10.90/4.57 YES 13.61/5.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 13.61/5.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.61/5.31 13.61/5.31 13.61/5.31 H-Termination with start terms of the given HASKELL could be proven: 13.61/5.31 13.61/5.31 (0) HASKELL 13.61/5.31 (1) LR [EQUIVALENT, 0 ms] 13.61/5.31 (2) HASKELL 13.61/5.31 (3) CR [EQUIVALENT, 0 ms] 13.61/5.31 (4) HASKELL 13.61/5.31 (5) IFR [EQUIVALENT, 0 ms] 13.61/5.31 (6) HASKELL 13.61/5.31 (7) BR [EQUIVALENT, 0 ms] 13.61/5.31 (8) HASKELL 13.61/5.31 (9) COR [EQUIVALENT, 6 ms] 13.61/5.31 (10) HASKELL 13.61/5.31 (11) NumRed [SOUND, 0 ms] 13.61/5.31 (12) HASKELL 13.61/5.31 (13) Narrow [SOUND, 0 ms] 13.61/5.31 (14) AND 13.61/5.31 (15) QDP 13.61/5.31 (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.61/5.31 (17) YES 13.61/5.31 (18) QDP 13.61/5.31 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.61/5.31 (20) YES 13.61/5.31 (21) QDP 13.61/5.31 (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.61/5.31 (23) YES 13.61/5.31 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (0) 13.61/5.31 Obligation: 13.61/5.31 mainModule Main 13.61/5.31 module Maybe where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 module List where { 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 elemIndices :: Eq a => a -> [a] -> [Int]; 13.61/5.31 elemIndices x = findIndices (== x); 13.61/5.31 13.61/5.31 findIndices :: (a -> Bool) -> [a] -> [Int]; 13.61/5.31 findIndices p xs = concatMap (\vv1 ->case vv1 of { 13.61/5.31 (x,i)-> if p x then i : [] else []; 13.61/5.31 _-> []; 13.61/5.31 } ) (zip xs (enumFrom 0)); 13.61/5.31 13.61/5.31 } 13.61/5.31 module Main where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (1) LR (EQUIVALENT) 13.61/5.31 Lambda Reductions: 13.61/5.31 The following Lambda expression 13.61/5.31 "\ab->(a,b)" 13.61/5.31 is transformed to 13.61/5.31 "zip0 a b = (a,b); 13.61/5.31 " 13.61/5.31 The following Lambda expression 13.61/5.31 "\vv1->case vv1 of { 13.61/5.31 (x,i) -> if p x then i : [] else []; 13.61/5.31 _ -> []} 13.61/5.31 " 13.61/5.31 is transformed to 13.61/5.31 "findIndices0 p vv1 = case vv1 of { 13.61/5.31 (x,i) -> if p x then i : [] else []; 13.61/5.31 _ -> []} 13.61/5.31 ; 13.61/5.31 " 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (2) 13.61/5.31 Obligation: 13.61/5.31 mainModule Main 13.61/5.31 module Maybe where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 module List where { 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 elemIndices :: Eq a => a -> [a] -> [Int]; 13.61/5.31 elemIndices x = findIndices (== x); 13.61/5.31 13.61/5.31 findIndices :: (a -> Bool) -> [a] -> [Int]; 13.61/5.31 findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0)); 13.61/5.31 13.61/5.31 findIndices0 p vv1 = case vv1 of { 13.61/5.31 (x,i)-> if p x then i : [] else []; 13.61/5.31 _-> []; 13.61/5.31 } ; 13.61/5.31 13.61/5.31 } 13.61/5.31 module Main where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (3) CR (EQUIVALENT) 13.61/5.31 Case Reductions: 13.61/5.31 The following Case expression 13.61/5.31 "case vv1 of { 13.61/5.31 (x,i) -> if p x then i : [] else []; 13.61/5.31 _ -> []} 13.61/5.31 " 13.61/5.31 is transformed to 13.61/5.31 "findIndices00 p (x,i) = if p x then i : [] else []; 13.61/5.31 findIndices00 p _ = []; 13.61/5.31 " 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (4) 13.61/5.31 Obligation: 13.61/5.31 mainModule Main 13.61/5.31 module Maybe where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 module List where { 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 elemIndices :: Eq a => a -> [a] -> [Int]; 13.61/5.31 elemIndices x = findIndices (== x); 13.61/5.31 13.61/5.31 findIndices :: (a -> Bool) -> [a] -> [Int]; 13.61/5.31 findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0)); 13.61/5.31 13.61/5.31 findIndices0 p vv1 = findIndices00 p vv1; 13.61/5.31 13.61/5.31 findIndices00 p (x,i) = if p x then i : [] else []; 13.61/5.31 findIndices00 p _ = []; 13.61/5.31 13.61/5.31 } 13.61/5.31 module Main where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (5) IFR (EQUIVALENT) 13.61/5.31 If Reductions: 13.61/5.31 The following If expression 13.61/5.31 "if p x then i : [] else []" 13.61/5.31 is transformed to 13.61/5.31 "findIndices000 i True = i : []; 13.61/5.31 findIndices000 i False = []; 13.61/5.31 " 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (6) 13.61/5.31 Obligation: 13.61/5.31 mainModule Main 13.61/5.31 module Maybe