/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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="primPlusInt vx3 vx4",fontsize=16,color="burlywood",shape="box"];47[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 6[label="",style="solid", color="burlywood", weight=3]; 48[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 7[label="",style="solid", color="burlywood", weight=3]; 6[label="primPlusInt (Pos vx30) vx4",fontsize=16,color="burlywood",shape="box"];49[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 8[label="",style="solid", color="burlywood", weight=3]; 50[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 50[label="",style="solid", color="burlywood", weight=9]; 50 -> 9[label="",style="solid", color="burlywood", weight=3]; 7[label="primPlusInt (Neg vx30) vx4",fontsize=16,color="burlywood",shape="box"];51[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 51[label="",style="solid", color="burlywood", weight=9]; 51 -> 10[label="",style="solid", color="burlywood", weight=3]; 52[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 52[label="",style="solid", color="burlywood", weight=9]; 52 -> 11[label="",style="solid", color="burlywood", weight=3]; 8[label="primPlusInt (Pos vx30) (Pos vx40)",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3]; 9[label="primPlusInt (Pos vx30) (Neg vx40)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 10[label="primPlusInt (Neg vx30) (Pos vx40)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 11[label="primPlusInt (Neg vx30) (Neg vx40)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 12[label="Pos (primPlusNat vx30 vx40)",fontsize=16,color="green",shape="box"];12 -> 16[label="",style="dashed", color="green", weight=3]; 13[label="primMinusNat vx30 vx40",fontsize=16,color="burlywood",shape="triangle"];53[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];13 -> 53[label="",style="solid", color="burlywood", weight=9]; 53 -> 17[label="",style="solid", color="burlywood", weight=3]; 54[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 54[label="",style="solid", color="burlywood", weight=9]; 54 -> 18[label="",style="solid", color="burlywood", weight=3]; 14 -> 13[label="",style="dashed", color="red", weight=0]; 14[label="primMinusNat vx40 vx30",fontsize=16,color="magenta"];14 -> 19[label="",style="dashed", color="magenta", weight=3]; 14 -> 20[label="",style="dashed", color="magenta", weight=3]; 15[label="Neg (primPlusNat vx30 vx40)",fontsize=16,color="green",shape="box"];15 -> 21[label="",style="dashed", color="green", weight=3]; 16[label="primPlusNat vx30 vx40",fontsize=16,color="burlywood",shape="triangle"];55[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 55[label="",style="solid", color="burlywood", weight=9]; 55 -> 22[label="",style="solid", color="burlywood", weight=3]; 56[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 56[label="",style="solid", color="burlywood", weight=9]; 56 -> 23[label="",style="solid", color="burlywood", weight=3]; 17[label="primMinusNat (Succ vx300) vx40",fontsize=16,color="burlywood",shape="box"];57[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];17 -> 57[label="",style="solid", color="burlywood", weight=9]; 57 -> 24[label="",style="solid", color="burlywood", weight=3]; 58[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 58[label="",style="solid", color="burlywood", weight=9]; 58 -> 25[label="",style="solid", color="burlywood", weight=3]; 18[label="primMinusNat Zero vx40",fontsize=16,color="burlywood",shape="box"];59[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];18 -> 59[label="",style="solid", color="burlywood", weight=9]; 59 -> 26[label="",style="solid", color="burlywood", weight=3]; 60[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 60[label="",style="solid", color="burlywood", weight=9]; 60 -> 27[label="",style="solid", color="burlywood", weight=3]; 19[label="vx40",fontsize=16,color="green",shape="box"];20[label="vx30",fontsize=16,color="green",shape="box"];21 -> 16[label="",style="dashed", color="red", weight=0]; 21[label="primPlusNat vx30 vx40",fontsize=16,color="magenta"];21 -> 28[label="",style="dashed", color="magenta", weight=3]; 21 -> 29[label="",style="dashed", color="magenta", weight=3]; 22[label="primPlusNat (Succ vx300) vx40",fontsize=16,color="burlywood",shape="box"];61[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];22 -> 61[label="",style="solid", color="burlywood", weight=9]; 61 -> 30[label="",style="solid", color="burlywood", weight=3]; 62[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 62[label="",style="solid", color="burlywood", weight=9]; 62 -> 31[label="",style="solid", color="burlywood", weight=3]; 23[label="primPlusNat Zero vx40",fontsize=16,color="burlywood",shape="box"];63[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];23 -> 63[label="",style="solid", color="burlywood", weight=9]; 63 -> 32[label="",style="solid", color="burlywood", weight=3]; 64[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 64[label="",style="solid", color="burlywood", weight=9]; 64 -> 33[label="",style="solid", color="burlywood", weight=3]; 24[label="primMinusNat (Succ vx300) (Succ vx400)",fontsize=16,color="black",shape="box"];24 -> 34[label="",style="solid", color="black", weight=3]; 25[label="primMinusNat (Succ vx300) Zero",fontsize=16,color="black",shape="box"];25 -> 35[label="",style="solid", color="black", weight=3]; 26[label="primMinusNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];26 -> 36[label="",style="solid", color="black", weight=3]; 27[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];27 -> 37[label="",style="solid", color="black", weight=3]; 28[label="vx30",fontsize=16,color="green",shape="box"];29[label="vx40",fontsize=16,color="green",shape="box"];30[label="primPlusNat (Succ vx300) (Succ vx400)",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3]; 31[label="primPlusNat (Succ vx300) Zero",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3]; 32[label="primPlusNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3]; 33[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3]; 34 -> 13[label="",style="dashed", color="red", weight=0]; 34[label="primMinusNat vx300 vx400",fontsize=16,color="magenta"];34 -> 42[label="",style="dashed", color="magenta", weight=3]; 34 -> 43[label="",style="dashed", color="magenta", weight=3]; 35[label="Pos (Succ vx300)",fontsize=16,color="green",shape="box"];36[label="Neg (Succ vx400)",fontsize=16,color="green",shape="box"];37[label="Pos Zero",fontsize=16,color="green",shape="box"];38[label="Succ (Succ (primPlusNat vx300 vx400))",fontsize=16,color="green",shape="box"];38 -> 44[label="",style="dashed", color="green", weight=3]; 39[label="Succ vx300",fontsize=16,color="green",shape="box"];40[label="Succ vx400",fontsize=16,color="green",shape="box"];41[label="Zero",fontsize=16,color="green",shape="box"];42[label="vx300",fontsize=16,color="green",shape="box"];43[label="vx400",fontsize=16,color="green",shape="box"];44 -> 16[label="",style="dashed", color="red", weight=0]; 44[label="primPlusNat vx300 vx400",fontsize=16,color="magenta"];44 -> 45[label="",style="dashed", color="magenta", weight=3]; 44 -> 46[label="",style="dashed", color="magenta", weight=3]; 45[label="vx300",fontsize=16,color="green",shape="box"];46[label="vx400",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNat(Succ(vx300), Succ(vx400)) -> new_primMinusNat(vx300, 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_primMinusNat(Succ(vx300), Succ(vx400)) -> new_primMinusNat(vx300, 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(vx300), Succ(vx400)) -> new_primPlusNat(vx300, vx400) 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(vx300), Succ(vx400)) -> new_primPlusNat(vx300, vx400) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (12) YES