/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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) QDPOrderProof [EQUIVALENT, 28 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) QDP (17) MNOCProof [EQUIVALENT, 0 ms] (18) QDP (19) NonTerminationLoopProof [COMPLETE, 5 ms] (20) NO (21) QDP (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] (23) YES (24) Narrow [COMPLETE, 0 ms] (25) 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"];57[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];6 -> 57[label="",style="solid", color="burlywood", weight=9]; 57 -> 7[label="",style="solid", color="burlywood", weight=3]; 58[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 58[label="",style="solid", color="burlywood", weight=9]; 58 -> 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 -> 13[label="",style="dashed", color="red", weight=0]; 11[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];11 -> 14[label="",style="dashed", color="magenta", weight=3]; 12[label="return []",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3]; 14[label="vx3 vx40",fontsize=16,color="green",shape="box"];14 -> 19[label="",style="dashed", color="green", weight=3]; 13[label="vx5 >>= sequence1 (map vx3 vx41)",fontsize=16,color="burlywood",shape="triangle"];59[label="vx5/vx50 : vx51",fontsize=10,color="white",style="solid",shape="box"];13 -> 59[label="",style="solid", color="burlywood", weight=9]; 59 -> 17[label="",style="solid", color="burlywood", weight=3]; 60[label="vx5/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 60[label="",style="solid", color="burlywood", weight=9]; 60 -> 18[label="",style="solid", color="burlywood", weight=3]; 15[label="[] : []",fontsize=16,color="green",shape="box"];19[label="vx40",fontsize=16,color="green",shape="box"];17[label="vx50 : vx51 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];17 -> 20[label="",style="solid", color="black", weight=3]; 18[label="[] >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3]; 20 -> 22[label="",style="dashed", color="red", weight=0]; 20[label="sequence1 (map vx3 vx41) vx50 ++ (vx51 >>= sequence1 (map vx3 vx41))",fontsize=16,color="magenta"];20 -> 23[label="",style="dashed", color="magenta", weight=3]; 21[label="[]",fontsize=16,color="green",shape="box"];23 -> 13[label="",style="dashed", color="red", weight=0]; 23[label="vx51 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];23 -> 24[label="",style="dashed", color="magenta", weight=3]; 22[label="sequence1 (map vx3 vx41) vx50 ++ vx6",fontsize=16,color="black",shape="triangle"];22 -> 25[label="",style="solid", color="black", weight=3]; 24[label="vx51",fontsize=16,color="green",shape="box"];25 -> 26[label="",style="dashed", color="red", weight=0]; 25[label="(sequence (map vx3 vx41) >>= sequence0 vx50) ++ vx6",fontsize=16,color="magenta"];25 -> 27[label="",style="dashed", color="magenta", weight=3]; 27 -> 6[label="",style="dashed", color="red", weight=0]; 27[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];27 -> 28[label="",style="dashed", color="magenta", weight=3]; 26[label="(vx7 >>= sequence0 vx50) ++ vx6",fontsize=16,color="burlywood",shape="triangle"];61[label="vx7/vx70 : vx71",fontsize=10,color="white",style="solid",shape="box"];26 -> 61[label="",style="solid", color="burlywood", weight=9]; 61 -> 29[label="",style="solid", color="burlywood", weight=3]; 62[label="vx7/[]",fontsize=10,color="white",style="solid",shape="box"];26 -> 62[label="",style="solid", color="burlywood", weight=9]; 62 -> 30[label="",style="solid", color="burlywood", weight=3]; 28[label="vx41",fontsize=16,color="green",shape="box"];29[label="(vx70 : vx71 >>= sequence0 vx50) ++ vx6",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3]; 30[label="([] >>= sequence0 vx50) ++ vx6",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3]; 31[label="(sequence0 vx50 vx70 ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3]; 32[label="[] ++ vx6",fontsize=16,color="black",shape="triangle"];32 -> 34[label="",style="solid", color="black", weight=3]; 33[label="(return (vx50 : vx70) ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3]; 34[label="vx6",fontsize=16,color="green",shape="box"];35[label="(((vx50 : vx70) : []) ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="black",shape="box"];35 -> 36[label="",style="solid", color="black", weight=3]; 36 -> 37[label="",style="dashed", color="red", weight=0]; 36[label="((vx50 : vx70) : [] ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="magenta"];36 -> 38[label="",style="dashed", color="magenta", weight=3]; 38 -> 32[label="",style="dashed", color="red", weight=0]; 38[label="[] ++ (vx71 >>= sequence0 vx50)",fontsize=16,color="magenta"];38 -> 39[label="",style="dashed", color="magenta", weight=3]; 37[label="((vx50 : vx70) : vx8) ++ vx6",fontsize=16,color="black",shape="triangle"];37 -> 40[label="",style="solid", color="black", weight=3]; 39[label="vx71 >>= sequence0 vx50",fontsize=16,color="burlywood",shape="triangle"];63[label="vx71/vx710 : vx711",fontsize=10,color="white",style="solid",shape="box"];39 -> 63[label="",style="solid", color="burlywood", weight=9]; 63 -> 41[label="",style="solid", color="burlywood", weight=3]; 64[label="vx71/[]",fontsize=10,color="white",style="solid",shape="box"];39 -> 64[label="",style="solid", color="burlywood", weight=9]; 64 -> 42[label="",style="solid", color="burlywood", weight=3]; 40[label="(vx50 : vx70) : vx8 ++ vx6",fontsize=16,color="green",shape="box"];40 -> 43[label="",style="dashed", color="green", weight=3]; 41[label="vx710 : vx711 >>= sequence0 vx50",fontsize=16,color="black",shape="box"];41 -> 44[label="",style="solid", color="black", weight=3]; 42[label="[] >>= sequence0 vx50",fontsize=16,color="black",shape="box"];42 -> 45[label="",style="solid", color="black", weight=3]; 43[label="vx8 ++ vx6",fontsize=16,color="burlywood",shape="triangle"];65[label="vx8/vx80 : vx81",fontsize=10,color="white",style="solid",shape="box"];43 -> 65[label="",style="solid", color="burlywood", weight=9]; 65 -> 46[label="",style="solid", color="burlywood", weight=3]; 66[label="vx8/[]",fontsize=10,color="white",style="solid",shape="box"];43 -> 66[label="",style="solid", color="burlywood", weight=9]; 66 -> 47[label="",style="solid", color="burlywood", weight=3]; 44 -> 43[label="",style="dashed", color="red", weight=0]; 44[label="sequence0 vx50 vx710 ++ (vx711 >>= sequence0 vx50)",fontsize=16,color="magenta"];44 -> 48[label="",style="dashed", color="magenta", weight=3]; 44 -> 49[label="",style="dashed", color="magenta", weight=3]; 45[label="[]",fontsize=16,color="green",shape="box"];46[label="(vx80 : vx81) ++ vx6",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3]; 47[label="[] ++ vx6",fontsize=16,color="black",shape="box"];47 -> 51[label="",style="solid", color="black", weight=3]; 48[label="sequence0 vx50 vx710",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3]; 49 -> 39[label="",style="dashed", color="red", weight=0]; 49[label="vx711 >>= sequence0 vx50",fontsize=16,color="magenta"];49 -> 53[label="",style="dashed", color="magenta", weight=3]; 50[label="vx80 : vx81 ++ vx6",fontsize=16,color="green",shape="box"];50 -> 54[label="",style="dashed", color="green", weight=3]; 