where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 module List where { 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 elemIndices :: Eq a => a -> [a] -> [Int]; 13.61/5.31 elemIndices x = findIndices (== x); 13.61/5.31 13.61/5.31 findIndices :: (a -> Bool) -> [a] -> [Int]; 13.61/5.31 findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0)); 13.61/5.31 13.61/5.31 findIndices0 p vv1 = findIndices00 p vv1; 13.61/5.31 13.61/5.31 findIndices00 p (x,i) = findIndices000 i (p x); 13.61/5.31 findIndices00 p _ = []; 13.61/5.31 13.61/5.31 findIndices000 i True = i : []; 13.61/5.31 findIndices000 i False = []; 13.61/5.31 13.61/5.31 } 13.61/5.31 module Main where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (7) BR (EQUIVALENT) 13.61/5.31 Replaced joker patterns by fresh variables and removed binding patterns. 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (8) 13.61/5.31 Obligation: 13.61/5.31 mainModule Main 13.61/5.31 module Maybe where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 module List where { 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 elemIndices :: Eq a => a -> [a] -> [Int]; 13.61/5.31 elemIndices x = findIndices (== x); 13.61/5.31 13.61/5.31 findIndices :: (a -> Bool) -> [a] -> [Int]; 13.61/5.31 findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0)); 13.61/5.31 13.61/5.31 findIndices0 p vv1 = findIndices00 p vv1; 13.61/5.31 13.61/5.31 findIndices00 p (x,i) = findIndices000 i (p x); 13.61/5.31 findIndices00 p wv = []; 13.61/5.31 13.61/5.31 findIndices000 i True = i : []; 13.61/5.31 findIndices000 i False = []; 13.61/5.31 13.61/5.31 } 13.61/5.31 module Main where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (9) COR (EQUIVALENT) 13.61/5.31 Cond Reductions: 13.61/5.31 The following Function with conditions 13.61/5.31 "undefined |Falseundefined; 13.61/5.31 " 13.61/5.31 is transformed to 13.61/5.31 "undefined = undefined1; 13.61/5.31 " 13.61/5.31 "undefined0 True = undefined; 13.61/5.31 " 13.61/5.31 "undefined1 = undefined0 False; 13.61/5.31 " 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (10) 13.61/5.31 Obligation: 13.61/5.31 mainModule Main 13.61/5.31 module Maybe where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 module List where { 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 elemIndices :: Eq a => a -> [a] -> [Int]; 13.61/5.31 elemIndices x = findIndices (== x); 13.61/5.31 13.61/5.31 findIndices :: (a -> Bool) -> [a] -> [Int]; 13.61/5.31 findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0)); 13.61/5.31 13.61/5.31 findIndices0 p vv1 = findIndices00 p vv1; 13.61/5.31 13.61/5.31 findIndices00 p (x,i) = findIndices000 i (p x); 13.61/5.31 findIndices00 p wv = []; 13.61/5.31 13.61/5.31 findIndices000 i True = i : []; 13.61/5.31 findIndices000 i False = []; 13.61/5.31 13.61/5.31 } 13.61/5.31 module Main where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (11) NumRed (SOUND) 13.61/5.31 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (12) 13.61/5.31 Obligation: 13.61/5.31 mainModule Main 13.61/5.31 module Maybe where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 module List where { 13.61/5.31 import qualified Main; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 elemIndices :: Eq a => a -> [a] -> [Int]; 13.61/5.31 elemIndices x = findIndices (== x); 13.61/5.31 13.61/5.31 findIndices :: (a -> Bool) -> [a] -> [Int]; 13.61/5.31 findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom (Pos Zero))); 13.61/5.31 13.61/5.31 findIndices0 p vv1 = findIndices00 p vv1; 13.61/5.31 13.61/5.31 findIndices00 p (x,i) = findIndices000 i (p x); 13.61/5.31 findIndices00 p wv = []; 13.61/5.31 13.61/5.31 findIndices000 i True = i : []; 13.61/5.31 findIndices000 i False = []; 13.61/5.31 13.61/5.31 } 13.61/5.31 module Main where { 13.61/5.31 import qualified List; 13.61/5.31 import qualified Maybe; 13.61/5.31 import qualified Prelude; 13.61/5.31 } 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (13) Narrow (SOUND) 13.61/5.31 Haskell To QDPs 13.61/5.31 13.61/5.31 digraph dp_graph { 13.61/5.31 node [outthreshold=100, inthreshold=100];1[label="List.elemIndices",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 13.61/5.31 3[label="List.elemIndices ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 13.61/5.31 4[label="List.elemIndices ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 13.61/5.31 5[label="List.findIndices (ww3 ==) ww4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 13.61/5.31 6[label="concatMap (List.findIndices0 (ww3 ==)) (zip ww4 (enumFrom (Pos Zero)))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 13.61/5.31 7[label="concat . map (List.findIndices0 (ww3 ==))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 13.61/5.31 8[label="concat (map (List.findIndices0 (ww3 ==)) (zip ww4 (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 13.61/5.31 9[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zip ww4 (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 13.61/5.31 10[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww4 (enumFrom (Pos Zero))))",fontsize=16,color="burlywood",shape="box"];266[label="ww4/ww40 : ww41",fontsize=10,color="white",style="solid",shape="box"];10 -> 266[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 266 -> 11[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 267[label="ww4/[]",fontsize=10,color="white",style="solid",shape="box"];10 -> 267[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 267 -> 12[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 11[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 (ww40 : ww41) (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 13.61/5.31 12[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 [] (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13.61/5.31 13[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 (ww40 : ww41) (numericEnumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 13.61/5.31 14[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) [])",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 13.61/5.31 15[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 (ww40 : ww41) (Pos Zero : (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 13.61/5.31 16[label="foldr (++) [] []",fontsize=16,color="black",shape="triangle"];16 -> 18[label="",style="solid", color="black", weight=3]; 13.61/5.31 17[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zip0 ww40 (Pos Zero) : zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 13.61/5.31 18[label="[]",fontsize=16,color="green",shape="box"];19[label="foldr (++) [] (List.findIndices0 (ww3 ==) (zip0 ww40 (Pos Zero)) : map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3]; 13.61/5.31 20[label="(++) List.findIndices0 (ww3 ==) (zip0 ww40 (Pos Zero)) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3]; 13.61/5.31 21[label="(++) List.findIndices00 (ww3 ==) (zip0 ww40 (Pos Zero)) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3]; 13.61/5.31 22[label="(++) List.findIndices00 (ww3 ==) (ww40,Pos Zero) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3]; 13.61/5.31 23[label="(++) List.findIndices000 (Pos Zero) (ww3 == ww40) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3]; 13.61/5.31 24[label="(++) List.findIndices000 (Pos Zero) (primEqChar ww3 ww40) foldr (++) [] (map (List.findIndices0 (primEqChar ww3)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];268[label="ww3/Char ww30",fontsize=10,color="white",style="solid",shape="box"];24 -> 268[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 268 -> 25[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 25[label="(++) List.findIndices000 (Pos Zero) (primEqChar (Char ww30) ww40) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];269[label="ww40/Char ww400",fontsize=10,color="white",style="solid",shape="box"];25 -> 269[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 269 -> 26[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 26[label="(++) List.findIndices000 (Pos Zero) (primEqChar (Char ww30) (Char ww400)) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];26 -> 27[label="",style="solid", color="black", weight=3]; 13.61/5.31 27 -> 59[label="",style="dashed", color="red", weight=0]; 13.61/5.31 27[label="(++) List.findIndices000 (Pos Zero) (primEqNat ww30 ww400) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];27 -> 60[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 27 -> 61[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 27 -> 62[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 60[label="ww30",fontsize=16,color="green",shape="box"];61[label="ww400",fontsize=16,color="green",shape="box"];62[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];270[label="ww41/ww410 : ww411",fontsize=10,color="white",style="solid",shape="box"];62 -> 270[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 270 -> 67[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 271[label="ww41/[]",fontsize=10,color="white",style="solid",shape="box"];62 -> 271[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 271 -> 68[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 59[label="(++) List.findIndices000 (Pos Zero) (primEqNat ww3000 ww40000) ww5",fontsize=16,color="burlywood",shape="triangle"];272[label="ww3000/Succ ww30000",fontsize=10,color="white",style="solid",shape="box"];59 -> 272[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 272 -> 69[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 273[label="ww3000/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 273[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 273 -> 70[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 67[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww410 : ww411) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];67 -> 71[label="",style="solid", color="black", weight=3]; 13.61/5.31 68[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 [] (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];68 -> 72[label="",style="solid", color="black", weight=3]; 13.61/5.31 69[label="(++) List.findIndices000 (Pos Zero) (primEqNat (Succ ww30000) ww40000) ww5",fontsize=16,color="burlywood",shape="box"];274[label="ww40000/Succ ww400000",fontsize=10,color="white",style="solid",shape="box"];69 -> 274[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 274 -> 73[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 275[label="ww40000/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 275[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 275 -> 74[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 70[label="(++) List.findIndices000 (Pos Zero) (primEqNat Zero ww40000) ww5",fontsize=16,color="burlywood",shape="box"];276[label="ww40000/Succ ww400000",fontsize=10,color="white",style="solid",shape="box"];70 -> 276[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 276 -> 75[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 277[label="ww40000/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 277[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 277 -> 76[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 71[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww410 : ww411) (Pos Zero + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];71 -> 77[label="",style="solid", color="black", weight=3]; 13.61/5.31 72[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) [])",fontsize=16,color="black",shape="triangle"];72 -> 78[label="",style="solid", color="black", weight=3]; 13.61/5.31 73[label="(++) List.findIndices000 (Pos Zero) (primEqNat (Succ ww30000) (Succ ww400000)) ww5",fontsize=16,color="black",shape="box"];73 -> 79[label="",style="solid", color="black", weight=3]; 13.61/5.31 74[label="(++) List.findIndices000 (Pos Zero) (primEqNat (Succ ww30000) Zero) ww5",fontsize=16,color="black",shape="box"];74 -> 80[label="",style="solid", color="black", weight=3]; 13.61/5.31 75[label="(++) List.findIndices000 (Pos Zero) (primEqNat Zero (Succ ww400000)) ww5",fontsize=16,color="black",shape="box"];75 -> 81[label="",style="solid", color="black", weight=3]; 13.61/5.31 76[label="(++) List.findIndices000 (Pos Zero) (primEqNat Zero Zero) ww5",fontsize=16,color="black",shape="box"];76 -> 82[label="",style="solid", color="black", weight=3]; 13.61/5.31 77[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww410 : ww411) (enforceWHNF (WHNF (Pos Zero + fromInt (Pos (Succ Zero)))) (numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];77 -> 83[label="",style="solid", color="black", weight=3]; 13.61/5.31 78 -> 16[label="",style="dashed", color="red", weight=0]; 13.61/5.31 78[label="foldr (++) [] []",fontsize=16,color="magenta"];79 -> 59[label="",style="dashed", color="red", weight=0]; 13.61/5.31 79[label="(++) List.findIndices000 (Pos Zero) (primEqNat ww30000 ww400000) ww5",fontsize=16,color="magenta"];79 -> 84[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 79 -> 85[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 80[label="(++) List.findIndices000 (Pos Zero) False ww5",fontsize=16,color="black",shape="triangle"];80 -> 86[label="",style="solid", color="black", weight=3]; 13.61/5.31 81 -> 80[label="",style="dashed", color="red", weight=0]; 13.61/5.31 81[label="(++) List.findIndices000 (Pos Zero) False ww5",fontsize=16,color="magenta"];82[label="(++) List.findIndices000 (Pos Zero) True ww5",fontsize=16,color="black",shape="box"];82 -> 87[label="",style="solid", color="black", weight=3]; 