7.69/3.60 YES 9.65/4.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.65/4.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.65/4.08 9.65/4.08 9.65/4.08 H-Termination with start terms of the given HASKELL could be proven: 9.65/4.08 9.65/4.08 (0) HASKELL 9.65/4.08 (1) BR [EQUIVALENT, 0 ms] 9.65/4.08 (2) HASKELL 9.65/4.08 (3) COR [EQUIVALENT, 0 ms] 9.65/4.08 (4) HASKELL 9.65/4.08 (5) NumRed [SOUND, 4 ms] 9.65/4.08 (6) HASKELL 9.65/4.08 (7) Narrow [EQUIVALENT, 0 ms] 9.65/4.08 (8) YES 9.65/4.08 9.65/4.08 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (0) 9.65/4.08 Obligation: 9.65/4.08 mainModule Main 9.65/4.08 module Main where { 9.65/4.08 import qualified Prelude; 9.65/4.08 } 9.65/4.08 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (1) BR (EQUIVALENT) 9.65/4.08 Replaced joker patterns by fresh variables and removed binding patterns. 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (2) 9.65/4.08 Obligation: 9.65/4.08 mainModule Main 9.65/4.08 module Main where { 9.65/4.08 import qualified Prelude; 9.65/4.08 } 9.65/4.08 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (3) COR (EQUIVALENT) 9.65/4.08 Cond Reductions: 9.65/4.08 The following Function with conditions 9.65/4.08 "absReal x|x >= 0x|otherwise`negate` x; 9.65/4.08 " 9.65/4.08 is transformed to 9.65/4.08 "absReal x = absReal2 x; 9.65/4.08 " 9.65/4.08 "absReal0 x True = `negate` x; 9.65/4.08 " 9.65/4.08 "absReal1 x True = x; 9.65/4.08 absReal1 x False = absReal0 x otherwise; 9.65/4.08 " 9.65/4.08 "absReal2 x = absReal1 x (x >= 0); 9.65/4.08 " 9.65/4.08 The following Function with conditions 9.65/4.08 "undefined |Falseundefined; 9.65/4.08 " 9.65/4.08 is transformed to 9.65/4.08 "undefined = undefined1; 9.65/4.08 " 9.65/4.08 "undefined0 True = undefined; 9.65/4.08 " 9.65/4.08 "undefined1 = undefined0 False; 9.65/4.08 " 9.65/4.08 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (4) 9.65/4.08 Obligation: 9.65/4.08 mainModule Main 9.65/4.08 module Main where { 9.65/4.08 import qualified Prelude; 9.65/4.08 } 9.65/4.08 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (5) NumRed (SOUND) 9.65/4.08 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (6) 9.65/4.08 Obligation: 9.65/4.08 mainModule Main 9.65/4.08 module Main where { 9.65/4.08 import qualified Prelude; 9.65/4.08 } 9.65/4.08 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (7) Narrow (EQUIVALENT) 9.65/4.08 Haskell To QDPs 9.65/4.08 9.65/4.08 digraph dp_graph { 9.65/4.08 node [outthreshold=100, inthreshold=100];1[label="abs",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.65/4.08 3[label="abs vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.65/4.08 4[label="absReal vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.65/4.08 5[label="absReal2 vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.65/4.08 6[label="absReal1 vx3 (vx3 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 9.65/4.08 7[label="absReal1 vx3 (compare vx3 (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 9.65/4.08 8[label="absReal1 vx3 (not (compare vx3 (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9.65/4.08 9[label="absReal1 vx3 (not (primCmpInt vx3 (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];41[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];9 -> 41[label="",style="solid", color="burlywood", weight=9]; 9.65/4.08 41 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.65/4.08 42[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];9 -> 42[label="",style="solid", color="burlywood", weight=9]; 9.65/4.08 42 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.65/4.08 10[label="absReal1 (Pos vx30) (not (primCmpInt (Pos vx30) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];43[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 43[label="",style="solid", color="burlywood", weight=9]; 9.65/4.08 43 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.65/4.08 44[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 44[label="",style="solid", color="burlywood", weight=9]; 9.65/4.08 44 -> 13[label="",style="solid", color="burlywood", weight=3]; 9.65/4.08 11[label="absReal1 (Neg vx30) (not (primCmpInt (Neg vx30) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];45[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];11 -> 45[label="",style="solid", color="burlywood", weight=9]; 9.65/4.08 45 -> 14[label="",style="solid", color="burlywood", weight=3]; 9.65/4.08 46[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 46[label="",style="solid", color="burlywood", weight=9]; 9.65/4.08 46 -> 15[label="",style="solid", color="burlywood", weight=3]; 9.65/4.08 12[label="absReal1 (Pos (Succ vx300)) (not (primCmpInt (Pos (Succ vx300)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 9.65/4.08 13[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 9.65/4.08 14[label="absReal1 (Neg (Succ vx300)) (not (primCmpInt (Neg (Succ vx300)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 9.65/4.08 15[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 9.65/4.08 16[label="absReal1 (Pos (Succ vx300)) (not (primCmpInt (Pos (Succ vx300)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 9.65/4.08 17[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 9.65/4.08 18[label="absReal1 (Neg (Succ vx300)) (not (primCmpInt (Neg (Succ vx300)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 9.65/4.08 19[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 9.65/4.08 20[label="absReal1 (Pos (Succ vx300)) (not (primCmpNat (Succ vx300) Zero == LT))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 9.65/4.08 21[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 9.65/4.08 22[label="absReal1 (Neg (Succ vx300)) (not (LT == LT))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3]; 9.65/4.08 23[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 9.65/4.08 24[label="absReal1 (Pos (Succ vx300)) (not (GT == LT))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 9.65/4.08 25[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 9.65/4.08 26[label="absReal1 (Neg (Succ vx300)) (not True)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 9.65/4.08 27[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3]; 9.65/4.08 28[label="absReal1 (Pos (Succ vx300)) (not False)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3]; 9.65/4.08 29[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 9.65/4.08 30[label="absReal1 (Neg (Succ vx300)) False",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3]; 9.65/4.08 31[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3]; 9.65/4.08 32[label="absReal1 (Pos (Succ vx300)) True",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3]; 9.65/4.08 33[label="Pos Zero",fontsize=16,color="green",shape="box"];34[label="absReal0 (Neg (Succ vx300)) otherwise",fontsize=16,color="black",shape="box"];34 -> 37[label="",style="solid", color="black", weight=3]; 9.65/4.08 35[label="Neg Zero",fontsize=16,color="green",shape="box"];36[label="Pos (Succ vx300)",fontsize=16,color="green",shape="box"];37[label="absReal0 (Neg (Succ vx300)) True",fontsize=16,color="black",shape="box"];37 -> 38[label="",style="solid", color="black", weight=3]; 9.65/4.08 38[label="`negate` Neg (Succ vx300)",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3]; 9.65/4.08 39[label="primNegInt (Neg (Succ vx300))",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3]; 9.65/4.08 40[label="Pos (Succ vx300)",fontsize=16,color="green",shape="box"];} 9.65/4.08 9.65/4.08 ---------------------------------------- 9.65/4.08 9.65/4.08 (8) 9.65/4.08 YES 9.77/4.18 EOF