/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) AND (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) QDPOrderProof [EQUIVALENT, 37 ms] (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) QDP (23) MNOCProof [EQUIVALENT, 0 ms] (24) QDP (25) NonTerminationLoopProof [COMPLETE, 0 ms] (26) NO (27) QDP (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] (29) YES (30) QDP (31) QDPSizeChangeProof [EQUIVALENT, 0 ms] (32) YES (33) Narrow [COMPLETE, 0 ms] (34) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\xs->return (x : xs)" is transformed to "sequence0 x xs = return (x : xs); " The following Lambda expression "\x->sequence cs >>= sequence0 x" is transformed to "sequence1 cs x = sequence cs >>= sequence0 x; " ---------------------------------------- (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; " ---------------------------------------- (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="mapM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="mapM vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="mapM vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="sequence . map vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="sequence (map vx3 vx4)",fontsize=16,color="burlywood",shape="triangle"];111[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];6 -> 111[label="",style="solid", color="burlywood", weight=9]; 111 -> 7[label="",style="solid", color="burlywood", weight=3]; 112[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 112[label="",style="solid", color="burlywood", weight=9]; 112 -> 8[label="",style="solid", color="burlywood", weight=3]; 7[label="sequence (map vx3 (vx40 : vx41))",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8[label="sequence (map vx3 [])",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9[label="sequence (vx3 vx40 : map vx3 vx41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10[label="sequence []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="blue",shape="box"];113[label=">>= :: (Maybe a) -> (a -> Maybe ([] a)) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];11 -> 113[label="",style="solid", color="blue", weight=9]; 113 -> 13[label="",style="solid", color="blue", weight=3]; 114[label=">>= :: (IO a) -> (a -> IO ([] a)) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];11 -> 114[label="",style="solid", color="blue", weight=9]; 114 -> 14[label="",style="solid", color="blue", weight=3]; 115[label=">>= :: ([] a) -> (a -> [] ([] a)) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];11 -> 115[label="",style="solid", color="blue", weight=9]; 115 -> 15[label="",style="solid", color="blue", weight=3]; 12[label="return []",fontsize=16,color="blue",shape="box"];116[label="return :: ([] a) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];12 -> 116[label="",style="solid", color="blue", weight=9]; 116 -> 16[label="",style="solid", color="blue", weight=3]; 117[label="return :: ([] a) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];12 -> 117[label="",style="solid", color="blue", weight=9]; 117 -> 17[label="",style="solid", color="blue", weight=3]; 118[label="return :: ([] a) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];12 -> 118[label="",style="solid", color="blue", weight=9]; 118 -> 18[label="",style="solid", color="blue", weight=3]; 13 -> 19[label="",style="dashed", color="red", weight=0]; 13[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];13 -> 20[label="",style="dashed", color="magenta", weight=3]; 14[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];14 -> 21[label="",style="solid", color="black", weight=3]; 15 -> 22[label="",style="dashed", color="red", weight=0]; 15[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];15 -> 23[label="",style="dashed", color="magenta", weight=3]; 16[label="return []",fontsize=16,color="black",shape="box"];16 -> 24[label="",style="solid", color="black", weight=3]; 17[label="return []",fontsize=16,color="black",shape="box"];17 -> 25[label="",style="solid", color="black", weight=3]; 18[label="return []",fontsize=16,color="black",shape="box"];18 -> 26[label="",style="solid", color="black", weight=3]; 20[label="vx3 vx40",fontsize=16,color="green",shape="box"];20 -> 27[label="",style="dashed", color="green", weight=3]; 19[label="vx5 >>= sequence1 (map vx3 vx41)",fontsize=16,color="burlywood",shape="triangle"];119[label="vx5/Nothing",fontsize=10,color="white",style="solid",shape="box"];19 -> 119[label="",style="solid", color="burlywood", weight=9]; 119 -> 28[label="",style="solid", color="burlywood", weight=3]; 120[label="vx5/Just vx50",fontsize=10,color="white",style="solid",shape="box"];19 -> 120[label="",style="solid", color="burlywood", weight=9]; 120 -> 29[label="",style="solid", color="burlywood", weight=3]; 21 -> 30[label="",style="dashed", color="red", weight=0]; 21[label="primbindIO (vx3 vx40) (sequence1 (map vx3 vx41))",fontsize=16,color="magenta"];21 -> 31[label="",style="dashed", color="magenta", weight=3]; 23[label="vx3 vx40",fontsize=16,color="green",shape="box"];23 -> 32[label="",style="dashed", color="green", weight=3]; 22[label="vx6 >>= sequence1 (map vx3 vx41)",fontsize=16,color="burlywood",shape="triangle"];121[label="vx6/vx60 : vx61",fontsize=10,color="white",style="solid",shape="box"];22 -> 121[label="",style="solid", color="burlywood", weight=9]; 121 -> 33[label="",style="solid", color="burlywood", weight=3]; 122[label="vx6/[]",fontsize=10,color="white",style="solid",shape="box"];22 -> 122[label="",style="solid", color="burlywood", weight=9]; 122 -> 34[label="",style="solid", color="burlywood", weight=3]; 24[label="Just []",fontsize=16,color="green",shape="box"];25[label="primretIO []",fontsize=16,color="black",shape="box"];25 -> 35[label="",style="solid", color="black", weight=3]; 26[label="[] : []",fontsize=16,color="green",shape="box"];27[label="vx40",fontsize=16,color="green",shape="box"];28[label="Nothing >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];28 -> 36[label="",style="solid", color="black", weight=3]; 29[label="Just vx50 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3]; 31[label="vx3 vx40",fontsize=16,color="green",shape="box"];31 -> 43[label="",style="dashed", color="green", weight=3]; 