/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) NumRed [SOUND, 0 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) AND (9) QDP (10) MNOCProof [EQUIVALENT, 0 ms] (11) QDP (12) NonTerminationLoopProof [COMPLETE, 0 ms] (13) NO (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] (16) YES (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) Narrow [COMPLETE, 0 ms] (24) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="enumFrom",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="enumFrom vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="numericEnumFrom vx3",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="vx3 : (numericEnumFrom $! vx3 + fromInt (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3]; 6[label="(numericEnumFrom $! vx3 + fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 8[label="",style="dashed", color="red", weight=0]; 7[label="(vx3 + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (vx3 + fromInt (Pos (Succ 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vx31",fontsize=10,color="white",style="solid",shape="box"];12 -> 147[label="",style="solid", color="burlywood", weight=9]; 147 -> 15[label="",style="solid", color="burlywood", weight=3]; 14 -> 10[label="",style="dashed", color="red", weight=0]; 14[label="vx3 + fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];13[label="enforceWHNF (WHNF vx5) vx4",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3]; 15[label="primPlusFloat (Float vx30 vx31) (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="vx4",fontsize=16,color="green",shape="box"];17[label="primPlusFloat (Float vx30 vx31) (primIntToFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 18[label="primPlusFloat (Float vx30 vx31) (Float (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 19[label="Float (vx30 * Pos (Succ Zero) + Pos (Succ Zero) * vx31) (vx31 * Pos (Succ Zero))",fontsize=16,color="green",shape="box"];19 -> 20[label="",style="dashed", color="green", weight=3]; 19 -> 21[label="",style="dashed", color="green", weight=3]; 20[label="vx30 * Pos (Succ Zero) + Pos (Succ Zero) * vx31",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3]; 21[label="vx31 * Pos (Succ Zero)",fontsize=16,color="black",shape="triangle"];21 -> 23[label="",style="solid", color="black", weight=3]; 22 -> 24[label="",style="dashed", color="red", weight=0]; 22[label="primPlusInt (vx30 * Pos (Succ Zero)) (Pos (Succ Zero) * vx31)",fontsize=16,color="magenta"];22 -> 25[label="",style="dashed", color="magenta", weight=3]; 23[label="primMulInt vx31 (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];148[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];23 -> 148[label="",style="solid", color="burlywood", weight=9]; 148 -> 26[label="",style="solid", color="burlywood", weight=3]; 149[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];23 -> 149[label="",style="solid", color="burlywood", weight=9]; 149 -> 27[label="",style="solid", color="burlywood", weight=3]; 25 -> 21[label="",style="dashed", color="red", weight=0]; 25[label="vx30 * Pos (Succ Zero)",fontsize=16,color="magenta"];25 -> 28[label="",style="dashed", color="magenta", weight=3]; 24[label="primPlusInt vx6 (Pos (Succ Zero) * vx31)",fontsize=16,color="burlywood",shape="triangle"];150[label="vx6/Pos vx60",fontsize=10,color="white",style="solid",shape="box"];24 -> 150[label="",style="solid", color="burlywood", weight=9]; 150 -> 29[label="",style="solid", color="burlywood", weight=3]; 151[label="vx6/Neg vx60",fontsize=10,color="white",style="solid",shape="box"];24 -> 151[label="",style="solid", color="burlywood", weight=9]; 151 -> 30[label="",style="solid", color="burlywood", weight=3]; 26[label="primMulInt (Pos vx310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];26 -> 31[label="",style="solid", color="black", weight=3]; 27[label="primMulInt (Neg vx310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 32[label="",style="solid", color="black", weight=3]; 28[label="vx30",fontsize=16,color="green",shape="box"];29[label="primPlusInt (Pos vx60) (Pos (Succ Zero) * vx31)",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 30[label="primPlusInt (Neg vx60) (Pos (Succ Zero) * vx31)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3]; 31[label="Pos (primMulNat vx310 (Succ Zero))",fontsize=16,color="green",shape="box"];31 -> 35[label="",style="dashed", color="green", weight=3]; 32[label="Neg (primMulNat vx310 (Succ Zero))",fontsize=16,color="green",shape="box"];32 -> 36[label="",style="dashed", color="green", weight=3]; 33[label="primPlusInt (Pos vx60) (primMulInt (Pos (Succ Zero)) vx31)",fontsize=16,color="burlywood",shape="box"];152[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];33 -> 152[label="",style="solid", color="burlywood", weight=9]; 152 -> 37[label="",style="solid", color="burlywood", weight=3]; 153[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];33 -> 153[label="",style="solid", color="burlywood", weight=9]; 153 -> 38[label="",style="solid", color="burlywood", weight=3]; 34[label="primPlusInt (Neg vx60) (primMulInt (Pos (Succ Zero)) vx31)",fontsize=16,color="burlywood",shape="box"];154[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];34 -> 154[label="",style="solid", color="burlywood", weight=9]; 154 -> 39[label="",style="solid", color="burlywood", weight=3]; 155[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];34 -> 155[label="",style="solid", color="burlywood", weight=9]; 155 -> 40[label="",style="solid", color="burlywood", weight=3]; 35[label="primMulNat vx310 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];156[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];35 -> 156[label="",style="solid", color="burlywood", weight=9]; 156 -> 41[label="",style="solid", color="burlywood", weight=3]; 157[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 157[label="",style="solid", color="burlywood", weight=9]; 157 -> 42[label="",style="solid", color="burlywood", weight=3]; 