10.49/4.68 YES 12.71/5.30 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 12.71/5.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.71/5.30 12.71/5.30 12.71/5.30 H-Termination with start terms of the given HASKELL could be proven: 12.71/5.30 12.71/5.30 (0) HASKELL 12.71/5.30 (1) LR [EQUIVALENT, 0 ms] 12.71/5.30 (2) HASKELL 12.71/5.30 (3) BR [EQUIVALENT, 0 ms] 12.71/5.30 (4) HASKELL 12.71/5.30 (5) COR [EQUIVALENT, 0 ms] 12.71/5.30 (6) HASKELL 12.71/5.30 (7) Narrow [SOUND, 0 ms] 12.71/5.30 (8) AND 12.71/5.30 (9) QDP 12.71/5.30 (10) TransformationProof [EQUIVALENT, 0 ms] 12.71/5.30 (11) QDP 12.71/5.30 (12) TransformationProof [EQUIVALENT, 0 ms] 12.71/5.30 (13) QDP 12.71/5.30 (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.71/5.30 (15) YES 12.71/5.30 (16) QDP 12.71/5.30 (17) DependencyGraphProof [EQUIVALENT, 0 ms] 12.71/5.30 (18) AND 12.71/5.30 (19) QDP 12.71/5.30 (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.71/5.30 (21) YES 12.71/5.30 (22) QDP 12.71/5.30 (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.71/5.30 (24) YES 12.71/5.30 (25) QDP 12.71/5.30 (26) TransformationProof [EQUIVALENT, 0 ms] 12.71/5.30 (27) QDP 12.71/5.30 (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.71/5.30 (29) YES 12.71/5.30 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (0) 12.71/5.30 Obligation: 12.71/5.30 mainModule Main 12.71/5.30 module FiniteMap where { 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 12.71/5.30 12.71/5.30 eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]; 12.71/5.30 eltsFM_LE fm fr = foldFM_LE (\key elt rest ->elt : rest) [] fr fm; 12.71/5.30 12.71/5.30 foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b; 12.71/5.30 foldFM_LE k z fr EmptyFM = z; 12.71/5.30 foldFM_LE k z fr (Branch key elt _ fm_l fm_r) | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r 12.71/5.30 | otherwise = foldFM_LE k z fr fm_l; 12.71/5.30 12.71/5.30 } 12.71/5.30 module Maybe where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 module Main where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (1) LR (EQUIVALENT) 12.71/5.30 Lambda Reductions: 12.71/5.30 The following Lambda expression 12.71/5.30 "\keyeltrest->elt : rest" 12.71/5.30 is transformed to 12.71/5.30 "eltsFM_LE0 key elt rest = elt : rest; 12.71/5.30 " 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (2) 12.71/5.30 Obligation: 12.71/5.30 mainModule Main 12.71/5.30 module FiniteMap where { 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 12.71/5.30 12.71/5.30 eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]; 12.71/5.30 eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm; 12.71/5.30 12.71/5.30 eltsFM_LE0 key elt rest = elt : rest; 12.71/5.30 12.71/5.30 foldFM_LE :: Ord b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a; 12.71/5.30 foldFM_LE k z fr EmptyFM = z; 12.71/5.30 foldFM_LE k z fr (Branch key elt _ fm_l fm_r) | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r 12.71/5.30 | otherwise = foldFM_LE k z fr fm_l; 12.71/5.30 12.71/5.30 } 12.71/5.30 module Maybe where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 module Main where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (3) BR (EQUIVALENT) 12.71/5.30 Replaced joker patterns by fresh variables and removed binding patterns. 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (4) 12.71/5.30 Obligation: 12.71/5.30 mainModule Main 12.71/5.30 module FiniteMap where { 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 12.71/5.30 12.71/5.30 eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]; 12.71/5.30 eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm; 12.71/5.30 12.71/5.30 eltsFM_LE0 key elt rest = elt : rest; 12.71/5.30 12.71/5.30 foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c; 12.71/5.30 foldFM_LE k z fr EmptyFM = z; 12.71/5.30 foldFM_LE k z fr (Branch key elt vy fm_l fm_r) | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r 12.71/5.30 | otherwise = foldFM_LE k z fr fm_l; 12.71/5.30 12.71/5.30 } 12.71/5.30 module Maybe where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 module Main where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (5) COR (EQUIVALENT) 12.71/5.30 Cond Reductions: 12.71/5.30 The following Function with conditions 12.71/5.30 "undefined |Falseundefined; 12.71/5.30 " 12.71/5.30 is transformed to 12.71/5.30 "undefined = undefined1; 12.71/5.30 " 12.71/5.30 "undefined0 True = undefined; 12.71/5.30 " 12.71/5.30 "undefined1 = undefined0 False; 12.71/5.30 " 12.71/5.30 The following Function with conditions 12.71/5.30 "foldFM_LE k z fr EmptyFM = z; 12.71/5.30 foldFM_LE k z fr (Branch key elt vy fm_l fm_r)|key <= frfoldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r|otherwisefoldFM_LE k z fr fm_l; 12.71/5.30 " 12.71/5.30 is transformed to 12.71/5.30 "foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM; 12.71/5.30 foldFM_LE k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r); 12.71/5.30 " 12.71/5.30 "foldFM_LE1 k z fr key elt vy fm_l fm_r True = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r; 12.71/5.30 foldFM_LE1 k z fr key elt vy fm_l fm_r False = foldFM_LE0 k z fr key elt vy fm_l fm_r otherwise; 12.71/5.30 " 12.71/5.30 "foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l; 12.71/5.30 " 12.71/5.30 "foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE1 k z fr key elt vy fm_l fm_r (key <= fr); 12.71/5.30 " 12.71/5.30 "foldFM_LE3 k z fr EmptyFM = z; 12.71/5.30 foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy; 12.71/5.30 " 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (6) 12.71/5.30 Obligation: 12.71/5.30 mainModule Main 12.71/5.30 module FiniteMap where { 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 12.71/5.30 12.71/5.30 eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]; 12.71/5.30 eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm; 12.71/5.30 12.71/5.30 eltsFM_LE0 key elt rest = elt : rest; 12.71/5.30 12.71/5.30 foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b; 12.71/5.30 foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM; 12.71/5.30 foldFM_LE k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r); 12.71/5.30 12.71/5.30 foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l; 12.71/5.30 12.71/5.30 foldFM_LE1 k z fr key elt vy fm_l fm_r True = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r; 12.71/5.30 foldFM_LE1 k z fr key elt vy fm_l fm_r False = foldFM_LE0 k z fr key elt vy fm_l fm_r otherwise; 12.71/5.30 12.71/5.30 foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE1 k z fr key elt vy fm_l fm_r (key <= fr); 12.71/5.30 12.71/5.30 foldFM_LE3 k z fr EmptyFM = z; 12.71/5.30 foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy; 12.71/5.30 12.71/5.30 } 12.71/5.30 module Maybe where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Main; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 module Main where { 12.71/5.30 import qualified FiniteMap; 12.71/5.30 import qualified Maybe; 12.71/5.30 import qualified Prelude; 12.71/5.30 } 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (7) Narrow (SOUND) 12.71/5.30 Haskell To QDPs 12.71/5.30 12.71/5.30 digraph dp_graph { 12.71/5.30 node [outthreshold=100, inthreshold=100];1[label="FiniteMap.eltsFM_LE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 12.71/5.30 3[label="FiniteMap.eltsFM_LE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 12.71/5.30 4[label="FiniteMap.eltsFM_LE wz3 wz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 12.71/5.30 5[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] wz4 wz3",fontsize=16,color="burlywood",shape="triangle"];114[label="wz3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 114[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 114 -> 6[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 115[label="wz3/FiniteMap.Branch wz30 wz31 wz32 wz33 wz34",fontsize=10,color="white",style="solid",shape="box"];5 -> 115[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 115 -> 7[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 6[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 12.71/5.30 7[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 12.71/5.30 8[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 12.71/5.30 9[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 12.71/5.30 10[label="[]",fontsize=16,color="green",shape="box"];11[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (wz30 <= wz4)",fontsize=16,color="burlywood",shape="box"];116[label="wz30/False",fontsize=10,color="white",style="solid",shape="box"];11 -> 116[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 116 -> 12[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 117[label="wz30/True",fontsize=10,color="white",style="solid",shape="box"];11 -> 117[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 117 -> 13[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 12[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] wz4 False wz31 wz32 wz33 wz34 (False <= wz4)",fontsize=16,color="burlywood",shape="box"];118[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];12 -> 118[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 118 -> 14[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 119[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];12 -> 119[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 119 -> 15[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 13[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] wz4 True wz31 wz32 wz33 wz34 (True <= wz4)",fontsize=16,color="burlywood",shape="box"];120[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];13 -> 120[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 120 -> 16[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 121[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];13 -> 121[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 121 -> 17[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 14[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] False False wz31 wz32 wz33 wz34 (False <= False)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 12.71/5.30 15[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] True False wz31 wz32 wz33 wz34 (False <= True)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 12.71/5.30 16[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] False True wz31 wz32 wz33 wz34 (True <= False)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 12.71/5.30 17[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] True True wz31 wz32 wz33 wz34 (True <= True)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 12.71/5.30 