/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) AND (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) 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="(*)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="(*) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="(*) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="primMulInt vx3 vx4",fontsize=16,color="burlywood",shape="box"];56[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 56[label="",style="solid", color="burlywood", weight=9]; 56 -> 6[label="",style="solid", color="burlywood", weight=3]; 57[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 57[label="",style="solid", color="burlywood", weight=9]; 57 -> 7[label="",style="solid", color="burlywood", weight=3]; 6[label="primMulInt (Pos vx30) vx4",fontsize=16,color="burlywood",shape="box"];58[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 58[label="",style="solid", color="burlywood", weight=9]; 58 -> 8[label="",style="solid", color="burlywood", weight=3]; 59[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 59[label="",style="solid", color="burlywood", weight=9]; 59 -> 9[label="",style="solid", color="burlywood", weight=3]; 7[label="primMulInt (Neg vx30) vx4",fontsize=16,color="burlywood",shape="box"];60[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 60[label="",style="solid", color="burlywood", weight=9]; 60 -> 10[label="",style="solid", color="burlywood", weight=3]; 61[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 61[label="",style="solid", color="burlywood", weight=9]; 61 -> 11[label="",style="solid", color="burlywood", weight=3]; 8[label="primMulInt (Pos vx30) (Pos vx40)",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3]; 9[label="primMulInt (Pos vx30) (Neg vx40)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 10[label="primMulInt (Neg vx30) (Pos vx40)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 11[label="primMulInt (Neg vx30) (Neg vx40)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 12[label="Pos (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];12 -> 16[label="",style="dashed", color="green", weight=3]; 13[label="Neg (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];13 -> 17[label="",style="dashed", color="green", weight=3]; 14[label="Neg (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];14 -> 18[label="",style="dashed", color="green", weight=3]; 15[label="Pos (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];15 -> 19[label="",style="dashed", color="green", weight=3]; 16[label="primMulNat vx30 vx40",fontsize=16,color="burlywood",shape="triangle"];62[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 62[label="",style="solid", color="burlywood", weight=9]; 62 -> 20[label="",style="solid", color="burlywood", weight=3]; 63[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 63[label="",style="solid", color="burlywood", weight=9]; 63 -> 21[label="",style="solid", color="burlywood", weight=3]; 17 -> 16[label="",style="dashed", color="red", weight=0]; 17[label="primMulNat vx30 vx40",fontsize=16,color="magenta"];17 -> 22[label="",style="dashed", color="magenta", weight=3]; 18 -> 16[label="",style="dashed", color="red", weight=0]; 18[label="primMulNat vx30 vx40",fontsize=16,color="magenta"];18 -> 23[label="",style="dashed", color="magenta", weight=3]; 19 -> 16[label="",style="dashed", color="red", weight=0]; 19[label="primMulNat vx30 vx40",fontsize=16,color="magenta"];19 -> 24[label="",style="dashed", color="magenta", weight=3]; 19 -> 25[label="",style="dashed", color="magenta", weight=3]; 20[label="primMulNat (Succ vx300) vx40",fontsize=16,color="burlywood",shape="box"];64[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];20 -> 64[label="",style="solid", color="burlywood", weight=9]; 64 -> 26[label="",style="solid", color="burlywood", weight=3]; 65[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 65[label="",style="solid", color="burlywood", weight=9]; 65 -> 27[label="",style="solid", color="burlywood", weight=3]; 21[label="primMulNat Zero vx40",fontsize=16,color="burlywood",shape="box"];66[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];21 -> 66[label="",style="solid", color="burlywood", weight=9]; 66 -> 28[label="",style="solid", color="burlywood", weight=3]; 67[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 67[label="",style="solid", color="burlywood", weight=9]; 67 -> 29[label="",style="solid", color="burlywood", weight=3]; 22[label="vx40",fontsize=16,color="green",shape="box"];23[label="vx30",fontsize=16,color="green",shape="box"];24[label="vx30",fontsize=16,color="green",shape="box"];25[label="vx40",fontsize=16,color="green",shape="box"];26[label="primMulNat (Succ vx300) (Succ vx400)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 27[label="primMulNat (Succ vx300) Zero",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3]; 