/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) Narrow [SOUND, 0 ms] (6) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (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) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="compare",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="compare vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="compare vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="primCmpInt vx3 vx4",fontsize=16,color="burlywood",shape="box"];66[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 66[label="",style="solid", color="burlywood", weight=9]; 66 -> 6[label="",style="solid", color="burlywood", weight=3]; 67[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 67[label="",style="solid", color="burlywood", weight=9]; 67 -> 7[label="",style="solid", color="burlywood", weight=3]; 6[label="primCmpInt (Pos vx30) vx4",fontsize=16,color="burlywood",shape="box"];68[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];6 -> 68[label="",style="solid", color="burlywood", weight=9]; 68 -> 8[label="",style="solid", color="burlywood", weight=3]; 69[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];6 -> 69[label="",style="solid", color="burlywood", weight=9]; 69 -> 9[label="",style="solid", color="burlywood", weight=3]; 7[label="primCmpInt (Neg vx30) vx4",fontsize=16,color="burlywood",shape="box"];70[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];7 -> 70[label="",style="solid", color="burlywood", weight=9]; 70 -> 10[label="",style="solid", color="burlywood", weight=3]; 71[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 71[label="",style="solid", color="burlywood", weight=9]; 71 -> 11[label="",style="solid", color="burlywood", weight=3]; 8[label="primCmpInt (Pos (Succ vx300)) vx4",fontsize=16,color="burlywood",shape="box"];72[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];8 -> 72[label="",style="solid", color="burlywood", weight=9]; 72 -> 12[label="",style="solid", color="burlywood", weight=3]; 73[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];8 -> 73[label="",style="solid", color="burlywood", weight=9]; 73 -> 13[label="",style="solid", color="burlywood", weight=3]; 9[label="primCmpInt (Pos Zero) vx4",fontsize=16,color="burlywood",shape="box"];74[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];9 -> 74[label="",style="solid", color="burlywood", weight=9]; 74 -> 14[label="",style="solid", color="burlywood", weight=3]; 75[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];9 -> 75[label="",style="solid", color="burlywood", weight=9]; 75 -> 15[label="",style="solid", color="burlywood", weight=3]; 10[label="primCmpInt (Neg (Succ vx300)) vx4",fontsize=16,color="burlywood",shape="box"];76[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];10 -> 76[label="",style="solid", color="burlywood", weight=9]; 76 -> 16[label="",style="solid", color="burlywood", weight=3]; 77[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];10 -> 77[label="",style="solid", color="burlywood", weight=9]; 77 -> 17[label="",style="solid", color="burlywood", weight=3]; 11[label="primCmpInt (Neg Zero) vx4",fontsize=16,color="burlywood",shape="box"];78[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];11 -> 78[label="",style="solid", color="burlywood", weight=9]; 78 -> 18[label="",style="solid", color="burlywood", weight=3]; 79[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];11 -> 79[label="",style="solid", color="burlywood", weight=9]; 79 -> 19[label="",style="solid", color="burlywood", weight=3]; 12[label="primCmpInt (Pos (Succ vx300)) (Pos vx40)",fontsize=16,color="black",shape="box"];12 -> 20[label="",style="solid", color="black", weight=3]; 13[label="primCmpInt (Pos (Succ vx300)) (Neg vx40)",fontsize=16,color="black",shape="box"];13 -> 21[label="",style="solid", color="black", weight=3]; 14[label="primCmpInt (Pos Zero) (Pos vx40)",fontsize=16,color="burlywood",shape="box"];80[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 80[label="",style="solid", color="burlywood", weight=9]; 80 -> 22[label="",style="solid", color="burlywood", weight=3]; 81[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 81[label="",style="solid", color="burlywood", weight=9]; 81 -> 23[label="",style="solid", color="burlywood", weight=3]; 