 -> 1962[label="",style="solid", color="black", weight=3]; 1961[label="pr2F3 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz89 (Pos Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1961 -> 1963[label="",style="solid", color="black", weight=3]; 1080[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) (primGEqNatS (Succ vuz57000) Zero))) (primEvenNat (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) (primGEqNatS (Succ vuz57000) Zero)))",fontsize=16,color="black",shape="box"];1080 -> 1092[label="",style="solid", color="black", weight=3]; 1081[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero))) (primEvenNat (primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];1081 -> 1093[label="",style="solid", color="black", weight=3]; 1082 -> 1059[label="",style="dashed", color="red", weight=0]; 1082[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos Zero) (primEvenNat Zero)",fontsize=16,color="magenta"];1083[label="pr2F0G2 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1083 -> 1094[label="",style="solid", color="black", weight=3]; 1962[label="pr2F3 (primEqInt (Pos (Succ vuz880)) (Pos Zero)) vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1962 -> 1964[label="",style="solid", color="black", weight=3]; 1963[label="pr2F3 (primEqInt (Pos Zero) (Pos Zero)) vuz89 (Pos Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1963 -> 1965[label="",style="solid", color="black", weight=3]; 1092[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) True)) (primEvenNat (primDivNatS0 (Succ (Succ vuz57000)) (Succ Zero) True))",fontsize=16,color="black",shape="box"];1092 -> 1104[label="",style="solid", color="black", weight=3]; 1093[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (primDivNatS0 (Succ Zero) (Succ Zero) True)) (primEvenNat (primDivNatS0 (Succ Zero) (Succ Zero) True))",fontsize=16,color="black",shape="box"];1093 -> 1105[label="",style="solid", color="black", weight=3]; 1094[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1094 -> 1106[label="",style="solid", color="black", weight=3]; 1964[label="pr2F3 False vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1964 -> 1966[label="",style="solid", color="black", weight=3]; 1965[label="pr2F3 True vuz89 (Pos Zero) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1965 -> 1967[label="",style="solid", color="black", weight=3]; 1104 -> 1318[label="",style="dashed", color="red", weight=0]; 1104[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (Succ (primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero))))) (primEvenNat (Succ (primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1104 -> 1319[label="",style="dashed", color="magenta", weight=3]; 1104 -> 1320[label="",style="dashed", color="magenta", weight=3]; 1104 -> 1321[label="",style="dashed", color="magenta", weight=3]; 1104 -> 1322[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1318[label="",style="dashed", color="red", weight=0]; 1105[label="pr2F0G1 vuz55 (vuz56 * vuz56) (Pos (Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))))) (primEvenNat (Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1105 -> 1323[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1324[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1325[label="",style="dashed", color="magenta", weight=3]; 1105 -> 1326[label="",style="dashed", color="magenta", weight=3]; 1106[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos Zero `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1106 -> 1116[label="",style="solid", color="black", weight=3]; 1966[label="pr2F0 vuz89 (Pos (Succ vuz880)) (vuz89 * vuz90)",fontsize=16,color="black",shape="box"];1966 -> 1968[label="",style="solid", color="black", weight=3]; 1967[label="vuz89 * vuz90",fontsize=16,color="blue",shape="box"];2134[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2134[label="",style="solid", color="blue", weight=9]; 2134 -> 1969[label="",style="solid", color="blue", weight=3]; 2135[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2135[label="",style="solid", color="blue", weight=9]; 2135 -> 1970[label="",style="solid", color="blue", weight=3]; 2136[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2136[label="",style="solid", color="blue", weight=9]; 2136 -> 1971[label="",style="solid", color="blue", weight=3]; 2137[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2137[label="",style="solid", color="blue", weight=9]; 2137 -> 1972[label="",style="solid", color="blue", weight=3]; 2138[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1967 -> 2138[label="",style="solid", color="blue", weight=9]; 2138 -> 1973[label="",style="solid", color="blue", weight=3]; 1319[label="Succ (primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1319 -> 1343[label="",style="dashed", color="green", weight=3]; 1320[label="primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];1320 -> 1344[label="",style="solid", color="black", weight=3]; 