10.85/4.63 YES 12.76/5.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 12.76/5.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.76/5.17 12.76/5.17 12.76/5.17 H-Termination with start terms of the given HASKELL could be proven: 12.76/5.17 12.76/5.17 (0) HASKELL 12.76/5.17 (1) BR [EQUIVALENT, 0 ms] 12.76/5.17 (2) HASKELL 12.76/5.17 (3) COR [EQUIVALENT, 0 ms] 12.76/5.17 (4) HASKELL 12.76/5.17 (5) Narrow [SOUND, 0 ms] 12.76/5.17 (6) QDP 12.76/5.17 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 12.76/5.17 (8) AND 12.76/5.17 (9) QDP 12.76/5.17 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/5.17 (11) YES 12.76/5.17 (12) QDP 12.76/5.17 (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.76/5.17 (14) YES 12.76/5.17 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (0) 12.76/5.17 Obligation: 12.76/5.17 mainModule Main 12.76/5.17 module FiniteMap where { 12.76/5.17 import qualified Main; 12.76/5.17 import qualified Maybe; 12.76/5.17 import qualified Prelude; 12.76/5.17 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 12.76/5.17 12.76/5.17 instance (Eq a, Eq b) => Eq FiniteMap a b where { 12.76/5.17 } 12.76/5.17 foldFM_GE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c; 12.76/5.17 foldFM_GE k z fr EmptyFM = z; 12.76/5.17 foldFM_GE k z fr (Branch key elt _ fm_l fm_r) | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l 12.76/5.17 | otherwise = foldFM_GE k z fr fm_r; 12.76/5.17 12.76/5.17 } 12.76/5.17 module Maybe where { 12.76/5.17 import qualified FiniteMap; 12.76/5.17 import qualified Main; 12.76/5.17 import qualified Prelude; 12.76/5.17 } 12.76/5.17 module Main where { 12.76/5.17 import qualified FiniteMap; 12.76/5.17 import qualified Maybe; 12.76/5.17 import qualified Prelude; 12.76/5.17 } 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (1) BR (EQUIVALENT) 12.76/5.17 Replaced joker patterns by fresh variables and removed binding patterns. 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (2) 12.76/5.17 Obligation: 12.76/5.17 mainModule Main 12.76/5.17 module FiniteMap where { 12.76/5.17 import qualified Main; 12.76/5.17 import qualified Maybe; 12.76/5.17 import qualified Prelude; 12.76/5.17 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 12.76/5.17 12.76/5.17 instance (Eq a, Eq b) => Eq FiniteMap b a where { 12.76/5.17 } 12.76/5.17 foldFM_GE :: Ord b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a; 12.76/5.17 foldFM_GE k z fr EmptyFM = z; 12.76/5.17 foldFM_GE k z fr (Branch key elt vy fm_l fm_r) | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l 12.76/5.17 | otherwise = foldFM_GE k z fr fm_r; 12.76/5.17 12.76/5.17 } 12.76/5.17 module Maybe where { 12.76/5.17 import qualified FiniteMap; 12.76/5.17 import qualified Main; 12.76/5.17 import qualified Prelude; 12.76/5.17 } 12.76/5.17 module Main where { 12.76/5.17 import qualified FiniteMap; 12.76/5.17 import qualified Maybe; 12.76/5.17 import qualified Prelude; 12.76/5.17 } 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (3) COR (EQUIVALENT) 12.76/5.17 Cond Reductions: 12.76/5.17 The following Function with conditions 12.76/5.17 "undefined |Falseundefined; 12.76/5.17 " 12.76/5.17 is transformed to 12.76/5.17 "undefined = undefined1; 12.76/5.17 " 12.76/5.17 "undefined0 True = undefined; 12.76/5.17 " 12.76/5.17 "undefined1 = undefined0 False; 12.76/5.17 " 12.76/5.17 The following Function with conditions 12.76/5.17 "foldFM_GE k z fr EmptyFM = z; 12.76/5.17 foldFM_GE k z fr (Branch key elt vy fm_l fm_r)|key >= frfoldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l|otherwisefoldFM_GE k z fr fm_r; 12.76/5.17 " 12.76/5.17 is transformed to 12.76/5.17 "foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM; 12.76/5.17 foldFM_GE k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r); 12.76/5.17 " 12.76/5.17 "foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r; 12.76/5.17 " 12.76/5.17 "foldFM_GE1 k z fr key elt vy fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l; 12.76/5.17 foldFM_GE1 k z fr key elt vy fm_l fm_r False = foldFM_GE0 k z fr key elt vy fm_l fm_r otherwise; 12.76/5.17 " 12.76/5.17 "foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE1 k z fr key elt vy fm_l fm_r (key >= fr); 12.76/5.17 " 12.76/5.17 "foldFM_GE3 k z fr EmptyFM = z; 12.76/5.17 foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy; 12.76/5.17 " 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (4) 12.76/5.17 Obligation: 12.76/5.17 mainModule Main 12.76/5.17 module FiniteMap where { 12.76/5.17 