15[label="primCmpInt (Pos Zero) (Neg vx40)",fontsize=16,color="burlywood",shape="box"];82[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];15 -> 82[label="",style="solid", color="burlywood", weight=9]; 82 -> 24[label="",style="solid", color="burlywood", weight=3]; 83[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];15 -> 83[label="",style="solid", color="burlywood", weight=9]; 83 -> 25[label="",style="solid", color="burlywood", weight=3]; 16[label="primCmpInt (Neg (Succ vx300)) (Pos vx40)",fontsize=16,color="black",shape="box"];16 -> 26[label="",style="solid", color="black", weight=3]; 17[label="primCmpInt (Neg (Succ vx300)) (Neg vx40)",fontsize=16,color="black",shape="box"];17 -> 27[label="",style="solid", color="black", weight=3]; 18[label="primCmpInt (Neg Zero) (Pos vx40)",fontsize=16,color="burlywood",shape="box"];84[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];18 -> 84[label="",style="solid", color="burlywood", weight=9]; 84 -> 28[label="",style="solid", color="burlywood", weight=3]; 85[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 85[label="",style="solid", color="burlywood", weight=9]; 85 -> 29[label="",style="solid", color="burlywood", weight=3]; 19[label="primCmpInt (Neg Zero) (Neg vx40)",fontsize=16,color="burlywood",shape="box"];86[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];19 -> 86[label="",style="solid", color="burlywood", weight=9]; 86 -> 30[label="",style="solid", color="burlywood", weight=3]; 87[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 87[label="",style="solid", color="burlywood", weight=9]; 87 -> 31[label="",style="solid", color="burlywood", weight=3]; 20[label="primCmpNat (Succ vx300) vx40",fontsize=16,color="burlywood",shape="triangle"];88[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];20 -> 88[label="",style="solid", color="burlywood", weight=9]; 88 -> 32[label="",style="solid", color="burlywood", weight=3]; 89[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 89[label="",style="solid", color="burlywood", weight=9]; 89 -> 33[label="",style="solid", color="burlywood", weight=3]; 21[label="GT",fontsize=16,color="green",shape="box"];22[label="primCmpInt (Pos Zero) (Pos (Succ vx400))",fontsize=16,color="black",shape="box"];22 -> 34[label="",style="solid", color="black", weight=3]; 23[label="primCmpInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];23 -> 35[label="",style="solid", color="black", weight=3]; 24[label="primCmpInt (Pos Zero) (Neg (Succ vx400))",fontsize=16,color="black",shape="box"];24 -> 36[label="",style="solid", color="black", weight=3]; 25[label="primCmpInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];25 -> 37[label="",style="solid", color="black", weight=3]; 26[label="LT",fontsize=16,color="green",shape="box"];27[label="primCmpNat vx40 (Succ vx300)",fontsize=16,color="burlywood",shape="triangle"];90[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];27 -> 90[label="",style="solid", color="burlywood", weight=9]; 90 -> 38[label="",style="solid", color="burlywood", weight=3]; 91[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 91[label="",style="solid", color="burlywood", weight=9]; 91 -> 39[label="",style="solid", color="burlywood", weight=3]; 28[label="primCmpInt (Neg Zero) (Pos (Succ vx400))",fontsize=16,color="black",shape="box"];28 -> 40[label="",style="solid", color="black", weight=3]; 29[label="primCmpInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];29 -> 41[label="",style="solid", color="black", weight=3]; 30[label="primCmpInt (Neg Zero) (Neg (Succ vx400))",fontsize=16,color="black",shape="box"];30 -> 42[label="",style="solid", color="black", weight=3]; 31[label="primCmpInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];31 -> 43[label="",style="solid", color="black", weight=3]; 32[label="primCmpNat (Succ vx300) (Succ vx400)",fontsize=16,color="black",shape="box"];32 -> 44[label="",style="solid", color="black", weight=3]; 33[label="primCmpNat (Succ vx300) Zero",fontsize=16,color="black",shape="box"];33 -> 45[label="",style="solid", color="black", weight=3]; 34 -> 27[label="",style="dashed", color="red", weight=0]; 34[label="primCmpNat Zero (Succ vx400)",fontsize=16,color="magenta"];34 -> 46[label="",style="dashed", color="magenta", weight=3]; 