1321[label="vuz55",fontsize=16,color="green",shape="box"];1322[label="vuz56",fontsize=16,color="green",shape="box"];1318[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat vuz71)",fontsize=16,color="burlywood",shape="triangle"];2139[label="vuz71/Succ vuz710",fontsize=10,color="white",style="solid",shape="box"];1318 -> 2139[label="",style="solid", color="burlywood", weight=9]; 2139 -> 1345[label="",style="solid", color="burlywood", weight=3]; 2140[label="vuz71/Zero",fontsize=10,color="white",style="solid",shape="box"];1318 -> 2140[label="",style="solid", color="burlywood", weight=9]; 2140 -> 1346[label="",style="solid", color="burlywood", weight=3]; 1323[label="Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1323 -> 1347[label="",style="dashed", color="green", weight=3]; 1324[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];1324 -> 1348[label="",style="solid", color="black", weight=3]; 1325[label="vuz55",fontsize=16,color="green",shape="box"];1326[label="vuz56",fontsize=16,color="green",shape="box"];1116[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos Zero) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1116 -> 1127[label="",style="solid", color="black", weight=3]; 1968[label="pr2F0G (vuz89 * vuz90) vuz89 (Pos (Succ vuz880))",fontsize=16,color="black",shape="box"];1968 -> 1974[label="",style="solid", color="black", weight=3]; 1969 -> 878[label="",style="dashed", color="red", weight=0]; 1969[label="vuz89 * vuz90",fontsize=16,color="magenta"];1969 -> 1975[label="",style="dashed", color="magenta", weight=3]; 1969 -> 1976[label="",style="dashed", color="magenta", weight=3]; 1970 -> 894[label="",style="dashed", color="red", weight=0]; 1970[label="vuz89 * vuz90",fontsize=16,color="magenta"];1970 -> 1977[label="",style="dashed", color="magenta", weight=3]; 1970 -> 1978[label="",style="dashed", color="magenta", weight=3]; 1971 -> 914[label="",style="dashed", color="red", weight=0]; 1971[label="vuz89 * vuz90",fontsize=16,color="magenta"];1971 -> 1979[label="",style="dashed", color="magenta", weight=3]; 1971 -> 1980[label="",style="dashed", color="magenta", weight=3]; 1972 -> 928[label="",style="dashed", color="red", weight=0]; 1972[label="vuz89 * vuz90",fontsize=16,color="magenta"];1972 -> 1981[label="",style="dashed", color="magenta", weight=3]; 1972 -> 1982[label="",style="dashed", color="magenta", weight=3]; 1973 -> 941[label="",style="dashed", color="red", weight=0]; 1973[label="vuz89 * vuz90",fontsize=16,color="magenta"];1973 -> 1983[label="",style="dashed", color="magenta", weight=3]; 1973 -> 1984[label="",style="dashed", color="magenta", weight=3]; 1343 -> 1320[label="",style="dashed", color="red", weight=0]; 1343[label="primDivNatS (primMinusNatS (Succ (Succ vuz57000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1344[label="primDivNatS (primMinusNatS (Succ vuz57000) Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1344 -> 1351[label="",style="solid", color="black", weight=3]; 1345[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat (Succ vuz710))",fontsize=16,color="burlywood",shape="box"];2141[label="vuz710/Succ vuz7100",fontsize=10,color="white",style="solid",shape="box"];1345 -> 2141[label="",style="solid", color="burlywood", weight=9]; 2141 -> 1352[label="",style="solid", color="burlywood", weight=3]; 2142[label="vuz710/Zero",fontsize=10,color="white",style="solid",shape="box"];1345 -> 2142[label="",style="solid", color="burlywood", weight=9]; 2142 -> 1353[label="",style="solid", color="burlywood", weight=3]; 1346[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];1346 -> 1354[label="",style="solid", color="black", weight=3]; 1347 -> 1324[label="",style="dashed", color="red", weight=0]; 1347[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1348[label="primDivNatS (primMinusNatS Zero Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1348 -> 1355[label="",style="solid", color="black", weight=3]; 1127 -> 991[label="",style="dashed", color="red", weight=0]; 1127[label="pr2F0G1 vuz55 (vuz56 * vuz56 * (vuz56 * vuz56)) (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos Zero) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1127 -> 1143[label="",style="dashed", color="magenta", weight=3]; 1127 -> 1144[label="",style="dashed", color="magenta", weight=3]; 1974[label="pr2F0G2 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880))",fontsize=16,color="black",shape="box"];1974 -> 1985[label="",style="solid", color="black", weight=3]; 1975[label="vuz89",fontsize=16,color="green",shape="box"];1976[label="vuz90",fontsize=16,color="green",shape="box"];878[label="vuz15 * vuz49",fontsize=16,color="black",shape="triangle"];878 -> 883[label="",style="solid", color="black", weight=3]; 1977[label="vuz90",fontsize=16,color="green",shape="box"];1978[label="vuz89",fontsize=16,color="green",shape="box"];1979[label="vuz90",fontsize=16,color="green",shape="box"];1980[label="vuz89",fontsize=16,color="green",shape="box"];914[label="vuz15 * vuz51",fontsize=16,color="black",shape="triangle"];914 -> 920[label="",style="solid", color="black", weight=3]; 