8.16/3.49 YES 9.57/3.93 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.57/3.93 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.57/3.93 9.57/3.93 9.57/3.93 H-Termination with start terms of the given HASKELL could be proven: 9.57/3.93 9.57/3.93 (0) HASKELL 9.57/3.93 (1) BR [EQUIVALENT, 0 ms] 9.57/3.93 (2) HASKELL 9.57/3.93 (3) COR [EQUIVALENT, 0 ms] 9.57/3.93 (4) HASKELL 9.57/3.93 (5) Narrow [SOUND, 0 ms] 9.57/3.93 (6) AND 9.57/3.93 (7) QDP 9.57/3.93 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.57/3.93 (9) YES 9.57/3.93 (10) QDP 9.57/3.93 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.57/3.93 (12) YES 9.57/3.93 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (0) 9.57/3.93 Obligation: 9.57/3.93 mainModule Main 9.57/3.93 module Main where { 9.57/3.93 import qualified Prelude; 9.57/3.93 } 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (1) BR (EQUIVALENT) 9.57/3.93 Replaced joker patterns by fresh variables and removed binding patterns. 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (2) 9.57/3.93 Obligation: 9.57/3.93 mainModule Main 9.57/3.93 module Main where { 9.57/3.93 import qualified Prelude; 9.57/3.93 } 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (3) COR (EQUIVALENT) 9.57/3.93 Cond Reductions: 9.57/3.93 The following Function with conditions 9.57/3.93 "undefined |Falseundefined; 9.57/3.93 " 9.57/3.93 is transformed to 9.57/3.93 "undefined = undefined1; 9.57/3.93 " 9.57/3.93 "undefined0 True = undefined; 9.57/3.93 " 9.57/3.93 "undefined1 = undefined0 False; 9.57/3.93 " 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (4) 9.57/3.93 Obligation: 9.57/3.93 mainModule Main 9.57/3.93 module Main where { 9.57/3.93 import qualified Prelude; 9.57/3.93 } 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (5) Narrow (SOUND) 9.57/3.93 Haskell To QDPs 9.57/3.93 9.57/3.93 digraph dp_graph { 9.57/3.93 node [outthreshold=100, inthreshold=100];1[label="logBase",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.57/3.93 3[label="logBase vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.57/3.93 4[label="logBase vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.57/3.93 5[label="log vx4 / log vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.57/3.93 6 -> 16[label="",style="dashed", color="red", weight=0]; 9.57/3.93 6[label="primDivFloat (log vx4) (log vx3)",fontsize=16,color="magenta"];6 -> 17[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 6 -> 18[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 17[label="log vx3",fontsize=16,color="black",shape="triangle"];17 -> 20[label="",style="solid", color="black", weight=3]; 9.57/3.93 18 -> 17[label="",style="dashed", color="red", weight=0]; 9.57/3.93 18[label="log vx4",fontsize=16,color="magenta"];18 -> 21[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 16[label="primDivFloat vx5 vx6",fontsize=16,color="burlywood",shape="triangle"];83[label="vx5/Float vx50 vx51",fontsize=10,color="white",style="solid",shape="box"];16 -> 83[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 83 -> 22[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 20[label="primLogFloat vx3",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3]; 9.57/3.93 21[label="vx4",fontsize=16,color="green",shape="box"];22[label="primDivFloat (Float vx50 vx51) vx6",fontsize=16,color="burlywood",shape="box"];84[label="vx6/Float vx60 vx61",fontsize=10,color="white",style="solid",shape="box"];22 -> 84[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 84 -> 24[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 23[label="terminator vx3",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 9.57/3.93 24[label="primDivFloat (Float vx50 vx51) (Float vx60 vx61)",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3]; 9.57/3.93 25[label="ter1m vx3",fontsize=16,color="green",shape="box"];25 -> 27[label="",style="dashed", color="green", weight=3]; 9.57/3.93 26[label="Float (vx50 * vx61) (vx51 * vx60)",fontsize=16,color="green",shape="box"];26 -> 28[label="",style="dashed", color="green", weight=3]; 9.57/3.93 26 -> 29[label="",style="dashed", color="green", weight=3]; 9.57/3.93 27[label="vx3",fontsize=16,color="green",shape="box"];28[label="vx50 * vx61",fontsize=16,color="black",shape="triangle"];28 -> 30[label="",style="solid", color="black", weight=3]; 9.57/3.93 29 -> 28[label="",style="dashed", color="red", weight=0]; 9.57/3.93 29[label="vx51 * vx60",fontsize=16,color="magenta"];29 -> 31[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 29 -> 32[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 30[label="primMulInt vx50 vx61",fontsize=16,color="burlywood",shape="box"];85[label="vx50/Pos vx500",fontsize=10,color="white",style="solid",shape="box"];30 -> 85[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 85 -> 33[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 86[label="vx50/Neg vx500",fontsize=10,color="white",style="solid",shape="box"];30 -> 86[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 86 -> 34[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 31[label="vx51",fontsize=16,color="green",shape="box"];32[label="vx60",fontsize=16,color="green",shape="box"];33[label="primMulInt (Pos vx500) vx61",fontsize=16,color="burlywood",shape="box"];87[label="vx61/Pos vx610",fontsize=10,color="white",style="solid",shape="box"];33 -> 87[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 87 -> 