34 -> 47[label="",style="dashed", color="magenta", weight=3]; 35[label="EQ",fontsize=16,color="green",shape="box"];36[label="GT",fontsize=16,color="green",shape="box"];37[label="EQ",fontsize=16,color="green",shape="box"];38[label="primCmpNat (Succ vx400) (Succ vx300)",fontsize=16,color="black",shape="box"];38 -> 48[label="",style="solid", color="black", weight=3]; 39[label="primCmpNat Zero (Succ vx300)",fontsize=16,color="black",shape="box"];39 -> 49[label="",style="solid", color="black", weight=3]; 40[label="LT",fontsize=16,color="green",shape="box"];41[label="EQ",fontsize=16,color="green",shape="box"];42 -> 20[label="",style="dashed", color="red", weight=0]; 42[label="primCmpNat (Succ vx400) Zero",fontsize=16,color="magenta"];42 -> 50[label="",style="dashed", color="magenta", weight=3]; 42 -> 51[label="",style="dashed", color="magenta", weight=3]; 43[label="EQ",fontsize=16,color="green",shape="box"];44[label="primCmpNat vx300 vx400",fontsize=16,color="burlywood",shape="triangle"];92[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];44 -> 92[label="",style="solid", color="burlywood", weight=9]; 92 -> 52[label="",style="solid", color="burlywood", weight=3]; 93[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];44 -> 93[label="",style="solid", color="burlywood", weight=9]; 93 -> 53[label="",style="solid", color="burlywood", weight=3]; 45[label="GT",fontsize=16,color="green",shape="box"];46[label="Zero",fontsize=16,color="green",shape="box"];47[label="vx400",fontsize=16,color="green",shape="box"];48 -> 44[label="",style="dashed", color="red", weight=0]; 48[label="primCmpNat vx400 vx300",fontsize=16,color="magenta"];48 -> 54[label="",style="dashed", color="magenta", weight=3]; 48 -> 55[label="",style="dashed", color="magenta", weight=3]; 49[label="LT",fontsize=16,color="green",shape="box"];50[label="vx400",fontsize=16,color="green",shape="box"];51[label="Zero",fontsize=16,color="green",shape="box"];52[label="primCmpNat (Succ vx3000) vx400",fontsize=16,color="burlywood",shape="box"];94[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];52 -> 94[label="",style="solid", color="burlywood", weight=9]; 94 -> 56[label="",style="solid", color="burlywood", weight=3]; 95[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 95[label="",style="solid", color="burlywood", weight=9]; 95 -> 57[label="",style="solid", color="burlywood", weight=3]; 53[label="primCmpNat Zero vx400",fontsize=16,color="burlywood",shape="box"];96[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];53 -> 96[label="",style="solid", color="burlywood", weight=9]; 96 -> 58[label="",style="solid", color="burlywood", weight=3]; 97[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];53 -> 97[label="",style="solid", color="burlywood", weight=9]; 97 -> 59[label="",style="solid", color="burlywood", weight=3]; 54[label="vx400",fontsize=16,color="green",shape="box"];55[label="vx300",fontsize=16,color="green",shape="box"];56[label="primCmpNat (Succ vx3000) (Succ vx4000)",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3]; 57[label="primCmpNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];57 -> 61[label="",style="solid", color="black", weight=3]; 58[label="primCmpNat Zero (Succ vx4000)",fontsize=16,color="black",shape="box"];58 -> 62[label="",style="solid", color="black", weight=3]; 59[label="primCmpNat Zero Zero",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3]; 60 -> 44[label="",style="dashed", color="red", weight=0]; 60[label="primCmpNat vx3000 vx4000",fontsize=16,color="magenta"];60 -> 64[label="",style="dashed", color="magenta", weight=3]; 60 -> 65[label="",style="dashed", color="magenta", weight=3]; 61[label="GT",fontsize=16,color="green",shape="box"];62[label="LT",fontsize=16,color="green",shape="box"];63[label="EQ",fontsize=16,color="green",shape="box"];64[label="vx3000",fontsize=16,color="green",shape="box"];65[label="vx4000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_primCmpNat(Succ(vx3000), Succ(vx4000)) -> new_primCmpNat(vx3000, vx4000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) 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_primCmpNat(Succ(vx3000), Succ(vx4000)) -> new_primCmpNat(vx3000, vx4000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (8) YES