1981[label="vuz89",fontsize=16,color="green",shape="box"];1982[label="vuz90",fontsize=16,color="green",shape="box"];928[label="vuz15 * vuz52",fontsize=16,color="black",shape="triangle"];928 -> 936[label="",style="solid", color="black", weight=3]; 1983[label="vuz90",fontsize=16,color="green",shape="box"];1984[label="vuz89",fontsize=16,color="green",shape="box"];941[label="vuz15 * vuz53",fontsize=16,color="black",shape="triangle"];941 -> 949[label="",style="solid", color="black", weight=3]; 1351[label="primDivNatS (Succ vuz57000) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1351 -> 1358[label="",style="solid", color="black", weight=3]; 1352[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat (Succ (Succ vuz7100)))",fontsize=16,color="black",shape="box"];1352 -> 1359[label="",style="solid", color="black", weight=3]; 1353[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];1353 -> 1360[label="",style="solid", color="black", weight=3]; 1354[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) True",fontsize=16,color="black",shape="box"];1354 -> 1361[label="",style="solid", color="black", weight=3]; 1355[label="primDivNatS Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];1355 -> 1362[label="",style="solid", color="black", weight=3]; 1143[label="Zero",fontsize=16,color="green",shape="box"];1144[label="vuz56 * vuz56",fontsize=16,color="blue",shape="box"];2143[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2143[label="",style="solid", color="blue", weight=9]; 2143 -> 1150[label="",style="solid", color="blue", weight=3]; 2144[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2144[label="",style="solid", color="blue", weight=9]; 2144 -> 1151[label="",style="solid", color="blue", weight=3]; 2145[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2145[label="",style="solid", color="blue", weight=9]; 2145 -> 1152[label="",style="solid", color="blue", weight=3]; 2146[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2146[label="",style="solid", color="blue", weight=9]; 2146 -> 1153[label="",style="solid", color="blue", weight=3]; 2147[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1144 -> 2147[label="",style="solid", color="blue", weight=9]; 2147 -> 1154[label="",style="solid", color="blue", weight=3]; 1985[label="pr2F0G1 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880)) (even (Pos (Succ vuz880)))",fontsize=16,color="black",shape="box"];1985 -> 1986[label="",style="solid", color="black", weight=3]; 883[label="error []",fontsize=16,color="red",shape="box"];920[label="error []",fontsize=16,color="red",shape="box"];936[label="primMulFloat vuz15 vuz52",fontsize=16,color="burlywood",shape="box"];2148[label="vuz15/Float vuz150 vuz151",fontsize=10,color="white",style="solid",shape="box"];936 -> 2148[label="",style="solid", color="burlywood", weight=9]; 2148 -> 950[label="",style="solid", color="burlywood", weight=3]; 949[label="error []",fontsize=16,color="red",shape="box"];1358[label="primDivNatS0 vuz57000 (Succ Zero) (primGEqNatS vuz57000 (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2149[label="vuz57000/Succ vuz570000",fontsize=10,color="white",style="solid",shape="box"];1358 -> 2149[label="",style="solid", color="burlywood", weight=9]; 2149 -> 1365[label="",style="solid", color="burlywood", weight=3]; 2150[label="vuz57000/Zero",fontsize=10,color="white",style="solid",shape="box"];1358 -> 2150[label="",style="solid", color="burlywood", weight=9]; 2150 -> 1366[label="",style="solid", color="burlywood", weight=3]; 1359 -> 1318[label="",style="dashed", color="red", weight=0]; 1359[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) (primEvenNat vuz7100)",fontsize=16,color="magenta"];1359 -> 1367[label="",style="dashed", color="magenta", weight=3]; 1360[label="pr2F0G1 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) False",fontsize=16,color="black",shape="box"];1360 -> 1368[label="",style="solid", color="black", weight=3]; 1361[label="pr2F0G vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1361 -> 1369[label="",style="solid", color="black", weight=3]; 1362[label="Zero",fontsize=16,color="green",shape="box"];1150 -> 229[label="",style="dashed", color="red", weight=0]; 1150[label="vuz56 * vuz56",fontsize=16,color="magenta"];1150 -> 1161[label="",style="dashed", color="magenta", weight=3]; 1151 -> 230[label="",style="dashed", color="red", weight=0]; 1151[label="vuz56 * vuz56",fontsize=16,color="magenta"];1151 -> 1162[label="",style="dashed", color="magenta", weight=3]; 1152 -> 231[label="",style="dashed", color="red", weight=0]; 1152[label="vuz56 * vuz56",fontsize=16,color="magenta"];1152 -> 1163[label="",style="dashed", color="magenta", weight=3]; 1153 -> 232[label="",style="dashed", color="red", weight=0]; 1153[label="vuz56 * vuz56",fontsize=16,color="magenta"];1153 -> 1164[label="",style="dashed", color="magenta", weight=3]; 1154 -> 233[label="",style="dashed", color="red", weight=0]; 1154[label="vuz56 * vuz56",fontsize=16,color="magenta"];1154 -> 1165[label="",style="dashed", color="magenta", weight=3]; 