35[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 88[label="vx61/Neg vx610",fontsize=10,color="white",style="solid",shape="box"];33 -> 88[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 88 -> 36[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 34[label="primMulInt (Neg vx500) vx61",fontsize=16,color="burlywood",shape="box"];89[label="vx61/Pos vx610",fontsize=10,color="white",style="solid",shape="box"];34 -> 89[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 89 -> 37[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 90[label="vx61/Neg vx610",fontsize=10,color="white",style="solid",shape="box"];34 -> 90[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 90 -> 38[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 35[label="primMulInt (Pos vx500) (Pos vx610)",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 9.57/3.93 36[label="primMulInt (Pos vx500) (Neg vx610)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 9.57/3.93 37[label="primMulInt (Neg vx500) (Pos vx610)",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3]; 9.57/3.93 38[label="primMulInt (Neg vx500) (Neg vx610)",fontsize=16,color="black",shape="box"];38 -> 42[label="",style="solid", color="black", weight=3]; 9.57/3.93 39[label="Pos (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];39 -> 43[label="",style="dashed", color="green", weight=3]; 9.57/3.93 40[label="Neg (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];40 -> 44[label="",style="dashed", color="green", weight=3]; 9.57/3.93 41[label="Neg (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];41 -> 45[label="",style="dashed", color="green", weight=3]; 9.57/3.93 42[label="Pos (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];42 -> 46[label="",style="dashed", color="green", weight=3]; 9.57/3.93 43[label="primMulNat vx500 vx610",fontsize=16,color="burlywood",shape="triangle"];91[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];43 -> 91[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 91 -> 47[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 92[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 92[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 92 -> 48[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 44 -> 43[label="",style="dashed", color="red", weight=0]; 9.57/3.93 44[label="primMulNat vx500 vx610",fontsize=16,color="magenta"];44 -> 49[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 45 -> 43[label="",style="dashed", color="red", weight=0]; 9.57/3.93 45[label="primMulNat vx500 vx610",fontsize=16,color="magenta"];45 -> 50[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 46 -> 43[label="",style="dashed", color="red", weight=0]; 9.57/3.93 46[label="primMulNat vx500 vx610",fontsize=16,color="magenta"];46 -> 51[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 46 -> 52[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 47[label="primMulNat (Succ vx5000) vx610",fontsize=16,color="burlywood",shape="box"];93[label="vx610/Succ vx6100",fontsize=10,color="white",style="solid",shape="box"];47 -> 93[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 93 -> 53[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 94[label="vx610/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 94[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 94 -> 54[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 48[label="primMulNat Zero vx610",fontsize=16,color="burlywood",shape="box"];95[label="vx610/Succ vx6100",fontsize=10,color="white",style="solid",shape="box"];48 -> 95[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 95 -> 55[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 96[label="vx610/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 96[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 96 -> 56[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 49[label="vx610",fontsize=16,color="green",shape="box"];50[label="vx500",fontsize=16,color="green",shape="box"];51[label="vx610",fontsize=16,color="green",shape="box"];52[label="vx500",fontsize=16,color="green",shape="box"];53[label="primMulNat (Succ vx5000) (Succ vx6100)",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3]; 9.57/3.93 54[label="primMulNat (Succ vx5000) Zero",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 9.57/3.93 55[label="primMulNat Zero (Succ vx6100)",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 9.57/3.93 56[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3]; 9.57/3.93 57 -> 61[label="",style="dashed", color="red", weight=0]; 9.57/3.93 57[label="primPlusNat (primMulNat vx5000 (Succ vx6100)) (Succ vx6100)",fontsize=16,color="magenta"];57 -> 62[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 58[label="Zero",fontsize=16,color="green",shape="box"];59[label="Zero",fontsize=16,color="green",shape="box"];60[label="Zero",fontsize=16,color="green",shape="box"];62 -> 43[label="",style="dashed", color="red", weight=0]; 9.57/3.93 62[label="primMulNat vx5000 (Succ vx6100)",fontsize=16,color="magenta"];62 -> 63[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 62 -> 64[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 61[label="primPlusNat vx7 (Succ vx6100)",fontsize=16,color="burlywood",shape="triangle"];97[label="vx7/Succ vx70",fontsize=10,color="white",style="solid",shape="box"];61 -> 97[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 97 -> 65[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 