30[label="primbindIO vx7 (sequence1 (map vx3 vx41))",fontsize=16,color="burlywood",shape="triangle"];123[label="vx7/IO vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 123[label="",style="solid", color="burlywood", weight=9]; 123 -> 39[label="",style="solid", color="burlywood", weight=3]; 124[label="vx7/AProVE_IO vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 124[label="",style="solid", color="burlywood", weight=9]; 124 -> 40[label="",style="solid", color="burlywood", weight=3]; 125[label="vx7/AProVE_Exception vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 125[label="",style="solid", color="burlywood", weight=9]; 125 -> 41[label="",style="solid", color="burlywood", weight=3]; 126[label="vx7/AProVE_Error vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 126[label="",style="solid", color="burlywood", weight=9]; 126 -> 42[label="",style="solid", color="burlywood", weight=3]; 32[label="vx40",fontsize=16,color="green",shape="box"];33[label="vx60 : vx61 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];33 -> 44[label="",style="solid", color="black", weight=3]; 34[label="[] >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];34 -> 45[label="",style="solid", color="black", weight=3]; 35[label="AProVE_IO []",fontsize=16,color="green",shape="box"];36[label="Nothing",fontsize=16,color="green",shape="box"];37[label="sequence1 (map vx3 vx41) vx50",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3]; 43[label="vx40",fontsize=16,color="green",shape="box"];39[label="primbindIO (IO vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];39 -> 47[label="",style="solid", color="black", weight=3]; 40[label="primbindIO (AProVE_IO vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];40 -> 48[label="",style="solid", color="black", weight=3]; 41[label="primbindIO (AProVE_Exception vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3]; 42[label="primbindIO (AProVE_Error vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];42 -> 50[label="",style="solid", color="black", weight=3]; 44 -> 51[label="",style="dashed", color="red", weight=0]; 44[label="sequence1 (map vx3 vx41) vx60 ++ (vx61 >>= sequence1 (map vx3 vx41))",fontsize=16,color="magenta"];44 -> 52[label="",style="dashed", color="magenta", weight=3]; 45[label="[]",fontsize=16,color="green",shape="box"];46 -> 53[label="",style="dashed", color="red", weight=0]; 46[label="sequence (map vx3 vx41) >>= sequence0 vx50",fontsize=16,color="magenta"];46 -> 54[label="",style="dashed", color="magenta", weight=3]; 47[label="error []",fontsize=16,color="red",shape="box"];48[label="sequence1 (map vx3 vx41) vx70",fontsize=16,color="black",shape="box"];48 -> 55[label="",style="solid", color="black", weight=3]; 49[label="AProVE_Exception vx70",fontsize=16,color="green",shape="box"];50[label="AProVE_Error vx70",fontsize=16,color="green",shape="box"];52 -> 22[label="",style="dashed", color="red", weight=0]; 52[label="vx61 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];52 -> 56[label="",style="dashed", color="magenta", weight=3]; 51[label="sequence1 (map vx3 vx41) vx60 ++ vx8",fontsize=16,color="black",shape="triangle"];51 -> 57[label="",style="solid", color="black", weight=3]; 54 -> 6[label="",style="dashed", color="red", weight=0]; 54[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];54 -> 58[label="",style="dashed", color="magenta", weight=3]; 53[label="vx9 >>= sequence0 vx50",fontsize=16,color="burlywood",shape="triangle"];127[label="vx9/Nothing",fontsize=10,color="white",style="solid",shape="box"];53 -> 127[label="",style="solid", color="burlywood", weight=9]; 127 -> 59[label="",style="solid", color="burlywood", weight=3]; 128[label="vx9/Just vx90",fontsize=10,color="white",style="solid",shape="box"];53 -> 128[label="",style="solid", color="burlywood", weight=9]; 128 -> 60[label="",style="solid", color="burlywood", weight=3]; 55 -> 61[label="",style="dashed", color="red", weight=0]; 55[label="sequence (map vx3 vx41) >>= sequence0 vx70",fontsize=16,color="magenta"];55 -> 62[label="",style="dashed", color="magenta", weight=3]; 56[label="vx61",fontsize=16,color="green",shape="box"];57 -> 63[label="",style="dashed", color="red", weight=0]; 57[label="(sequence (map vx3 vx41) >>= sequence0 vx60) ++ vx8",fontsize=16,color="magenta"];57 -> 64[label="",style="dashed", color="magenta", weight=3]; 58[label="vx41",fontsize=16,color="green",shape="box"];59[label="Nothing >>= sequence0 vx50",fontsize=16,color="black",shape="box"];59 -> 65[label="",style="solid", color="black", weight=3]; 60[label="Just vx90 >>= sequence0 vx50",fontsize=16,color="black",shape="box"];60 -> 66[label="",style="solid", color="black", weight=3]; 62 -> 6[label="",style="dashed", color="red", weight=0]; 62[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];62 -> 67[label="",style="dashed", color="magenta", weight=3]; 61[label="vx10 >>= sequence0 vx70",fontsize=16,color="black",shape="triangle"];61 -> 68[label="",style="solid", color="black", weight=3]; 64 -> 6[label="",style="dashed", color="red", weight=0]; 64[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];64 -> 69[label="",style="dashed", color="magenta", weight=3]; 63[label="(vx11 >>= sequence0 vx60) ++ vx8",fontsize=16,color="burlywood",shape="triangle"];129[label="vx11/vx110 : vx111",fontsize=10,color="white",style="solid",shape="box"];63 -> 129[label="",style="solid", color="burlywood", weight=9]; 129 -> 70[label="",style="solid", color="burlywood", weight=3]; 130[label="vx11/[]",fontsize=10,color="white",style="solid",shape="box"];63 -> 130[label="",style="solid", color="burlywood", weight=9]; 130 -> 71[label="",style="solid", color="burlywood", weight=3]; 65[label="Nothing",fontsize=16,color="green",shape="box"];66[label="sequence0 vx50 vx90",fontsize=16,color="black",shape="box"];66 -> 72[label="",style="solid", color="black", weight=3]; 67[label="vx41",fontsize=16,color="green",shape="box"];68[label="primbindIO vx10 (sequence0 vx70)",fontsize=16,color="burlywood",shape="box"];131[label="vx10/IO vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 131[label="",style="solid", color="burlywood", weight=9]; 131 -> 73[label="",style="solid", color="burlywood", weight=3]; 132[label="vx10/AProVE_IO vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 132[label="",style="solid", color="burlywood", weight=9]; 132 -> 74[label="",style="solid", color="burlywood", weight=3]; 133[label="vx10/AProVE_Exception vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 133[label="",style="solid", color="burlywood", weight=9]; 133 -> 75[label="",style="solid", color="burlywood", weight=3]; 134[label="vx10/AProVE_Error vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 134[label="",style="solid", color="burlywood", weight=9]; 134 -> 76[label="",style="solid", color="burlywood", weight=3]; 69[label="vx41",fontsize=16,color="green",shape="box"];70[label="(vx110 : vx111 >>= sequence0 vx60) ++ vx8",fontsize=16,color="black",shape="box"];70 -> 77[label="",style="solid", color="black", weight=3]; 71[label="([] >>= sequence0 vx60) ++ vx8",fontsize=16,color="black",shape="box"];71 -> 78[label="",style="solid", color="black", weight=3]; 72[label="return (vx50 : vx90)",fontsize=16,color="black",shape="box"];72 -> 79[label="",style="solid", color="black", weight=3]; 73[label="primbindIO (IO vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];73 -> 80[label="",style="solid", color="black", weight=3]; 74[label="primbindIO (AProVE_IO vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];74 -> 81[label="",style="solid", color="black", weight=3]; 75[label="primbindIO (AProVE_Exception vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];75 -> 82[label="",style="solid", color="black", weight=3]; 76[label="primbindIO (AProVE_Error vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];76 -> 83[label="",style="solid", color="black", weight=3]; 77[label="(sequence0 vx60 vx110 ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="black",shape="box"];77 -> 84[label="",style="solid", color="black", weight=3]; 78[label="[] ++ vx8",fontsize=16,color="black",shape="triangle"];78 -> 85[label="",style="solid", color="black", weight=3]; 79[label="Just (vx50 : vx90)",fontsize=16,color="green",shape="box"];80[label="error []",fontsize=16,color="red",shape="box"];81[label="sequence0 vx70 vx100",fontsize=16,color="black",shape="box"];81 -> 86[label="",style="solid", color="black", weight=3]; 82[label="AProVE_Exception vx100",fontsize=16,color="green",shape="box"];83[label="AProVE_Error vx100",fontsize=16,color="green",shape="box"];84[label="(return (vx60 : vx110) ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="black",shape="box"];84 -> 87[label="",style="solid", color="black", weight=3]; 85[label="vx8",fontsize=16,color="green",shape="box"];86[label="return (vx70 : vx100)",fontsize=16,color="black",shape="box"];86 -> 88[label="",style="solid", color="black", weight=3]; 87[label="(((vx60 : vx110) : []) ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="black",shape="box"];87 -> 89[label="",style="solid", color="black", weight=3]; 88[label="primretIO (vx70 : vx100)",fontsize=16,color="black",shape="box"];88 -> 90[label="",style="solid", color="black", weight=3]; 89 -> 91[label="",style="dashed", color="red", weight=0]; 89[label="((vx60 : vx110) : [] ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="magenta"];89 -> 92[label="",style="dashed", color="magenta", weight=3]; 90[label="AProVE_IO (vx70 : vx100)",fontsize=16,color="green",shape="box"];92 -> 78[label="",style="dashed", color="red", weight=0]; 92[label="[] ++ (vx111 >>= sequence0 vx60)",fontsize=16,color="magenta"];92 -> 93[label="",style="dashed", color="magenta", weight=3]; 91[label="((vx60 : vx110) : vx12) ++ vx8",fontsize=16,color="black",shape="triangle"];91 -> 94[label="",style="solid", color="black", weight=3]; 93[label="vx111 >>= sequence0 vx60",fontsize=16,color="burlywood",shape="triangle"];135[label="vx111/vx1110 : vx1111",fontsize=10,color="white",style="solid",shape="box"];93 -> 135[label="",style="solid", color="burlywood", weight=9]; 135 -> 95[label="",style="solid", color="burlywood", weight=3]; 136[label="vx111/[]",fontsize=10,color="white",style="solid",shape="box"];93 -> 136[label="",style="solid", color="burlywood", weight=9]; 136 -> 96[label="",style="solid", color="burlywood", weight=3]; 94[label="(vx60 : vx110) : vx12 ++ vx8",fontsize=16,color="green",shape="box"];94 -> 97[label="",style="dashed", color="green", weight=3]; 95[label="vx1110 : vx1111 >>= sequence0 vx60",fontsize=16,color="black",shape="box"];95 -> 98[label="",style="solid", color="black", weight=3]; 96[label="[] >>= sequence0 vx60",fontsize=16,color="black",shape="box"];96 -> 99[label="",style="solid", color="black", weight=3]; 97[label="vx12 ++ vx8",fontsize=16,color="burlywood",shape="triangle"];137[label="vx12/vx120 : vx121",fontsize=10,color="white",style="solid",shape="box"];97 -> 137[label="",style="solid", color="burlywood", weight=9]; 137 -> 100[label="",style="solid", color="burlywood", weight=3]; 138[label="vx12/[]",fontsize=10,color="white",style="solid",shape="box"];97 -> 138[label="",style="solid", color="burlywood", weight=9]; 138 -> 101[label="",style="solid", color="burlywood", weight=3]; 98 -> 97[label="",style="dashed", color="red", weight=0]; 98[label="sequence0 vx60 vx1110 ++ (vx1111 >>= sequence0 vx60)",fontsize=16,color="magenta"];98 -> 102[label="",style="dashed", color="magenta", weight=3]; 98 -> 103[label="",style="dashed", color="magenta", weight=3]; 99[label="[]",fontsize=16,color="green",shape="box"];100[label="(vx120 : vx121) ++ vx8",fontsize=16,color="black",shape="box"];100 -> 104[label="",style="solid", color="black", weight=3]; 101[label="[] ++ vx8",fontsize=16,color="black",shape="box"];101 -> 105[label="",style="solid", color="black", weight=3]; 102 -> 93[label="",style="dashed", color="red", weight=0]; 102[label="vx1111 >>= sequence0 vx60",fontsize=16,color="magenta"];102 -> 106[label="",style="dashed", color="magenta", weight=3]; 103[label="sequence0 vx60 vx1110",fontsize=16,color="black",shape="box"];103 -> 107[label="",style="solid", color="black", weight=3]; 104[label="vx120 : vx121 ++ vx8",fontsize=16,color="green",shape="box"];104 -> 108[label="",style="dashed", color="green", weight=3]; 105[label="vx8",fontsize=16,color="green",shape="box"];106[label="vx1111",fontsize=16,color="green",shape="box"];107[label="return (vx60 : vx1110)",fontsize=16,color="black",shape="box"];107 -> 109[label="",style="solid", color="black", weight=3]; 108 -> 97[label="",style="dashed", color="red", weight=0]; 108[label="vx121 ++ vx8",fontsize=16,color="magenta"];108 -> 110[label="",style="dashed", color="magenta", weight=3]; 109[label="(vx60 : vx1110) : []",fontsize=16,color="green",shape="box"];110[label="vx121",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs(:(vx1110, vx1111), vx60, h) -> new_gtGtEs(vx1111, vx60, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) 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_gtGtEs(:(vx1110, vx1111), vx60, h) -> new_gtGtEs(vx1111, vx60, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_sequence(vx3, :(vx40, vx41), ty_Maybe, h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) new_gtGtEs1(vx3, vx41, h, ba) -> new_psPs0(vx3, vx41, h, ba) new_gtGtEs0(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_Maybe, h, ba) new_sequence(vx3, :(vx40, vx41), ty_[], h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) new_gtGtEs1(vx3, vx41, h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) new_sequence(vx3, :(vx40, vx41), ty_IO, h, ba) -> new_primbindIO(vx3, vx41, h, ba) new_primbindIO(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_IO, h, ba) new_psPs0(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_[], h, ba) The TRS R consists of the following rules: new_psPs4(vx8, h) -> vx8 new_psPs2([], vx60, vx8, h) -> new_psPs4(vx8, h) new_psPs1(:(vx120, vx121), vx8, h) -> :(vx120, new_psPs1(vx121, vx8, h)) new_gtGtEs3([], vx60, h) -> [] new_psPs3(vx60, vx110, vx12, vx8, h) -> :(:(vx60, vx110), new_psPs1(vx12, vx8, h)) new_gtGtEs2([], vx3, vx41, h, ba) -> [] new_gtGtEs3(:(vx1110, vx1111), vx60, h) -> new_psPs1(:(:(vx60, vx1110), []), new_gtGtEs3(vx1111, vx60, h), h) new_psPs2(:(vx110, vx111), vx60, vx8, h) -> new_psPs3(vx60, vx110, new_psPs4(new_gtGtEs3(vx111, vx60, h), h), vx8, h) new_gtGtEs2(:(vx60, vx61), vx3, vx41, h, ba) -> new_psPs5(vx3, vx41, vx60, new_gtGtEs2(vx61, vx3, vx41, h, ba), h, ba) new_psPs1([], vx8, h) -> vx8 new_psPs5(vx3, vx41, vx60, vx8, h, ba) -> new_psPs2(new_sequence0(vx3, vx41, ty_[], h, ba), vx60, vx8, h) The set Q consists of the following terms: new_gtGtEs2(:(x0, x1), x2, x3, x4, x5) new_psPs3(x0, x1, x2, x3, x4) new_gtGtEs2([], x0, x1, x2, x3) new_gtGtEs3([], x0, x1) new_psPs5(x0, x1, x2, x3, x4, x5) new_psPs1(:(x0, x1), x2, x3) new_psPs1([], x0, x1) new_psPs4(x0, x1) new_gtGtEs3(:(x0, x1), x2, x3) new_psPs2([], x0, x1, x2) new_psPs2(:(x0, x1), x2, x3, x4) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (13) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs. ---------------------------------------- (14) Complex Obligation (AND) ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_primbindIO(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_IO, h, ba) new_sequence(vx3, :(vx40, vx41), ty_IO, h, ba) -> new_primbindIO(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs4(vx8, h) -> vx8 new_psPs2([], vx60, vx8, h) -> new_psPs4(vx8, h) new_psPs1(:(vx120, vx121), vx8, h) -> :(vx120, new_psPs1(vx121, vx8, h)) new_gtGtEs3([], vx60, h) -> [] new_psPs3(vx60, vx110, vx12, vx8, h) -> :(:(vx60, vx110), new_psPs1(vx12, vx8, h)) new_gtGtEs2([], vx3, vx41, h, ba) -> [] new_gtGtEs3(:(vx1110, vx1111), vx60, h) -> new_psPs1(:(:(vx60, vx1110), []), new_gtGtEs3(vx1111, vx60, h), h) new_psPs2(:(vx110, vx111), vx60, vx8, h) -> new_psPs3(vx60, vx110, new_psPs4(new_gtGtEs3(vx111, vx60, h), h), vx8, h) new_gtGtEs2(:(vx60, vx61), vx3, vx41, h, ba) -> new_psPs5(vx3, vx41, vx60, new_gtGtEs2(vx61, vx3, vx41, h, ba), h, ba) new_psPs1([], vx8, h) -> vx8 new_psPs5(vx3, vx41, vx60, vx8, h, ba) -> new_psPs2(new_sequence0(vx3, vx41, ty_[], h, ba), vx60, vx8, h) The set Q consists of the following terms: new_gtGtEs2(:(x0, x1), x2, x3, x4, x5) new_psPs3(x0, x1, x2, x3, x4) new_gtGtEs2([], x0, x1, x2, x3) new_gtGtEs3([], x0, x1) new_psPs5(x0, x1, x2, x3, x4, x5) new_psPs1(:(x0, x1), x2, x3) new_psPs1([], x0, x1) new_psPs4(x0, x1) new_gtGtEs3(:(x0, x1), x2, x3) new_psPs2([], x0, x1, x2) new_psPs2(:(x0, x1), x2, x3, x4) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) 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_sequence(vx3, :(vx40, vx41), ty_IO, h, ba) -> new_primbindIO(vx3, vx41, h, ba) The graph contains the following edges 1 >= 1, 2 > 2, 4 >= 3, 5 >= 4 *new_primbindIO(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_IO, h, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5 ---------------------------------------- (17) YES ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs0(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_[], h, ba) new_sequence(vx3, :(vx40, vx41), ty_[], h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) new_gtGtEs1(vx3, vx41, h, ba) -> new_psPs0(vx3, vx41, h, ba) new_gtGtEs1(vx3, vx41, h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs4(vx8, h) -> vx8 new_psPs2([], vx60, vx8, h) -> new_psPs4(vx8, h) new_psPs1(:(vx120, vx121), vx8, h) -> :(vx120, new_psPs1(vx121, vx8, h)) new_gtGtEs3([], vx60, h) -> [] new_psPs3(vx60, vx110, vx12, vx8, h) -> :(:(vx60, vx110), new_psPs1(vx12, vx8, h)) new_gtGtEs2([], vx3, vx41, h, ba) -> [] new_gtGtEs3(:(vx1110, vx1111), vx60, h) -> new_psPs1(:(:(vx60, vx1110), []), new_gtGtEs3(vx1111, vx60, h), h) new_psPs2(:(vx110, vx111), vx60, vx8, h) -> new_psPs3(vx60, vx110, new_psPs4(new_gtGtEs3(vx111, vx60, h), h), vx8, h) new_gtGtEs2(:(vx60, vx61), vx3, vx41, h, ba) -> new_psPs5(vx3, vx41, vx60, new_gtGtEs2(vx61, vx3, vx41, h, ba), h, ba) new_psPs1([], vx8, h) -> vx8 new_psPs5(vx3, vx41, vx60, vx8, h, ba) -> new_psPs2(new_sequence0(vx3, vx41, ty_[], h, ba), vx60, vx8, h) The set Q consists of the following terms: new_gtGtEs2(:(x0, x1), x2, x3, x4, x5) new_psPs3(x0, x1, x2, x3, x4) new_gtGtEs2([], x0, x1, x2, x3) new_gtGtEs3([], x0, x1) new_psPs5(x0, x1, x2, x3, x4, x5) new_psPs1(:(x0, x1), x2, x3) new_psPs1([], x0, x1) new_psPs4(x0, x1) new_gtGtEs3(:(x0, x1), x2, x3) new_psPs2([], x0, x1, x2) new_psPs2(:(x0, x1), x2, x3, x4) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (19) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gtGtEs1(vx3, vx41, h, ba) -> new_psPs0(vx3, vx41, h, ba) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(:(x_1, x_2)) = 