import qualified Main; 12.76/5.17 import qualified Maybe; 12.76/5.17 import qualified Prelude; 12.76/5.17 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 12.76/5.17 12.76/5.17 instance (Eq a, Eq b) => Eq FiniteMap a b where { 12.76/5.17 } 12.76/5.17 foldFM_GE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c; 12.76/5.17 foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM; 12.76/5.17 foldFM_GE k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r); 12.76/5.17 12.76/5.17 foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r; 12.76/5.17 12.76/5.17 foldFM_GE1 k z fr key elt vy fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l; 12.76/5.17 foldFM_GE1 k z fr key elt vy fm_l fm_r False = foldFM_GE0 k z fr key elt vy fm_l fm_r otherwise; 12.76/5.17 12.76/5.17 foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE1 k z fr key elt vy fm_l fm_r (key >= fr); 12.76/5.17 12.76/5.17 foldFM_GE3 k z fr EmptyFM = z; 12.76/5.17 foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy; 12.76/5.17 12.76/5.17 } 12.76/5.17 module Maybe where { 12.76/5.17 import qualified FiniteMap; 12.76/5.17 import qualified Main; 12.76/5.17 import qualified Prelude; 12.76/5.17 } 12.76/5.17 module Main where { 12.76/5.17 import qualified FiniteMap; 12.76/5.17 import qualified Maybe; 12.76/5.17 import qualified Prelude; 12.76/5.17 } 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (5) Narrow (SOUND) 12.76/5.17 Haskell To QDPs 12.76/5.17 12.76/5.17 digraph dp_graph { 12.76/5.17 node [outthreshold=100, inthreshold=100];1[label="FiniteMap.foldFM_GE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 12.76/5.17 3[label="FiniteMap.foldFM_GE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 12.76/5.17 4[label="FiniteMap.foldFM_GE wz3 wz4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 12.76/5.17 5[label="FiniteMap.foldFM_GE wz3 wz4 wz5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3]; 12.76/5.17 6[label="FiniteMap.foldFM_GE wz3 wz4 wz5 wz6",fontsize=16,color="burlywood",shape="triangle"];345[label="wz6/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6 -> 345[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 345 -> 7[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 346[label="wz6/FiniteMap.Branch wz60 wz61 wz62 wz63 wz64",fontsize=10,color="white",style="solid",shape="box"];6 -> 346[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 346 -> 8[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 7[label="FiniteMap.foldFM_GE wz3 wz4 wz5 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 12.76/5.17 8[label="FiniteMap.foldFM_GE wz3 wz4 wz5 (FiniteMap.Branch wz60 wz61 wz62 wz63 wz64)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 12.76/5.17 9[label="FiniteMap.foldFM_GE3 wz3 wz4 wz5 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 12.76/5.17 10[label="FiniteMap.foldFM_GE2 wz3 wz4 wz5 (FiniteMap.Branch wz60 wz61 wz62 wz63 wz64)",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 12.76/5.17 11[label="wz4",fontsize=16,color="green",shape="box"];12[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (wz60 >= wz5)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 12.76/5.17 13[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (compare wz60 wz5 /= LT)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 12.76/5.17 14[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (compare wz60 wz5 == LT))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 12.76/5.17 15[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (primCmpChar wz60 wz5 == LT))",fontsize=16,color="burlywood",shape="box"];347[label="wz60/Char wz600",fontsize=10,color="white",style="solid",shape="box"];15 -> 347[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 347 -> 16[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 16[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 (Char wz600) wz61 wz62 wz63 wz64 (not (primCmpChar (Char wz600) wz5 == LT))",fontsize=16,color="burlywood",shape="box"];348[label="wz5/Char wz50",fontsize=10,color="white",style="solid",shape="box"];16 -> 348[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 348 -> 17[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 17[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char wz50) (Char wz600) wz61 wz62 wz63 wz64 (not (primCmpChar (Char wz600) (Char wz50) == LT))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 12.76/5.17 18[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char wz50) (Char wz600) wz61 wz62 