9.47/4.39 YES 11.71/4.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 11.71/4.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.71/4.96 11.71/4.96 11.71/4.96 H-Termination with start terms of the given HASKELL could be proven: 11.71/4.96 11.71/4.96 (0) HASKELL 11.71/4.96 (1) BR [EQUIVALENT, 0 ms] 11.71/4.96 (2) HASKELL 11.71/4.96 (3) COR [EQUIVALENT, 0 ms] 11.71/4.96 (4) HASKELL 11.71/4.96 (5) NumRed [SOUND, 0 ms] 11.71/4.96 (6) HASKELL 11.71/4.96 (7) Narrow [EQUIVALENT, 4 ms] 11.71/4.96 (8) YES 11.71/4.96 11.71/4.96 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (0) 11.71/4.96 Obligation: 11.71/4.96 mainModule Main 11.71/4.96 module FiniteMap where { 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 11.71/4.96 11.71/4.96 instance (Eq a, Eq b) => Eq FiniteMap b a where { 11.71/4.96 } 11.71/4.96 isEmptyFM :: FiniteMap b a -> Bool; 11.71/4.96 isEmptyFM fm = sizeFM fm == 0; 11.71/4.96 11.71/4.96 sizeFM :: FiniteMap b a -> Int; 11.71/4.96 sizeFM EmptyFM = 0; 11.71/4.96 sizeFM (Branch _ _ size _ _) = size; 11.71/4.96 11.71/4.96 } 11.71/4.96 module Maybe where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 module Main where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (1) BR (EQUIVALENT) 11.71/4.96 Replaced joker patterns by fresh variables and removed binding patterns. 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (2) 11.71/4.96 Obligation: 11.71/4.96 mainModule Main 11.71/4.96 module FiniteMap where { 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 11.71/4.96 11.71/4.96 instance (Eq a, Eq b) => Eq FiniteMap b a where { 11.71/4.96 } 11.71/4.96 isEmptyFM :: FiniteMap b a -> Bool; 11.71/4.96 isEmptyFM fm = sizeFM fm == 0; 11.71/4.96 11.71/4.96 sizeFM :: FiniteMap a b -> Int; 11.71/4.96 sizeFM EmptyFM = 0; 11.71/4.96 sizeFM (Branch wu wv size ww wx) = size; 11.71/4.96 11.71/4.96 } 11.71/4.96 module Maybe where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 module Main where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (3) COR (EQUIVALENT) 11.71/4.96 Cond Reductions: 11.71/4.96 The following Function with conditions 11.71/4.96 "undefined |Falseundefined; 11.71/4.96 " 11.71/4.96 is transformed to 11.71/4.96 "undefined = undefined1; 11.71/4.96 " 11.71/4.96 "undefined0 True = undefined; 11.71/4.96 " 11.71/4.96 "undefined1 = undefined0 False; 11.71/4.96 " 11.71/4.96 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (4) 11.71/4.96 Obligation: 11.71/4.96 mainModule Main 11.71/4.96 module FiniteMap where { 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 11.71/4.96 11.71/4.96 instance (Eq a, Eq b) => Eq FiniteMap a b where { 11.71/4.96 } 11.71/4.96 isEmptyFM :: FiniteMap b a -> Bool; 11.71/4.96 isEmptyFM fm = sizeFM fm == 0; 11.71/4.96 11.71/4.96 sizeFM :: FiniteMap a b -> Int; 11.71/4.96 sizeFM EmptyFM = 0; 11.71/4.96 sizeFM (Branch wu wv size ww wx) = size; 11.71/4.96 11.71/4.96 } 11.71/4.96 module Maybe where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 module Main where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (5) NumRed (SOUND) 11.71/4.96 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (6) 11.71/4.96 Obligation: 11.71/4.96 mainModule Main 11.71/4.96 module FiniteMap where { 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 11.71/4.96 11.71/4.96 instance (Eq a, Eq b) => Eq FiniteMap a b where { 11.71/4.96 } 11.71/4.96 isEmptyFM :: FiniteMap a b -> Bool; 11.71/4.96 isEmptyFM fm = sizeFM fm == Pos Zero; 11.71/4.96 11.71/4.96 sizeFM :: FiniteMap a b -> Int; 11.71/4.96 sizeFM EmptyFM = Pos Zero; 11.71/4.96 sizeFM (Branch wu wv size ww wx) = size; 11.71/4.96 11.71/4.96 } 11.71/4.96 module Maybe where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Main; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 module Main where { 11.71/4.96 import qualified FiniteMap; 11.71/4.96 import qualified Maybe; 11.71/4.96 import qualified Prelude; 11.71/4.96 } 11.71/4.96 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (7) Narrow (EQUIVALENT) 11.71/4.96 Haskell To QDPs 11.71/4.96 11.71/4.96 digraph dp_graph { 11.71/4.96 node [outthreshold=100, inthreshold=100];1[label="FiniteMap.isEmptyFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 11.71/4.96 3[label="FiniteMap.isEmptyFM wy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 11.71/4.96 4[label="FiniteMap.sizeFM wy3 == Pos Zero",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 11.71/4.96 5[label="primEqInt (FiniteMap.sizeFM wy3) (Pos Zero)",fontsize=16,color="burlywood",shape="box"];21[label="wy3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 21[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 21 -> 6[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 22[label="wy3/FiniteMap.Branch wy30 wy31 wy32 wy33 wy34",fontsize=10,color="white",style="solid",shape="box"];5 -> 22[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 22 -> 7[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 6[label="primEqInt (FiniteMap.sizeFM FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 11.71/4.96 7[label="primEqInt (FiniteMap.sizeFM (FiniteMap.Branch wy30 wy31 wy32 wy33 wy34)) (Pos Zero)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 11.71/4.96 8[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 11.71/4.96 9[label="primEqInt wy32 (Pos Zero)",fontsize=16,color="burlywood",shape="box"];23[label="wy32/Pos wy320",fontsize=10,color="white",style="solid",shape="box"];9 -> 23[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 23 -> 11[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 24[label="wy32/Neg wy320",fontsize=10,color="white",style="solid",shape="box"];9 -> 24[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 24 -> 12[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 10[label="True",fontsize=16,color="green",shape="box"];11[label="primEqInt (Pos wy320) (Pos Zero)",fontsize=16,color="burlywood",shape="box"];25[label="wy320/Succ wy3200",fontsize=10,color="white",style="solid",shape="box"];11 -> 25[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 25 -> 13[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 26[label="wy320/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 26[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 26 -> 14[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 12[label="primEqInt (Neg wy320) (Pos Zero)",fontsize=16,color="burlywood",shape="box"];27[label="wy320/Succ wy3200",fontsize=10,color="white",style="solid",shape="box"];12 -> 27[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 27 -> 15[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 28[label="wy320/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 28[label="",style="solid", color="burlywood", weight=9]; 11.71/4.96 28 -> 16[label="",style="solid", color="burlywood", weight=3]; 11.71/4.96 13[label="primEqInt (Pos (Succ wy3200)) (Pos Zero)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 11.71/4.96 14[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 11.71/4.96 15[label="primEqInt (Neg (Succ wy3200)) (Pos Zero)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 11.71/4.96 16[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 11.71/4.96 17[label="False",fontsize=16,color="green",shape="box"];18[label="True",fontsize=16,color="green",shape="box"];19[label="False",fontsize=16,color="green",shape="box"];20[label="True",fontsize=16,color="green",shape="box"];} 11.71/4.96 11.71/4.96 ---------------------------------------- 11.71/4.96 11.71/4.96 (8) 11.71/4.96 YES 11.71/5.01 EOF