98[label="vx7/Zero",fontsize=10,color="white",style="solid",shape="box"];61 -> 98[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 98 -> 66[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 63[label="Succ vx6100",fontsize=16,color="green",shape="box"];64[label="vx5000",fontsize=16,color="green",shape="box"];65[label="primPlusNat (Succ vx70) (Succ vx6100)",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3]; 9.57/3.93 66[label="primPlusNat Zero (Succ vx6100)",fontsize=16,color="black",shape="box"];66 -> 68[label="",style="solid", color="black", weight=3]; 9.57/3.93 67[label="Succ (Succ (primPlusNat vx70 vx6100))",fontsize=16,color="green",shape="box"];67 -> 69[label="",style="dashed", color="green", weight=3]; 9.57/3.93 68[label="Succ vx6100",fontsize=16,color="green",shape="box"];69[label="primPlusNat vx70 vx6100",fontsize=16,color="burlywood",shape="triangle"];99[label="vx70/Succ vx700",fontsize=10,color="white",style="solid",shape="box"];69 -> 99[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 99 -> 70[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 100[label="vx70/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 100[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 100 -> 71[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 70[label="primPlusNat (Succ vx700) vx6100",fontsize=16,color="burlywood",shape="box"];101[label="vx6100/Succ vx61000",fontsize=10,color="white",style="solid",shape="box"];70 -> 101[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 101 -> 72[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 102[label="vx6100/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 102[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 102 -> 73[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 71[label="primPlusNat Zero vx6100",fontsize=16,color="burlywood",shape="box"];103[label="vx6100/Succ vx61000",fontsize=10,color="white",style="solid",shape="box"];71 -> 103[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 103 -> 74[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 104[label="vx6100/Zero",fontsize=10,color="white",style="solid",shape="box"];71 -> 104[label="",style="solid", color="burlywood", weight=9]; 9.57/3.93 104 -> 75[label="",style="solid", color="burlywood", weight=3]; 9.57/3.93 72[label="primPlusNat (Succ vx700) (Succ vx61000)",fontsize=16,color="black",shape="box"];72 -> 76[label="",style="solid", color="black", weight=3]; 9.57/3.93 73[label="primPlusNat (Succ vx700) Zero",fontsize=16,color="black",shape="box"];73 -> 77[label="",style="solid", color="black", weight=3]; 9.57/3.93 74[label="primPlusNat Zero (Succ vx61000)",fontsize=16,color="black",shape="box"];74 -> 78[label="",style="solid", color="black", weight=3]; 9.57/3.93 75[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];75 -> 79[label="",style="solid", color="black", weight=3]; 9.57/3.93 76[label="Succ (Succ (primPlusNat vx700 vx61000))",fontsize=16,color="green",shape="box"];76 -> 80[label="",style="dashed", color="green", weight=3]; 9.57/3.93 77[label="Succ vx700",fontsize=16,color="green",shape="box"];78[label="Succ vx61000",fontsize=16,color="green",shape="box"];79[label="Zero",fontsize=16,color="green",shape="box"];80 -> 69[label="",style="dashed", color="red", weight=0]; 9.57/3.93 80[label="primPlusNat vx700 vx61000",fontsize=16,color="magenta"];80 -> 81[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 80 -> 82[label="",style="dashed", color="magenta", weight=3]; 9.57/3.93 81[label="vx61000",fontsize=16,color="green",shape="box"];82[label="vx700",fontsize=16,color="green",shape="box"];} 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (6) 9.57/3.93 Complex Obligation (AND) 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (7) 9.57/3.93 Obligation: 9.57/3.93 Q DP problem: 9.57/3.93 The TRS P consists of the following rules: 9.57/3.93 9.57/3.93 new_primMulNat(Succ(vx5000), Succ(vx6100)) -> new_primMulNat(vx5000, Succ(vx6100)) 9.57/3.93 9.57/3.93 R is empty. 9.57/3.93 Q is empty. 9.57/3.93 We have to consider all minimal (P,Q,R)-chains. 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (8) QDPSizeChangeProof (EQUIVALENT) 9.57/3.93 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. 9.57/3.93 9.57/3.93 From the DPs we obtained the following set of size-change graphs: 9.57/3.93 *new_primMulNat(Succ(vx5000), Succ(vx6100)) -> new_primMulNat(vx5000, Succ(vx6100)) 9.57/3.93 The graph contains the following edges 1 > 1, 2 >= 2 9.57/3.93 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (9) 9.57/3.93 YES 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (10) 9.57/3.93 Obligation: 9.57/3.93 Q DP problem: 9.57/3.93 The TRS P consists of the following rules: 9.57/3.93 9.57/3.93 new_primPlusNat(Succ(vx700), Succ(vx61000)) -> new_primPlusNat(vx700, vx61000) 9.57/3.93 9.57/3.93 R is empty. 9.57/3.93 Q is empty. 9.57/3.93 We have to consider all minimal (P,Q,R)-chains. 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (11) QDPSizeChangeProof (EQUIVALENT) 9.57/3.93 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. 9.57/3.93 9.57/3.93 From the DPs we obtained the following set of size-change graphs: 9.57/3.93 *new_primPlusNat(Succ(vx700), Succ(vx61000)) -> new_primPlusNat(vx700, vx61000) 9.57/3.93 The graph contains the following edges 1 > 1, 2 > 2 9.57/3.93 9.57/3.93 9.57/3.93 ---------------------------------------- 9.57/3.93 9.57/3.93 (12) 9.57/3.93 YES 9.83/4.00 EOF