/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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="logBase",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="logBase vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="logBase vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="log vx4 / log vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6 -> 16[label="",style="dashed", color="red", weight=0]; 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88 -> 36[label="",style="solid", color="burlywood", weight=3]; 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]; 89 -> 37[label="",style="solid", color="burlywood", weight=3]; 90[label="vx61/Neg vx610",fontsize=10,color="white",style="solid",shape="box"];34 -> 90[label="",style="solid", color="burlywood", weight=9]; 90 -> 38[label="",style="solid", color="burlywood", weight=3]; 35[label="primMulInt (Pos vx500) (Pos vx610)",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 36[label="primMulInt (Pos vx500) (Neg vx610)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 37[label="primMulInt (Neg vx500) (Pos vx610)",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3]; 38[label="primMulInt (Neg vx500) (Neg vx610)",fontsize=16,color="black",shape="box"];38 -> 42[label="",style="solid", color="black", weight=3]; 39[label="Pos (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];39 -> 43[label="",style="dashed", color="green", weight=3]; 40[label="Neg (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];40 -> 44[label="",style="dashed", color="green", weight=3]; 41[label="Neg (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];41 -> 45[label="",style="dashed", color="green", weight=3]; 42[label="Pos (primMulNat vx500 vx610)",fontsize=16,color="green",shape="box"];42 -> 46[label="",style="dashed", color="green", weight=3]; 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]; 91 -> 47[label="",style="solid", color="burlywood", weight=3]; 92[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 92[label="",style="solid", color="burlywood", weight=9]; 92 -> 48[label="",style="solid", color="burlywood", weight=3]; 44 -> 43[label="",style="dashed", color="red", weight=0]; 44[label="primMulNat vx500 vx610",fontsize=16,color="magenta"];44 -> 49[label="",style="dashed", color="magenta", weight=3]; 45 -> 43[label="",style="dashed", color="red", weight=0]; 45[label="primMulNat vx500 vx610",fontsize=16,color="magenta"];45 -> 50[label="",style="dashed", color="magenta", weight=3]; 46 -> 43[label="",style="dashed", color="red", weight=0]; 46[label="primMulNat vx500 vx610",fontsize=16,color="magenta"];46 -> 51[label="",style="dashed", color="magenta", weight=3]; 46 -> 52[label="",style="dashed", color="magenta", weight=3]; 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]; 93 -> 53[label="",style="solid", color="burlywood", weight=3]; 94[label="vx610/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 94[label="",style="solid", color="burlywood", weight=9]; 94 -> 54[label="",style="solid", color="burlywood", weight=3]; 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]; 95 -> 55[label="",style="solid", color="burlywood", weight=3]; 96[label="vx610/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 96[label="",style="solid", color="burlywood", weight=9]; 96 -> 56[label="",style="solid", color="burlywood", weight=3]; 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]; 54[label="primMulNat (Succ vx5000) Zero",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 55[label="primMulNat Zero (Succ vx6100)",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 56[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3]; 57 -> 61[label="",style="dashed", color="red", weight=0]; 57[label="primPlusNat (primMulNat vx5000 (Succ vx6100)) (Succ vx6100)",fontsize=16,color="magenta"];57 -> 62[label="",style="dashed", color="magenta", weight=3]; 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]; 62[label="primMulNat vx5000 (Succ vx6100)",fontsize=16,color="magenta"];62 -> 63[label="",style="dashed", color="magenta", weight=3]; 62 -> 64[label="",style="dashed", color="magenta", weight=3]; 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]; 97 -> 65[label="",style="solid", color="burlywood", weight=3]; 98[label="vx7/Zero",fontsize=10,color="white",style="solid",shape="box"];61 -> 98[label="",style="solid", color="burlywood", weight=9]; 98 -> 66[label="",style="solid", color="burlywood", weight=3]; 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]; 66[label="primPlusNat Zero (Succ vx6100)",fontsize=16,color="black",shape="box"];66 -> 68[label="",style="solid", color="black", weight=3]; 67[label="Succ (Succ (primPlusNat vx70 vx6100))",fontsize=16,color="green",shape="box"];67 -> 69[label="",style="dashed", color="green", weight=3]; 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]; 99 -> 70[label="",style="solid", color="burlywood", weight=3]; 100[label="vx70/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 100[label="",style="solid", color="burlywood", weight=9]; 100 -> 71[label="",style="solid", color="burlywood", weight=3]; 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]; 101 -> 72[label="",style="solid", color="burlywood", weight=3]; 102[label="vx6100/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 102[label="",style="solid", color="burlywood", weight=9]; 102 -> 73[label="",style="solid", color="burlywood", weight=3]; 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]; 103 -> 74[label="",style="solid", color="burlywood", weight=3]; 104[label="vx6100/Zero",fontsize=10,color="white",style="solid",shape="box"];71 -> 104[label="",style="solid", color="burlywood", weight=9]; 104 -> 75[label="",style="solid", color="burlywood", weight=3]; 72[label="primPlusNat (Succ vx700) (Succ vx61000)",fontsize=16,color="black",shape="box"];72 -> 76[label="",style="solid", color="black", weight=3]; 73[label="primPlusNat (Succ vx700) Zero",fontsize=16,color="black",shape="box"];73 -> 77[label="",style="solid", color="black", weight=3]; 74[label="primPlusNat Zero (Succ vx61000)",fontsize=16,color="black",shape="box"];74 -> 78[label="",style="solid", color="black", weight=3]; 75[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];75 -> 79[label="",style="solid", color="black", weight=3]; 76[label="Succ (Succ (primPlusNat vx700 vx61000))",fontsize=16,color="green",shape="box"];76 -> 80[label="",style="dashed", color="green", weight=3]; 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]; 80[label="primPlusNat vx700 vx61000",fontsize=16,color="magenta"];80 -> 81[label="",style="dashed", color="magenta", weight=3]; 80 -> 82[label="",style="dashed", color="magenta", weight=3]; 81[label="vx700",fontsize=16,color="green",shape="box"];82[label="vx61000",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(vx5000), Succ(vx6100)) -> new_primMulNat(vx5000, Succ(vx6100)) 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(vx5000), Succ(vx6100)) -> new_primMulNat(vx5000, Succ(vx6100)) 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(vx700), Succ(vx61000)) -> new_primPlusNat(vx700, vx61000) 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(vx700), Succ(vx61000)) -> new_primPlusNat(vx700, vx61000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (12) YES