wz63 wz64 (not (primCmpNat wz600 wz50 == LT))",fontsize=16,color="burlywood",shape="box"];349[label="wz600/Succ wz6000",fontsize=10,color="white",style="solid",shape="box"];18 -> 349[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 349 -> 19[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 350[label="wz600/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 350[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 350 -> 20[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 19[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char wz50) (Char (Succ wz6000)) wz61 wz62 wz63 wz64 (not (primCmpNat (Succ wz6000) wz50 == LT))",fontsize=16,color="burlywood",shape="box"];351[label="wz50/Succ wz500",fontsize=10,color="white",style="solid",shape="box"];19 -> 351[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 351 -> 21[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 352[label="wz50/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 352[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 352 -> 22[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 20[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char wz50) (Char Zero) wz61 wz62 wz63 wz64 (not (primCmpNat Zero wz50 == LT))",fontsize=16,color="burlywood",shape="box"];353[label="wz50/Succ wz500",fontsize=10,color="white",style="solid",shape="box"];20 -> 353[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 353 -> 23[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 354[label="wz50/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 354[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 354 -> 24[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 21[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char (Succ wz500)) 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25[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char (Succ wz500)) (Char (Succ wz6000)) wz61 wz62 wz63 wz64 (not (primCmpNat wz6000 wz500 == LT))",fontsize=16,color="magenta"];25 -> 239[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 240[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 241[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 242[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 243[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 244[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 245[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 246[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 247[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 25 -> 248[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 26[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char Zero) (Char (Succ wz6000)) wz61 wz62 wz63 wz64 (not (GT == LT))",fontsize=16,color="black",shape="box"];26 -> 31[label="",style="solid", color="black", weight=3]; 12.76/5.17 27[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char (Succ wz500)) (Char Zero) wz61 wz62 wz63 wz64 (not (LT == LT))",fontsize=16,color="black",shape="box"];27 -> 32[label="",style="solid", color="black", weight=3]; 12.76/5.17 28[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char Zero) (Char Zero) wz61 wz62 wz63 wz64 (not (EQ == LT))",fontsize=16,color="black",shape="box"];28 -> 33[label="",style="solid", color="black", weight=3]; 12.76/5.17 239[label="wz500",fontsize=16,color="green",shape="box"];240[label="wz3",fontsize=16,color="green",shape="box"];241[label="wz4",fontsize=16,color="green",shape="box"];242[label="wz500",fontsize=16,color="green",shape="box"];243[label="wz62",fontsize=16,color="green",shape="box"];244[label="wz6000",fontsize=16,color="green",shape="box"];245[label="wz61",fontsize=16,color="green",shape="box"];246[label="wz63",fontsize=16,color="green",shape="box"];247[label="wz64",fontsize=16,color="green",shape="box"];248[label="wz6000",fontsize=16,color="green",shape="box"];238[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat wz42 wz43 == LT))",fontsize=16,color="burlywood",shape="triangle"];355[label="wz42/Succ wz420",fontsize=10,color="white",style="solid",shape="box"];238 -> 355[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 355 -> 309[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 356[label="wz42/Zero",fontsize=10,color="white",style="solid",shape="box"];238 -> 356[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 356 -> 310[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 31[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char Zero) (Char (Succ wz6000)) wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];31 -> 38[label="",style="solid", color="black", weight=3]; 12.76/5.17 32[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char (Succ wz500)) (Char Zero) wz61 wz62 wz63 wz64 (not True)",fontsize=16,color="black",shape="box"];32 -> 39[label="",style="solid", color="black", weight=3]; 12.76/5.17 33[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char Zero) (Char Zero) wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];33 -> 40[label="",style="solid", color="black", weight=3]; 12.76/5.17 309[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat (Succ wz420) wz43 == LT))",fontsize=16,color="burlywood",shape="box"];357[label="wz43/Succ wz430",fontsize=10,color="white",style="solid",shape="box"];309 -> 357[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 357 -> 311[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 358[label="wz43/Zero",fontsize=10,color="white",style="solid",shape="box"];309 -> 358[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 358 -> 312[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 310[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat Zero wz43 == LT))",fontsize=16,color="burlywood",shape="box"];359[label="wz43/Succ wz430",fontsize=10,color="white",style="solid",shape="box"];310 -> 359[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 359 -> 313[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 360[label="wz43/Zero",fontsize=10,color="white",style="solid",shape="box"];310 -> 360[label="",style="solid", color="burlywood", weight=9]; 12.76/5.17 360 -> 314[label="",style="solid", color="burlywood", weight=3]; 12.76/5.17 38[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char Zero) (Char (Succ wz6000)) wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3]; 12.76/5.17 39[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char (Succ wz500)) (Char Zero) wz61 wz62 wz63 wz64 False",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3]; 12.76/5.17 40[label="FiniteMap.foldFM_GE1 wz3 wz4 (Char Zero) (Char Zero) wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3]; 12.76/5.17 311[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat (Succ wz420) (Succ wz430) == LT))",fontsize=16,color="black",shape="box"];311 -> 315[label="",style="solid", color="black", weight=3]; 12.76/5.17 312[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat (Succ wz420) Zero == LT))",fontsize=16,color="black",shape="box"];312 -> 316[label="",style="solid", color="black", weight=3]; 12.76/5.17 313[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat Zero (Succ wz430) == LT))",fontsize=16,color="black",shape="box"];313 -> 317[label="",style="solid", color="black", weight=3]; 12.76/5.17 314[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat Zero Zero == LT))",fontsize=16,color="black",shape="box"];314 -> 318[label="",style="solid", color="black", weight=3]; 12.76/5.17 45 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 45[label="FiniteMap.foldFM_GE wz3 (wz3 (Char (Succ wz6000)) wz61 (FiniteMap.foldFM_GE wz3 wz4 (Char Zero) wz64)) (Char Zero) wz63",fontsize=16,color="magenta"];45 -> 53[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 45 -> 54[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 45 -> 55[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 46[label="FiniteMap.foldFM_GE0 wz3 wz4 (Char (Succ wz500)) (Char Zero) wz61 wz62 wz63 wz64 otherwise",fontsize=16,color="black",shape="box"];46 -> 56[label="",style="solid", color="black", weight=3]; 12.76/5.17 47 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 47[label="FiniteMap.foldFM_GE wz3 (wz3 (Char Zero) wz61 (FiniteMap.foldFM_GE wz3 wz4 (Char Zero) wz64)) (Char Zero) wz63",fontsize=16,color="magenta"];47 -> 57[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 47 -> 58[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 47 -> 59[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 315 -> 238[label="",style="dashed", color="red", weight=0]; 12.76/5.17 315[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (primCmpNat wz420 wz430 == LT))",fontsize=16,color="magenta"];315 -> 319[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 315 -> 320[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 316[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (GT == LT))",fontsize=16,color="black",shape="box"];316 -> 321[label="",style="solid", color="black", weight=3]; 12.76/5.17 317[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (LT == LT))",fontsize=16,color="black",shape="box"];317 -> 322[label="",style="solid", color="black", weight=3]; 12.76/5.17 318[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not (EQ == LT))",fontsize=16,color="black",shape="box"];318 -> 323[label="",style="solid", color="black", weight=3]; 12.76/5.17 53[label="wz3 (Char (Succ wz6000)) wz61 (FiniteMap.foldFM_GE wz3 wz4 (Char Zero) wz64)",fontsize=16,color="green",shape="box"];53 -> 67[label="",style="dashed", color="green", weight=3]; 12.76/5.17 53 -> 68[label="",style="dashed", color="green", weight=3]; 12.76/5.17 53 -> 69[label="",style="dashed", color="green", weight=3]; 12.76/5.17 54[label="wz63",fontsize=16,color="green",shape="box"];55[label="Char Zero",fontsize=16,color="green",shape="box"];56[label="FiniteMap.foldFM_GE0 wz3 wz4 (Char (Succ wz500)) (Char Zero) wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];56 -> 70[label="",style="solid", color="black", weight=3]; 12.76/5.17 57[label="wz3 (Char Zero) wz61 (FiniteMap.foldFM_GE wz3 wz4 (Char Zero) wz64)",fontsize=16,color="green",shape="box"];57 -> 71[label="",style="dashed", color="green", weight=3]; 12.76/5.17 57 -> 72[label="",style="dashed", color="green", weight=3]; 12.76/5.17 57 -> 73[label="",style="dashed", color="green", weight=3]; 12.76/5.17 58[label="wz63",fontsize=16,color="green",shape="box"];59[label="Char Zero",fontsize=16,color="green",shape="box"];319[label="wz430",fontsize=16,color="green",shape="box"];320[label="wz420",fontsize=16,color="green",shape="box"];321[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not False)",fontsize=16,color="black",shape="triangle"];321 -> 324[label="",style="solid", color="black", weight=3]; 12.76/5.17 322[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not True)",fontsize=16,color="black",shape="box"];322 -> 325[label="",style="solid", color="black", weight=3]; 12.76/5.17 323 -> 321[label="",style="dashed", color="red", weight=0]; 12.76/5.17 323[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 (not False)",fontsize=16,color="magenta"];67[label="Char (Succ wz6000)",fontsize=16,color="green",shape="box"];68[label="wz61",fontsize=16,color="green",shape="box"];69 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 69[label="FiniteMap.foldFM_GE wz3 wz4 (Char Zero) wz64",fontsize=16,color="magenta"];69 -> 81[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 69 -> 82[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 70 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 70[label="FiniteMap.foldFM_GE wz3 wz4 (Char (Succ wz500)) wz64",fontsize=16,color="magenta"];70 -> 83[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 70 -> 84[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 71[label="Char Zero",fontsize=16,color="green",shape="box"];72[label="wz61",fontsize=16,color="green",shape="box"];73 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 73[label="FiniteMap.foldFM_GE wz3 wz4 (Char Zero) wz64",fontsize=16,color="magenta"];73 -> 85[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 73 -> 86[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 324[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 True",fontsize=16,color="black",shape="box"];324 -> 326[label="",style="solid", color="black", weight=3]; 12.76/5.17 325[label="FiniteMap.foldFM_GE1 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 False",fontsize=16,color="black",shape="box"];325 -> 327[label="",style="solid", color="black", weight=3]; 12.76/5.17 81[label="wz64",fontsize=16,color="green",shape="box"];82[label="Char Zero",fontsize=16,color="green",shape="box"];83[label="wz64",fontsize=16,color="green",shape="box"];84[label="Char (Succ wz500)",fontsize=16,color="green",shape="box"];85[label="wz64",fontsize=16,color="green",shape="box"];86[label="Char Zero",fontsize=16,color="green",shape="box"];326 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 326[label="FiniteMap.foldFM_GE wz34 (wz34 (Char (Succ wz37)) wz38 (FiniteMap.foldFM_GE wz34 wz35 (Char (Succ wz36)) wz41)) (Char (Succ wz36)) wz40",fontsize=16,color="magenta"];326 -> 328[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 326 -> 329[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 326 -> 330[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 326 -> 331[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 327[label="FiniteMap.foldFM_GE0 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 otherwise",fontsize=16,color="black",shape="box"];327 -> 