36 -> 35[label="",style="dashed", color="red", weight=0]; 36[label="primMulNat vx310 (Succ Zero)",fontsize=16,color="magenta"];36 -> 43[label="",style="dashed", color="magenta", weight=3]; 37[label="primPlusInt (Pos vx60) (primMulInt (Pos (Succ Zero)) (Pos vx310))",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3]; 38[label="primPlusInt (Pos vx60) (primMulInt (Pos (Succ Zero)) (Neg vx310))",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3]; 39[label="primPlusInt (Neg vx60) (primMulInt (Pos (Succ Zero)) (Pos vx310))",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3]; 40[label="primPlusInt (Neg vx60) (primMulInt (Pos (Succ Zero)) (Neg vx310))",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3]; 41[label="primMulNat (Succ vx3100) (Succ Zero)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3]; 42[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3]; 43[label="vx310",fontsize=16,color="green",shape="box"];44[label="primPlusInt (Pos vx60) (Pos (primMulNat (Succ Zero) vx310))",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3]; 45[label="primPlusInt (Pos vx60) (Neg (primMulNat (Succ Zero) vx310))",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3]; 46[label="primPlusInt (Neg vx60) (Pos (primMulNat (Succ Zero) vx310))",fontsize=16,color="black",shape="box"];46 -> 52[label="",style="solid", color="black", weight=3]; 47[label="primPlusInt (Neg vx60) (Neg (primMulNat (Succ Zero) vx310))",fontsize=16,color="black",shape="box"];47 -> 53[label="",style="solid", color="black", weight=3]; 48 -> 54[label="",style="dashed", color="red", weight=0]; 48[label="primPlusNat (primMulNat vx3100 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];48 -> 55[label="",style="dashed", color="magenta", weight=3]; 49[label="Zero",fontsize=16,color="green",shape="box"];50[label="Pos (primPlusNat vx60 (primMulNat (Succ Zero) vx310))",fontsize=16,color="green",shape="box"];50 -> 56[label="",style="dashed", color="green", weight=3]; 51[label="primMinusNat vx60 (primMulNat (Succ Zero) 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(primPlusNat vx60 (primMulNat (Succ Zero) vx310))",fontsize=16,color="green",shape="box"];53 -> 61[label="",style="dashed", color="green", weight=3]; 55 -> 35[label="",style="dashed", color="red", weight=0]; 55[label="primMulNat vx3100 (Succ Zero)",fontsize=16,color="magenta"];55 -> 62[label="",style="dashed", color="magenta", weight=3]; 54[label="primPlusNat vx7 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];162[label="vx7/Succ vx70",fontsize=10,color="white",style="solid",shape="box"];54 -> 162[label="",style="solid", color="burlywood", weight=9]; 162 -> 63[label="",style="solid", color="burlywood", weight=3]; 163[label="vx7/Zero",fontsize=10,color="white",style="solid",shape="box"];54 -> 163[label="",style="solid", color="burlywood", weight=9]; 163 -> 64[label="",style="solid", color="burlywood", weight=3]; 56[label="primPlusNat vx60 (primMulNat (Succ Zero) vx310)",fontsize=16,color="burlywood",shape="triangle"];164[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];56 -> 164[label="",style="solid", color="burlywood", weight=9]; 164 -> 65[label="",style="solid", color="burlywood", weight=3]; 165[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 165[label="",style="solid", color="burlywood", weight=9]; 165 -> 66[label="",style="solid", color="burlywood", weight=3]; 57[label="primMinusNat (Succ vx600) (primMulNat (Succ Zero) vx310)",fontsize=16,color="burlywood",shape="box"];166[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];57 -> 166[label="",style="solid", color="burlywood", weight=9]; 166 -> 67[label="",style="solid", color="burlywood", weight=3]; 167[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 167[label="",style="solid", color="burlywood", weight=9]; 167 -> 68[label="",style="solid", color="burlywood", weight=3]; 58[label="primMinusNat Zero (primMulNat (Succ Zero) vx310)",fontsize=16,color="burlywood",shape="box"];168[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];58 -> 168[label="",style="solid", color="burlywood", weight=9]; 168 -> 69[label="",style="solid", color="burlywood", weight=3]; 169[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 169[label="",style="solid", color="burlywood", weight=9]; 169 -> 70[label="",style="solid", color="burlywood", weight=3]; 59[label="primMinusNat (primMulNat (Succ Zero) (Succ vx3100)) vx60",fontsize=16,color="black",shape="box"];59 -> 71[label="",style="solid", color="black", weight=3]; 60[label="primMinusNat (primMulNat (Succ Zero) Zero) vx60",fontsize=16,color="black",shape="box"];60 -> 72[label="",style="solid", color="black", weight=3]; 61 -> 56[label="",style="dashed", color="red", weight=0]; 61[label="primPlusNat vx60 (primMulNat (Succ Zero) vx310)",fontsize=16,color="magenta"];61 -> 73[label="",style="dashed", color="magenta", weight=3]; 61 -> 74[label="",style="dashed", color="magenta", weight=3]; 62[label="vx3100",fontsize=16,color="green",shape="box"];63[label="primPlusNat (Succ vx70) (Succ Zero)",fontsize=16,color="black",shape="box"];63 -> 75[label="",style="solid", color="black", weight=3]; 64[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];64 -> 76[label="",style="solid", color="black", weight=3]; 65[label="primPlusNat (Succ vx600) (primMulNat (Succ Zero) vx310)",fontsize=16,color="burlywood",shape="box"];170[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];65 -> 170[label="",style="solid", color="burlywood", weight=9]; 170 -> 77[label="",style="solid", color="burlywood", weight=3]; 171[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 171[label="",style="solid", color="burlywood", weight=9]; 171 -> 78[label="",style="solid", color="burlywood", weight=3]; 66[label="primPlusNat Zero (primMulNat (Succ Zero) vx310)",fontsize=16,color="burlywood",shape="box"];172[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];66 -> 