8.18/3.64 YES 9.61/4.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.61/4.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.61/4.10 9.61/4.10 9.61/4.10 H-Termination with start terms of the given HASKELL could be proven: 9.61/4.10 9.61/4.10 (0) HASKELL 9.61/4.10 (1) BR [EQUIVALENT, 0 ms] 9.61/4.10 (2) HASKELL 9.61/4.10 (3) COR [EQUIVALENT, 0 ms] 9.61/4.10 (4) HASKELL 9.61/4.10 (5) Narrow [SOUND, 0 ms] 9.61/4.10 (6) QDP 9.61/4.10 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.61/4.10 (8) YES 9.61/4.10 9.61/4.10 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (0) 9.61/4.10 Obligation: 9.61/4.10 mainModule Main 9.61/4.10 module Main where { 9.61/4.10 import qualified Prelude; 9.61/4.10 } 9.61/4.10 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (1) BR (EQUIVALENT) 9.61/4.10 Replaced joker patterns by fresh variables and removed binding patterns. 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (2) 9.61/4.10 Obligation: 9.61/4.10 mainModule Main 9.61/4.10 module Main where { 9.61/4.10 import qualified Prelude; 9.61/4.10 } 9.61/4.10 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (3) COR (EQUIVALENT) 9.61/4.10 Cond Reductions: 9.61/4.10 The following Function with conditions 9.61/4.10 "undefined |Falseundefined; 9.61/4.10 " 9.61/4.10 is transformed to 9.61/4.10 "undefined = undefined1; 9.61/4.10 " 9.61/4.10 "undefined0 True = undefined; 9.61/4.10 " 9.61/4.10 "undefined1 = undefined0 False; 9.61/4.10 " 9.61/4.10 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (4) 9.61/4.10 Obligation: 9.61/4.10 mainModule Main 9.61/4.10 module Main where { 9.61/4.10 import qualified Prelude; 9.61/4.10 } 9.61/4.10 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (5) Narrow (SOUND) 9.61/4.10 Haskell To QDPs 9.61/4.10 9.61/4.10 digraph dp_graph { 9.61/4.10 node [outthreshold=100, inthreshold=100];1[label="(>)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.61/4.10 3[label="(>) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.61/4.10 4[label="(>) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.61/4.10 5[label="compare vx3 vx4 == GT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.61/4.10 6[label="primCmpInt vx3 vx4 == GT",fontsize=16,color="burlywood",shape="box"];70[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];6 -> 70[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 70 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 71[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];6 -> 71[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 71 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 7[label="primCmpInt (Pos vx30) vx4 == GT",fontsize=16,color="burlywood",shape="box"];72[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];7 -> 72[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 72 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 73[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 73[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 73 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 8[label="primCmpInt (Neg vx30) vx4 == GT",fontsize=16,color="burlywood",shape="box"];74[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 74[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 74 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 75[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 75[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 75 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 9[label="primCmpInt (Pos (Succ vx300)) vx4 == GT",fontsize=16,color="burlywood",shape="box"];76[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];9 -> 76[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 76 -> 13[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 77[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];9 -> 77[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 77 -> 14[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 10[label="primCmpInt (Pos Zero) vx4 == GT",fontsize=16,color="burlywood",shape="box"];78[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];10 -> 78[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 78 -> 15[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 79[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];10 -> 79[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 79 -> 16[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 11[label="primCmpInt (Neg (Succ vx300)) vx4 == GT",fontsize=16,color="burlywood",shape="box"];80[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];11 -> 80[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 80 -> 17[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 81[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];11 -> 81[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 81 -> 18[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 12[label="primCmpInt (Neg Zero) vx4 == GT",fontsize=16,color="burlywood",shape="box"];82[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 82[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 82 -> 19[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 83[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 83[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 83 -> 20[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 13[label="primCmpInt (Pos (Succ vx300)) (Pos vx40) == GT",fontsize=16,color="black",shape="box"];13 -> 21[label="",style="solid", color="black", weight=3]; 9.61/4.10 14[label="primCmpInt (Pos (Succ vx300)) (Neg vx40) == GT",fontsize=16,color="black",shape="box"];14 -> 