332[label="",style="solid", color="black", weight=3]; 12.76/5.17 328[label="wz34 (Char (Succ wz37)) wz38 (FiniteMap.foldFM_GE wz34 wz35 (Char (Succ wz36)) wz41)",fontsize=16,color="green",shape="box"];328 -> 333[label="",style="dashed", color="green", weight=3]; 12.76/5.17 328 -> 334[label="",style="dashed", color="green", weight=3]; 12.76/5.17 328 -> 335[label="",style="dashed", color="green", weight=3]; 12.76/5.17 329[label="wz40",fontsize=16,color="green",shape="box"];330[label="Char (Succ wz36)",fontsize=16,color="green",shape="box"];331[label="wz34",fontsize=16,color="green",shape="box"];332[label="FiniteMap.foldFM_GE0 wz34 wz35 (Char (Succ wz36)) (Char (Succ wz37)) wz38 wz39 wz40 wz41 True",fontsize=16,color="black",shape="box"];332 -> 336[label="",style="solid", color="black", weight=3]; 12.76/5.17 333[label="Char (Succ wz37)",fontsize=16,color="green",shape="box"];334[label="wz38",fontsize=16,color="green",shape="box"];335 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 335[label="FiniteMap.foldFM_GE wz34 wz35 (Char (Succ wz36)) wz41",fontsize=16,color="magenta"];335 -> 337[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 335 -> 338[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 335 -> 339[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 335 -> 340[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 336 -> 6[label="",style="dashed", color="red", weight=0]; 12.76/5.17 336[label="FiniteMap.foldFM_GE wz34 wz35 (Char (Succ wz36)) wz41",fontsize=16,color="magenta"];336 -> 341[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 336 -> 342[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 336 -> 343[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 336 -> 344[label="",style="dashed", color="magenta", weight=3]; 12.76/5.17 337[label="wz35",fontsize=16,color="green",shape="box"];338[label="wz41",fontsize=16,color="green",shape="box"];339[label="Char (Succ wz36)",fontsize=16,color="green",shape="box"];340[label="wz34",fontsize=16,color="green",shape="box"];341[label="wz35",fontsize=16,color="green",shape="box"];342[label="wz41",fontsize=16,color="green",shape="box"];343[label="Char (Succ wz36)",fontsize=16,color="green",shape="box"];344[label="wz34",fontsize=16,color="green",shape="box"];} 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (6) 12.76/5.17 Obligation: 12.76/5.17 Q DP problem: 12.76/5.17 The TRS P consists of the following rules: 12.76/5.17 12.76/5.17 new_foldFM_GE(wz3, Char(Succ(wz500)), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE1(wz3, wz500, wz6000, wz61, wz62, wz63, wz64, wz6000, wz500, bb, bc) 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz63, bb, bc) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Zero, Zero, h, ba) -> new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) 12.76/5.17 new_foldFM_GE(wz3, Char(Succ(wz500)), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Succ(wz500)), wz64, bb, bc) 12.76/5.17 new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz40, h, ba) 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz63, bb, bc) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Zero, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Zero, Succ(wz430), h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz64, bb, bc) 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz64, bb, bc) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Succ(wz430), h, ba) -> new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, wz420, wz430, h, ba) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Zero, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz40, h, ba) 12.76/5.17 12.76/5.17 R is empty. 12.76/5.17 Q is empty. 12.76/5.17 We have to consider all minimal (P,Q,R)-chains. 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (7) DependencyGraphProof (EQUIVALENT) 12.76/5.17 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (8) 12.76/5.17 Complex Obligation (AND) 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (9) 12.76/5.17 Obligation: 12.76/5.17 Q DP problem: 12.76/5.17 The TRS P consists of the following rules: 12.76/5.17 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz63, bb, bc) 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz63, bb, bc) 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz64, bb, bc) 12.76/5.17 new_foldFM_GE(wz3, Char(Zero), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz64, bb, bc) 12.76/5.17 12.76/5.17 R is empty. 12.76/5.17 Q is empty. 