7.90/3.55 YES 9.31/3.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.31/3.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.31/3.98 9.31/3.98 9.31/3.98 H-Termination with start terms of the given HASKELL could be proven: 9.31/3.98 9.31/3.98 (0) HASKELL 9.31/3.98 (1) BR [EQUIVALENT, 0 ms] 9.31/3.98 (2) HASKELL 9.31/3.98 (3) COR [EQUIVALENT, 0 ms] 9.31/3.98 (4) HASKELL 9.31/3.98 (5) Narrow [SOUND, 0 ms] 9.31/3.98 (6) AND 9.31/3.98 (7) QDP 9.31/3.98 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.31/3.98 (9) YES 9.31/3.98 (10) QDP 9.31/3.98 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.31/3.98 (12) YES 9.31/3.98 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (0) 9.31/3.98 Obligation: 9.31/3.98 mainModule Main 9.31/3.98 module Main where { 9.31/3.98 import qualified Prelude; 9.31/3.98 } 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (1) BR (EQUIVALENT) 9.31/3.98 Replaced joker patterns by fresh variables and removed binding patterns. 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (2) 9.31/3.98 Obligation: 9.31/3.98 mainModule Main 9.31/3.98 module Main where { 9.31/3.98 import qualified Prelude; 9.31/3.98 } 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (3) COR (EQUIVALENT) 9.31/3.98 Cond Reductions: 9.31/3.98 The following Function with conditions 9.31/3.98 "undefined |Falseundefined; 9.31/3.98 " 9.31/3.98 is transformed to 9.31/3.98 "undefined = undefined1; 9.31/3.98 " 9.31/3.98 "undefined0 True = undefined; 9.31/3.98 " 9.31/3.98 "undefined1 = undefined0 False; 9.31/3.98 " 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (4) 9.31/3.98 Obligation: 9.31/3.98 mainModule Main 9.31/3.98 module Main where { 9.31/3.98 import qualified Prelude; 9.31/3.98 } 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (5) Narrow (SOUND) 9.31/3.98 Haskell To QDPs 9.31/3.98 9.31/3.98 digraph dp_graph { 9.31/3.98 node [outthreshold=100, inthreshold=100];1[label="(**)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.31/3.98 3[label="(**) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.31/3.98 4[label="(**) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.31/3.98 5[label="exp (log vx3 * vx4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.31/3.98 6[label="primExpFloat (log vx3 * vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 9.31/3.98 7[label="terminator (log vx3 * vx4)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 9.31/3.98 8[label="ter0m (log vx3 * vx4)",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3]; 9.31/3.98 9[label="log vx3 * vx4",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 9.31/3.98 10 -> 14[label="",style="dashed", color="red", weight=0]; 9.31/3.98 10[label="primMulFloat (log vx3) vx4",fontsize=16,color="magenta"];10 -> 15[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 15[label="log vx3",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 9.31/3.98 14[label="primMulFloat vx5 vx4",fontsize=16,color="burlywood",shape="triangle"];82[label="vx5/Float vx50 vx51",fontsize=10,color="white",style="solid",shape="box"];14 -> 82[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 82 -> 20[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 19[label="primLogFloat vx3",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3]; 9.31/3.98 20[label="primMulFloat (Float vx50 vx51) vx4",fontsize=16,color="burlywood",shape="box"];83[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];20 -> 83[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 83 -> 23[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 22[label="terminator vx3",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3]; 9.31/3.98 23[label="primMulFloat (Float vx50 vx51) (Float vx40 vx41)",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 9.31/3.98 24[label="ter2m vx3",fontsize=16,color="green",shape="box"];24 -> 26[label="",style="dashed", color="green", weight=3]; 9.31/3.98 25[label="Float (vx50 * vx40) (vx51 * vx41)",fontsize=16,color="green",shape="box"];25 -> 27[label="",style="dashed", color="green", weight=3]; 9.31/3.98 25 -> 28[label="",style="dashed", color="green", weight=3]; 9.31/3.98 26[label="vx3",fontsize=16,color="green",shape="box"];27[label="vx50 * vx40",fontsize=16,color="black",shape="triangle"];27 -> 29[label="",style="solid", color="black", weight=3]; 9.31/3.98 28 -> 27[label="",style="dashed", color="red", weight=0]; 9.31/3.98 28[label="vx51 * vx41",fontsize=16,color="magenta"];28 -> 30[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 28 -> 31[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 29[label="primMulInt vx50 vx40",fontsize=16,color="burlywood",shape="box"];84[label="vx50/Pos vx500",fontsize=10,color="white",style="solid",shape="box"];29 -> 84[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 84 -> 32[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 85[label="vx50/Neg vx500",fontsize=10,color="white",style="solid",shape="box"];29 -> 85[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 85 -> 33[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 30[label="vx41",fontsize=16,color="green",shape="box"];31[label="vx51",fontsize=16,color="green",shape="box"];32[label="primMulInt (Pos vx500) vx40",fontsize=16,color="burlywood",shape="box"];86[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];32 -> 86[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 