18[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] False False wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 12.71/5.30 19[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] True False wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 12.71/5.30 20[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] False True wz31 wz32 wz33 wz34 False",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 12.71/5.30 21[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] True True wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 12.71/5.30 22 -> 26[label="",style="dashed", color="red", weight=0]; 12.71/5.30 22[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] False wz33)) False wz34",fontsize=16,color="magenta"];22 -> 27[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 23 -> 28[label="",style="dashed", color="red", weight=0]; 12.71/5.30 23[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] True wz33)) True wz34",fontsize=16,color="magenta"];23 -> 29[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 24[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 [] False True wz31 wz32 wz33 wz34 otherwise",fontsize=16,color="black",shape="box"];24 -> 30[label="",style="solid", color="black", weight=3]; 12.71/5.30 25 -> 31[label="",style="dashed", color="red", weight=0]; 12.71/5.30 25[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz31 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] True wz33)) True wz34",fontsize=16,color="magenta"];25 -> 32[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 27 -> 5[label="",style="dashed", color="red", weight=0]; 12.71/5.30 27[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] False wz33",fontsize=16,color="magenta"];27 -> 33[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 27 -> 34[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 26[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz5) False wz34",fontsize=16,color="burlywood",shape="triangle"];122[label="wz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];26 -> 122[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 122 -> 35[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 123[label="wz34/FiniteMap.Branch wz340 wz341 wz342 wz343 wz344",fontsize=10,color="white",style="solid",shape="box"];26 -> 123[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 123 -> 36[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 29 -> 5[label="",style="dashed", color="red", weight=0]; 12.71/5.30 29[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] True wz33",fontsize=16,color="magenta"];29 -> 37[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 29 -> 38[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 28[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz6) True wz34",fontsize=16,color="burlywood",shape="triangle"];124[label="wz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];28 -> 124[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 124 -> 39[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 125[label="wz34/FiniteMap.Branch wz340 wz341 wz342 wz343 wz344",fontsize=10,color="white",style="solid",shape="box"];28 -> 125[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 125 -> 40[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 30[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 [] False True wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];30 -> 41[label="",style="solid", color="black", weight=3]; 12.71/5.30 32 -> 5[label="",style="dashed", color="red", weight=0]; 12.71/5.30 32[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] True wz33",fontsize=16,color="magenta"];32 -> 42[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 32 -> 43[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 31[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz31 wz7) True wz34",fontsize=16,color="burlywood",shape="triangle"];126[label="wz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];31 -> 126[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 126 -> 44[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 127[label="wz34/FiniteMap.Branch wz340 wz341 wz342 wz343 wz344",fontsize=10,color="white",style="solid",shape="box"];31 -> 127[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 127 -> 45[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 33[label="False",fontsize=16,color="green",shape="box"];34[label="wz33",fontsize=16,color="green",shape="box"];35[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz5) False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];35 -> 46[label="",style="solid", color="black", weight=3]; 12.71/5.30 36[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz5) False (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];36 -> 47[label="",style="solid", color="black", weight=3]; 12.71/5.30 37[label="True",fontsize=16,color="green",shape="box"];38[label="wz33",fontsize=16,color="green",shape="box"];39[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz6) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3]; 12.71/5.30 40[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz6) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3]; 12.71/5.30 41 -> 5[label="",style="dashed", color="red", weight=0]; 12.71/5.30 41[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] False