1 + x_2 POL(new_gtGtEs1(x_1, x_2, x_3, x_4)) = 1 + x_2 POL(new_psPs0(x_1, x_2, x_3, x_4)) = x_2 POL(new_sequence(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_3 POL(ty_[]) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: none ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs0(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_[], h, ba) new_sequence(vx3, :(vx40, vx41), ty_[], h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) new_gtGtEs1(vx3, vx41, h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs4(vx8, h) -> vx8 new_psPs2([], vx60, vx8, h) -> new_psPs4(vx8, h) new_psPs1(:(vx120, vx121), vx8, h) -> :(vx120, new_psPs1(vx121, vx8, h)) new_gtGtEs3([], vx60, h) -> [] new_psPs3(vx60, vx110, vx12, vx8, h) -> :(:(vx60, vx110), new_psPs1(vx12, vx8, h)) new_gtGtEs2([], vx3, vx41, h, ba) -> [] new_gtGtEs3(:(vx1110, vx1111), vx60, h) -> new_psPs1(:(:(vx60, vx1110), []), new_gtGtEs3(vx1111, vx60, h), h) new_psPs2(:(vx110, vx111), vx60, vx8, h) -> new_psPs3(vx60, vx110, new_psPs4(new_gtGtEs3(vx111, vx60, h), h), vx8, h) new_gtGtEs2(:(vx60, vx61), vx3, vx41, h, ba) -> new_psPs5(vx3, vx41, vx60, new_gtGtEs2(vx61, vx3, vx41, h, ba), h, ba) new_psPs1([], vx8, h) -> vx8 new_psPs5(vx3, vx41, vx60, vx8, h, ba) -> new_psPs2(new_sequence0(vx3, vx41, ty_[], h, ba), vx60, vx8, h) The set Q consists of the following terms: new_gtGtEs2(:(x0, x1), x2, x3, x4, x5) new_psPs3(x0, x1, x2, x3, x4) new_gtGtEs2([], x0, x1, x2, x3) new_gtGtEs3([], x0, x1) new_psPs5(x0, x1, x2, x3, x4, x5) new_psPs1(:(x0, x1), x2, x3) new_psPs1([], x0, x1) new_psPs4(x0, x1) new_gtGtEs3(:(x0, x1), x2, x3) new_psPs2([], x0, x1, x2) new_psPs2(:(x0, x1), x2, x3, x4) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs1(vx3, vx41, h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs4(vx8, h) -> vx8 new_psPs2([], vx60, vx8, h) -> new_psPs4(vx8, h) new_psPs1(:(vx120, vx121), vx8, h) -> :(vx120, new_psPs1(vx121, vx8, h)) new_gtGtEs3([], vx60, h) -> [] new_psPs3(vx60, vx110, vx12, vx8, h) -> :(:(vx60, vx110), new_psPs1(vx12, vx8, h)) new_gtGtEs2([], vx3, vx41, h, ba) -> [] new_gtGtEs3(:(vx1110, vx1111), vx60, h) -> new_psPs1(:(:(vx60, vx1110), []), new_gtGtEs3(vx1111, vx60, h), h) new_psPs2(:(vx110, vx111), vx60, vx8, h) -> new_psPs3(vx60, vx110, new_psPs4(new_gtGtEs3(vx111, vx60, h), h), vx8, h) new_gtGtEs2(:(vx60, vx61), vx3, vx41, h, ba) -> new_psPs5(vx3, vx41, vx60, new_gtGtEs2(vx61, vx3, vx41, h, ba), h, ba) new_psPs1([], vx8, h) -> vx8 new_psPs5(vx3, vx41, vx60, vx8, h, ba) -> new_psPs2(new_sequence0(vx3, vx41, ty_[], h, ba), vx60, vx8, h) The set Q consists of the following terms: new_gtGtEs2(:(x0, x1), x2, x3, x4, x5) new_psPs3(x0, x1, x2, x3, x4) new_gtGtEs2([], x0, x1, x2, x3) new_gtGtEs3([], x0, x1) new_psPs5(x0, x1, x2, x3, x4, x5) new_psPs1(:(x0, x1), x2, x3) new_psPs1([], x0, x1) new_psPs4(x0, x1) new_gtGtEs3(:(x0, x1), x2, x3) new_psPs2([], x0, x1, x2) new_psPs2(:(x0, x1), x2, x3, x4) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (23) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs1(vx3, vx41, h, ba) -> new_gtGtEs1(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs4(vx8, h) -> vx8 new_psPs2([], vx60, vx8, h) -> new_psPs4(vx8, h) new_psPs1(:(vx120, vx121), vx8, h) -> :(vx120, new_psPs1(vx121, vx8, h)) new_gtGtEs3([], vx60, h) -> [] new_psPs3(vx60, vx110, vx12, vx8, h) -> :(:(vx60, vx110), new_psPs1(vx12, vx8, h)) new_gtGtEs2([], vx3, vx41, h, ba) -> [] new_gtGtEs3(:(vx1110, vx1111), vx60, h) -> new_psPs1(:(:(vx60, vx1110), []), new_gtGtEs3(vx1111, vx60, h), h) new_psPs2(:(vx110, vx111), vx60, vx8, h) -> new_psPs3(vx60, vx110, new_psPs4(new_gtGtEs3(vx111, vx60, h), h), vx8, h) new_gtGtEs2(:(vx60, vx61), vx3, vx41, h, ba) -> new_psPs5(vx3, vx41, vx60, new_gtGtEs2(vx61, vx3, vx41, h, ba), h, ba) new_psPs1([], vx8, h) -> vx8 new_psPs5(vx3, vx41, vx60, vx8, h, ba) -> new_psPs2(new_sequence0(vx3, vx41, ty_[], h, ba), vx60, vx8, h) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (25) 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_gtGtEs1(vx3, vx41, h, ba) evaluates to t =new_gtGtEs1(vx3, vx41, h, ba) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_gtGtEs1(vx3, vx41, h, ba) to new_gtGtEs1(vx3, vx41, h, ba). ---------------------------------------- (26) NO ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs0(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_Maybe, h, ba) new_sequence(vx3, :(vx40, vx41), ty_Maybe, h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs4(vx8, h) -> vx8 new_psPs2([], vx60, vx8, h) -> new_psPs4(vx8, h) new_psPs1(:(vx120, vx121), vx8, h) -> :(vx120, new_psPs1(vx121, vx8, h)) new_gtGtEs3([], vx60, h) -> [] new_psPs3(vx60, vx110, vx12, vx8, h) -> :(:(vx60, vx110), new_psPs1(vx12, vx8, h)) new_gtGtEs2([], vx3, vx41, h, ba) -> [] new_gtGtEs3(:(vx1110, vx1111), vx60, h) -> new_psPs1(:(:(vx60, vx1110), []), new_gtGtEs3(vx1111, vx60, h), h) new_psPs2(:(vx110, vx111), vx60, vx8, h) -> new_psPs3(vx60, vx110, new_psPs4(new_gtGtEs3(vx111, vx60, h), h), vx8, h) new_gtGtEs2(:(vx60, vx61), vx3, vx41, h, ba) -> new_psPs5(vx3, vx41, vx60, new_gtGtEs2(vx61, vx3, vx41, h, ba), h, ba) new_psPs1([], vx8, h) -> vx8 new_psPs5(vx3, vx41, vx60, vx8, h, ba) -> new_psPs2(new_sequence0(vx3, vx41, ty_[], h, ba), vx60, vx8, h) The set Q consists of the following terms: new_gtGtEs2(:(x0, x1), x2, x3, x4, x5) new_psPs3(x0, x1, x2, x3, x4) new_gtGtEs2([], x0, x1, x2, x3) new_gtGtEs3([], x0, x1) new_psPs5(x0, x1, x2, x3, x4, x5) new_psPs1(:(x0, x1), x2, x3) new_psPs1([], x0, x1) new_psPs4(x0, x1) new_gtGtEs3(:(x0, x1), x2, x3) new_psPs2([], x0, x1, x2) new_psPs2(:(x0, x1), x2, x3, x4) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) 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_sequence(vx3, :(vx40, vx41), ty_Maybe, h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) The graph contains the following edges 1 >= 1, 2 > 2, 4 >= 3, 5 >= 4 *new_gtGtEs0(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, ty_Maybe, h, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5 ---------------------------------------- (29) YES ---------------------------------------- (30) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(vx120, vx121), vx8, h) -> new_psPs(vx121, vx8, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (31) 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_psPs(:(vx120, vx121), vx8, h) -> new_psPs(vx121, vx8, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (32) YES ---------------------------------------- (33) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="mapM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="mapM vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="mapM vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="sequence . map vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="sequence (map vx3 vx4)",fontsize=16,color="burlywood",shape="triangle"];111[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];6 -> 111[label="",style="solid", color="burlywood", weight=9]; 111 -> 7[label="",style="solid", color="burlywood", weight=3]; 112[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 112[label="",style="solid", color="burlywood", weight=9]; 112 -> 8[label="",style="solid", color="burlywood", weight=3]; 7[label="sequence (map vx3 (vx40 : vx41))",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8[label="sequence (map vx3 [])",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9[label="sequence (vx3 vx40 : map vx3 vx41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10[label="sequence []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="blue",shape="box"];113[label=">>= :: (Maybe a) -> (a -> Maybe ([] a)) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];11 -> 113[label="",style="solid", color="blue", weight=9]; 113 -> 13[label="",style="solid", color="blue", weight=3]; 114[label=">>= :: (IO a) -> (a -> IO ([] a)) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];11 -> 114[label="",style="solid", color="blue", weight=9]; 114 -> 14[label="",style="solid", color="blue", weight=3]; 115[label=">>= :: ([] a) -> (a -> [] ([] a)) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];11 -> 115[label="",style="solid", color="blue", weight=9]; 115 -> 15[label="",style="solid", color="blue", weight=3]; 12[label="return []",fontsize=16,color="blue",shape="box"];116[label="return :: ([] a) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];12 -> 116[label="",style="solid", color="blue", weight=9]; 116 -> 16[label="",style="solid", color="blue", weight=3]; 117[label="return :: ([] a) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];12 -> 117[label="",style="solid", color="blue", weight=9]; 117 -> 17[label="",style="solid", color="blue", weight=3]; 118[label="return :: ([] a) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];12 -> 118[label="",style="solid", color="blue", weight=9]; 118 -> 18[label="",style="solid", color="blue", weight=3]; 13 -> 19[label="",style="dashed", color="red", weight=0]; 13[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];13 -> 20[label="",style="dashed", color="magenta", weight=3]; 14[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];14 -> 21[label="",style="solid", color="black", weight=3]; 15 -> 22[label="",style="dashed", color="red", weight=0]; 15[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];15 -> 23[label="",style="dashed", color="magenta", weight=3]; 16[label="return []",fontsize=16,color="black",shape="box"];16 -> 24[label="",style="solid", color="black", weight=3]; 17[label="return []",fontsize=16,color="black",shape="box"];17 -> 25[label="",style="solid", color="black", weight=3]; 18[label="return []",fontsize=16,color="black",shape="box"];18 -> 26[label="",style="solid", color="black", weight=3]; 20[label="vx3 vx40",fontsize=16,color="green",shape="box"];20 -> 27[label="",style="dashed", color="green", weight=3]; 19[label="vx5 >>= sequence1 (map vx3 vx41)",fontsize=16,color="burlywood",shape="triangle"];119[label="vx5/Nothing",fontsize=10,color="white",style="solid",shape="box"];19 -> 119[label="",style="solid", color="burlywood", weight=9]; 119 -> 28[label="",style="solid", color="burlywood", weight=3]; 120[label="vx5/Just vx50",fontsize=10,color="white",style="solid",shape="box"];19 -> 120[label="",style="solid", color="burlywood", weight=9]; 120 -> 29[label="",style="solid", color="burlywood", weight=3]; 21 -> 30[label="",style="dashed", color="red", weight=0]; 21[label="primbindIO (vx3 vx40) (sequence1 (map vx3 vx41))",fontsize=16,color="magenta"];21 -> 31[label="",style="dashed", color="magenta", weight=3]; 23[label="vx3 vx40",fontsize=16,color="green",shape="box"];23 -> 32[label="",style="dashed", color="green", weight=3]; 22[label="vx6 >>= sequence1 (map vx3 vx41)",fontsize=16,color="burlywood",shape="triangle"];121[label="vx6/vx60 : vx61",fontsize=10,color="white",style="solid",shape="box"];22 -> 121[label="",style="solid", color="burlywood", weight=9]; 121 -> 33[label="",style="solid", color="burlywood", weight=3]; 122[label="vx6/[]",fontsize=10,color="white",style="solid",shape="box"];22 -> 122[label="",style="solid", color="burlywood", weight=9]; 122 -> 34[label="",style="solid", color="burlywood", weight=3]; 24[label="Just []",fontsize=16,color="green",shape="box"];25[label="primretIO []",fontsize=16,color="black",shape="box"];25 -> 35[label="",style="solid", color="black", weight=3]; 26[label="[] : []",fontsize=16,color="green",shape="box"];27[label="vx40",fontsize=16,color="green",shape="box"];28[label="Nothing >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];28 -> 36[label="",style="solid", color="black", weight=3]; 29[label="Just vx50 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3]; 31[label="vx3 vx40",fontsize=16,color="green",shape="box"];31 -> 43[label="",style="dashed", color="green", weight=3]; 30[label="primbindIO vx7 (sequence1 (map vx3 vx41))",fontsize=16,color="burlywood",shape="triangle"];123[label="vx7/IO vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 123[label="",style="solid", color="burlywood", weight=9]; 123 -> 39[label="",style="solid", color="burlywood", weight=3]; 124[label="vx7/AProVE_IO vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 124[label="",style="solid", color="burlywood", weight=9]; 124 -> 40[label="",style="solid", color="burlywood", weight=3]; 125[label="vx7/AProVE_Exception vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 125[label="",style="solid", color="burlywood", weight=9]; 125 -> 41[label="",style="solid", color="burlywood", weight=3]; 126[label="vx7/AProVE_Error vx70",fontsize=10,color="white",style="solid",shape="box"];30 -> 126[label="",style="solid", color="burlywood", weight=9]; 126 -> 42[label="",style="solid", color="burlywood", weight=3]; 32[label="vx40",fontsize=16,color="green",shape="box"];33[label="vx60 : vx61 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];33 -> 44[label="",style="solid", color="black", weight=3]; 34[label="[] >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];34 -> 45[label="",style="solid", color="black", weight=3]; 35[label="AProVE_IO []",fontsize=16,color="green",shape="box"];36[label="Nothing",fontsize=16,color="green",shape="box"];37[label="sequence1 (map vx3 vx41) vx50",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3]; 43[label="vx40",fontsize=16,color="green",shape="box"];39[label="primbindIO (IO vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];39 -> 47[label="",style="solid", color="black", weight=3]; 40[label="primbindIO (AProVE_IO vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];40 -> 48[label="",style="solid", color="black", weight=3]; 41[label="primbindIO (AProVE_Exception vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3]; 42[label="primbindIO (AProVE_Error vx70) (sequence1 (map vx3 vx41))",fontsize=16,color="black",shape="box"];42 -> 50[label="",style="solid", color="black", weight=3]; 44 -> 51[label="",style="dashed", color="red", weight=0]; 44[label="sequence1 (map vx3 vx41) vx60 ++ (vx61 >>= sequence1 (map vx3 vx41))",fontsize=16,color="magenta"];44 -> 52[label="",style="dashed", color="magenta", weight=3]; 45[label="[]",fontsize=16,color="green",shape="box"];46 -> 53[label="",style="dashed", color="red", weight=0]; 46[label="sequence (map vx3 vx41) >>= sequence0 vx50",fontsize=16,color="magenta"];46 -> 54[label="",style="dashed", color="magenta", weight=3]; 47[label="error []",fontsize=16,color="red",shape="box"];48[label="sequence1 (map vx3 vx41) vx70",fontsize=16,color="black",shape="box"];48 -> 55[label="",style="solid", color="black", weight=3]; 49[label="AProVE_Exception vx70",fontsize=16,color="green",shape="box"];50[label="AProVE_Error vx70",fontsize=16,color="green",shape="box"];52 -> 22[label="",style="dashed", color="red", weight=0]; 52[label="vx61 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];52 -> 56[label="",style="dashed", color="magenta", weight=3]; 51[label="sequence1 (map vx3 vx41) vx60 ++ vx8",fontsize=16,color="black",shape="triangle"];51 -> 57[label="",style="solid", color="black", weight=3]; 54 -> 6[label="",style="dashed", color="red", weight=0]; 54[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];54 -> 58[label="",style="dashed", color="magenta", weight=3]; 53[label="vx9 >>= sequence0 vx50",fontsize=16,color="burlywood",shape="triangle"];127[label="vx9/Nothing",fontsize=10,color="white",style="solid",shape="box"];53 -> 127[label="",style="solid", color="burlywood", weight=9]; 127 -> 59[label="",style="solid", color="burlywood", weight=3]; 128[label="vx9/Just vx90",fontsize=10,color="white",style="solid",shape="box"];53 -> 128[label="",style="solid", color="burlywood", weight=9]; 128 -> 60[label="",style="solid", color="burlywood", weight=3]; 55 -> 61[label="",style="dashed", color="red", weight=0]; 55[label="sequence (map vx3 vx41) >>= sequence0 vx70",fontsize=16,color="magenta"];55 -> 62[label="",style="dashed", color="magenta", weight=3]; 56[label="vx61",fontsize=16,color="green",shape="box"];57 -> 63[label="",style="dashed", color="red", weight=0]; 57[label="(sequence (map vx3 vx41) >>= sequence0 vx60) ++ vx8",fontsize=16,color="magenta"];57 -> 64[label="",style="dashed", color="magenta", weight=3]; 58[label="vx41",fontsize=16,color="green",shape="box"];59[label="Nothing >>= sequence0 vx50",fontsize=16,color="black",shape="box"];59 -> 65[label="",style="solid", color="black", weight=3]; 60[label="Just vx90 >>= sequence0 vx50",fontsize=16,color="black",shape="box"];60 -> 66[label="",style="solid", color="black", weight=3]; 62 -> 6[label="",style="dashed", color="red", weight=0]; 62[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];62 -> 67[label="",style="dashed", color="magenta", weight=3]; 61[label="vx10 >>= sequence0 vx70",fontsize=16,color="black",shape="triangle"];61 -> 68[label="",style="solid", color="black", weight=3]; 64 -> 6[label="",style="dashed", color="red", weight=0]; 64[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];64 -> 69[label="",style="dashed", color="magenta", weight=3]; 63[label="(vx11 >>= sequence0 vx60) ++ vx8",fontsize=16,color="burlywood",shape="triangle"];129[label="vx11/vx110 : vx111",fontsize=10,color="white",style="solid",shape="box"];63 -> 129[label="",style="solid", color="burlywood", weight=9]; 129 -> 70[label="",style="solid", color="burlywood", weight=3]; 130[label="vx11/[]",fontsize=10,color="white",style="solid",shape="box"];63 -> 130[label="",style="solid", color="burlywood", weight=9]; 130 -> 71[label="",style="solid", color="burlywood", weight=3]; 65[label="Nothing",fontsize=16,color="green",shape="box"];66[label="sequence0 vx50 vx90",fontsize=16,color="black",shape="box"];66 -> 72[label="",style="solid", color="black", weight=3]; 67[label="vx41",fontsize=16,color="green",shape="box"];68[label="primbindIO vx10 (sequence0 vx70)",fontsize=16,color="burlywood",shape="box"];131[label="vx10/IO vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 131[label="",style="solid", color="burlywood", weight=9]; 131 -> 73[label="",style="solid", color="burlywood", weight=3]; 132[label="vx10/AProVE_IO vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 132[label="",style="solid", color="burlywood", weight=9]; 132 -> 74[label="",style="solid", color="burlywood", weight=3]; 133[label="vx10/AProVE_Exception vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 133[label="",style="solid", color="burlywood", weight=9]; 133 -> 75[label="",style="solid", color="burlywood", weight=3]; 134[label="vx10/AProVE_Error vx100",fontsize=10,color="white",style="solid",shape="box"];68 -> 