/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) NumRed [SOUND, 0 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; genericLength :: Num b => [a] -> b; genericLength [] = 0; genericLength (_ : l) = 1 + genericLength l; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; genericLength :: Num b => [a] -> b; genericLength [] = 0; genericLength (vy : l) = 1 + genericLength l; } module Main where { import qualified List; import qualified Maybe; 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 Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; genericLength :: Num b => [a] -> b; genericLength [] = 0; genericLength (vy : l) = 1 + genericLength l; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (6) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; genericLength :: Num b => [a] -> b; genericLength [] = fromInt (Pos Zero); genericLength (vy : l) = fromInt (Pos (Succ Zero)) + genericLength l; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.genericLength",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.genericLength vz3",fontsize=16,color="burlywood",shape="triangle"];36[label="vz3/vz30 : vz31",fontsize=10,color="white",style="solid",shape="box"];3 -> 36[label="",style="solid", color="burlywood", weight=9]; 36 -> 4[label="",style="solid", color="burlywood", weight=3]; 37[label="vz3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 37[label="",style="solid", color="burlywood", weight=9]; 37 -> 5[label="",style="solid", color="burlywood", weight=3]; 4[label="List.genericLength (vz30 : vz31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 5[label="List.genericLength []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6 -> 8[label="",style="dashed", color="red", weight=0]; 6[label="fromInt (Pos (Succ Zero)) + List.genericLength vz31",fontsize=16,color="magenta"];6 -> 9[label="",style="dashed", color="magenta", weight=3]; 7[label="fromInt (Pos Zero)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3]; 9 -> 3[label="",style="dashed", color="red", weight=0]; 9[label="List.genericLength vz31",fontsize=16,color="magenta"];9 -> 11[label="",style="dashed", color="magenta", weight=3]; 8[label="fromInt (Pos (Succ Zero)) + vz4",fontsize=16,color="black",shape="triangle"];8 -> 12[label="",style="solid", color="black", weight=3]; 10[label="Pos Zero",fontsize=16,color="green",shape="box"];11[label="vz31",fontsize=16,color="green",shape="box"];12[label="primPlusInt (fromInt (Pos (Succ Zero))) vz4",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 13[label="primPlusInt (Pos (Succ Zero)) vz4",fontsize=16,color="burlywood",shape="box"];38[label="vz4/Pos vz40",fontsize=10,color="white",style="solid",shape="box"];13 -> 38[label="",style="solid", color="burlywood", weight=9]; 38 -> 14[label="",style="solid", color="burlywood", weight=3]; 39[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];13 -> 39[label="",style="solid", color="burlywood", weight=9]; 39 -> 15[label="",style="solid", color="burlywood", weight=3]; 14[label="primPlusInt (Pos (Succ Zero)) (Pos vz40)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="primPlusInt (Pos (Succ Zero)) (Neg vz40)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="Pos (primPlusNat (Succ Zero) vz40)",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3]; 17[label="primMinusNat (Succ Zero) vz40",fontsize=16,color="burlywood",shape="box"];40[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];17 -> 40[label="",style="solid", color="burlywood", weight=9]; 40 -> 19[label="",style="solid", color="burlywood", weight=3]; 41[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 41[label="",style="solid", color="burlywood", weight=9]; 41 -> 20[label="",style="solid", color="burlywood", weight=3]; 18[label="primPlusNat (Succ Zero) vz40",fontsize=16,color="burlywood",shape="box"];42[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];18 -> 42[label="",style="solid", color="burlywood", weight=9]; 42 -> 21[label="",style="solid", color="burlywood", weight=3]; 43[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 43[label="",style="solid", color="burlywood", weight=9]; 43 -> 22[label="",style="solid", color="burlywood", weight=3]; 19[label="primMinusNat (Succ Zero) (Succ vz400)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="primPlusNat (Succ Zero) (Succ vz400)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3]; 23[label="primMinusNat Zero vz400",fontsize=16,color="burlywood",shape="box"];44[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];23 -> 44[label="",style="solid", color="burlywood", weight=9]; 44 -> 27[label="",style="solid", color="burlywood", weight=3]; 45[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 45[label="",style="solid", color="burlywood", weight=9]; 45 -> 28[label="",style="solid", color="burlywood", weight=3]; 24[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];25[label="Succ (Succ (primPlusNat Zero vz400))",fontsize=16,color="green",shape="box"];25 -> 29[label="",style="dashed", color="green", weight=3]; 26[label="Succ Zero",fontsize=16,color="green",shape="box"];27[label="primMinusNat Zero (Succ vz4000)",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3]; 28[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3]; 29[label="primPlusNat Zero vz400",fontsize=16,color="burlywood",shape="box"];46[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];29 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 32[label="",style="solid", color="burlywood", weight=3]; 47[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 33[label="",style="solid", color="burlywood", weight=3]; 30[label="Neg (Succ vz4000)",fontsize=16,color="green",shape="box"];31[label="Pos Zero",fontsize=16,color="green",shape="box"];32[label="primPlusNat Zero (Succ vz4000)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3]; 33[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3]; 34[label="Succ vz4000",fontsize=16,color="green",shape="box"];35[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: new_genericLength(:(vz30, vz31), ba) -> new_genericLength(vz31, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (9) 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_genericLength(:(vz30, vz31), ba) -> new_genericLength(vz31, ba) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (10) YES