13.61/5.31 83[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww410 : ww411) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero))))) (numericEnumFrom (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero))))))))",fontsize=16,color="black",shape="box"];83 -> 88[label="",style="solid", color="black", weight=3]; 13.61/5.31 84[label="ww30000",fontsize=16,color="green",shape="box"];85[label="ww400000",fontsize=16,color="green",shape="box"];86[label="(++) [] ww5",fontsize=16,color="black",shape="triangle"];86 -> 89[label="",style="solid", color="black", weight=3]; 13.61/5.31 87[label="(++) (Pos Zero : []) ww5",fontsize=16,color="black",shape="box"];87 -> 90[label="",style="solid", color="black", weight=3]; 13.61/5.31 88[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww410 : ww411) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (Pos (Succ Zero)))) (numericEnumFrom (primPlusInt (Pos Zero) (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];88 -> 91[label="",style="solid", color="black", weight=3]; 13.61/5.31 89[label="ww5",fontsize=16,color="green",shape="box"];90[label="Pos Zero : [] ++ ww5",fontsize=16,color="green",shape="box"];90 -> 92[label="",style="dashed", color="green", weight=3]; 13.61/5.31 91[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww410 : ww411) (enforceWHNF (WHNF (Pos (primPlusNat Zero (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero)))))))",fontsize=16,color="black",shape="box"];91 -> 93[label="",style="solid", color="black", weight=3]; 13.61/5.31 92 -> 86[label="",style="dashed", color="red", weight=0]; 13.61/5.31 92[label="[] ++ ww5",fontsize=16,color="magenta"];93 -> 172[label="",style="dashed", color="red", weight=0]; 13.61/5.31 93[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww410 : ww411) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero))))))",fontsize=16,color="magenta"];93 -> 173[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 93 -> 174[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 93 -> 175[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 173[label="ww410",fontsize=16,color="green",shape="box"];174[label="Zero",fontsize=16,color="green",shape="box"];175[label="ww411",fontsize=16,color="green",shape="box"];172[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww4110 : ww4111) (numericEnumFrom (Pos (primPlusNat ww7 (Succ Zero))))))",fontsize=16,color="black",shape="triangle"];172 -> 177[label="",style="solid", color="black", weight=3]; 13.61/5.31 177[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww4110 : ww4111) (Pos (primPlusNat ww7 (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];177 -> 178[label="",style="solid", color="black", weight=3]; 13.61/5.31 178[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero))) : zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];178 -> 179[label="",style="solid", color="black", weight=3]; 13.61/5.31 179[label="foldr (++) [] (List.findIndices0 (primEqChar (Char ww30)) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero)))) : map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];179 -> 180[label="",style="solid", color="black", weight=3]; 13.61/5.31 180[label="(++) List.findIndices0 (primEqChar (Char ww30)) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero)))) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];180 -> 181[label="",style="solid", color="black", weight=3]; 13.61/5.31 181[label="(++) List.findIndices00 (primEqChar (Char ww30)) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero)))) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];181 -> 182[label="",style="solid", color="black", weight=3]; 13.61/5.31 182[label="(++) List.findIndices00 (primEqChar (Char ww30)) (ww4110,Pos (primPlusNat ww7 (Succ Zero))) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];182 -> 183[label="",style="solid", color="black", weight=3]; 13.61/5.31 183[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqChar (Char ww30) ww4110) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];278[label="ww4110/Char ww41100",fontsize=10,color="white",style="solid",shape="box"];183 -> 278[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 278 -> 184[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 184[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqChar (Char ww30) (Char ww41100)) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];184 -> 185[label="",style="solid", color="black", weight=3]; 13.61/5.31 