1986[label="pr2F0G1 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880)) (primEvenInt (Pos (Succ vuz880)))",fontsize=16,color="black",shape="box"];1986 -> 1987[label="",style="solid", color="black", weight=3]; 950[label="primMulFloat (Float vuz150 vuz151) vuz52",fontsize=16,color="burlywood",shape="box"];2151[label="vuz52/Float vuz520 vuz521",fontsize=10,color="white",style="solid",shape="box"];950 -> 2151[label="",style="solid", color="burlywood", weight=9]; 2151 -> 978[label="",style="solid", color="burlywood", weight=3]; 1365[label="primDivNatS0 (Succ vuz570000) (Succ Zero) (primGEqNatS (Succ vuz570000) (Succ Zero))",fontsize=16,color="black",shape="box"];1365 -> 1372[label="",style="solid", color="black", weight=3]; 1366[label="primDivNatS0 Zero (Succ Zero) (primGEqNatS Zero (Succ Zero))",fontsize=16,color="black",shape="box"];1366 -> 1373[label="",style="solid", color="black", weight=3]; 1367[label="vuz7100",fontsize=16,color="green",shape="box"];1368[label="pr2F0G0 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) otherwise",fontsize=16,color="black",shape="box"];1368 -> 1374[label="",style="solid", color="black", weight=3]; 1369[label="pr2F0G2 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];1369 -> 1375[label="",style="solid", color="black", weight=3]; 1161[label="vuz56",fontsize=16,color="green",shape="box"];229 -> 878[label="",style="dashed", color="red", weight=0]; 229[label="vuz7 * vuz7",fontsize=16,color="magenta"];229 -> 879[label="",style="dashed", color="magenta", weight=3]; 229 -> 880[label="",style="dashed", color="magenta", weight=3]; 1162[label="vuz56",fontsize=16,color="green",shape="box"];230 -> 894[label="",style="dashed", color="red", weight=0]; 230[label="vuz7 * vuz7",fontsize=16,color="magenta"];230 -> 899[label="",style="dashed", color="magenta", weight=3]; 230 -> 900[label="",style="dashed", color="magenta", weight=3]; 1163[label="vuz56",fontsize=16,color="green",shape="box"];231 -> 914[label="",style="dashed", color="red", weight=0]; 231[label="vuz7 * vuz7",fontsize=16,color="magenta"];231 -> 915[label="",style="dashed", color="magenta", weight=3]; 231 -> 916[label="",style="dashed", color="magenta", weight=3]; 1164[label="vuz56",fontsize=16,color="green",shape="box"];232 -> 928[label="",style="dashed", color="red", weight=0]; 232[label="vuz7 * vuz7",fontsize=16,color="magenta"];232 -> 929[label="",style="dashed", color="magenta", weight=3]; 232 -> 930[label="",style="dashed", color="magenta", weight=3]; 1165[label="vuz56",fontsize=16,color="green",shape="box"];233 -> 941[label="",style="dashed", color="red", weight=0]; 233[label="vuz7 * vuz7",fontsize=16,color="magenta"];233 -> 942[label="",style="dashed", color="magenta", weight=3]; 233 -> 943[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2020[label="",style="dashed", color="red", weight=0]; 1987[label="pr2F0G1 (vuz89 * vuz90) vuz89 (Pos (Succ vuz880)) (primEvenNat (Succ vuz880))",fontsize=16,color="magenta"];1987 -> 2021[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2022[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2023[label="",style="dashed", color="magenta", weight=3]; 1987 -> 2024[label="",style="dashed", color="magenta", weight=3]; 978[label="primMulFloat (Float vuz150 vuz151) (Float vuz520 vuz521)",fontsize=16,color="black",shape="box"];978 -> 1020[label="",style="solid", color="black", weight=3]; 1372[label="primDivNatS0 (Succ vuz570000) (Succ Zero) (primGEqNatS vuz570000 Zero)",fontsize=16,color="burlywood",shape="box"];2152[label="vuz570000/Succ vuz5700000",fontsize=10,color="white",style="solid",shape="box"];1372 -> 2152[label="",style="solid", color="burlywood", weight=9]; 2152 -> 1382[label="",style="solid", color="burlywood", weight=3]; 2153[label="vuz570000/Zero",fontsize=10,color="white",style="solid",shape="box"];1372 -> 2153[label="",style="solid", color="burlywood", weight=9]; 2153 -> 1383[label="",style="solid", color="burlywood", weight=3]; 1373[label="primDivNatS0 Zero (Succ Zero) False",fontsize=16,color="black",shape="box"];1373 -> 1384[label="",style="solid", color="black", weight=3]; 1374[label="pr2F0G0 vuz68 (vuz69 * vuz69) (Pos (Succ vuz70)) True",fontsize=16,color="black",shape="box"];1374 -> 1385[label="",style="solid", color="black", weight=3]; 1375[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1375 -> 1386[label="",style="solid", color="black", weight=3]; 879[label="vuz7",fontsize=16,color="green",shape="box"];880[label="vuz7",fontsize=16,color="green",shape="box"];899[label="vuz7",fontsize=16,color="green",shape="box"];900[label="vuz7",fontsize=16,color="green",shape="box"];915[label="vuz7",fontsize=16,color="green",shape="box"];916[label="vuz7",fontsize=16,color="green",shape="box"];929[label="vuz7",fontsize=16,color="green",shape="box"];930[label="vuz7",fontsize=16,color="green",shape="box"];942[label="vuz7",fontsize=16,color="green",shape="box"];943[label="vuz7",fontsize=16,color="green",shape="box"];2021[label="Succ vuz880",fontsize=16,color="green",shape="box"];2022[label="vuz89",fontsize=16,color="green",shape="box"];2023[label="vuz90",fontsize=16,color="green",shape="box"];2024[label="vuz880",fontsize=16,color="green",shape="box"];2020[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat vuz95)",fontsize=16,color="burlywood",shape="triangle"];2154[label="vuz95/Succ vuz950",fontsize=10,color="white",style="solid",shape="box"];2020 -> 2154[label="",style="solid", color="burlywood", weight=9]; 2154 -> 2037[label="",style="solid", color="burlywood", weight=3]; 2155[label="vuz95/Zero",fontsize=10,color="white",style="solid",shape="box"];2020 -> 2155[label="",style="solid", color="burlywood", weight=9]; 2155 -> 2038[label="",style="solid", color="burlywood", weight=3]; 1020[label="Float (vuz150 * vuz520) (vuz151 * vuz521)",fontsize=16,color="green",shape="box"];1020 -> 1032[label="",style="dashed", color="green", weight=3]; 1020 -> 1033[label="",style="dashed", color="green", weight=3]; 1382[label="primDivNatS0 (Succ (Succ vuz5700000)) (Succ Zero) (primGEqNatS (Succ vuz5700000) Zero)",fontsize=16,color="black",shape="box"];1382 -> 1398[label="",style="solid", color="black", weight=3]; 1383[label="primDivNatS0 (Succ Zero) (Succ Zero) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1383 -> 1399[label="",style="solid", color="black", weight=3]; 1384[label="Zero",fontsize=16,color="green",shape="box"];1385[label="pr2F (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="black",shape="box"];1385 -> 1400[label="",style="solid", color="black", weight=3]; 1386[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz70) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];1386 -> 1401[label="",style="solid", color="black", weight=3]; 2037[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat (Succ vuz950))",fontsize=16,color="burlywood",shape="box"];2156[label="vuz950/Succ vuz9500",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2156[label="",style="solid", color="burlywood", weight=9]; 2156 -> 2039[label="",style="solid", color="burlywood", weight=3]; 2157[label="vuz950/Zero",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2157[label="",style="solid", color="burlywood", weight=9]; 2157 -> 2040[label="",style="solid", color="burlywood", weight=3]; 2038[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat Zero)",fontsize=16,color="black",shape="box"];2038 -> 2041[label="",style="solid", color="black", weight=3]; 1032 -> 894[label="",style="dashed", color="red", weight=0]; 1032[label="vuz150 * vuz520",fontsize=16,color="magenta"];1032 -> 1046[label="",style="dashed", color="magenta", weight=3]; 1032 -> 1047[label="",style="dashed", color="magenta", weight=3]; 1033 -> 894[label="",style="dashed", color="red", weight=0]; 1033[label="vuz151 * vuz521",fontsize=16,color="magenta"];1033 -> 1048[label="",style="dashed", color="magenta", weight=3]; 1033 -> 1049[label="",style="dashed", color="magenta", weight=3]; 1398[label="primDivNatS0 (Succ (Succ vuz5700000)) (Succ Zero) True",fontsize=16,color="black",shape="box"];1398 -> 1413[label="",style="solid", color="black", weight=3]; 1399[label="primDivNatS0 (Succ Zero) (Succ Zero) True",fontsize=16,color="black",shape="box"];1399 -> 1414[label="",style="solid", color="black", weight=3]; 1400[label="pr2F4 (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="black",shape="box"];1400 -> 1415[label="",style="solid", color="black", weight=3]; 1401[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (primQuotInt (Pos (Succ vuz70)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz70)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];1401 -> 1416[label="",style="solid", color="black", weight=3]; 2039[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat (Succ (Succ vuz9500)))",fontsize=16,color="black",shape="box"];2039 -> 2042[label="",style="solid", color="black", weight=3]; 2040[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];2040 -> 2043[label="",style="solid", color="black", weight=3]; 2041[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) True",fontsize=16,color="black",shape="box"];2041 -> 2044[label="",style="solid", color="black", weight=3]; 1046[label="vuz520",fontsize=16,color="green",shape="box"];1047[label="vuz150",fontsize=16,color="green",shape="box"];1048[label="vuz521",fontsize=16,color="green",shape="box"];1049[label="vuz151",fontsize=16,color="green",shape="box"];1413[label="Succ (primDivNatS (primMinusNatS (Succ (Succ vuz5700000)) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1413 -> 1423[label="",style="dashed", color="green", weight=3]; 1414[label="Succ (primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];1414 -> 1424[label="",style="dashed", color="green", weight=3]; 1415[label="pr2F3 (Pos (Succ vuz70) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="black",shape="box"];1415 -> 1425[label="",style="solid", color="black", weight=3]; 1416 -> 991[label="",style="dashed", color="red", weight=0]; 1416[label="pr2F0G1 vuz68 (vuz69 * vuz69 * (vuz69 * vuz69)) (primQuotInt (Pos (Succ vuz70)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz70)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];1416 -> 1426[label="",style="dashed", color="magenta", weight=3]; 1416 -> 1427[label="",style="dashed", color="magenta", weight=3]; 1416 -> 1428[label="",style="dashed", color="magenta", weight=3]; 2042 -> 2020[label="",style="dashed", color="red", weight=0]; 2042[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) (primEvenNat vuz9500)",fontsize=16,color="magenta"];2042 -> 2045[label="",style="dashed", color="magenta", weight=3]; 2043[label="pr2F0G1 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) False",fontsize=16,color="black",shape="box"];2043 -> 2046[label="",style="solid", color="black", weight=3]; 2044[label="pr2F0G (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];2044 -> 2047[label="",style="solid", color="black", weight=3]; 1423 -> 1320[label="",style="dashed", color="red", weight=0]; 1423[label="primDivNatS (primMinusNatS (Succ (Succ vuz5700000)) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1423 -> 1430[label="",style="dashed", color="magenta", weight=3]; 1424 -> 1324[label="",style="dashed", color="red", weight=0]; 1424[label="primDivNatS (primMinusNatS (Succ Zero) (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];1425 -> 1922[label="",style="dashed", color="red", weight=0]; 1425[label="pr2F3 (primEqInt (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) (vuz69 * vuz69) (Pos (Succ vuz70) - fromInt (Pos (Succ Zero))) (vuz69 * vuz69 * vuz68)",fontsize=16,color="magenta"];1425 -> 1926[label="",style="dashed", color="magenta", weight=3]; 1425 -> 1927[label="",style="dashed", color="magenta", weight=3]; 1425 -> 1928[label="",style="dashed", color="magenta", weight=3]; 1426[label="Succ vuz70",fontsize=16,color="green",shape="box"];1427[label="vuz68",fontsize=16,color="green",shape="box"];1428[label="vuz69 * vuz69",fontsize=16,color="blue",shape="box"];2158[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2158[label="",style="solid", color="blue", weight=9]; 2158 -> 1432[label="",style="solid", color="blue", weight=3]; 2159[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2159[label="",style="solid", color="blue", weight=9]; 2159 -> 1433[label="",style="solid", color="blue", weight=3]; 2160[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2160[label="",style="solid", color="blue", weight=9]; 2160 -> 1434[label="",style="solid", color="blue", weight=3]; 2161[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2161[label="",style="solid", color="blue", weight=9]; 2161 -> 1435[label="",style="solid", color="blue", weight=3]; 2162[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1428 -> 2162[label="",style="solid", color="blue", weight=9]; 2162 -> 1436[label="",style="solid", color="blue", weight=3]; 2045[label="vuz9500",fontsize=16,color="green",shape="box"];2046[label="pr2F0G0 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) otherwise",fontsize=16,color="black",shape="box"];2046 -> 2048[label="",style="solid", color="black", weight=3]; 2047[label="pr2F0G2 (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];2047 -> 2049[label="",style="solid", color="black", weight=3]; 1430[label="vuz5700000",fontsize=16,color="green",shape="box"];1926[label="vuz70",fontsize=16,color="green",shape="box"];1927[label="vuz69 * vuz69",fontsize=16,color="blue",shape="box"];2163[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2163[label="",style="solid", color="blue", weight=9]; 2163 -> 1945[label="",style="solid", color="blue", weight=3]; 2164[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2164[label="",style="solid", color="blue", weight=9]; 2164 -> 1946[label="",style="solid", color="blue", weight=3]; 2165[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2165[label="",style="solid", color="blue", weight=9]; 2165 -> 1947[label="",style="solid", color="blue", weight=3]; 2166[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2166[label="",style="solid", color="blue", weight=9]; 2166 -> 1948[label="",style="solid", color="blue", weight=3]; 2167[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1927 -> 2167[label="",style="solid", color="blue", weight=9]; 2167 -> 1949[label="",style="solid", color="blue", weight=3]; 1928[label="vuz68",fontsize=16,color="green",shape="box"];1432 -> 229[label="",style="dashed", color="red", weight=0]; 1432[label="vuz69 * vuz69",fontsize=16,color="magenta"];1432 -> 1440[label="",style="dashed", color="magenta", weight=3]; 1433 -> 230[label="",style="dashed", color="red", weight=0]; 1433[label="vuz69 * vuz69",fontsize=16,color="magenta"];1433 -> 1441[label="",style="dashed", color="magenta", weight=3]; 1434 -> 231[label="",style="dashed", color="red", weight=0]; 1434[label="vuz69 * vuz69",fontsize=16,color="magenta"];1434 -> 1442[label="",style="dashed", color="magenta", weight=3]; 1435 -> 232[label="",style="dashed", color="red", weight=0]; 1435[label="vuz69 * vuz69",fontsize=16,color="magenta"];1435 -> 1443[label="",style="dashed", color="magenta", weight=3]; 1436 -> 233[label="",style="dashed", color="red", weight=0]; 1436[label="vuz69 * vuz69",fontsize=16,color="magenta"];1436 -> 1444[label="",style="dashed", color="magenta", weight=3]; 2048[label="pr2F0G0 (vuz92 * vuz93) vuz92 (Pos (Succ vuz94)) True",fontsize=16,color="black",shape="box"];2048 -> 2050[label="",style="solid", color="black", weight=3]; 2049[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))) (even (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];2049 -> 2051[label="",style="solid", color="black", weight=3]; 1945 -> 229[label="",style="dashed", color="red", weight=0]; 1945[label="vuz69 * vuz69",fontsize=16,color="magenta"];1945 -> 1951[label="",style="dashed", color="magenta", weight=3]; 1946 -> 230[label="",style="dashed", color="red", weight=0]; 1946[label="vuz69 * vuz69",fontsize=16,color="magenta"];1946 -> 1952[label="",style="dashed", color="magenta", weight=3]; 1947 -> 231[label="",style="dashed", color="red", weight=0]; 1947[label="vuz69 * vuz69",fontsize=16,color="magenta"];1947 -> 1953[label="",style="dashed", color="magenta", weight=3]; 1948 -> 232[label="",style="dashed", color="red", weight=0]; 1948[label="vuz69 * vuz69",fontsize=16,color="magenta"];1948 -> 1954[label="",style="dashed", color="magenta", weight=3]; 1949 -> 233[label="",style="dashed", color="red", weight=0]; 1949[label="vuz69 * vuz69",fontsize=16,color="magenta"];1949 -> 1955[label="",style="dashed", color="magenta", weight=3]; 1440[label="vuz69",fontsize=16,color="green",shape="box"];1441[label="vuz69",fontsize=16,color="green",shape="box"];1442[label="vuz69",fontsize=16,color="green",shape="box"];1443[label="vuz69",fontsize=16,color="green",shape="box"];1444[label="vuz69",fontsize=16,color="green",shape="box"];2050[label="pr2F vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="black",shape="box"];2050 -> 2052[label="",style="solid", color="black", weight=3]; 2051[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))) (primEvenInt (Pos (Succ vuz94) `quot` fromInt (Pos (Succ (Succ Zero)))))",fontsize=16,color="black",shape="box"];2051 -> 2053[label="",style="solid", color="black", weight=3]; 1951[label="vuz69",fontsize=16,color="green",shape="box"];1952[label="vuz69",fontsize=16,color="green",shape="box"];1953[label="vuz69",fontsize=16,color="green",shape="box"];1954[label="vuz69",fontsize=16,color="green",shape="box"];1955[label="vuz69",fontsize=16,color="green",shape="box"];2052[label="pr2F4 vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="black",shape="box"];2052 -> 2054[label="",style="solid", color="black", weight=3]; 2053[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (primQuotInt (Pos (Succ vuz94)) (fromInt (Pos (Succ (Succ Zero))))) (primEvenInt (primQuotInt (Pos (Succ vuz94)) (fromInt (Pos (Succ (Succ Zero))))))",fontsize=16,color="black",shape="box"];2053 -> 2055[label="",style="solid", color="black", weight=3]; 2054[label="pr2F3 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="black",shape="box"];2054 -> 2056[label="",style="solid", color="black", weight=3]; 2055 -> 991[label="",style="dashed", color="red", weight=0]; 2055[label="pr2F0G1 (vuz92 * vuz93) (vuz92 * vuz92) (primQuotInt (Pos (Succ vuz94)) (Pos (Succ (Succ Zero)))) (primEvenInt (primQuotInt (Pos (Succ vuz94)) (Pos (Succ (Succ Zero)))))",fontsize=16,color="magenta"];2055 -> 2057[label="",style="dashed", color="magenta", weight=3]; 2055 -> 2058[label="",style="dashed", color="magenta", weight=3]; 2055 -> 2059[label="",style="dashed", color="magenta", weight=3]; 2056 -> 1922[label="",style="dashed", color="red", weight=0]; 2056[label="pr2F3 (primEqInt (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) vuz92 (Pos (Succ vuz94) - fromInt (Pos (Succ Zero))) (vuz92 * (vuz92 * vuz93))",fontsize=16,color="magenta"];2056 -> 2060[label="",style="dashed", color="magenta", weight=3]; 2056 -> 2061[label="",style="dashed", color="magenta", weight=3]; 2056 -> 2062[label="",style="dashed", color="magenta", weight=3]; 2057[label="Succ vuz94",fontsize=16,color="green",shape="box"];2058[label="vuz92 * vuz93",fontsize=16,color="blue",shape="box"];2168[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2168[label="",style="solid", color="blue", weight=9]; 2168 -> 2063[label="",style="solid", color="blue", weight=3]; 2169[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2169[label="",style="solid", color="blue", weight=9]; 2169 -> 2064[label="",style="solid", color="blue", weight=3]; 2170[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2170[label="",style="solid", color="blue", weight=9]; 2170 -> 2065[label="",style="solid", color="blue", weight=3]; 2171[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2171[label="",style="solid", color="blue", weight=9]; 2171 -> 2066[label="",style="solid", color="blue", weight=3]; 2172[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];2058 -> 2172[label="",style="solid", color="blue", weight=9]; 