86 -> 34[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 87[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];32 -> 87[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 87 -> 35[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 33[label="primMulInt (Neg vx500) vx40",fontsize=16,color="burlywood",shape="box"];88[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];33 -> 88[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 88 -> 36[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 89[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];33 -> 89[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 89 -> 37[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 34[label="primMulInt (Pos vx500) (Pos vx400)",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3]; 9.31/3.98 35[label="primMulInt (Pos vx500) (Neg vx400)",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 9.31/3.98 36[label="primMulInt (Neg vx500) (Pos vx400)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 9.31/3.98 37[label="primMulInt (Neg vx500) (Neg vx400)",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3]; 9.31/3.98 38[label="Pos (primMulNat vx500 vx400)",fontsize=16,color="green",shape="box"];38 -> 42[label="",style="dashed", color="green", weight=3]; 9.31/3.98 39[label="Neg (primMulNat vx500 vx400)",fontsize=16,color="green",shape="box"];39 -> 43[label="",style="dashed", color="green", weight=3]; 9.31/3.98 40[label="Neg (primMulNat vx500 vx400)",fontsize=16,color="green",shape="box"];40 -> 44[label="",style="dashed", color="green", weight=3]; 9.31/3.98 41[label="Pos (primMulNat vx500 vx400)",fontsize=16,color="green",shape="box"];41 -> 45[label="",style="dashed", color="green", weight=3]; 9.31/3.98 42[label="primMulNat vx500 vx400",fontsize=16,color="burlywood",shape="triangle"];90[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];42 -> 90[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 90 -> 46[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 91[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];42 -> 91[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 91 -> 47[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 43 -> 42[label="",style="dashed", color="red", weight=0]; 9.31/3.98 43[label="primMulNat vx500 vx400",fontsize=16,color="magenta"];43 -> 48[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 44 -> 42[label="",style="dashed", color="red", weight=0]; 9.31/3.98 44[label="primMulNat vx500 vx400",fontsize=16,color="magenta"];44 -> 49[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 45 -> 42[label="",style="dashed", color="red", weight=0]; 9.31/3.98 45[label="primMulNat vx500 vx400",fontsize=16,color="magenta"];45 -> 50[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 45 -> 51[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 46[label="primMulNat (Succ vx5000) vx400",fontsize=16,color="burlywood",shape="box"];92[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];46 -> 92[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 92 -> 52[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 93[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 93[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 93 -> 53[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 47[label="primMulNat Zero vx400",fontsize=16,color="burlywood",shape="box"];94[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];47 -> 94[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 94 -> 54[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 95[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 95[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 95 -> 55[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 48[label="vx400",fontsize=16,color="green",shape="box"];49[label="vx500",fontsize=16,color="green",shape="box"];50[label="vx400",fontsize=16,color="green",shape="box"];51[label="vx500",fontsize=16,color="green",shape="box"];52[label="primMulNat (Succ vx5000) (Succ vx4000)",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 9.31/3.98 53[label="primMulNat (Succ vx5000) Zero",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3]; 9.31/3.98 54[label="primMulNat Zero (Succ vx4000)",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 9.31/3.98 55[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 9.31/3.98 56 -> 60[label="",style="dashed", color="red", weight=0]; 9.31/3.98 56[label="primPlusNat (primMulNat vx5000 (Succ vx4000)) (Succ vx4000)",fontsize=16,color="magenta"];56 -> 61[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 57[label="Zero",fontsize=16,color="green",shape="box"];58[label="Zero",fontsize=16,color="green",shape="box"];59[label="Zero",fontsize=16,color="green",shape="box"];61 -> 42[label="",style="dashed", color="red", weight=0]; 9.31/3.98 61[label="primMulNat vx5000 (Succ vx4000)",fontsize=16,color="magenta"];61 -> 62[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 61 -> 63[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 60[label="primPlusNat vx6 (Succ vx4000)",fontsize=16,color="burlywood",shape="triangle"];96[label="vx6/Succ vx60",fontsize=10,color="white",style="solid",shape="box"];60 -> 96[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 96 -> 64[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 