172[label="",style="solid", color="burlywood", weight=9]; 172 -> 79[label="",style="solid", color="burlywood", weight=3]; 173[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];66 -> 173[label="",style="solid", color="burlywood", weight=9]; 173 -> 80[label="",style="solid", color="burlywood", weight=3]; 67[label="primMinusNat (Succ vx600) (primMulNat (Succ Zero) (Succ vx3100))",fontsize=16,color="black",shape="box"];67 -> 81[label="",style="solid", color="black", weight=3]; 68[label="primMinusNat (Succ vx600) (primMulNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];68 -> 82[label="",style="solid", color="black", weight=3]; 69[label="primMinusNat Zero (primMulNat (Succ Zero) (Succ vx3100))",fontsize=16,color="black",shape="box"];69 -> 83[label="",style="solid", color="black", weight=3]; 70[label="primMinusNat Zero (primMulNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];70 -> 84[label="",style="solid", color="black", weight=3]; 71[label="primMinusNat (primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)) vx60",fontsize=16,color="black",shape="box"];71 -> 85[label="",style="solid", color="black", weight=3]; 72[label="primMinusNat Zero vx60",fontsize=16,color="burlywood",shape="triangle"];174[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];72 -> 174[label="",style="solid", color="burlywood", weight=9]; 174 -> 86[label="",style="solid", color="burlywood", weight=3]; 175[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 175[label="",style="solid", color="burlywood", weight=9]; 175 -> 87[label="",style="solid", color="burlywood", weight=3]; 73[label="vx60",fontsize=16,color="green",shape="box"];74[label="vx310",fontsize=16,color="green",shape="box"];75[label="Succ (Succ (primPlusNat vx70 Zero))",fontsize=16,color="green",shape="box"];75 -> 88[label="",style="dashed", color="green", weight=3]; 76[label="Succ Zero",fontsize=16,color="green",shape="box"];77[label="primPlusNat (Succ vx600) (primMulNat (Succ Zero) (Succ vx3100))",fontsize=16,color="black",shape="box"];77 -> 89[label="",style="solid", color="black", weight=3]; 78[label="primPlusNat (Succ vx600) (primMulNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];78 -> 90[label="",style="solid", color="black", weight=3]; 79[label="primPlusNat Zero (primMulNat (Succ Zero) (Succ vx3100))",fontsize=16,color="black",shape="box"];79 -> 91[label="",style="solid", color="black", weight=3]; 80[label="primPlusNat Zero (primMulNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];80 -> 92[label="",style="solid", color="black", weight=3]; 81[label="primMinusNat (Succ vx600) (primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100))",fontsize=16,color="black",shape="box"];81 -> 93[label="",style="solid", color="black", weight=3]; 82[label="primMinusNat (Succ vx600) Zero",fontsize=16,color="black",shape="box"];82 -> 94[label="",style="solid", color="black", weight=3]; 83 -> 72[label="",style="dashed", color="red", weight=0]; 83[label="primMinusNat Zero (primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100))",fontsize=16,color="magenta"];83 -> 95[label="",style="dashed", color="magenta", weight=3]; 84 -> 72[label="",style="dashed", color="red", weight=0]; 84[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];84 -> 96[label="",style="dashed", color="magenta", weight=3]; 85[label="primMinusNat (primPlusNat Zero (Succ vx3100)) vx60",fontsize=16,color="black",shape="box"];85 -> 97[label="",style="solid", color="black", weight=3]; 86[label="primMinusNat Zero (Succ vx600)",fontsize=16,color="black",shape="box"];86 -> 98[label="",style="solid", color="black", weight=3]; 87[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];87 -> 99[label="",style="solid", color="black", weight=3]; 88[label="primPlusNat vx70 Zero",fontsize=16,color="burlywood",shape="triangle"];176[label="vx70/Succ vx700",fontsize=10,color="white",style="solid",shape="box"];88 -> 176[label="",style="solid", color="burlywood", weight=9]; 176 -> 100[label="",style="solid", color="burlywood", weight=3]; 177[label="vx70/Zero",fontsize=10,color="white",style="solid",shape="box"];88 -> 177[label="",style="solid", color="burlywood", weight=9]; 177 -> 101[label="",style="solid", color="burlywood", weight=3]; 89[label="primPlusNat (Succ vx600) (primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100))",fontsize=16,color="black",shape="box"];89 -> 102[label="",style="solid", color="black", weight=3]; 90 -> 88[label="",style="dashed", color="red", weight=0]; 90[label="primPlusNat (Succ vx600) Zero",fontsize=16,color="magenta"];90 -> 103[label="",style="dashed", color="magenta", weight=3]; 91[label="primPlusNat Zero (primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100))",fontsize=16,color="black",shape="box"];91 -> 104[label="",style="solid", color="black", weight=3]; 92 -> 88[label="",style="dashed", color="red", weight=0]; 92[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];92 -> 105[label="",style="dashed", color="magenta", weight=3]; 93[label="primMinusNat (Succ vx600) (primPlusNat Zero (Succ vx3100))",fontsize=16,color="black",shape="box"];93 -> 106[label="",style="solid", color="black", weight=3]; 94[label="Pos (Succ vx600)",fontsize=16,color="green",shape="box"];95[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];95 -> 107[label="",style="solid", color="black", weight=3]; 96[label="Zero",fontsize=16,color="green",shape="box"];97[label="primMinusNat (Succ vx3100) vx60",fontsize=16,color="burlywood",shape="triangle"];178[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];97 -> 178[label="",style="solid", color="burlywood", weight=9]; 178 -> 108[label="",style="solid", color="burlywood", weight=3]; 179[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];97 -> 179[label="",style="solid", color="burlywood", weight=9]; 179 -> 109[label="",style="solid", color="burlywood", weight=3]; 98[label="Neg (Succ vx600)",fontsize=16,color="green",shape="box"];99[label="Pos