28[label="primMulNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3]; 29[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 30 -> 34[label="",style="dashed", color="red", weight=0]; 30[label="primPlusNat (primMulNat vx300 (Succ vx400)) (Succ vx400)",fontsize=16,color="magenta"];30 -> 35[label="",style="dashed", color="magenta", weight=3]; 31[label="Zero",fontsize=16,color="green",shape="box"];32[label="Zero",fontsize=16,color="green",shape="box"];33[label="Zero",fontsize=16,color="green",shape="box"];35 -> 16[label="",style="dashed", color="red", weight=0]; 35[label="primMulNat vx300 (Succ vx400)",fontsize=16,color="magenta"];35 -> 36[label="",style="dashed", color="magenta", weight=3]; 35 -> 37[label="",style="dashed", color="magenta", weight=3]; 34[label="primPlusNat vx5 (Succ vx400)",fontsize=16,color="burlywood",shape="triangle"];68[label="vx5/Succ vx50",fontsize=10,color="white",style="solid",shape="box"];34 -> 68[label="",style="solid", color="burlywood", weight=9]; 68 -> 38[label="",style="solid", color="burlywood", weight=3]; 69[label="vx5/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 69[label="",style="solid", color="burlywood", weight=9]; 69 -> 39[label="",style="solid", color="burlywood", weight=3]; 36[label="vx300",fontsize=16,color="green",shape="box"];37[label="Succ vx400",fontsize=16,color="green",shape="box"];38[label="primPlusNat (Succ vx50) (Succ vx400)",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3]; 39[label="primPlusNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];39 -> 41[label="",style="solid", color="black", weight=3]; 40[label="Succ (Succ (primPlusNat vx50 vx400))",fontsize=16,color="green",shape="box"];40 -> 42[label="",style="dashed", color="green", weight=3]; 41[label="Succ vx400",fontsize=16,color="green",shape="box"];42[label="primPlusNat vx50 vx400",fontsize=16,color="burlywood",shape="triangle"];70[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];42 -> 70[label="",style="solid", color="burlywood", weight=9]; 70 -> 43[label="",style="solid", color="burlywood", weight=3]; 71[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];42 -> 71[label="",style="solid", color="burlywood", weight=9]; 71 -> 44[label="",style="solid", color="burlywood", weight=3]; 43[label="primPlusNat (Succ vx500) vx400",fontsize=16,color="burlywood",shape="box"];72[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];43 -> 72[label="",style="solid", color="burlywood", weight=9]; 72 -> 45[label="",style="solid", color="burlywood", weight=3]; 73[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 73[label="",style="solid", color="burlywood", weight=9]; 73 -> 46[label="",style="solid", color="burlywood", weight=3]; 44[label="primPlusNat Zero vx400",fontsize=16,color="burlywood",shape="box"];74[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];44 -> 74[label="",style="solid", color="burlywood", weight=9]; 74 -> 47[label="",style="solid", color="burlywood", weight=3]; 75[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];44 -> 75[label="",style="solid", color="burlywood", weight=9]; 75 -> 48[label="",style="solid", color="burlywood", weight=3]; 45[label="primPlusNat (Succ vx500) (Succ vx4000)",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3]; 46[label="primPlusNat (Succ vx500) Zero",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3]; 47[label="primPlusNat Zero (Succ vx4000)",fontsize=16,color="black",shape="box"];47 -> 51[label="",style="solid", color="black", weight=3]; 48[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3]; 49[label="Succ (Succ (primPlusNat vx500 vx4000))",fontsize=16,color="green",shape="box"];49 -> 53[label="",style="dashed", color="green", weight=3]; 50[label="Succ vx500",fontsize=16,color="green",shape="box"];51[label="Succ vx4000",fontsize=16,color="green",shape="box"];52[label="Zero",fontsize=16,color="green",shape="box"];53 -> 42[label="",style="dashed", color="red", weight=0]; 53[label="primPlusNat vx500 vx4000",fontsize=16,color="magenta"];53 -> 54[label="",style="dashed", color="magenta", weight=3]; 53 -> 55[label="",style="dashed", color="magenta", weight=3]; 54[label="vx500",fontsize=16,color="green",shape="box"];55[label="vx4000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(vx300), Succ(vx400)) -> new_primMulNat(vx300, Succ(vx400)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (8) 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_primMulNat(Succ(vx300), Succ(vx400)) -> new_primMulNat(vx300, Succ(vx400)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (9) YES ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vx500), Succ(vx4000)) -> new_primPlusNat(vx500, vx4000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (11) 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_primPlusNat(Succ(vx500), Succ(vx4000)) -> new_primPlusNat(vx500, vx4000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (12) YES