wz33",fontsize=16,color="magenta"];41 -> 50[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 41 -> 51[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 42[label="True",fontsize=16,color="green",shape="box"];43[label="wz33",fontsize=16,color="green",shape="box"];44[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz31 wz7) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];44 -> 52[label="",style="solid", color="black", weight=3]; 12.71/5.30 45[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz31 wz7) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];45 -> 53[label="",style="solid", color="black", weight=3]; 12.71/5.30 46[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz5) False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];46 -> 54[label="",style="solid", color="black", weight=3]; 12.71/5.30 47[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz5) False (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];47 -> 55[label="",style="solid", color="black", weight=3]; 12.71/5.30 48[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz6) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];48 -> 56[label="",style="solid", color="black", weight=3]; 12.71/5.30 49[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz6) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];49 -> 57[label="",style="solid", color="black", weight=3]; 12.71/5.30 50[label="False",fontsize=16,color="green",shape="box"];51[label="wz33",fontsize=16,color="green",shape="box"];52[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz31 wz7) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];52 -> 58[label="",style="solid", color="black", weight=3]; 12.71/5.30 53[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz31 wz7) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];53 -> 59[label="",style="solid", color="black", weight=3]; 12.71/5.30 54[label="FiniteMap.eltsFM_LE0 False wz31 wz5",fontsize=16,color="black",shape="triangle"];54 -> 60[label="",style="solid", color="black", weight=3]; 12.71/5.30 55 -> 61[label="",style="dashed", color="red", weight=0]; 12.71/5.30 55[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz5) False wz340 wz341 wz342 wz343 wz344 (wz340 <= False)",fontsize=16,color="magenta"];55 -> 62[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 56 -> 54[label="",style="dashed", color="red", weight=0]; 12.71/5.30 56[label="FiniteMap.eltsFM_LE0 False wz31 wz6",fontsize=16,color="magenta"];56 -> 63[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 57 -> 64[label="",style="dashed", color="red", weight=0]; 12.71/5.30 57[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz31 wz6) True wz340 wz341 wz342 wz343 wz344 (wz340 <= True)",fontsize=16,color="magenta"];57 -> 65[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 58[label="FiniteMap.eltsFM_LE0 True wz31 wz7",fontsize=16,color="black",shape="triangle"];58 -> 67[label="",style="solid", color="black", weight=3]; 12.71/5.30 59 -> 64[label="",style="dashed", color="red", weight=0]; 12.71/5.30 59[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz31 wz7) True wz340 wz341 wz342 wz343 wz344 (wz340 <= True)",fontsize=16,color="magenta"];59 -> 66[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 60[label="wz31 : wz5",fontsize=16,color="green",shape="box"];62 -> 54[label="",style="dashed", color="red", weight=0]; 12.71/5.30 62[label="FiniteMap.eltsFM_LE0 False wz31 wz5",fontsize=16,color="magenta"];61[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz8 False wz340 wz341 wz342 wz343 wz344 (wz340 <= False)",fontsize=16,color="burlywood",shape="triangle"];128[label="wz340/False",fontsize=10,color="white",style="solid",shape="box"];61 -> 128[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 128 -> 68[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 129[label="wz340/True",fontsize=10,color="white",style="solid",shape="box"];61 -> 129[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 129 -> 69[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 63[label="wz6",fontsize=16,color="green",shape="box"];65 -> 54[label="",style="dashed", color="red", weight=0]; 12.71/5.30 65[label="FiniteMap.eltsFM_LE0 False wz31 wz6",fontsize=16,color="magenta"];65 -> 70[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 64[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz9 True wz340 wz341 wz342 wz343 wz344 (wz340 <= True)",fontsize=16,color="burlywood",shape="triangle"];130[label="wz340/False",fontsize=10,color="white",style="solid",shape="box"];64 -> 130[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 130 -> 71[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 131[label="wz340/True",fontsize=10,color="white",style="solid",shape="box"];64 -> 131[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 131 -> 72[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 67[label="wz31 : wz7",fontsize=16,color="green",shape="box"];66 -> 58[label="",style="dashed", color="red", weight=0]; 12.71/5.30 66[label="FiniteMap.eltsFM_LE0 True wz31 wz7",fontsize=16,color="magenta"];68[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz8 False False wz341 wz342 wz343 wz344 (False <= False)",fontsize=16,color="black",shape="box"];68 -> 73[label="",style="solid", color="black", weight=3]; 12.71/5.30 69[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz8 False True wz341 wz342 wz343 wz344 (True <= False)",fontsize=16,color="black",shape="box"];69 -> 74[label="",style="solid", color="black", weight=3]; 12.71/5.30 70[label="wz6",fontsize=16,color="green",shape="box"];71[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz9 True False wz341 wz342 wz343 wz344 (False <= True)",fontsize=16,color="black",shape="box"];71 -> 75[label="",style="solid", color="black", weight=3]; 12.71/5.30 72[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz9 True True wz341 wz342 wz343 wz344 (True <= True)",fontsize=16,color="black",shape="box"];72 -> 76[label="",style="solid", color="black", weight=3]; 12.71/5.30 73[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz8 False False wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];73 -> 77[label="",style="solid", color="black", weight=3]; 12.71/5.30 74[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz8 False True wz341 wz342 wz343 wz344 False",fontsize=16,color="black",shape="box"];74 -> 78[label="",style="solid", color="black", weight=3]; 12.71/5.30 75[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz9 True False wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];75 -> 79[label="",style="solid", color="black", weight=3]; 12.71/5.30 76[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz9 True True wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];76 -> 80[label="",style="solid", color="black", weight=3]; 12.71/5.30 77 -> 26[label="",style="dashed", color="red", weight=0]; 12.71/5.30 77[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz8 False wz343)) False wz344",fontsize=16,color="magenta"];77 -> 81[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 77 -> 82[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 77 -> 83[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 78[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz8 False True wz341 wz342 wz343 wz344 otherwise",fontsize=16,color="black",shape="box"];78 -> 84[label="",style="solid", color="black", weight=3]; 12.71/5.30 79 -> 28[label="",style="dashed", color="red", weight=0]; 12.71/5.30 79[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 False wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz9 True wz343)) True wz344",fontsize=16,color="magenta"];79 -> 85[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 79 -> 86[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 79 -> 87[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 80 -> 31[label="",style="dashed", color="red", weight=0]; 12.71/5.30 80[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 True wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz9 True wz343)) True wz344",fontsize=16,color="magenta"];80 -> 88[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 80 -> 89[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 80 -> 90[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 81[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz8 False wz343",fontsize=16,color="burlywood",shape="triangle"];132[label="wz343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];81 -> 132[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 132 -> 91[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 133[label="wz343/FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434",fontsize=10,color="white",style="solid",shape="box"];81 -> 133[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 133 -> 92[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 82[label="wz344",fontsize=16,color="green",shape="box"];83[label="wz341",fontsize=16,color="green",shape="box"];84[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz8 False True wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];84 -> 93[label="",style="solid", color="black", weight=3]; 12.71/5.30 85[label="wz344",fontsize=16,color="green",shape="box"];86[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz9 True wz343",fontsize=16,color="burlywood",shape="triangle"];134[label="wz343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];86 -> 134[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 134 -> 94[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 135[label="wz343/FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434",fontsize=10,color="white",style="solid",shape="box"];86 -> 135[label="",style="solid", color="burlywood", weight=9]; 12.71/5.30 135 -> 95[label="",style="solid", color="burlywood", weight=3]; 12.71/5.30 87[label="wz341",fontsize=16,color="green",shape="box"];88 -> 86[label="",style="dashed", color="red", weight=0]; 12.71/5.30 88[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz9 True wz343",fontsize=16,color="magenta"];89[label="wz344",fontsize=16,color="green",shape="box"];90[label="wz341",fontsize=16,color="green",shape="box"];91[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz8 False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];91 -> 96[label="",style="solid", color="black", weight=3]; 12.71/5.30 92[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz8 False (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];92 -> 97[label="",style="solid", color="black", weight=3]; 12.71/5.30 93 -> 81[label="",style="dashed", color="red", weight=0]; 