12.76/5.17 We have to consider all minimal (P,Q,R)-chains. 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (10) QDPSizeChangeProof (EQUIVALENT) 12.76/5.17 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. 12.76/5.17 12.76/5.17 From the DPs we obtained the following set of size-change graphs: 12.76/5.17 *new_foldFM_GE(wz3, Char(Zero), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz63, bb, bc) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE(wz3, Char(Zero), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz63, bb, bc) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE(wz3, Char(Zero), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz64, bb, bc) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE(wz3, Char(Zero), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Zero), wz64, bb, bc) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (11) 12.76/5.17 YES 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (12) 12.76/5.17 Obligation: 12.76/5.17 Q DP problem: 12.76/5.17 The TRS P consists of the following rules: 12.76/5.17 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Zero, Zero, h, ba) -> new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) 12.76/5.17 new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz40, h, ba) 12.76/5.17 new_foldFM_GE(wz3, Char(Succ(wz500)), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE1(wz3, wz500, wz6000, wz61, wz62, wz63, wz64, wz6000, wz500, bb, bc) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Zero, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 new_foldFM_GE(wz3, Char(Succ(wz500)), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Succ(wz500)), wz64, bb, bc) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Zero, Succ(wz430), h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Succ(wz430), h, ba) -> new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, wz420, wz430, h, ba) 12.76/5.17 new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Zero, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz40, h, ba) 12.76/5.17 new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 12.76/5.17 R is empty. 12.76/5.17 Q is empty. 12.76/5.17 We have to consider all minimal (P,Q,R)-chains. 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (13) QDPSizeChangeProof (EQUIVALENT) 12.76/5.17 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. 12.76/5.17 12.76/5.17 From the DPs we obtained the following set of size-change graphs: 12.76/5.17 *new_foldFM_GE(wz3, Char(Succ(wz500)), Branch(Char(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE1(wz3, wz500, wz6000, wz61, wz62, wz63, wz64, wz6000, wz500, bb, bc) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 3 > 8, 2 > 9, 4 >= 10, 5 >= 11 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Succ(wz430), h, ba) -> new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, wz420, wz430, h, ba) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10, 11 >= 11 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE(wz3, Char(Succ(wz500)), Branch(Char(Zero), wz61, wz62, wz63, wz64), bb, bc) -> new_foldFM_GE(wz3, Char(Succ(wz500)), wz64, bb, bc) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Zero, Zero, h, ba) -> new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) 12.76/5.17 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 8, 11 >= 9 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz40, h, ba) 12.76/5.17 The graph contains the following edges 1 >= 1, 6 >= 3, 8 >= 4, 9 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE10(wz34, wz36, wz37, wz38, wz39, wz40, wz41, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 The graph contains the following edges 1 >= 1, 7 >= 3, 8 >= 4, 9 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Zero, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 The graph contains the following edges 1 >= 1, 7 >= 3, 10 >= 4, 11 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Zero, Succ(wz430), h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz41, h, ba) 12.76/5.17 The graph contains the following edges 1 >= 1, 7 >= 3, 10 >= 4, 11 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 *new_foldFM_GE1(wz34, wz36, wz37, wz38, wz39, wz40, wz41, Succ(wz420), Zero, h, ba) -> new_foldFM_GE(wz34, Char(Succ(wz36)), wz40, h, ba) 12.76/5.17 The graph contains the following edges 1 >= 1, 6 >= 3, 10 >= 4, 11 >= 5 12.76/5.17 12.76/5.17 12.76/5.17 ---------------------------------------- 12.76/5.17 12.76/5.17 (14) 12.76/5.17 YES 12.86/5.21 EOF