Zero",fontsize=16,color="green",shape="box"];100[label="primPlusNat (Succ vx700) Zero",fontsize=16,color="black",shape="box"];100 -> 110[label="",style="solid", color="black", weight=3]; 101[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];101 -> 111[label="",style="solid", color="black", weight=3]; 102[label="primPlusNat (Succ vx600) (primPlusNat Zero (Succ vx3100))",fontsize=16,color="black",shape="box"];102 -> 112[label="",style="solid", color="black", weight=3]; 103[label="Succ vx600",fontsize=16,color="green",shape="box"];104[label="primPlusNat Zero (primPlusNat Zero (Succ vx3100))",fontsize=16,color="black",shape="box"];104 -> 113[label="",style="solid", color="black", weight=3]; 105[label="Zero",fontsize=16,color="green",shape="box"];106 -> 97[label="",style="dashed", color="red", weight=0]; 106[label="primMinusNat (Succ vx600) (Succ vx3100)",fontsize=16,color="magenta"];106 -> 114[label="",style="dashed", color="magenta", weight=3]; 106 -> 115[label="",style="dashed", color="magenta", weight=3]; 107[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="triangle"];107 -> 116[label="",style="solid", color="black", weight=3]; 108[label="primMinusNat (Succ vx3100) (Succ vx600)",fontsize=16,color="black",shape="box"];108 -> 117[label="",style="solid", color="black", weight=3]; 109[label="primMinusNat (Succ vx3100) Zero",fontsize=16,color="black",shape="box"];109 -> 118[label="",style="solid", color="black", weight=3]; 110[label="Succ vx700",fontsize=16,color="green",shape="box"];111[label="Zero",fontsize=16,color="green",shape="box"];112[label="primPlusNat (Succ vx600) (Succ vx3100)",fontsize=16,color="black",shape="box"];112 -> 119[label="",style="solid", color="black", weight=3]; 113 -> 107[label="",style="dashed", color="red", weight=0]; 113[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="magenta"];113 -> 120[label="",style="dashed", color="magenta", weight=3]; 114[label="Succ vx3100",fontsize=16,color="green",shape="box"];115[label="vx600",fontsize=16,color="green",shape="box"];116[label="Succ vx3100",fontsize=16,color="green",shape="box"];117[label="primMinusNat vx3100 vx600",fontsize=16,color="burlywood",shape="triangle"];180[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];117 -> 180[label="",style="solid", color="burlywood", weight=9]; 180 -> 121[label="",style="solid", color="burlywood", weight=3]; 181[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];117 -> 181[label="",style="solid", color="burlywood", weight=9]; 181 -> 122[label="",style="solid", color="burlywood", weight=3]; 118[label="Pos (Succ vx3100)",fontsize=16,color="green",shape="box"];119[label="Succ (Succ (primPlusNat vx600 vx3100))",fontsize=16,color="green",shape="box"];119 -> 123[label="",style="dashed", color="green", weight=3]; 120[label="vx3100",fontsize=16,color="green",shape="box"];121[label="primMinusNat (Succ vx31000) vx600",fontsize=16,color="burlywood",shape="box"];182[label="vx600/Succ vx6000",fontsize=10,color="white",style="solid",shape="box"];121 -> 182[label="",style="solid", color="burlywood", weight=9]; 182 -> 124[label="",style="solid", color="burlywood", weight=3]; 183[label="vx600/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 183[label="",style="solid", color="burlywood", weight=9]; 183 -> 125[label="",style="solid", color="burlywood", weight=3]; 122[label="primMinusNat Zero vx600",fontsize=16,color="burlywood",shape="box"];184[label="vx600/Succ vx6000",fontsize=10,color="white",style="solid",shape="box"];122 -> 184[label="",style="solid", color="burlywood", weight=9]; 184 -> 126[label="",style="solid", color="burlywood", weight=3]; 185[label="vx600/Zero",fontsize=10,color="white",style="solid",shape="box"];122 -> 185[label="",style="solid", color="burlywood", weight=9]; 185 -> 127[label="",style="solid", color="burlywood", weight=3]; 123[label="primPlusNat vx600 vx3100",fontsize=16,color="burlywood",shape="triangle"];186[label="vx600/Succ vx6000",fontsize=10,color="white",style="solid",shape="box"];123 -> 186[label="",style="solid", color="burlywood", weight=9]; 186 -> 128[label="",style="solid", color="burlywood", weight=3]; 187[label="vx600/Zero",fontsize=10,color="white",style="solid",shape="box"];123 -> 187[label="",style="solid", color="burlywood", weight=9]; 187 -> 129[label="",style="solid", color="burlywood", weight=3]; 124[label="primMinusNat (Succ vx31000) (Succ vx6000)",fontsize=16,color="black",shape="box"];124 -> 130[label="",style="solid", color="black", weight=3]; 125[label="primMinusNat (Succ vx31000) Zero",fontsize=16,color="black",shape="box"];125 -> 131[label="",style="solid", color="black", weight=3]; 126[label="primMinusNat Zero (Succ vx6000)",fontsize=16,color="black",shape="box"];126 -> 132[label="",style="solid", color="black", weight=3]; 127[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];127 -> 133[label="",style="solid", color="black", weight=3]; 128[label="primPlusNat (Succ vx6000) vx3100",fontsize=16,color="burlywood",shape="box"];188[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];128 -> 188[label="",style="solid", color="burlywood", weight=9]; 188 -> 134[label="",style="solid", color="burlywood", weight=3]; 189[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];128 -> 189[label="",style="solid", color="burlywood", weight=9]; 189 -> 135[label="",style="solid", color="burlywood", weight=3]; 129[label="primPlusNat Zero vx3100",fontsize=16,color="burlywood",shape="box"];190[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];129 -> 190[label="",style="solid", color="burlywood", weight=9]; 190 -> 136[label="",style="solid", color="burlywood", weight=3]; 191[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];129 -> 191[label="",style="solid", color="burlywood", weight=9]; 191 -> 137[label="",style="solid", color="burlywood", weight=3]; 130 -> 117[label="",style="dashed", color="red", weight=0]; 130[label="primMinusNat vx31000 vx6000",fontsize=16,color="magenta"];130 -> 138[label="",style="dashed", color="magenta", weight=3]; 130 -> 139[label="",style="dashed", color="magenta", weight=3]; 131[label="Pos (Succ vx31000)",fontsize=16,color="green",shape="box"];132[label="Neg (Succ vx6000)",fontsize=16,color="green",shape="box"];133[label="Pos Zero",fontsize=16,color="green",shape="box"];134[label="primPlusNat (Succ vx6000) (Succ vx31000)",fontsize=16,color="black",shape="box"];134 -> 140[label="",style="solid", color="black", weight=3]; 135[label="primPlusNat (Succ vx6000) Zero",fontsize=16,color="black",shape="box"];135 -> 141[label="",style="solid", color="black", weight=3]; 136[label="primPlusNat Zero (Succ vx31000)",fontsize=16,color="black",shape="box"];136 -> 142[label="",style="solid", color="black", weight=3]; 137[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];137 -> 143[label="",style="solid", color="black", weight=3]; 138[label="vx6000",fontsize=16,color="green",shape="box"];139[label="vx31000",fontsize=16,color="green",shape="box"];140[label="Succ (Succ (primPlusNat vx6000 vx31000))",fontsize=16,color="green",shape="box"];140 -> 144[label="",style="dashed", color="green", weight=3]; 141[label="Succ vx6000",fontsize=16,color="green",shape="box"];142[label="Succ vx31000",fontsize=16,color="green",shape="box"];143[label="Zero",fontsize=16,color="green",shape="box"];144 -> 123[label="",style="dashed", color="red", weight=0]; 144[label="primPlusNat vx6000 vx31000",fontsize=16,color="magenta"];144 -> 145[label="",style="dashed", color="magenta", weight=3]; 144 -> 146[label="",style="dashed", color="magenta", weight=3]; 145[label="vx31000",fontsize=16,color="green",shape="box"];146[label="vx6000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: new_numericEnumFrom(vx3) -> new_numericEnumFrom(new_ps(vx3)) The TRS R consists of the following rules: new_sr(Pos(vx310)) -> Pos(new_primMulNat0(vx310)) new_primMulNat0(Succ(vx3100)) -> new_primPlusNat2(new_primMulNat0(vx3100)) new_primMinusNat1(vx3100, Zero) -> Pos(Succ(vx3100)) new_primPlusInt(Neg(vx60), Pos(Succ(vx3100))) -> new_primMinusNat1(vx3100, vx60) new_primPlusInt(Pos(Zero), Neg(Zero)) -> new_primMinusNat0(Zero) new_primMinusNat0(Zero) -> Pos(Zero) new_primPlusNat4(Succ(vx6000), Succ(vx31000)) -> Succ(Succ(new_primPlusNat4(vx6000, vx31000))) new_primPlusNat4(Succ(vx6000), Zero) -> Succ(vx6000) new_primPlusNat4(Zero, Succ(vx31000)) -> Succ(vx31000) new_primPlusInt(Neg(vx60), Neg(vx310)) -> Neg(new_primPlusNat3(vx60, vx310)) new_sr(Neg(vx310)) -> Neg(new_primMulNat0(vx310)) new_primPlusNat3(Succ(vx600), Zero) -> new_primPlusNat0(Succ(vx600)) new_primPlusInt(Neg(vx60), Pos(Zero)) -> new_primMinusNat0(vx60) new_primPlusNat2(Succ(vx70)) -> Succ(Succ(new_primPlusNat0(vx70))) new_primMinusNat1(vx3100, Succ(vx600)) -> new_primMinusNat2(vx3100, vx600) new_primMinusNat2(Zero, Zero) -> Pos(Zero) new_primPlusNat2(Zero) -> Succ(Zero) new_primPlusNat3(Zero, Zero) -> new_primPlusNat0(Zero) new_primMinusNat0(Succ(vx600)) -> Neg(Succ(vx600)) new_primPlusNat1(vx3100) -> Succ(vx3100) new_primPlusInt(Pos(Succ(vx600)), Neg(Succ(vx3100))) -> new_primMinusNat1(vx600, Succ(vx3100)) new_primPlusInt(Pos(Zero), Neg(Succ(vx3100))) -> new_primMinusNat0(new_primPlusNat1(vx3100)) new_primPlusNat3(Succ(vx600), Succ(vx3100)) -> Succ(Succ(new_primPlusNat4(vx600, vx3100))) new_primPlusInt(Pos(vx60), Pos(vx310)) -> Pos(new_primPlusNat3(vx60, vx310)) new_primPlusNat3(Zero, Succ(vx3100)) -> new_primPlusNat1(vx3100) new_primPlusNat4(Zero, Zero) -> Zero new_primMinusNat2(Zero, Succ(vx6000)) -> Neg(Succ(vx6000)) new_primPlusInt(Pos(Succ(vx600)), Neg(Zero)) -> Pos(Succ(vx600)) new_primPlusNat0(Succ(vx700)) -> Succ(vx700) new_ps(Float(vx30, vx31)) -> Float(new_primPlusInt(new_sr(vx30), vx31), new_sr(vx31)) new_primMinusNat2(Succ(vx31000), Succ(vx6000)) -> new_primMinusNat2(vx31000, vx6000) new_primMinusNat2(Succ(vx31000), Zero) -> Pos(Succ(vx31000)) new_primMulNat0(Zero) -> Zero new_primPlusNat0(Zero) -> Zero The set Q consists of the following terms: new_primPlusInt(Pos(Zero), Neg(Succ(x0))) new_primPlusNat4(Succ(x0), Succ(x1)) new_primPlusNat4(Zero, Zero) new_primPlusNat3(Succ(x0), Zero) new_primMinusNat2(Succ(x0), Zero) new_primMinusNat2(Zero, Zero) new_primPlusNat2(Zero) new_primPlusNat3(Zero, Zero) new_primPlusNat0(Succ(x0)) new_primMulNat0(Zero) new_primPlusInt(Neg(x0), Neg(x1)) new_primMinusNat1(x0, Succ(x1)) new_primPlusInt(Neg(x0), Pos(Succ(x1))) new_primPlusInt(Pos(Zero), Neg(Zero)) new_primPlusInt(Pos(x0), Pos(x1)) new_primPlusInt(Neg(x0), Pos(Zero)) new_primPlusNat1(x0) new_primMinusNat1(x0, Zero) new_ps(Float(x0, x1)) new_sr(Pos(x0)) new_primMinusNat2(Zero, Succ(x0)) new_primMinusNat0(Zero) new_primPlusInt(Pos(Succ(x0)), Neg(Zero)) new_sr(Neg(x0)) new_primMinusNat0(Succ(x0)) new_primPlusNat4(Succ(x0), Zero) new_primPlusInt(Pos(Succ(x0)), Neg(Succ(x1))) new_primPlusNat4(Zero, Succ(x0)) new_primPlusNat0(Zero) new_primMinusNat2(Succ(x0), Succ(x1)) new_primMulNat0(Succ(x0)) new_primPlusNat3(Succ(x0), Succ(x1)) new_primPlusNat2(Succ(x0)) new_primPlusNat3(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: new_numericEnumFrom(vx3) -> new_numericEnumFrom(new_ps(vx3)) The TRS R consists of the following rules: new_sr(Pos(vx310)) -> Pos(new_primMulNat0(vx310)) new_primMulNat0(Succ(vx3100)) -> new_primPlusNat2(new_primMulNat0(vx3100)) new_primMinusNat1(vx3100, Zero) -> Pos(Succ(vx3100)) new_primPlusInt(Neg(vx60), Pos(Succ(vx3100))) -> new_primMinusNat1(vx3100, vx60) new_primPlusInt(Pos(Zero), Neg(Zero)) -> new_primMinusNat0(Zero) new_primMinusNat0(Zero) -> Pos(Zero) new_primPlusNat4(Succ(vx6000), Succ(vx31000)) -> Succ(Succ(new_primPlusNat4(vx6000, vx31000))) new_primPlusNat4(Succ(vx6000), Zero) -> Succ(vx6000) new_primPlusNat4(Zero, Succ(vx31000)) -> Succ(vx31000) new_primPlusInt(Neg(vx60), Neg(vx310)) -> Neg(new_primPlusNat3(vx60, vx310)) new_sr(Neg(vx310)) -> Neg(new_primMulNat0(vx310)) new_primPlusNat3(Succ(vx600), Zero) -> new_primPlusNat0(Succ(vx600)) new_primPlusInt(Neg(vx60), Pos(Zero)) -> new_primMinusNat0(vx60) new_primPlusNat2(Succ(vx70)) -> Succ(Succ(new_primPlusNat0(vx70))) new_primMinusNat1(vx3100, Succ(vx600)) -> new_primMinusNat2(vx3100, vx600) new_primMinusNat2(Zero, Zero) -> Pos(Zero) new_primPlusNat2(Zero) -> Succ(Zero) new_primPlusNat3(Zero, Zero) -> new_primPlusNat0(Zero) new_primMinusNat0(Succ(vx600)) -> Neg(Succ(vx600)) new_primPlusNat1(vx3100) -> Succ(vx3100) new_primPlusInt(Pos(Succ(vx600)), Neg(Succ(vx3100))) -> new_primMinusNat1(vx600, Succ(vx3100)) new_primPlusInt(Pos(Zero), Neg(Succ(vx3100))) -> new_primMinusNat0(new_primPlusNat1(vx3100)) new_primPlusNat3(Succ(vx600), Succ(vx3100)) -> Succ(Succ(new_primPlusNat4(vx600, vx3100))) new_primPlusInt(Pos(vx60), Pos(vx310)) -> Pos(new_primPlusNat3(vx60, vx310)) new_primPlusNat3(Zero, Succ(vx3100)) -> new_primPlusNat1(vx3100) new_primPlusNat4(Zero, Zero) -> Zero new_primMinusNat2(Zero, Succ(vx6000)) -> Neg(Succ(vx6000)) new_primPlusInt(Pos(Succ(vx600)), Neg(Zero)) -> Pos(Succ(vx600)) new_primPlusNat0(Succ(vx700)) -> Succ(vx700) new_ps(Float(vx30, vx31)) -> Float(new_primPlusInt(new_sr(vx30), vx31), new_sr(vx31)) new_primMinusNat2(Succ(vx31000), Succ(vx6000)) -> new_primMinusNat2(vx31000, vx6000) new_primMinusNat2(Succ(vx31000), Zero) -> Pos(Succ(vx31000)) new_primMulNat0(Zero) -> Zero new_primPlusNat0(Zero) -> Zero Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (12) 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_numericEnumFrom(vx3) evaluates to t =new_numericEnumFrom(new_ps(vx3)) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [vx3 / new_ps(vx3)] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_numericEnumFrom(vx3) to new_numericEnumFrom(new_ps(vx3)). ---------------------------------------- (13) NO ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(vx3100)) -> new_primMulNat(vx3100) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (15) 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(vx3100)) -> new_primMulNat(vx3100) The graph contains the following edges 1 > 1 ---------------------------------------- (16) YES ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNat(Succ(vx31000), Succ(vx6000)) -> new_primMinusNat(vx31000, vx6000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primMinusNat(Succ(vx31000), Succ(vx6000)) -> new_primMinusNat(vx31000, vx6000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vx6000), Succ(vx31000)) -> new_primPlusNat(vx6000, vx31000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) 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(vx6000), Succ(vx31000)) -> new_primPlusNat(vx6000, vx31000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (22) YES ---------------------------------------- (23) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="enumFrom",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="enumFrom vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="numericEnumFrom vx3",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="vx3 : (numericEnumFrom $! vx3 + fromInt (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3]; 6[label="(numericEnumFrom $! vx3 + fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 8[label="",style="dashed", color="red", weight=0]; 7[label="(vx3 + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (vx3 + fromInt (Pos (Succ Zero))))",fontsize=16,color="magenta"];7 -> 9[label="",style="dashed", color="magenta", weight=3]; 9 -> 4[label="",style="dashed", color="red", weight=0]; 9[label="numericEnumFrom (vx3 + fromInt (Pos (Succ Zero)))",fontsize=16,color="magenta"];9 -> 10[label="",style="dashed", color="magenta", weight=3]; 8[label="(vx3 + fromInt (Pos (Succ Zero)) `seq` vx4)",fontsize=16,color="black",shape="triangle"];8 -> 11[label="",style="solid", color="black", weight=3]; 10[label="vx3 + fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3]; 11 -> 13[label="",style="dashed", color="red", weight=0]; 11[label="enforceWHNF (WHNF (vx3 + fromInt (Pos (Succ Zero)))) vx4",fontsize=16,color="magenta"];11 -> 14[label="",style="dashed", color="magenta", weight=3]; 12[label="primPlusFloat vx3 (fromInt (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];147[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];12 -> 147[label="",style="solid", color="burlywood", weight=9]; 147 -> 15[label="",style="solid", color="burlywood", weight=3]; 14 -> 10[label="",style="dashed", color="red", weight=0]; 14[label="vx3 + fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];13[label="enforceWHNF (WHNF vx5) vx4",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3]; 15[label="primPlusFloat (Float vx30 vx31) (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="vx4",fontsize=16,color="green",shape="box"];17[label="primPlusFloat (Float vx30 vx31) (primIntToFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 18[label="primPlusFloat (Float vx30 vx31) (Float (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 19[label="Float (vx30 * Pos (Succ Zero) + Pos (Succ Zero) * vx31) (vx31 * Pos (Succ Zero))",fontsize=16,color="green",shape="box"];19 -> 20[label="",style="dashed", color="green", weight=3]; 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157 -> 42[label="",style="solid", color="burlywood", weight=3]; 36 -> 35[label="",style="dashed", color="red", weight=0]; 36[label="primMulNat vx310 (Succ Zero)",fontsize=16,color="magenta"];36 -> 43[label="",style="dashed", color="magenta", weight=3]; 37[label="primPlusInt (Pos vx60) (primMulInt (Pos (Succ Zero)) (Pos vx310))",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3]; 38[label="primPlusInt (Pos vx60) (primMulInt (Pos (Succ Zero)) (Neg vx310))",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3]; 39[label="primPlusInt (Neg vx60) (primMulInt (Pos (Succ Zero)) (Pos vx310))",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3]; 40[label="primPlusInt (Neg vx60) (primMulInt (Pos (Succ Zero)) (Neg vx310))",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3]; 41[label="primMulNat (Succ vx3100) (Succ Zero)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3]; 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61 -> 74[label="",style="dashed", color="magenta", weight=3]; 62[label="vx3100",fontsize=16,color="green",shape="box"];63[label="primPlusNat (Succ vx70) (Succ Zero)",fontsize=16,color="black",shape="box"];63 -> 75[label="",style="solid", color="black", weight=3]; 64[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];64 -> 76[label="",style="solid", color="black", weight=3]; 65[label="primPlusNat (Succ vx600) (primMulNat (Succ Zero) vx310)",fontsize=16,color="burlywood",shape="box"];170[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];65 -> 170[label="",style="solid", color="burlywood", weight=9]; 170 -> 77[label="",style="solid", color="burlywood", weight=3]; 171[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 171[label="",style="solid", color="burlywood", weight=9]; 171 -> 78[label="",style="solid", color="burlywood", weight=3]; 66[label="primPlusNat Zero (primMulNat (Succ Zero) vx310)",fontsize=16,color="burlywood",shape="box"];172[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];66 -> 172[label="",style="solid", color="burlywood", weight=9]; 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72[label="primMinusNat Zero vx60",fontsize=16,color="burlywood",shape="triangle"];174[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];72 -> 174[label="",style="solid", color="burlywood", weight=9]; 174 -> 86[label="",style="solid", color="burlywood", weight=3]; 175[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 175[label="",style="solid", color="burlywood", weight=9]; 175 -> 87[label="",style="solid", color="burlywood", weight=3]; 73[label="vx60",fontsize=16,color="green",shape="box"];74[label="vx310",fontsize=16,color="green",shape="box"];75[label="Succ (Succ (primPlusNat vx70 Zero))",fontsize=16,color="green",shape="box"];75 -> 88[label="",style="dashed", color="green", weight=3]; 76[label="Succ Zero",fontsize=16,color="green",shape="box"];77[label="primPlusNat (Succ vx600) (primMulNat (Succ Zero) (Succ vx3100))",fontsize=16,color="black",shape="box"];77 -> 89[label="",style="solid", color="black", weight=3]; 78[label="primPlusNat (Succ vx600) (primMulNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];78 -> 90[label="",style="solid", color="black", weight=3]; 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85[label="primMinusNat (primPlusNat Zero (Succ vx3100)) vx60",fontsize=16,color="black",shape="box"];85 -> 97[label="",style="solid", color="black", weight=3]; 86[label="primMinusNat Zero (Succ vx600)",fontsize=16,color="black",shape="box"];86 -> 98[label="",style="solid", color="black", weight=3]; 87[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];87 -> 99[label="",style="solid", color="black", weight=3]; 88[label="primPlusNat vx70 Zero",fontsize=16,color="burlywood",shape="triangle"];176[label="vx70/Succ vx700",fontsize=10,color="white",style="solid",shape="box"];88 -> 176[label="",style="solid", color="burlywood", weight=9]; 176 -> 100[label="",style="solid", color="burlywood", weight=3]; 177[label="vx70/Zero",fontsize=10,color="white",style="solid",shape="box"];88 -> 177[label="",style="solid", color="burlywood", weight=9]; 177 -> 101[label="",style="solid", color="burlywood", weight=3]; 89[label="primPlusNat (Succ vx600) (primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100))",fontsize=16,color="black",shape="box"];89 -> 102[label="",style="solid", color="black", weight=3]; 90 -> 88[label="",style="dashed", color="red", weight=0]; 90[label="primPlusNat (Succ vx600) Zero",fontsize=16,color="magenta"];90 -> 103[label="",style="dashed", color="magenta", weight=3]; 91[label="primPlusNat Zero (primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100))",fontsize=16,color="black",shape="box"];91 -> 104[label="",style="solid", color="black", weight=3]; 92 -> 88[label="",style="dashed", color="red", weight=0]; 92[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];92 -> 105[label="",style="dashed", color="magenta", weight=3]; 93[label="primMinusNat (Succ vx600) (primPlusNat Zero (Succ vx3100))",fontsize=16,color="black",shape="box"];93 -> 106[label="",style="solid", color="black", weight=3]; 94[label="Pos (Succ vx600)",fontsize=16,color="green",shape="box"];95[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];95 -> 107[label="",style="solid", color="black", weight=3]; 96[label="Zero",fontsize=16,color="green",shape="box"];97[label="primMinusNat (Succ vx3100) vx60",fontsize=16,color="burlywood",shape="triangle"];178[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];97 -> 178[label="",style="solid", color="burlywood", weight=9]; 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105[label="Zero",fontsize=16,color="green",shape="box"];106 -> 97[label="",style="dashed", color="red", weight=0]; 106[label="primMinusNat (Succ vx600) (Succ vx3100)",fontsize=16,color="magenta"];106 -> 114[label="",style="dashed", color="magenta", weight=3]; 106 -> 115[label="",style="dashed", color="magenta", weight=3]; 107[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="triangle"];107 -> 116[label="",style="solid", color="black", weight=3]; 108[label="primMinusNat (Succ vx3100) (Succ vx600)",fontsize=16,color="black",shape="box"];108 -> 117[label="",style="solid", color="black", weight=3]; 109[label="primMinusNat (Succ vx3100) Zero",fontsize=16,color="black",shape="box"];109 -> 118[label="",style="solid", color="black", weight=3]; 110[label="Succ vx700",fontsize=16,color="green",shape="box"];111[label="Zero",fontsize=16,color="green",shape="box"];112[label="primPlusNat (Succ vx600) (Succ vx3100)",fontsize=16,color="black",shape="box"];112 -> 119[label="",style="solid", color="black", weight=3]; 113 -> 107[label="",style="dashed", color="red", weight=0]; 