2172 -> 2067[label="",style="solid", color="blue", weight=3]; 2059[label="vuz92",fontsize=16,color="green",shape="box"];2060[label="vuz94",fontsize=16,color="green",shape="box"];2061[label="vuz92",fontsize=16,color="green",shape="box"];2062[label="vuz92 * vuz93",fontsize=16,color="blue",shape="box"];2173[label="* :: (Ratio a) -> (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2173[label="",style="solid", color="blue", weight=9]; 2173 -> 2068[label="",style="solid", color="blue", weight=3]; 2174[label="* :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2174[label="",style="solid", color="blue", weight=9]; 2174 -> 2069[label="",style="solid", color="blue", weight=3]; 2175[label="* :: Double -> Double -> Double",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2175[label="",style="solid", color="blue", weight=9]; 2175 -> 2070[label="",style="solid", color="blue", weight=3]; 2176[label="* :: Float -> Float -> Float",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2176[label="",style="solid", color="blue", weight=9]; 2176 -> 2071[label="",style="solid", color="blue", weight=3]; 2177[label="* :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];2062 -> 2177[label="",style="solid", color="blue", weight=9]; 2177 -> 2072[label="",style="solid", color="blue", weight=3]; 2063 -> 878[label="",style="dashed", color="red", weight=0]; 2063[label="vuz92 * vuz93",fontsize=16,color="magenta"];2063 -> 2073[label="",style="dashed", color="magenta", weight=3]; 2063 -> 2074[label="",style="dashed", color="magenta", weight=3]; 2064 -> 894[label="",style="dashed", color="red", weight=0]; 2064[label="vuz92 * vuz93",fontsize=16,color="magenta"];2064 -> 2075[label="",style="dashed", color="magenta", weight=3]; 2064 -> 2076[label="",style="dashed", color="magenta", weight=3]; 2065 -> 914[label="",style="dashed", color="red", weight=0]; 2065[label="vuz92 * vuz93",fontsize=16,color="magenta"];2065 -> 2077[label="",style="dashed", color="magenta", weight=3]; 2065 -> 2078[label="",style="dashed", color="magenta", weight=3]; 2066 -> 928[label="",style="dashed", color="red", weight=0]; 2066[label="vuz92 * vuz93",fontsize=16,color="magenta"];2066 -> 2079[label="",style="dashed", color="magenta", weight=3]; 2066 -> 2080[label="",style="dashed", color="magenta", weight=3]; 2067 -> 941[label="",style="dashed", color="red", weight=0]; 2067[label="vuz92 * vuz93",fontsize=16,color="magenta"];2067 -> 2081[label="",style="dashed", color="magenta", weight=3]; 2067 -> 2082[label="",style="dashed", color="magenta", weight=3]; 2068 -> 878[label="",style="dashed", color="red", weight=0]; 2068[label="vuz92 * vuz93",fontsize=16,color="magenta"];2068 -> 2083[label="",style="dashed", color="magenta", weight=3]; 2068 -> 2084[label="",style="dashed", color="magenta", weight=3]; 2069 -> 894[label="",style="dashed", color="red", weight=0]; 2069[label="vuz92 * vuz93",fontsize=16,color="magenta"];2069 -> 2085[label="",style="dashed", color="magenta", weight=3]; 2069 -> 2086[label="",style="dashed", color="magenta", weight=3]; 2070 -> 914[label="",style="dashed", color="red", weight=0]; 2070[label="vuz92 * vuz93",fontsize=16,color="magenta"];2070 -> 2087[label="",style="dashed", color="magenta", weight=3]; 2070 -> 2088[label="",style="dashed", color="magenta", weight=3]; 2071 -> 928[label="",style="dashed", color="red", weight=0]; 2071[label="vuz92 * vuz93",fontsize=16,color="magenta"];2071 -> 2089[label="",style="dashed", color="magenta", weight=3]; 2071 -> 2090[label="",style="dashed", color="magenta", weight=3]; 2072 -> 941[label="",style="dashed", color="red", weight=0]; 2072[label="vuz92 * vuz93",fontsize=16,color="magenta"];2072 -> 2091[label="",style="dashed", color="magenta", weight=3]; 2072 -> 2092[label="",style="dashed", color="magenta", weight=3]; 2073[label="vuz92",fontsize=16,color="green",shape="box"];2074[label="vuz93",fontsize=16,color="green",shape="box"];2075[label="vuz93",fontsize=16,color="green",shape="box"];2076[label="vuz92",fontsize=16,color="green",shape="box"];2077[label="vuz93",fontsize=16,color="green",shape="box"];2078[label="vuz92",fontsize=16,color="green",shape="box"];2079[label="vuz92",fontsize=16,color="green",shape="box"];2080[label="vuz93",fontsize=16,color="green",shape="box"];2081[label="vuz93",fontsize=16,color="green",shape="box"];2082[label="vuz92",fontsize=16,color="green",shape="box"];2083[label="vuz92",fontsize=16,color="green",shape="box"];2084[label="vuz93",fontsize=16,color="green",shape="box"];2085[label="vuz93",fontsize=16,color="green",shape="box"];2086[label="vuz92",fontsize=16,color="green",shape="box"];2087[label="vuz93",fontsize=16,color="green",shape="box"];2088[label="vuz92",fontsize=16,color="green",shape="box"];2089[label="vuz92",fontsize=16,color="green",shape="box"];2090[label="vuz93",fontsize=16,color="green",shape="box"];2091[label="vuz93",fontsize=16,color="green",shape="box"];2092[label="vuz92",fontsize=16,color="green",shape="box"];} ---------------------------------------- (45) TRUE