134[label="",style="solid", color="burlywood", weight=9]; 134 -> 76[label="",style="solid", color="burlywood", weight=3]; 69[label="vx41",fontsize=16,color="green",shape="box"];70[label="(vx110 : vx111 >>= sequence0 vx60) ++ vx8",fontsize=16,color="black",shape="box"];70 -> 77[label="",style="solid", color="black", weight=3]; 71[label="([] >>= sequence0 vx60) ++ vx8",fontsize=16,color="black",shape="box"];71 -> 78[label="",style="solid", color="black", weight=3]; 72[label="return (vx50 : vx90)",fontsize=16,color="black",shape="box"];72 -> 79[label="",style="solid", color="black", weight=3]; 73[label="primbindIO (IO vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];73 -> 80[label="",style="solid", color="black", weight=3]; 74[label="primbindIO (AProVE_IO vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];74 -> 81[label="",style="solid", color="black", weight=3]; 75[label="primbindIO (AProVE_Exception vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];75 -> 82[label="",style="solid", color="black", weight=3]; 76[label="primbindIO (AProVE_Error vx100) (sequence0 vx70)",fontsize=16,color="black",shape="box"];76 -> 83[label="",style="solid", color="black", weight=3]; 77[label="(sequence0 vx60 vx110 ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="black",shape="box"];77 -> 84[label="",style="solid", color="black", weight=3]; 78[label="[] ++ vx8",fontsize=16,color="black",shape="triangle"];78 -> 85[label="",style="solid", color="black", weight=3]; 79[label="Just (vx50 : vx90)",fontsize=16,color="green",shape="box"];80[label="error []",fontsize=16,color="red",shape="box"];81[label="sequence0 vx70 vx100",fontsize=16,color="black",shape="box"];81 -> 86[label="",style="solid", color="black", weight=3]; 82[label="AProVE_Exception vx100",fontsize=16,color="green",shape="box"];83[label="AProVE_Error vx100",fontsize=16,color="green",shape="box"];84[label="(return (vx60 : vx110) ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="black",shape="box"];84 -> 87[label="",style="solid", color="black", weight=3]; 85[label="vx8",fontsize=16,color="green",shape="box"];86[label="return (vx70 : vx100)",fontsize=16,color="black",shape="box"];86 -> 88[label="",style="solid", color="black", weight=3]; 87[label="(((vx60 : vx110) : []) ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="black",shape="box"];87 -> 89[label="",style="solid", color="black", weight=3]; 88[label="primretIO (vx70 : vx100)",fontsize=16,color="black",shape="box"];88 -> 90[label="",style="solid", color="black", weight=3]; 89 -> 91[label="",style="dashed", color="red", weight=0]; 89[label="((vx60 : vx110) : [] ++ (vx111 >>= sequence0 vx60)) ++ vx8",fontsize=16,color="magenta"];89 -> 92[label="",style="dashed", color="magenta", weight=3]; 90[label="AProVE_IO (vx70 : vx100)",fontsize=16,color="green",shape="box"];92 -> 78[label="",style="dashed", color="red", weight=0]; 92[label="[] ++ (vx111 >>= sequence0 vx60)",fontsize=16,color="magenta"];92 -> 93[label="",style="dashed", color="magenta", weight=3]; 91[label="((vx60 : vx110) : vx12) ++ vx8",fontsize=16,color="black",shape="triangle"];91 -> 94[label="",style="solid", color="black", weight=3]; 93[label="vx111 >>= sequence0 vx60",fontsize=16,color="burlywood",shape="triangle"];135[label="vx111/vx1110 : vx1111",fontsize=10,color="white",style="solid",shape="box"];93 -> 135[label="",style="solid", color="burlywood", weight=9]; 135 -> 95[label="",style="solid", color="burlywood", weight=3]; 136[label="vx111/[]",fontsize=10,color="white",style="solid",shape="box"];93 -> 136[label="",style="solid", color="burlywood", weight=9]; 136 -> 96[label="",style="solid", color="burlywood", weight=3]; 94[label="(vx60 : vx110) : vx12 ++ vx8",fontsize=16,color="green",shape="box"];94 -> 97[label="",style="dashed", color="green", weight=3]; 95[label="vx1110 : vx1111 >>= sequence0 vx60",fontsize=16,color="black",shape="box"];95 -> 98[label="",style="solid", color="black", weight=3]; 96[label="[] >>= sequence0 vx60",fontsize=16,color="black",shape="box"];96 -> 99[label="",style="solid", color="black", weight=3]; 97[label="vx12 ++ vx8",fontsize=16,color="burlywood",shape="triangle"];137[label="vx12/vx120 : vx121",fontsize=10,color="white",style="solid",shape="box"];97 -> 137[label="",style="solid", color="burlywood", weight=9]; 137 -> 100[label="",style="solid", color="burlywood", weight=3]; 138[label="vx12/[]",fontsize=10,color="white",style="solid",shape="box"];97 -> 138[label="",style="solid", color="burlywood", weight=9]; 138 -> 101[label="",style="solid", color="burlywood", weight=3]; 98 -> 97[label="",style="dashed", color="red", weight=0]; 98[label="sequence0 vx60 vx1110 ++ (vx1111 >>= sequence0 vx60)",fontsize=16,color="magenta"];98 -> 102[label="",style="dashed", color="magenta", weight=3]; 98 -> 103[label="",style="dashed", color="magenta", weight=3]; 99[label="[]",fontsize=16,color="green",shape="box"];100[label="(vx120 : vx121) ++ vx8",fontsize=16,color="black",shape="box"];100 -> 104[label="",style="solid", color="black", weight=3]; 101[label="[] ++ vx8",fontsize=16,color="black",shape="box"];101 -> 105[label="",style="solid", color="black", weight=3]; 102 -> 93[label="",style="dashed", color="red", weight=0]; 102[label="vx1111 >>= sequence0 vx60",fontsize=16,color="magenta"];102 -> 106[label="",style="dashed", color="magenta", weight=3]; 103[label="sequence0 vx60 vx1110",fontsize=16,color="black",shape="box"];103 -> 107[label="",style="solid", color="black", weight=3]; 104[label="vx120 : vx121 ++ vx8",fontsize=16,color="green",shape="box"];104 -> 108[label="",style="dashed", color="green", weight=3]; 105[label="vx8",fontsize=16,color="green",shape="box"];106[label="vx1111",fontsize=16,color="green",shape="box"];107[label="return (vx60 : vx1110)",fontsize=16,color="black",shape="box"];107 -> 109[label="",style="solid", color="black", weight=3]; 108 -> 97[label="",style="dashed", color="red", weight=0]; 108[label="vx121 ++ vx8",fontsize=16,color="magenta"];108 -> 110[label="",style="dashed", color="magenta", weight=3]; 109[label="(vx60 : vx1110) : []",fontsize=16,color="green",shape="box"];110[label="vx121",fontsize=16,color="green",shape="box"];} ---------------------------------------- (34) TRUE