51[label="vx6",fontsize=16,color="green",shape="box"];52[label="return (vx50 : vx710)",fontsize=16,color="black",shape="box"];52 -> 55[label="",style="solid", color="black", weight=3]; 53[label="vx711",fontsize=16,color="green",shape="box"];54 -> 43[label="",style="dashed", color="red", weight=0]; 54[label="vx81 ++ vx6",fontsize=16,color="magenta"];54 -> 56[label="",style="dashed", color="magenta", weight=3]; 55[label="(vx50 : vx710) : []",fontsize=16,color="green",shape="box"];56[label="vx81",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(:(vx710, vx711), vx50, h) -> new_gtGtEs(vx711, vx50, 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(:(vx710, vx711), vx50, h) -> new_gtGtEs(vx711, vx50, 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), h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) new_gtGtEs0(vx3, vx41, h, ba) -> new_psPs0(vx3, vx41, h, ba) new_gtGtEs0(vx3, vx41, h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) new_psPs0(vx3, vx41, h, ba) -> new_sequence(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs1([], vx50, vx6, h) -> new_psPs3(vx6, h) new_psPs5(:(vx80, vx81), vx6, h) -> :(vx80, new_psPs5(vx81, vx6, h)) new_gtGtEs1(:(vx50, vx51), vx3, vx41, h, ba) -> new_psPs4(vx3, vx41, vx50, new_gtGtEs1(vx51, vx3, vx41, h, ba), h, ba) new_psPs4(vx3, vx41, vx50, vx6, h, ba) -> new_psPs1(new_sequence0(vx3, vx41, h, ba), vx50, vx6, h) new_gtGtEs1([], vx3, vx41, h, ba) -> [] new_psPs1(:(vx70, vx71), vx50, vx6, h) -> new_psPs2(vx50, vx70, new_psPs3(new_gtGtEs2(vx71, vx50, h), h), vx6, h) new_gtGtEs2([], vx50, h) -> [] new_psPs5([], vx6, h) -> vx6 new_psPs2(vx50, vx70, vx8, vx6, h) -> :(:(vx50, vx70), new_psPs5(vx8, vx6, h)) new_psPs3(vx6, h) -> vx6 new_gtGtEs2(:(vx710, vx711), vx50, h) -> new_psPs5(:(:(vx50, vx710), []), new_gtGtEs2(vx711, vx50, h), h) The set Q consists of the following terms: new_psPs4(x0, x1, x2, x3, x4, x5) new_psPs1([], x0, x1, x2) new_gtGtEs2([], x0, x1) new_psPs1(:(x0, x1), x2, x3, x4) new_gtGtEs2(:(x0, x1), x2, x3) new_gtGtEs1([], x0, x1, x2, x3) new_psPs5([], x0, x1) new_psPs3(x0, x1) new_psPs2(x0, x1, x2, x3, x4) new_psPs5(:(x0, x1), x2, x3) new_gtGtEs1(:(x0, x1), x2, x3, x4, x5) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (13) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_psPs0(vx3, vx41, h, ba) -> new_sequence(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_gtGtEs0(x_1, x_2, x_3, x_4)) = 1 + x_2 POL(new_psPs0(x_1, x_2, x_3, x_4)) = 1 + x_2 POL(new_sequence(x_1, x_2, x_3, x_4)) = x_2 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: none ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: new_sequence(vx3, :(vx40, vx41), h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) new_gtGtEs0(vx3, vx41, h, ba) -> new_psPs0(vx3, vx41, h, ba) new_gtGtEs0(vx3, vx41, h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs1([], vx50, vx6, h) -> new_psPs3(vx6, h) new_psPs5(:(vx80, vx81), vx6, h) -> :(vx80, new_psPs5(vx81, vx6, h)) new_gtGtEs1(:(vx50, vx51), vx3, vx41, h, ba) -> new_psPs4(vx3, vx41, vx50, new_gtGtEs1(vx51, vx3, vx41, h, ba), h, ba) new_psPs4(vx3, vx41, vx50, vx6, h, ba) -> new_psPs1(new_sequence0(vx3, vx41, h, ba), vx50, vx6, h) new_gtGtEs1([], vx3, vx41, h, ba) -> [] new_psPs1(:(vx70, vx71), vx50, vx6, h) -> new_psPs2(vx50, vx70, new_psPs3(new_gtGtEs2(vx71, vx50, h), h), vx6, h) new_gtGtEs2([], vx50, h) -> [] new_psPs5([], vx6, h) -> vx6 new_psPs2(vx50, vx70, vx8, vx6, h) -> :(:(vx50, vx70), new_psPs5(vx8, vx6, h)) new_psPs3(vx6, h) -> vx6 new_gtGtEs2(:(vx710, vx711), vx50, h) -> new_psPs5(:(:(vx50, vx710), []), new_gtGtEs2(vx711, vx50, h), h) The