7.92/3.57 YES 9.82/4.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.82/4.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.82/4.10 9.82/4.10 9.82/4.10 H-Termination with start terms of the given HASKELL could be proven: 9.82/4.10 9.82/4.10 (0) HASKELL 9.82/4.10 (1) BR [EQUIVALENT, 0 ms] 9.82/4.10 (2) HASKELL 9.82/4.10 (3) COR [EQUIVALENT, 0 ms] 9.82/4.10 (4) HASKELL 9.82/4.10 (5) NumRed [SOUND, 0 ms] 9.82/4.10 (6) HASKELL 9.82/4.10 (7) Narrow [EQUIVALENT, 11 ms] 9.82/4.10 (8) YES 9.82/4.10 9.82/4.10 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (0) 9.82/4.10 Obligation: 9.82/4.10 mainModule Main 9.82/4.10 module Main where { 9.82/4.10 import qualified Prelude; 9.82/4.10 } 9.82/4.10 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (1) BR (EQUIVALENT) 9.82/4.10 Replaced joker patterns by fresh variables and removed binding patterns. 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (2) 9.82/4.10 Obligation: 9.82/4.10 mainModule Main 9.82/4.10 module Main where { 9.82/4.10 import qualified Prelude; 9.82/4.10 } 9.82/4.10 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (3) COR (EQUIVALENT) 9.82/4.10 Cond Reductions: 9.82/4.10 The following Function with conditions 9.82/4.10 "undefined |Falseundefined; 9.82/4.10 " 9.82/4.10 is transformed to 9.82/4.10 "undefined = undefined1; 9.82/4.10 " 9.82/4.10 "undefined0 True = undefined; 9.82/4.10 " 9.82/4.10 "undefined1 = undefined0 False; 9.82/4.10 " 9.82/4.10 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (4) 9.82/4.10 Obligation: 9.82/4.10 mainModule Main 9.82/4.10 module Main where { 9.82/4.10 import qualified Prelude; 9.82/4.10 } 9.82/4.10 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (5) NumRed (SOUND) 9.82/4.10 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (6) 9.82/4.10 Obligation: 9.82/4.10 mainModule Main 9.82/4.10 module Main where { 9.82/4.10 import qualified Prelude; 9.82/4.10 } 9.82/4.10 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (7) Narrow (EQUIVALENT) 9.82/4.10 Haskell To QDPs 9.82/4.10 9.82/4.10 digraph dp_graph { 9.82/4.10 node [outthreshold=100, inthreshold=100];1[label="recip",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.82/4.10 3[label="recip vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.82/4.10 4[label="fromInt (Pos (Succ Zero)) / vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.82/4.10 5[label="primDivFloat (fromInt (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.82/4.10 6[label="primDivFloat (primIntToFloat (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 9.82/4.10 7[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="box"];27[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];7 -> 27[label="",style="solid", color="burlywood", weight=9]; 9.82/4.10 27 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.82/4.10 8[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float vx30 vx31)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9.82/4.10 9[label="Float (Pos (Succ Zero) * vx31) (Pos (Succ Zero) * vx30)",fontsize=16,color="green",shape="box"];9 -> 10[label="",style="dashed", color="green", weight=3]; 9.82/4.10 9 -> 11[label="",style="dashed", color="green", weight=3]; 9.82/4.10 10[label="Pos (Succ Zero) * vx31",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3]; 9.82/4.10 11 -> 10[label="",style="dashed", color="red", weight=0]; 9.82/4.10 11[label="Pos (Succ Zero) * vx30",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3]; 9.82/4.10 12[label="primMulInt (Pos (Succ Zero)) vx31",fontsize=16,color="burlywood",shape="box"];28[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];12 -> 28[label="",style="solid", color="burlywood", weight=9]; 9.82/4.10 28 -> 14[label="",style="solid", color="burlywood", weight=3]; 9.82/4.10 29[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];12 -> 29[label="",style="solid", color="burlywood", weight=9]; 9.82/4.10 29 -> 15[label="",style="solid", color="burlywood", weight=3]; 9.82/4.10 13[label="vx30",fontsize=16,color="green",shape="box"];14[label="primMulInt (Pos (Succ Zero)) (Pos vx310)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 9.82/4.10 15[label="primMulInt (Pos (Succ Zero)) (Neg vx310)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 9.82/4.10 16[label="Pos (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3]; 9.82/4.10 17[label="Neg (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];17 -> 19[label="",style="dashed", color="green", weight=3]; 9.82/4.10 18[label="primMulNat (Succ Zero) vx310",fontsize=16,color="burlywood",shape="triangle"];30[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];18 -> 30[label="",style="solid", color="burlywood", weight=9]; 9.82/4.10 30 -> 20[label="",style="solid", color="burlywood", weight=3]; 9.82/4.10 31[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 31[label="",style="solid", color="burlywood", weight=9]; 9.82/4.10 31 -> 21[label="",style="solid", color="burlywood", weight=3]; 9.82/4.10 19 -> 18[label="",style="dashed", color="red", weight=0]; 9.82/4.10 19[label="primMulNat (Succ Zero) vx310",fontsize=16,color="magenta"];19 -> 22[label="",style="dashed", color="magenta", weight=3]; 9.82/4.10 20[label="primMulNat (Succ Zero) (Succ vx3100)",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3]; 9.82/4.10 21[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3]; 9.82/4.10 22[label="vx310",fontsize=16,color="green",shape="box"];23[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 9.82/4.10 24[label="Zero",fontsize=16,color="green",shape="box"];25[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3]; 9.82/4.10 26[label="Succ vx3100",fontsize=16,color="green",shape="box"];} 9.82/4.10 9.82/4.10 ---------------------------------------- 9.82/4.10 9.82/4.10 (8) 9.82/4.10 YES 10.00/4.18 EOF