7.59/3.51 YES 9.44/3.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.44/3.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.44/3.96 9.44/3.96 9.44/3.96 H-Termination with start terms of the given HASKELL could be proven: 9.44/3.96 9.44/3.96 (0) HASKELL 9.44/3.96 (1) BR [EQUIVALENT, 0 ms] 9.44/3.96 (2) HASKELL 9.44/3.96 (3) COR [EQUIVALENT, 0 ms] 9.44/3.96 (4) HASKELL 9.44/3.96 (5) Narrow [SOUND, 0 ms] 9.44/3.96 (6) AND 9.44/3.96 (7) QDP 9.44/3.96 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.44/3.96 (9) YES 9.44/3.96 (10) QDP 9.44/3.96 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.44/3.96 (12) YES 9.44/3.96 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (0) 9.44/3.96 Obligation: 9.44/3.96 mainModule Main 9.44/3.96 module Main where { 9.44/3.96 import qualified Prelude; 9.44/3.96 } 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (1) BR (EQUIVALENT) 9.44/3.96 Replaced joker patterns by fresh variables and removed binding patterns. 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (2) 9.44/3.96 Obligation: 9.44/3.96 mainModule Main 9.44/3.96 module Main where { 9.44/3.96 import qualified Prelude; 9.44/3.96 } 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (3) COR (EQUIVALENT) 9.44/3.96 Cond Reductions: 9.44/3.96 The following Function with conditions 9.44/3.96 "undefined |Falseundefined; 9.44/3.96 " 9.44/3.96 is transformed to 9.44/3.96 "undefined = undefined1; 9.44/3.96 " 9.44/3.96 "undefined0 True = undefined; 9.44/3.96 " 9.44/3.96 "undefined1 = undefined0 False; 9.44/3.96 " 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (4) 9.44/3.96 Obligation: 9.44/3.96 mainModule Main 9.44/3.96 module Main where { 9.44/3.96 import qualified Prelude; 9.44/3.96 } 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (5) Narrow (SOUND) 9.44/3.96 Haskell To QDPs 9.44/3.96 9.44/3.96 digraph dp_graph { 9.44/3.96 node [outthreshold=100, inthreshold=100];1[label="(/)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.44/3.96 3[label="(/) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.44/3.96 4[label="(/) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.44/3.96 5[label="primDivFloat vx3 vx4",fontsize=16,color="burlywood",shape="box"];64[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 64[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 64 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 6[label="primDivFloat (Float vx30 vx31) vx4",fontsize=16,color="burlywood",shape="box"];65[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];6 -> 65[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 65 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 7[label="primDivFloat (Float vx30 vx31) (Float vx40 vx41)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 9.44/3.96 8[label="Float (vx30 * vx41) (vx31 * vx40)",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3]; 9.44/3.96 8 -> 10[label="",style="dashed", color="green", weight=3]; 9.44/3.96 9[label="vx30 * vx41",fontsize=16,color="black",shape="triangle"];9 -> 11[label="",style="solid", color="black", weight=3]; 9.44/3.96 10 -> 9[label="",style="dashed", color="red", weight=0]; 9.44/3.96 10[label="vx31 * vx40",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 10 -> 13[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 11[label="primMulInt vx30 vx41",fontsize=16,color="burlywood",shape="box"];66[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];11 -> 66[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 66 -> 14[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 67[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];11 -> 67[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 67 -> 15[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 12[label="vx31",fontsize=16,color="green",shape="box"];13[label="vx40",fontsize=16,color="green",shape="box"];14[label="primMulInt (Pos vx300) vx41",fontsize=16,color="burlywood",shape="box"];68[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];14 -> 68[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 68 -> 16[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 69[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];14 -> 69[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 69 -> 17[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 15[label="primMulInt (Neg vx300) vx41",fontsize=16,color="burlywood",shape="box"];70[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];15 -> 70[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 70 -> 18[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 71[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];15 -> 71[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 71 -> 19[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 16[label="primMulInt (Pos vx300) (Pos vx410)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 9.44/3.96 17[label="primMulInt (Pos vx300) (Neg vx410)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 9.44/3.96 18[label="primMulInt (Neg vx300) (Pos vx410)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 9.44/3.96 19[label="primMulInt (Neg vx300) (Neg vx410)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 9.44/3.96 20[label="Pos (primMulNat vx300 vx410)",fontsize=16,color="green",shape="box"];20 -> 24[label="",style="dashed", color="green", weight=3]; 9.44/3.96 21[label="Neg (primMulNat vx300 vx410)",fontsize=16,color="green",shape="box"];21 -> 25[label="",style="dashed", color="green", weight=3]; 9.44/3.96 22[label="Neg (primMulNat vx300 vx410)",fontsize=16,color="green",shape="box"];22 -> 26[label="",style="dashed", color="green", weight=3]; 9.44/3.96 23[label="Pos (primMulNat vx300 vx410)",fontsize=16,color="green",shape="box"];23 -> 27[label="",style="dashed", color="green", weight=3]; 9.44/3.96 24[label="primMulNat vx300 vx410",fontsize=16,color="burlywood",shape="triangle"];72[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];24 -> 72[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 72 -> 28[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 73[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 73[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 73 -> 29[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 25 -> 24[label="",style="dashed", color="red", weight=0]; 9.44/3.96 25[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];25 -> 30[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 26 -> 24[label="",style="dashed", color="red", weight=0]; 9.44/3.96 26[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];26 -> 31[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 27 -> 24[label="",style="dashed", color="red", weight=0]; 9.44/3.96 27[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];27 -> 32[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 27 -> 33[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 28[label="primMulNat (Succ vx3000) vx410",fontsize=16,color="burlywood",shape="box"];74[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];28 -> 74[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 74 -> 34[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 75[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 75[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 75 -> 35[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 29[label="primMulNat Zero vx410",fontsize=16,color="burlywood",shape="box"];76[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];29 -> 76[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 76 -> 36[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 77[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 77[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 77 -> 37[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 30[label="vx410",fontsize=16,color="green",shape="box"];31[label="vx300",fontsize=16,color="green",shape="box"];32[label="vx300",fontsize=16,color="green",shape="box"];33[label="vx410",fontsize=16,color="green",shape="box"];34[label="primMulNat (Succ vx3000) (Succ vx4100)",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3]; 9.44/3.96 35[label="primMulNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 9.44/3.96 36[label="primMulNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 9.44/3.96 37[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3]; 9.44/3.96 38 -> 42[label="",style="dashed", color="red", weight=0]; 9.44/3.96 38[label="primPlusNat (primMulNat vx3000 (Succ vx4100)) (Succ vx4100)",fontsize=16,color="magenta"];38 -> 43[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 39[label="Zero",fontsize=16,color="green",shape="box"];40[label="Zero",fontsize=16,color="green",shape="box"];41[label="Zero",fontsize=16,color="green",shape="box"];43 -> 24[label="",style="dashed", color="red", weight=0]; 9.44/3.96 43[label="primMulNat vx3000 (Succ vx4100)",fontsize=16,color="magenta"];43 -> 44[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 43 -> 45[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 42[label="primPlusNat vx5 (Succ vx4100)",fontsize=16,color="burlywood",shape="triangle"];78[label="vx5/Succ vx50",fontsize=10,color="white",style="solid",shape="box"];42 -> 78[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 78 -> 46[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 79[label="vx5/Zero",fontsize=10,color="white",style="solid",shape="box"];42 -> 79[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 79 -> 47[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 44[label="vx3000",fontsize=16,color="green",shape="box"];45[label="Succ vx4100",fontsize=16,color="green",shape="box"];46[label="primPlusNat (Succ vx50) (Succ vx4100)",fontsize=16,color="black",shape="box"];46 -> 48[label="",style="solid", color="black", weight=3]; 9.44/3.96 47[label="primPlusNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];47 -> 49[label="",style="solid", color="black", weight=3]; 9.44/3.96 48[label="Succ (Succ (primPlusNat vx50 vx4100))",fontsize=16,color="green",shape="box"];48 -> 50[label="",style="dashed", color="green", weight=3]; 9.44/3.96 49[label="Succ vx4100",fontsize=16,color="green",shape="box"];50[label="primPlusNat vx50 vx4100",fontsize=16,color="burlywood",shape="triangle"];80[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];50 -> 80[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 80 -> 51[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 81[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 81[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 81 -> 52[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 51[label="primPlusNat (Succ vx500) vx4100",fontsize=16,color="burlywood",shape="box"];82[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];51 -> 82[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 82 -> 53[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 83[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 83[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 83 -> 54[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 52[label="primPlusNat Zero vx4100",fontsize=16,color="burlywood",shape="box"];84[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];52 -> 84[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 84 -> 55[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 85[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 85[label="",style="solid", color="burlywood", weight=9]; 9.44/3.96 85 -> 56[label="",style="solid", color="burlywood", weight=3]; 9.44/3.96 53[label="primPlusNat (Succ vx500) (Succ vx41000)",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3]; 9.44/3.96 54[label="primPlusNat (Succ vx500) Zero",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 9.44/3.96 55[label="primPlusNat Zero (Succ vx41000)",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 9.44/3.96 56[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3]; 9.44/3.96 57[label="Succ (Succ (primPlusNat vx500 vx41000))",fontsize=16,color="green",shape="box"];57 -> 61[label="",style="dashed", color="green", weight=3]; 9.44/3.96 58[label="Succ vx500",fontsize=16,color="green",shape="box"];59[label="Succ vx41000",fontsize=16,color="green",shape="box"];60[label="Zero",fontsize=16,color="green",shape="box"];61 -> 50[label="",style="dashed", color="red", weight=0]; 9.44/3.96 61[label="primPlusNat vx500 vx41000",fontsize=16,color="magenta"];61 -> 62[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 61 -> 63[label="",style="dashed", color="magenta", weight=3]; 9.44/3.96 62[label="vx41000",fontsize=16,color="green",shape="box"];63[label="vx500",fontsize=16,color="green",shape="box"];} 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (6) 9.44/3.96 Complex Obligation (AND) 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (7) 9.44/3.96 Obligation: 9.44/3.96 Q DP problem: 9.44/3.96 The TRS P consists of the following rules: 9.44/3.96 9.44/3.96 new_primMulNat(Succ(vx3000), Succ(vx4100)) -> new_primMulNat(vx3000, Succ(vx4100)) 9.44/3.96 9.44/3.96 R is empty. 9.44/3.96 Q is empty. 9.44/3.96 We have to consider all minimal (P,Q,R)-chains. 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (8) QDPSizeChangeProof (EQUIVALENT) 9.44/3.96 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. 9.44/3.96 9.44/3.96 From the DPs we obtained the following set of size-change graphs: 9.44/3.96 *new_primMulNat(Succ(vx3000), Succ(vx4100)) -> new_primMulNat(vx3000, Succ(vx4100)) 9.44/3.96 The graph contains the following edges 1 > 1, 2 >= 2 9.44/3.96 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (9) 9.44/3.96 YES 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (10) 9.44/3.96 Obligation: 9.44/3.96 Q DP problem: 9.44/3.96 The TRS P consists of the following rules: 9.44/3.96 9.44/3.96 new_primPlusNat(Succ(vx500), Succ(vx41000)) -> new_primPlusNat(vx500, vx41000) 9.44/3.96 9.44/3.96 R is empty. 9.44/3.96 Q is empty. 9.44/3.96 We have to consider all minimal (P,Q,R)-chains. 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (11) QDPSizeChangeProof (EQUIVALENT) 9.44/3.96 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. 9.44/3.96 9.44/3.96 From the DPs we obtained the following set of size-change graphs: 9.44/3.96 *new_primPlusNat(Succ(vx500), Succ(vx41000)) -> new_primPlusNat(vx500, vx41000) 9.44/3.96 The graph contains the following edges 1 > 1, 2 > 2 9.44/3.96 9.44/3.96 9.44/3.96 ---------------------------------------- 9.44/3.96 9.44/3.96 (12) 9.44/3.96 YES 9.48/4.00 EOF