set Q consists of the following terms: new_psPs4(x0, x1, x2, x3, x4, x5) new_psPs1([], x0, x1, x2) new_gtGtEs2([], x0, x1) new_psPs1(:(x0, x1), x2, x3, x4) new_gtGtEs2(:(x0, x1), x2, x3) new_gtGtEs1([], x0, x1, x2, x3) new_psPs5([], x0, x1) new_psPs3(x0, x1) new_psPs2(x0, x1, x2, x3, x4) new_psPs5(:(x0, x1), x2, x3) new_gtGtEs1(:(x0, x1), x2, x3, x4, x5) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (15) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (16) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs0(vx3, vx41, h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs1([], vx50, vx6, h) -> new_psPs3(vx6, h) new_psPs5(:(vx80, vx81), vx6, h) -> :(vx80, new_psPs5(vx81, vx6, h)) new_gtGtEs1(:(vx50, vx51), vx3, vx41, h, ba) -> new_psPs4(vx3, vx41, vx50, new_gtGtEs1(vx51, vx3, vx41, h, ba), h, ba) new_psPs4(vx3, vx41, vx50, vx6, h, ba) -> new_psPs1(new_sequence0(vx3, vx41, h, ba), vx50, vx6, h) new_gtGtEs1([], vx3, vx41, h, ba) -> [] new_psPs1(:(vx70, vx71), vx50, vx6, h) -> new_psPs2(vx50, vx70, new_psPs3(new_gtGtEs2(vx71, vx50, h), h), vx6, h) new_gtGtEs2([], vx50, h) -> [] new_psPs5([], vx6, h) -> vx6 new_psPs2(vx50, vx70, vx8, vx6, h) -> :(:(vx50, vx70), new_psPs5(vx8, vx6, h)) new_psPs3(vx6, h) -> vx6 new_gtGtEs2(:(vx710, vx711), vx50, h) -> new_psPs5(:(:(vx50, vx710), []), new_gtGtEs2(vx711, vx50, h), h) The set Q consists of the following terms: new_psPs4(x0, x1, x2, x3, x4, x5) new_psPs1([], x0, x1, x2) new_gtGtEs2([], x0, x1) new_psPs1(:(x0, x1), x2, x3, x4) new_gtGtEs2(:(x0, x1), x2, x3) new_gtGtEs1([], x0, x1, x2, x3) new_psPs5([], x0, x1) new_psPs3(x0, x1) new_psPs2(x0, x1, x2, x3, x4) new_psPs5(:(x0, x1), x2, x3) new_gtGtEs1(:(x0, x1), x2, x3, x4, x5) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (17) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs0(vx3, vx41, h, ba) -> new_gtGtEs0(vx3, vx41, h, ba) The TRS R consists of the following rules: new_psPs1([], vx50, vx6, h) -> new_psPs3(vx6, h) new_psPs5(:(vx80, vx81), vx6, h) -> :(vx80, new_psPs5(vx81, vx6, h)) new_gtGtEs1(:(vx50, vx51), vx3, vx41, h, ba) -> new_psPs4(vx3, vx41, vx50, new_gtGtEs1(vx51, vx3, vx41, h, ba), h, ba) new_psPs4(vx3, vx41, vx50, vx6, h, ba) -> new_psPs1(new_sequence0(vx3, vx41, h, ba), vx50, vx6, h) new_gtGtEs1([], vx3, vx41, h, ba) -> [] new_psPs1(:(vx70, vx71), vx50, vx6, h) -> new_psPs2(vx50, vx70, new_psPs3(new_gtGtEs2(vx71, vx50, h), h), vx6, h) new_gtGtEs2([], vx50, h) -> [] new_psPs5([], vx6, h) -> vx6 new_psPs2(vx50, vx70, vx8, vx6, h) -> :(:(vx50, vx70), new_psPs5(vx8, vx6, h)) new_psPs3(vx6, h) -> vx6 new_gtGtEs2(:(vx710, vx711), vx50, h) -> new_psPs5(:(:(vx50, vx710), []), new_gtGtEs2(vx711, vx50, h), h) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (19) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_gtGtEs0(vx3, vx41, h, ba) evaluates to t =new_gtGtEs0(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_gtGtEs0(vx3, vx41, h, ba) to new_gtGtEs0(vx3, vx41, h, ba). ---------------------------------------- (20) NO ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(vx80, vx81), vx6, h) -> new_psPs(vx81, vx6, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (22) 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(:(vx80, vx81), vx6, h) -> new_psPs(vx81, vx6, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (23) YES ---------------------------------------- (24) 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"];57[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];6 -> 57[label="",style="solid", color="burlywood", weight=9]; 57 -> 7[label="",style="solid", color="burlywood", weight=3]; 