12.71/5.30 93[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz8 False wz343",fontsize=16,color="magenta"];94[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];94 -> 98[label="",style="solid", color="black", weight=3]; 12.71/5.30 95[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz9 True (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];95 -> 99[label="",style="solid", color="black", weight=3]; 12.71/5.30 96[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 wz8 False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];96 -> 100[label="",style="solid", color="black", weight=3]; 12.71/5.30 97[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 wz8 False (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];97 -> 101[label="",style="solid", color="black", weight=3]; 12.71/5.30 98[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];98 -> 102[label="",style="solid", color="black", weight=3]; 12.71/5.30 99[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 wz9 True (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];99 -> 103[label="",style="solid", color="black", weight=3]; 12.71/5.30 100[label="wz8",fontsize=16,color="green",shape="box"];101 -> 61[label="",style="dashed", color="red", weight=0]; 12.71/5.30 101[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz8 False wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= False)",fontsize=16,color="magenta"];101 -> 104[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 101 -> 105[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 101 -> 106[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 101 -> 107[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 101 -> 108[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 102[label="wz9",fontsize=16,color="green",shape="box"];103 -> 64[label="",style="dashed", color="red", weight=0]; 12.71/5.30 103[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz9 True wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= True)",fontsize=16,color="magenta"];103 -> 109[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 103 -> 110[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 103 -> 111[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 103 -> 112[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 103 -> 113[label="",style="dashed", color="magenta", weight=3]; 12.71/5.30 104[label="wz3430",fontsize=16,color="green",shape="box"];105[label="wz3432",fontsize=16,color="green",shape="box"];106[label="wz3434",fontsize=16,color="green",shape="box"];107[label="wz3433",fontsize=16,color="green",shape="box"];108[label="wz3431",fontsize=16,color="green",shape="box"];109[label="wz3430",fontsize=16,color="green",shape="box"];110[label="wz3432",fontsize=16,color="green",shape="box"];111[label="wz3434",fontsize=16,color="green",shape="box"];112[label="wz3433",fontsize=16,color="green",shape="box"];113[label="wz3431",fontsize=16,color="green",shape="box"];} 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (8) 12.71/5.30 Complex Obligation (AND) 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (9) 12.71/5.30 Obligation: 12.71/5.30 Q DP problem: 12.71/5.30 The TRS P consists of the following rules: 12.71/5.30 12.71/5.30 new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.30 new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h) 12.71/5.30 new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.30 new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 12.71/5.30 The TRS R consists of the following rules: 12.71/5.30 12.71/5.30 new_foldFM_LE4(wz31, wz7, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz7, h) 12.71/5.30 new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5) 12.71/5.30 new_foldFM_LE0(wz9, EmptyFM, h) -> wz9 12.71/5.30 new_foldFM_LE5(wz31, wz6, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz6, h) 12.71/5.30 new_foldFM_LE5(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 new_foldFM_LE10(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 new_foldFM_LE4(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 new_foldFM_LE0(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.30 new_eltsFM_LE00(wz31, wz7, h) -> :(wz31, wz7) 12.71/5.30 new_foldFM_LE10(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 12.71/5.30 The set Q consists of the following terms: 12.71/5.30 12.71/5.30 new_foldFM_LE10(x0, True, x1, x2, x3, x4, x5) 12.71/5.30 new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6) 12.71/5.30 new_eltsFM_LE00(x0, x1, x2) 12.71/5.30 new_foldFM_LE0(x0, EmptyFM, x1) 12.71/5.30 new_foldFM_LE10(x0, False, x1, x2, x3, x4, x5) 12.71/5.30 new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.30 new_foldFM_LE4(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.30 new_foldFM_LE4(x0, x1, EmptyFM, x2) 12.71/5.30 new_eltsFM_LE0(x0, x1, x2) 12.71/5.30 new_foldFM_LE5(x0, x1, EmptyFM, x2) 12.71/5.30 12.71/5.30 We have to consider all minimal (P,Q,R)-chains. 