22[label="",style="solid", color="black", weight=3]; 9.61/4.10 15[label="primCmpInt (Pos Zero) (Pos vx40) == GT",fontsize=16,color="burlywood",shape="box"];84[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];15 -> 84[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 84 -> 23[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 85[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];15 -> 85[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 85 -> 24[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 16[label="primCmpInt (Pos Zero) (Neg vx40) == GT",fontsize=16,color="burlywood",shape="box"];86[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];16 -> 86[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 86 -> 25[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 87[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 87[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 87 -> 26[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 17[label="primCmpInt (Neg (Succ vx300)) (Pos vx40) == GT",fontsize=16,color="black",shape="box"];17 -> 27[label="",style="solid", color="black", weight=3]; 9.61/4.10 18[label="primCmpInt (Neg (Succ vx300)) (Neg vx40) == GT",fontsize=16,color="black",shape="box"];18 -> 28[label="",style="solid", color="black", weight=3]; 9.61/4.10 19[label="primCmpInt (Neg Zero) (Pos vx40) == GT",fontsize=16,color="burlywood",shape="box"];88[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];19 -> 88[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 88 -> 29[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 89[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 89[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 89 -> 30[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 20[label="primCmpInt (Neg Zero) (Neg vx40) == GT",fontsize=16,color="burlywood",shape="box"];90[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];20 -> 90[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 90 -> 31[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 91[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 91[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 91 -> 32[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 21[label="primCmpNat (Succ vx300) vx40 == GT",fontsize=16,color="burlywood",shape="triangle"];92[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];21 -> 92[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 92 -> 33[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 93[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 93[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 93 -> 34[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 22[label="GT == GT",fontsize=16,color="black",shape="triangle"];22 -> 35[label="",style="solid", color="black", weight=3]; 9.61/4.10 23[label="primCmpInt (Pos Zero) (Pos (Succ vx400)) == GT",fontsize=16,color="black",shape="box"];23 -> 36[label="",style="solid", color="black", weight=3]; 9.61/4.10 24[label="primCmpInt (Pos Zero) (Pos Zero) == GT",fontsize=16,color="black",shape="box"];24 -> 37[label="",style="solid", color="black", weight=3]; 9.61/4.10 25[label="primCmpInt (Pos Zero) (Neg (Succ vx400)) == GT",fontsize=16,color="black",shape="box"];25 -> 38[label="",style="solid", color="black", weight=3]; 9.61/4.10 26[label="primCmpInt (Pos Zero) (Neg Zero) == GT",fontsize=16,color="black",shape="box"];26 -> 39[label="",style="solid", color="black", weight=3]; 9.61/4.10 27[label="LT == GT",fontsize=16,color="black",shape="triangle"];27 -> 40[label="",style="solid", color="black", weight=3]; 9.61/4.10 28[label="primCmpNat vx40 (Succ vx300) == GT",fontsize=16,color="burlywood",shape="triangle"];94[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];28 -> 94[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 94 -> 41[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 95[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 95[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 95 -> 42[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 29[label="primCmpInt (Neg Zero) (Pos (Succ vx400)) == GT",fontsize=16,color="black",shape="box"];29 -> 43[label="",style="solid", color="black", weight=3]; 9.61/4.10 30[label="primCmpInt (Neg Zero) (Pos Zero) == GT",fontsize=16,color="black",shape="box"];30 -> 44[label="",style="solid", color="black", weight=3]; 9.61/4.10 31[label="primCmpInt (Neg Zero) (Neg (Succ vx400)) == GT",fontsize=16,color="black",shape="box"];31 -> 45[label="",style="solid", color="black", weight=3]; 9.61/4.10 32[label="primCmpInt (Neg Zero) (Neg Zero) == GT",fontsize=16,color="black",shape="box"];32 -> 46[label="",style="solid", color="black", weight=3]; 9.61/4.10 33[label="primCmpNat (Succ vx300) (Succ vx400) == GT",fontsize=16,color="black",shape="box"];33 -> 47[label="",style="solid", color="black", weight=3]; 9.61/4.10 34[label="primCmpNat (Succ vx300) Zero == GT",fontsize=16,color="black",shape="box"];34 -> 48[label="",style="solid", color="black", weight=3]; 9.61/4.10 35[label="True",fontsize=16,color="green",shape="box"];36 -> 28[label="",style="dashed", color="red", weight=0]; 9.61/4.10 36[label="primCmpNat Zero (Succ vx400) == GT",fontsize=16,color="magenta"];36 -> 49[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 36 -> 50[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 37[label="EQ == GT",fontsize=16,color="black",shape="triangle"];37 -> 51[label="",style="solid", color="black", weight=3]; 9.61/4.10 38 -> 22[label="",style="dashed", color="red", weight=0]; 9.61/4.10 38[label="GT == GT",fontsize=16,color="magenta"];39 -> 37[label="",style="dashed", color="red", weight=0]; 9.61/4.10 39[label="EQ == GT",fontsize=16,color="magenta"];40[label="False",fontsize=16,color="green",shape="box"];41[label="primCmpNat (Succ vx400) (Succ vx300) == GT",fontsize=16,color="black",shape="box"];41 -> 52[label="",style="solid", color="black", weight=3]; 9.61/4.10 42[label="primCmpNat Zero (Succ vx300) == GT",fontsize=16,color="black",shape="box"];42 -> 53[label="",style="solid", color="black", weight=3]; 9.61/4.10 43 -> 27[label="",style="dashed", color="red", weight=0]; 9.61/4.10 43[label="LT == GT",fontsize=16,color="magenta"];44 -> 37[label="",style="dashed", color="red", weight=0]; 9.61/4.10 44[label="EQ == GT",fontsize=16,color="magenta"];45 -> 21[label="",style="dashed", color="red", weight=0]; 9.61/4.10 45[label="primCmpNat (Succ vx400) Zero == GT",fontsize=16,color="magenta"];45 -> 54[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 45 -> 55[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 46 -> 37[label="",style="dashed", color="red", weight=0]; 9.61/4.10 46[label="EQ == GT",fontsize=16,color="magenta"];47[label="primCmpNat vx300 vx400 == GT",fontsize=16,color="burlywood",shape="triangle"];96[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];47 -> 96[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 96 -> 56[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 97[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 97[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 97 -> 57[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 48 -> 22[label="",style="dashed", color="red", weight=0]; 9.61/4.10 48[label="GT == GT",fontsize=16,color="magenta"];49[label="vx400",fontsize=16,color="green",shape="box"];50[label="Zero",fontsize=16,color="green",shape="box"];51[label="False",fontsize=16,color="green",shape="box"];52 -> 47[label="",style="dashed", color="red", weight=0]; 9.61/4.10 52[label="primCmpNat vx400 vx300 == GT",fontsize=16,color="magenta"];52 -> 58[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 52 -> 59[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 53 -> 27[label="",style="dashed", color="red", weight=0]; 9.61/4.10 53[label="LT == GT",fontsize=16,color="magenta"];54[label="vx400",fontsize=16,color="green",shape="box"];55[label="Zero",fontsize=16,color="green",shape="box"];56[label="primCmpNat (Succ vx3000) vx400 == GT",fontsize=16,color="burlywood",shape="box"];98[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];56 -> 98[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 98 -> 60[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 99[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 99[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 99 -> 61[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 57[label="primCmpNat Zero vx400 == GT",fontsize=16,color="burlywood",shape="box"];100[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];57 -> 100[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 100 -> 62[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 101[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 101[label="",style="solid", color="burlywood", weight=9]; 9.61/4.10 101 -> 63[label="",style="solid", color="burlywood", weight=3]; 9.61/4.10 58[label="vx400",fontsize=16,color="green",shape="box"];59[label="vx300",fontsize=16,color="green",shape="box"];60[label="primCmpNat (Succ vx3000) (Succ vx4000) == GT",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3]; 9.61/4.10 61[label="primCmpNat (Succ vx3000) Zero == GT",fontsize=16,color="black",shape="box"];61 -> 65[label="",style="solid", color="black", weight=3]; 9.61/4.10 62[label="primCmpNat Zero (Succ vx4000) == GT",fontsize=16,color="black",shape="box"];62 -> 66[label="",style="solid", color="black", weight=3]; 9.61/4.10 63[label="primCmpNat Zero Zero == GT",fontsize=16,color="black",shape="box"];63 -> 67[label="",style="solid", color="black", weight=3]; 9.61/4.10 64 -> 47[label="",style="dashed", color="red", weight=0]; 9.61/4.10 64[label="primCmpNat vx3000 vx4000 == GT",fontsize=16,color="magenta"];64 -> 68[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 64 -> 69[label="",style="dashed", color="magenta", weight=3]; 9.61/4.10 65 -> 22[label="",style="dashed", color="red", weight=0]; 9.61/4.10 65[label="GT == GT",fontsize=16,color="magenta"];66 -> 27[label="",style="dashed", color="red", weight=0]; 9.61/4.10 66[label="LT == GT",fontsize=16,color="magenta"];67 -> 37[label="",style="dashed", color="red", weight=0]; 9.61/4.10 67[label="EQ == GT",fontsize=16,color="magenta"];68[label="vx3000",fontsize=16,color="green",shape="box"];69[label="vx4000",fontsize=16,color="green",shape="box"];} 9.61/4.10 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (6) 9.61/4.10 Obligation: 9.61/4.10 Q DP problem: 9.61/4.10 The TRS P consists of the following rules: 9.61/4.10 9.61/4.10 new_esEs(Succ(vx3000), Succ(vx4000)) -> new_esEs(vx3000, vx4000) 9.61/4.10 9.61/4.10 R is empty. 9.61/4.10 Q is empty. 9.61/4.10 We have to consider all minimal (P,Q,R)-chains. 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (7) QDPSizeChangeProof (EQUIVALENT) 9.61/4.10 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. 9.61/4.10 9.61/4.10 From the DPs we obtained the following set of size-change graphs: 9.61/4.10 *new_esEs(Succ(vx3000), Succ(vx4000)) -> new_esEs(vx3000, vx4000) 9.61/4.10 The graph contains the following edges 1 > 1, 2 > 2 9.61/4.10 9.61/4.10 9.61/4.10 ---------------------------------------- 9.61/4.10 9.61/4.10 (8) 9.61/4.10 YES 9.82/4.13 EOF