113[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="magenta"];113 -> 120[label="",style="dashed", color="magenta", weight=3]; 114[label="Succ vx3100",fontsize=16,color="green",shape="box"];115[label="vx600",fontsize=16,color="green",shape="box"];116[label="Succ vx3100",fontsize=16,color="green",shape="box"];117[label="primMinusNat vx3100 vx600",fontsize=16,color="burlywood",shape="triangle"];180[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];117 -> 180[label="",style="solid", color="burlywood", weight=9]; 180 -> 121[label="",style="solid", color="burlywood", weight=3]; 181[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];117 -> 181[label="",style="solid", color="burlywood", weight=9]; 181 -> 122[label="",style="solid", color="burlywood", weight=3]; 118[label="Pos (Succ vx3100)",fontsize=16,color="green",shape="box"];119[label="Succ (Succ (primPlusNat vx600 vx3100))",fontsize=16,color="green",shape="box"];119 -> 123[label="",style="dashed", color="green", weight=3]; 120[label="vx3100",fontsize=16,color="green",shape="box"];121[label="primMinusNat (Succ vx31000) vx600",fontsize=16,color="burlywood",shape="box"];182[label="vx600/Succ vx6000",fontsize=10,color="white",style="solid",shape="box"];121 -> 182[label="",style="solid", color="burlywood", weight=9]; 182 -> 124[label="",style="solid", color="burlywood", weight=3]; 183[label="vx600/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 183[label="",style="solid", color="burlywood", weight=9]; 183 -> 125[label="",style="solid", color="burlywood", weight=3]; 122[label="primMinusNat Zero vx600",fontsize=16,color="burlywood",shape="box"];184[label="vx600/Succ vx6000",fontsize=10,color="white",style="solid",shape="box"];122 -> 184[label="",style="solid", color="burlywood", weight=9]; 184 -> 126[label="",style="solid", color="burlywood", weight=3]; 185[label="vx600/Zero",fontsize=10,color="white",style="solid",shape="box"];122 -> 185[label="",style="solid", color="burlywood", weight=9]; 185 -> 127[label="",style="solid", color="burlywood", weight=3]; 123[label="primPlusNat vx600 vx3100",fontsize=16,color="burlywood",shape="triangle"];186[label="vx600/Succ vx6000",fontsize=10,color="white",style="solid",shape="box"];123 -> 186[label="",style="solid", color="burlywood", weight=9]; 186 -> 128[label="",style="solid", color="burlywood", weight=3]; 187[label="vx600/Zero",fontsize=10,color="white",style="solid",shape="box"];123 -> 187[label="",style="solid", color="burlywood", weight=9]; 187 -> 129[label="",style="solid", color="burlywood", weight=3]; 124[label="primMinusNat (Succ vx31000) (Succ vx6000)",fontsize=16,color="black",shape="box"];124 -> 130[label="",style="solid", color="black", weight=3]; 125[label="primMinusNat (Succ vx31000) Zero",fontsize=16,color="black",shape="box"];125 -> 131[label="",style="solid", color="black", weight=3]; 126[label="primMinusNat Zero (Succ vx6000)",fontsize=16,color="black",shape="box"];126 -> 132[label="",style="solid", color="black", weight=3]; 127[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];127 -> 133[label="",style="solid", color="black", weight=3]; 128[label="primPlusNat (Succ vx6000) vx3100",fontsize=16,color="burlywood",shape="box"];188[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];128 -> 188[label="",style="solid", color="burlywood", weight=9]; 188 -> 134[label="",style="solid", color="burlywood", weight=3]; 189[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];128 -> 189[label="",style="solid", color="burlywood", weight=9]; 189 -> 135[label="",style="solid", color="burlywood", weight=3]; 129[label="primPlusNat Zero vx3100",fontsize=16,color="burlywood",shape="box"];190[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];129 -> 190[label="",style="solid", color="burlywood", weight=9]; 190 -> 136[label="",style="solid", color="burlywood", weight=3]; 191[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];129 -> 191[label="",style="solid", color="burlywood", weight=9]; 191 -> 137[label="",style="solid", color="burlywood", weight=3]; 130 -> 117[label="",style="dashed", color="red", weight=0]; 130[label="primMinusNat vx31000 vx6000",fontsize=16,color="magenta"];130 -> 138[label="",style="dashed", color="magenta", weight=3]; 130 -> 139[label="",style="dashed", color="magenta", weight=3]; 131[label="Pos (Succ vx31000)",fontsize=16,color="green",shape="box"];132[label="Neg (Succ vx6000)",fontsize=16,color="green",shape="box"];133[label="Pos Zero",fontsize=16,color="green",shape="box"];134[label="primPlusNat (Succ vx6000) (Succ vx31000)",fontsize=16,color="black",shape="box"];134 -> 140[label="",style="solid", color="black", weight=3]; 135[label="primPlusNat (Succ vx6000) Zero",fontsize=16,color="black",shape="box"];135 -> 141[label="",style="solid", color="black", weight=3]; 136[label="primPlusNat Zero (Succ vx31000)",fontsize=16,color="black",shape="box"];136 -> 142[label="",style="solid", color="black", weight=3]; 137[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];137 -> 143[label="",style="solid", color="black", weight=3]; 138[label="vx6000",fontsize=16,color="green",shape="box"];139[label="vx31000",fontsize=16,color="green",shape="box"];140[label="Succ (Succ (primPlusNat vx6000 vx31000))",fontsize=16,color="green",shape="box"];140 -> 144[label="",style="dashed", color="green", weight=3]; 141[label="Succ vx6000",fontsize=16,color="green",shape="box"];142[label="Succ vx31000",fontsize=16,color="green",shape="box"];143[label="Zero",fontsize=16,color="green",shape="box"];144 -> 123[label="",style="dashed", color="red", weight=0]; 144[label="primPlusNat vx6000 vx31000",fontsize=16,color="magenta"];144 -> 145[label="",style="dashed", color="magenta", weight=3]; 144 -> 146[label="",style="dashed", color="magenta", weight=3]; 145[label="vx31000",fontsize=16,color="green",shape="box"];146[label="vx6000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (24) TRUE