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (10) TransformationProof (EQUIVALENT) 12.71/5.30 By rewriting [LPAR04] the rule new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]: 12.71/5.30 12.71/5.30 (new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h)) 12.71/5.30 12.71/5.30 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (11) 12.71/5.30 Obligation: 12.71/5.30 Q DP problem: 12.71/5.30 The TRS P consists of the following rules: 12.71/5.30 12.71/5.30 new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.30 new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h) 12.71/5.30 new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.30 new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 12.71/5.30 The TRS R consists of the following rules: 12.71/5.30 12.71/5.30 new_foldFM_LE4(wz31, wz7, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz7, h) 12.71/5.30 new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5) 12.71/5.30 new_foldFM_LE0(wz9, EmptyFM, h) -> wz9 12.71/5.30 new_foldFM_LE5(wz31, wz6, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz6, h) 12.71/5.30 new_foldFM_LE5(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 new_foldFM_LE10(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 new_foldFM_LE4(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.30 new_foldFM_LE0(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.30 new_eltsFM_LE00(wz31, wz7, h) -> :(wz31, wz7) 12.71/5.30 new_foldFM_LE10(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.30 12.71/5.30 The set Q consists of the following terms: 12.71/5.30 12.71/5.30 new_foldFM_LE10(x0, True, x1, x2, x3, x4, x5) 12.71/5.30 new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6) 12.71/5.30 new_eltsFM_LE00(x0, x1, x2) 12.71/5.30 new_foldFM_LE0(x0, EmptyFM, x1) 12.71/5.30 new_foldFM_LE10(x0, False, x1, x2, x3, x4, x5) 12.71/5.30 new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.30 new_foldFM_LE4(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.30 new_foldFM_LE4(x0, x1, EmptyFM, x2) 12.71/5.30 new_eltsFM_LE0(x0, x1, x2) 12.71/5.30 new_foldFM_LE5(x0, x1, EmptyFM, x2) 12.71/5.30 12.71/5.30 We have to consider all minimal (P,Q,R)-chains. 12.71/5.30 ---------------------------------------- 12.71/5.30 12.71/5.30 (12) TransformationProof (EQUIVALENT) 12.71/5.30 By rewriting [LPAR04] the rule new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]: 12.71/5.30 12.71/5.30 (new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h)) 12.71/5.31 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (13) 12.71/5.31 Obligation: 12.71/5.31 Q DP problem: 12.71/5.31 The TRS P consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h) 12.71/5.31 new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.31 new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.31 new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 12.71/5.31 The TRS R consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE4(wz31, wz7, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz7, h) 12.71/5.31 new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5) 12.71/5.31 new_foldFM_LE0(wz9, EmptyFM, h) -> wz9 12.71/5.31 new_foldFM_LE5(wz31, wz6, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz6, h) 12.71/5.31 new_foldFM_LE5(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 new_foldFM_LE10(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.31 new_foldFM_LE4(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 new_foldFM_LE0(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_eltsFM_LE00(wz31, wz7, h) -> :(wz31, wz7) 12.71/5.31 new_foldFM_LE10(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.31 12.71/5.31 The set Q consists of the following terms: 12.71/5.31 12.71/5.31 new_foldFM_LE10(x0, True, x1, x2, x3, x4, x5) 12.71/5.31 new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6) 12.71/5.31 new_eltsFM_LE00(x0, x1, x2) 12.71/5.31 new_foldFM_LE0(x0, EmptyFM, x1) 12.71/5.31 new_foldFM_LE10(x0, False, x1, x2, x3, x4, x5) 12.71/5.31 new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.31 new_foldFM_LE4(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.31 new_foldFM_LE4(x0, x1, EmptyFM, x2) 12.71/5.31 new_eltsFM_LE0(x0, x1, x2) 12.71/5.31 new_foldFM_LE5(x0, x1, EmptyFM, x2) 12.71/5.31 12.71/5.31 We have to consider all minimal (P,Q,R)-chains. 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (14) QDPSizeChangeProof (EQUIVALENT) 12.71/5.31 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. 12.71/5.31 12.71/5.31 From the DPs we obtained the following set of size-change graphs: 12.71/5.31 *new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.31 The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h) 12.71/5.31 The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4 12.71/5.31 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (15) 12.71/5.31 YES 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (16) 12.71/5.31 Obligation: 12.71/5.31 Q DP problem: 12.71/5.31 The TRS P consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE13(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h) 12.71/5.31 new_foldFM_LE13(False, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h) 12.71/5.31 new_foldFM_LE13(False, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h) 12.71/5.31 new_foldFM_LE13(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h) 12.71/5.31 12.71/5.31 R is empty. 12.71/5.31 Q is empty. 12.71/5.31 We have to consider all minimal (P,Q,R)-chains. 