97[label="vx6/Zero",fontsize=10,color="white",style="solid",shape="box"];60 -> 97[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 97 -> 65[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 62[label="Succ vx4000",fontsize=16,color="green",shape="box"];63[label="vx5000",fontsize=16,color="green",shape="box"];64[label="primPlusNat (Succ vx60) (Succ vx4000)",fontsize=16,color="black",shape="box"];64 -> 66[label="",style="solid", color="black", weight=3]; 9.31/3.98 65[label="primPlusNat Zero (Succ vx4000)",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3]; 9.31/3.98 66[label="Succ (Succ (primPlusNat vx60 vx4000))",fontsize=16,color="green",shape="box"];66 -> 68[label="",style="dashed", color="green", weight=3]; 9.31/3.98 67[label="Succ vx4000",fontsize=16,color="green",shape="box"];68[label="primPlusNat vx60 vx4000",fontsize=16,color="burlywood",shape="triangle"];98[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];68 -> 98[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 98 -> 69[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 99[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];68 -> 99[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 99 -> 70[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 69[label="primPlusNat (Succ vx600) vx4000",fontsize=16,color="burlywood",shape="box"];100[label="vx4000/Succ vx40000",fontsize=10,color="white",style="solid",shape="box"];69 -> 100[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 100 -> 71[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 101[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 101[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 101 -> 72[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 70[label="primPlusNat Zero vx4000",fontsize=16,color="burlywood",shape="box"];102[label="vx4000/Succ vx40000",fontsize=10,color="white",style="solid",shape="box"];70 -> 102[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 102 -> 73[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 103[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 103[label="",style="solid", color="burlywood", weight=9]; 9.31/3.98 103 -> 74[label="",style="solid", color="burlywood", weight=3]; 9.31/3.98 71[label="primPlusNat (Succ vx600) (Succ vx40000)",fontsize=16,color="black",shape="box"];71 -> 75[label="",style="solid", color="black", weight=3]; 9.31/3.98 72[label="primPlusNat (Succ vx600) Zero",fontsize=16,color="black",shape="box"];72 -> 76[label="",style="solid", color="black", weight=3]; 9.31/3.98 73[label="primPlusNat Zero (Succ vx40000)",fontsize=16,color="black",shape="box"];73 -> 77[label="",style="solid", color="black", weight=3]; 9.31/3.98 74[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];74 -> 78[label="",style="solid", color="black", weight=3]; 9.31/3.98 75[label="Succ (Succ (primPlusNat vx600 vx40000))",fontsize=16,color="green",shape="box"];75 -> 79[label="",style="dashed", color="green", weight=3]; 9.31/3.98 76[label="Succ vx600",fontsize=16,color="green",shape="box"];77[label="Succ vx40000",fontsize=16,color="green",shape="box"];78[label="Zero",fontsize=16,color="green",shape="box"];79 -> 68[label="",style="dashed", color="red", weight=0]; 9.31/3.98 79[label="primPlusNat vx600 vx40000",fontsize=16,color="magenta"];79 -> 80[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 79 -> 81[label="",style="dashed", color="magenta", weight=3]; 9.31/3.98 80[label="vx40000",fontsize=16,color="green",shape="box"];81[label="vx600",fontsize=16,color="green",shape="box"];} 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (6) 9.31/3.98 Complex Obligation (AND) 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (7) 9.31/3.98 Obligation: 9.31/3.98 Q DP problem: 9.31/3.98 The TRS P consists of the following rules: 9.31/3.98 9.31/3.98 new_primMulNat(Succ(vx5000), Succ(vx4000)) -> new_primMulNat(vx5000, Succ(vx4000)) 9.31/3.98 9.31/3.98 R is empty. 9.31/3.98 Q is empty. 9.31/3.98 We have to consider all minimal (P,Q,R)-chains. 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (8) QDPSizeChangeProof (EQUIVALENT) 9.31/3.98 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. 9.31/3.98 9.31/3.98 From the DPs we obtained the following set of size-change graphs: 9.31/3.98 *new_primMulNat(Succ(vx5000), Succ(vx4000)) -> new_primMulNat(vx5000, Succ(vx4000)) 9.31/3.98 The graph contains the following edges 1 > 1, 2 >= 2 9.31/3.98 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (9) 9.31/3.98 YES 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (10) 9.31/3.98 Obligation: 9.31/3.98 Q DP problem: 9.31/3.98 The TRS P consists of the following rules: 9.31/3.98 9.31/3.98 new_primPlusNat(Succ(vx600), Succ(vx40000)) -> new_primPlusNat(vx600, vx40000) 9.31/3.98 9.31/3.98 R is empty. 9.31/3.98 Q is empty. 9.31/3.98 We have to consider all minimal (P,Q,R)-chains. 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (11) QDPSizeChangeProof (EQUIVALENT) 9.31/3.98 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. 9.31/3.98 9.31/3.98 From the DPs we obtained the following set of size-change graphs: 9.31/3.98 *new_primPlusNat(Succ(vx600), Succ(vx40000)) -> new_primPlusNat(vx600, vx40000) 9.31/3.98 The graph contains the following edges 1 > 1, 2 > 2 9.31/3.98 9.31/3.98 9.31/3.98 ---------------------------------------- 9.31/3.98 9.31/3.98 (12) 9.31/3.98 YES 9.61/4.02 EOF