185 -> 218[label="",style="dashed", color="red", weight=0]; 13.61/5.31 185[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat ww30 ww41100) foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];185 -> 219[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 185 -> 220[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 185 -> 221[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 219[label="ww30",fontsize=16,color="green",shape="box"];220[label="ww41100",fontsize=16,color="green",shape="box"];221[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];279[label="ww4111/ww41110 : ww41111",fontsize=10,color="white",style="solid",shape="box"];221 -> 279[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 279 -> 226[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 280[label="ww4111/[]",fontsize=10,color="white",style="solid",shape="box"];221 -> 280[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 280 -> 227[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 218[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat ww3000 ww4110000) ww8",fontsize=16,color="burlywood",shape="triangle"];281[label="ww3000/Succ ww30000",fontsize=10,color="white",style="solid",shape="box"];218 -> 281[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 281 -> 228[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 282[label="ww3000/Zero",fontsize=10,color="white",style="solid",shape="box"];218 -> 282[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 282 -> 229[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 226[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww41110 : ww41111) (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];226 -> 230[label="",style="solid", color="black", weight=3]; 13.61/5.31 227[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 [] (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];227 -> 231[label="",style="solid", color="black", weight=3]; 13.61/5.31 228[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat (Succ ww30000) ww4110000) ww8",fontsize=16,color="burlywood",shape="box"];283[label="ww4110000/Succ ww41100000",fontsize=10,color="white",style="solid",shape="box"];228 -> 283[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 283 -> 232[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 284[label="ww4110000/Zero",fontsize=10,color="white",style="solid",shape="box"];228 -> 284[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 284 -> 233[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 229[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat Zero ww4110000) ww8",fontsize=16,color="burlywood",shape="box"];285[label="ww4110000/Succ ww41100000",fontsize=10,color="white",style="solid",shape="box"];229 -> 285[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 285 -> 234[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 286[label="ww4110000/Zero",fontsize=10,color="white",style="solid",shape="box"];229 -> 286[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 286 -> 235[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 230[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww41110 : ww41111) (Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];230 -> 236[label="",style="solid", color="black", weight=3]; 13.61/5.31 231 -> 72[label="",style="dashed", color="red", weight=0]; 13.61/5.31 231[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) [])",fontsize=16,color="magenta"];232[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat (Succ ww30000) (Succ ww41100000)) ww8",fontsize=16,color="black",shape="box"];232 -> 237[label="",style="solid", color="black", weight=3]; 13.61/5.31 233[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat (Succ ww30000) Zero) ww8",fontsize=16,color="black",shape="box"];233 -> 238[label="",style="solid", color="black", weight=3]; 13.61/5.31 234[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat Zero (Succ ww41100000)) ww8",fontsize=16,color="black",shape="box"];234 -> 239[label="",style="solid", color="black", weight=3]; 13.61/5.31 235[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat Zero Zero) ww8",fontsize=16,color="black",shape="box"];235 -> 240[label="",style="solid", color="black", weight=3]; 13.61/5.31 236[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww41110 : ww41111) (enforceWHNF (WHNF (Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];236 -> 241[label="",style="solid", color="black", weight=3]; 13.61/5.31 237 -> 