58[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 58[label="",style="solid", color="burlywood", weight=9]; 58 -> 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 -> 13[label="",style="dashed", color="red", weight=0]; 11[label="vx3 vx40 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];11 -> 14[label="",style="dashed", color="magenta", weight=3]; 12[label="return []",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3]; 14[label="vx3 vx40",fontsize=16,color="green",shape="box"];14 -> 19[label="",style="dashed", color="green", weight=3]; 13[label="vx5 >>= sequence1 (map vx3 vx41)",fontsize=16,color="burlywood",shape="triangle"];59[label="vx5/vx50 : vx51",fontsize=10,color="white",style="solid",shape="box"];13 -> 59[label="",style="solid", color="burlywood", weight=9]; 59 -> 17[label="",style="solid", color="burlywood", weight=3]; 60[label="vx5/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 60[label="",style="solid", color="burlywood", weight=9]; 60 -> 18[label="",style="solid", color="burlywood", weight=3]; 15[label="[] : []",fontsize=16,color="green",shape="box"];19[label="vx40",fontsize=16,color="green",shape="box"];17[label="vx50 : vx51 >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];17 -> 20[label="",style="solid", color="black", weight=3]; 18[label="[] >>= sequence1 (map vx3 vx41)",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3]; 20 -> 22[label="",style="dashed", color="red", weight=0]; 20[label="sequence1 (map vx3 vx41) vx50 ++ (vx51 >>= sequence1 (map vx3 vx41))",fontsize=16,color="magenta"];20 -> 23[label="",style="dashed", color="magenta", weight=3]; 21[label="[]",fontsize=16,color="green",shape="box"];23 -> 13[label="",style="dashed", color="red", weight=0]; 23[label="vx51 >>= sequence1 (map vx3 vx41)",fontsize=16,color="magenta"];23 -> 24[label="",style="dashed", color="magenta", weight=3]; 22[label="sequence1 (map vx3 vx41) vx50 ++ vx6",fontsize=16,color="black",shape="triangle"];22 -> 25[label="",style="solid", color="black", weight=3]; 24[label="vx51",fontsize=16,color="green",shape="box"];25 -> 26[label="",style="dashed", color="red", weight=0]; 25[label="(sequence (map vx3 vx41) >>= sequence0 vx50) ++ vx6",fontsize=16,color="magenta"];25 -> 27[label="",style="dashed", color="magenta", weight=3]; 27 -> 6[label="",style="dashed", color="red", weight=0]; 27[label="sequence (map vx3 vx41)",fontsize=16,color="magenta"];27 -> 28[label="",style="dashed", color="magenta", weight=3]; 26[label="(vx7 >>= sequence0 vx50) ++ vx6",fontsize=16,color="burlywood",shape="triangle"];61[label="vx7/vx70 : vx71",fontsize=10,color="white",style="solid",shape="box"];26 -> 61[label="",style="solid", color="burlywood", weight=9]; 61 -> 29[label="",style="solid", color="burlywood", weight=3]; 62[label="vx7/[]",fontsize=10,color="white",style="solid",shape="box"];26 -> 62[label="",style="solid", color="burlywood", weight=9]; 62 -> 30[label="",style="solid", color="burlywood", weight=3]; 28[label="vx41",fontsize=16,color="green",shape="box"];29[label="(vx70 : vx71 >>= sequence0 vx50) ++ vx6",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3]; 30[label="([] >>= sequence0 vx50) ++ vx6",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3]; 31[label="(sequence0 vx50 vx70 ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3]; 32[label="[] ++ vx6",fontsize=16,color="black",shape="triangle"];32 -> 34[label="",style="solid", color="black", weight=3]; 33[label="(return (vx50 : vx70) ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3]; 34[label="vx6",fontsize=16,color="green",shape="box"];35[label="(((vx50 : vx70) : []) ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="black",shape="box"];35 -> 36[label="",style="solid", color="black", weight=3]; 36 -> 37[label="",style="dashed", color="red", weight=0]; 36[label="((vx50 : vx70) : [] ++ (vx71 >>= sequence0 vx50)) ++ vx6",fontsize=16,color="magenta"];36 -> 38[label="",style="dashed", color="magenta", weight=3]; 38 -> 32[label="",style="dashed", color="red", weight=0]; 38[label="[] ++ (vx71 >>= sequence0 vx50)",fontsize=16,color="magenta"];38 -> 39[label="",style="dashed", color="magenta", weight=3]; 37[label="((vx50 : vx70) : vx8) ++ vx6",fontsize=16,color="black",shape="triangle"];37 -> 40[label="",style="solid", color="black", weight=3]; 39[label="vx71 >>= sequence0 vx50",fontsize=16,color="burlywood",shape="triangle"];63[label="vx71/vx710 : vx711",fontsize=10,color="white",style="solid",shape="box"];39 -> 63[label="",style="solid", color="burlywood", weight=9]; 63 -> 41[label="",style="solid", color="burlywood", weight=3]; 64[label="vx71/[]",fontsize=10,color="white",style="solid",shape="box"];39 -> 64[label="",style="solid", color="burlywood", weight=9]; 64 -> 42[label="",style="solid", color="burlywood", weight=3]; 40[label="(vx50 : vx70) : vx8 ++ vx6",fontsize=16,color="green",shape="box"];40 -> 43[label="",style="dashed", color="green", weight=3]; 41[label="vx710 : vx711 >>= sequence0 vx50",fontsize=16,color="black",shape="box"];41 -> 44[label="",style="solid", color="black", weight=3]; 42[label="[] >>= sequence0 vx50",fontsize=16,color="black",shape="box"];42 -> 45[label="",style="solid", color="black", weight=3]; 43[label="vx8 ++ vx6",fontsize=16,color="burlywood",shape="triangle"];65[label="vx8/vx80 : vx81",fontsize=10,color="white",style="solid",shape="box"];43 -> 65[label="",style="solid", color="burlywood", weight=9]; 65 -> 46[label="",style="solid", color="burlywood", weight=3]; 66[label="vx8/[]",fontsize=10,color="white",style="solid",shape="box"];43 -> 66[label="",style="solid", color="burlywood", weight=9]; 66 -> 47[label="",style="solid", color="burlywood", weight=3]; 44 -> 43[label="",style="dashed", color="red", weight=0]; 44[label="sequence0 vx50 vx710 ++ (vx711 >>= sequence0 vx50)",fontsize=16,color="magenta"];44 -> 48[label="",style="dashed", color="magenta", weight=3]; 44 -> 49[label="",style="dashed", color="magenta", weight=3]; 45[label="[]",fontsize=16,color="green",shape="box"];46[label="(vx80 : vx81) ++ vx6",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3]; 47[label="[] ++ vx6",fontsize=16,color="black",shape="box"];47 -> 51[label="",style="solid", color="black", weight=3]; 48[label="sequence0 vx50 vx710",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3]; 49 -> 39[label="",style="dashed", color="red", weight=0]; 49[label="vx711 >>= sequence0 vx50",fontsize=16,color="magenta"];49 -> 53[label="",style="dashed", color="magenta", weight=3]; 50[label="vx80 : vx81 ++ vx6",fontsize=16,color="green",shape="box"];50 -> 54[label="",style="dashed", color="green", weight=3]; 51[label="vx6",fontsize=16,color="green",shape="box"];52[label="return (vx50 : vx710)",fontsize=16,color="black",shape="box"];52 -> 55[label="",style="solid", color="black", weight=3]; 53[label="vx711",fontsize=16,color="green",shape="box"];54 -> 43[label="",style="dashed", color="red", weight=0]; 54[label="vx81 ++ vx6",fontsize=16,color="magenta"];54 -> 56[label="",style="dashed", color="magenta", weight=3]; 55[label="(vx50 : vx710) : []",fontsize=16,color="green",shape="box"];56[label="vx81",fontsize=16,color="green",shape="box"];} ---------------------------------------- (25) TRUE