218[label="",style="dashed", color="red", weight=0]; 13.61/5.31 237[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (primEqNat ww30000 ww41100000) ww8",fontsize=16,color="magenta"];237 -> 242[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 237 -> 243[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 238[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) False ww8",fontsize=16,color="black",shape="triangle"];238 -> 244[label="",style="solid", color="black", weight=3]; 13.61/5.31 239 -> 238[label="",style="dashed", color="red", weight=0]; 13.61/5.31 239[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) False ww8",fontsize=16,color="magenta"];240[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) True ww8",fontsize=16,color="black",shape="box"];240 -> 245[label="",style="solid", color="black", weight=3]; 13.61/5.31 241[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww41110 : ww41111) (enforceWHNF (WHNF (primPlusInt (Pos (primPlusNat ww7 (Succ Zero))) (fromInt (Pos (Succ Zero))))) (numericEnumFrom (primPlusInt (Pos (primPlusNat ww7 (Succ Zero))) (fromInt (Pos (Succ Zero))))))))",fontsize=16,color="black",shape="box"];241 -> 246[label="",style="solid", color="black", weight=3]; 13.61/5.31 242[label="ww30000",fontsize=16,color="green",shape="box"];243[label="ww41100000",fontsize=16,color="green",shape="box"];244 -> 86[label="",style="dashed", color="red", weight=0]; 13.61/5.31 244[label="(++) [] ww8",fontsize=16,color="magenta"];244 -> 247[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 245[label="(++) (Pos (primPlusNat ww7 (Succ Zero)) : []) ww8",fontsize=16,color="black",shape="box"];245 -> 248[label="",style="solid", color="black", weight=3]; 13.61/5.31 246[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww41110 : ww41111) (enforceWHNF (WHNF (primPlusInt (Pos (primPlusNat ww7 (Succ Zero))) (Pos (Succ Zero)))) (numericEnumFrom (primPlusInt (Pos (primPlusNat ww7 (Succ Zero))) (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];246 -> 249[label="",style="solid", color="black", weight=3]; 13.61/5.31 247[label="ww8",fontsize=16,color="green",shape="box"];248[label="Pos (primPlusNat ww7 (Succ Zero)) : [] ++ ww8",fontsize=16,color="green",shape="box"];248 -> 250[label="",style="dashed", color="green", weight=3]; 13.61/5.31 248 -> 251[label="",style="dashed", color="green", weight=3]; 13.61/5.31 249[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww41110 : ww41111) (enforceWHNF (WHNF (Pos (primPlusNat (primPlusNat ww7 (Succ Zero)) (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat (primPlusNat ww7 (Succ Zero)) (Succ Zero)))))))",fontsize=16,color="black",shape="box"];249 -> 252[label="",style="solid", color="black", weight=3]; 13.61/5.31 250[label="primPlusNat ww7 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];287[label="ww7/Succ ww70",fontsize=10,color="white",style="solid",shape="box"];250 -> 287[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 287 -> 253[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 288[label="ww7/Zero",fontsize=10,color="white",style="solid",shape="box"];250 -> 288[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 288 -> 254[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 251 -> 86[label="",style="dashed", color="red", weight=0]; 13.61/5.31 251[label="[] ++ ww8",fontsize=16,color="magenta"];251 -> 255[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 252 -> 172[label="",style="dashed", color="red", weight=0]; 13.61/5.31 252[label="foldr (++) [] (map (List.findIndices0 (primEqChar (Char ww30))) (zipWith zip0 (ww41110 : ww41111) (numericEnumFrom (Pos (primPlusNat (primPlusNat ww7 (Succ Zero)) (Succ Zero))))))",fontsize=16,color="magenta"];252 -> 256[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 252 -> 257[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 252 -> 258[label="",style="dashed", color="magenta", weight=3]; 13.61/5.31 253[label="primPlusNat (Succ ww70) (Succ Zero)",fontsize=16,color="black",shape="box"];253 -> 259[label="",style="solid", color="black", weight=3]; 13.61/5.31 254[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];254 -> 260[label="",style="solid", color="black", weight=3]; 13.61/5.31 255[label="ww8",fontsize=16,color="green",shape="box"];256[label="ww41110",fontsize=16,color="green",shape="box"];257 -> 250[label="",style="dashed", color="red", weight=0]; 13.61/5.31 257[label="primPlusNat ww7 (Succ Zero)",fontsize=16,color="magenta"];258[label="ww41111",fontsize=16,color="green",shape="box"];259[label="Succ (Succ (primPlusNat ww70 Zero))",fontsize=16,color="green",shape="box"];259 -> 261[label="",style="dashed", color="green", weight=3]; 13.61/5.31 260[label="Succ Zero",fontsize=16,color="green",shape="box"];261[label="primPlusNat ww70 Zero",fontsize=16,color="burlywood",shape="box"];289[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];261 -> 289[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 289 -> 262[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 290[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];261 -> 290[label="",style="solid", color="burlywood", weight=9]; 13.61/5.31 290 -> 263[label="",style="solid", color="burlywood", weight=3]; 13.61/5.31 262[label="primPlusNat (Succ ww700) Zero",fontsize=16,color="black",shape="box"];262 -> 264[label="",style="solid", color="black", weight=3]; 13.61/5.31 263[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];263 -> 265[label="",style="solid", color="black", weight=3]; 13.61/5.31 264[label="Succ ww700",fontsize=16,color="green",shape="box"];265[label="Zero",fontsize=16,color="green",shape="box"];} 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (14) 13.61/5.31 Complex Obligation (AND) 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (15) 13.61/5.31 Obligation: 13.61/5.31 Q DP problem: 13.61/5.31 The TRS P consists of the following rules: 13.61/5.31 13.61/5.31 new_psPs0(Succ(ww30000), Succ(ww400000), ww5) -> new_psPs0(ww30000, ww400000, ww5) 13.61/5.31 13.61/5.31 R is empty. 13.61/5.31 Q is empty. 13.61/5.31 We have to consider all minimal (P,Q,R)-chains. 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (16) QDPSizeChangeProof (EQUIVALENT) 13.61/5.31 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. 13.61/5.31 13.61/5.31 From the DPs we obtained the following set of size-change graphs: 13.61/5.31 *new_psPs0(Succ(ww30000), Succ(ww400000), ww5) -> new_psPs0(ww30000, ww400000, ww5) 13.61/5.31 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 13.61/5.31 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (17) 13.61/5.31 YES 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (18) 13.61/5.31 Obligation: 13.61/5.31 Q DP problem: 13.61/5.31 The TRS P consists of the following rules: 13.61/5.31 13.61/5.31 new_psPs(ww7, Succ(ww30000), Succ(ww41100000), ww8) -> new_psPs(ww7, ww30000, ww41100000, ww8) 13.61/5.31 13.61/5.31 R is empty. 13.61/5.31 Q is empty. 13.61/5.31 We have to consider all minimal (P,Q,R)-chains. 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (19) QDPSizeChangeProof (EQUIVALENT) 13.61/5.31 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. 13.61/5.31 13.61/5.31 From the DPs we obtained the following set of size-change graphs: 13.61/5.31 *new_psPs(ww7, Succ(ww30000), Succ(ww41100000), ww8) -> new_psPs(ww7, ww30000, ww41100000, ww8) 13.61/5.31 The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4 13.61/5.31 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (20) 13.61/5.31 YES 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (21) 13.61/5.31 Obligation: 13.61/5.31 Q DP problem: 13.61/5.31 The TRS P consists of the following rules: 13.61/5.31 13.61/5.31 new_foldr(ww30, Char(ww41100), :(ww41110, ww41111), ww7) -> new_foldr(ww30, ww41110, ww41111, new_primPlusNat(ww7)) 13.61/5.31 13.61/5.31 The TRS R consists of the following rules: 13.61/5.31 13.61/5.31 new_primPlusNat(Succ(ww70)) -> Succ(Succ(new_primPlusNat0(ww70))) 13.61/5.31 new_primPlusNat(Zero) -> Succ(Zero) 13.61/5.31 new_primPlusNat0(Succ(ww700)) -> Succ(ww700) 13.61/5.31 new_primPlusNat0(Zero) -> Zero 13.61/5.31 13.61/5.31 The set Q consists of the following terms: 13.61/5.31 13.61/5.31 new_primPlusNat(Succ(x0)) 13.61/5.31 new_primPlusNat0(Zero) 13.61/5.31 new_primPlusNat0(Succ(x0)) 13.61/5.31 new_primPlusNat(Zero) 13.61/5.31 13.61/5.31 We have to consider all minimal (P,Q,R)-chains. 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (22) QDPSizeChangeProof (EQUIVALENT) 13.61/5.31 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. 13.61/5.31 13.61/5.31 From the DPs we obtained the following set of size-change graphs: 13.61/5.31 *new_foldr(ww30, Char(ww41100), :(ww41110, ww41111), ww7) -> new_foldr(ww30, ww41110, ww41111, new_primPlusNat(ww7)) 13.61/5.31 The graph contains the following edges 1 >= 1, 3 > 2, 3 > 3 13.61/5.31 13.61/5.31 13.61/5.31 ---------------------------------------- 13.61/5.31 13.61/5.31 (23) 13.61/5.31 YES 13.80/7.65 EOF