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (17) DependencyGraphProof (EQUIVALENT) 12.71/5.31 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (18) 12.71/5.31 Complex Obligation (AND) 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (19) 12.71/5.31 Obligation: 12.71/5.31 Q DP problem: 12.71/5.31 The TRS P consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE13(False, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h) 12.71/5.31 new_foldFM_LE13(False, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h) 12.71/5.31 12.71/5.31 R is empty. 12.71/5.31 Q is empty. 12.71/5.31 We have to consider all minimal (P,Q,R)-chains. 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (20) QDPSizeChangeProof (EQUIVALENT) 12.71/5.31 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. 12.71/5.31 12.71/5.31 From the DPs we obtained the following set of size-change graphs: 12.71/5.31 *new_foldFM_LE13(False, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE13(False, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 12.71/5.31 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (21) 12.71/5.31 YES 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (22) 12.71/5.31 Obligation: 12.71/5.31 Q DP problem: 12.71/5.31 The TRS P consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE13(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h) 12.71/5.31 new_foldFM_LE13(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h) 12.71/5.31 12.71/5.31 R is empty. 12.71/5.31 Q is empty. 12.71/5.31 We have to consider all minimal (P,Q,R)-chains. 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (23) QDPSizeChangeProof (EQUIVALENT) 12.71/5.31 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. 12.71/5.31 12.71/5.31 From the DPs we obtained the following set of size-change graphs: 12.71/5.31 *new_foldFM_LE13(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE13(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 12.71/5.31 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (24) 12.71/5.31 YES 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (25) 12.71/5.31 Obligation: 12.71/5.31 Q DP problem: 12.71/5.31 The TRS P consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE11(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz8, wz343, h) 12.71/5.31 new_foldFM_LE8(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 new_foldFM_LE11(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h) 12.71/5.31 new_foldFM_LE11(wz8, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 12.71/5.31 The TRS R consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE9(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE12(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5) 12.71/5.31 new_foldFM_LE7(wz8, EmptyFM, h) -> wz8 12.71/5.31 new_foldFM_LE7(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE12(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_foldFM_LE9(wz31, wz5, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz5, h) 12.71/5.31 new_foldFM_LE12(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz8, wz343, h) 12.71/5.31 new_foldFM_LE12(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h) 12.71/5.31 12.71/5.31 The set Q consists of the following terms: 12.71/5.31 12.71/5.31 new_foldFM_LE9(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.31 new_foldFM_LE12(x0, False, x1, x2, x3, x4, x5) 12.71/5.31 new_foldFM_LE9(x0, x1, EmptyFM, x2) 12.71/5.31 new_foldFM_LE12(x0, True, x1, x2, x3, x4, x5) 12.71/5.31 new_eltsFM_LE0(x0, x1, x2) 12.71/5.31 new_foldFM_LE7(x0, EmptyFM, x1) 12.71/5.31 new_foldFM_LE7(x0, Branch(x1, x2, x3, x4, x5), x6) 12.71/5.31 12.71/5.31 We have to consider all minimal (P,Q,R)-chains. 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (26) TransformationProof (EQUIVALENT) 12.71/5.31 By rewriting [LPAR04] the rule new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]: 12.71/5.31 12.71/5.31 (new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h)) 12.71/5.31 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (27) 12.71/5.31 Obligation: 12.71/5.31 Q DP problem: 12.71/5.31 The TRS P consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE11(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz8, wz343, h) 12.71/5.31 new_foldFM_LE8(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_foldFM_LE11(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h) 12.71/5.31 new_foldFM_LE11(wz8, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 12.71/5.31 The TRS R consists of the following rules: 12.71/5.31 12.71/5.31 new_foldFM_LE9(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE12(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5) 12.71/5.31 new_foldFM_LE7(wz8, EmptyFM, h) -> wz8 12.71/5.31 new_foldFM_LE7(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE12(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 new_foldFM_LE9(wz31, wz5, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz5, h) 12.71/5.31 new_foldFM_LE12(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz8, wz343, h) 12.71/5.31 new_foldFM_LE12(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h) 12.71/5.31 12.71/5.31 The set Q consists of the following terms: 12.71/5.31 12.71/5.31 new_foldFM_LE9(x0, x1, Branch(x2, x3, x4, x5, x6), x7) 12.71/5.31 new_foldFM_LE12(x0, False, x1, x2, x3, x4, x5) 12.71/5.31 new_foldFM_LE9(x0, x1, EmptyFM, x2) 12.71/5.31 new_foldFM_LE12(x0, True, x1, x2, x3, x4, x5) 12.71/5.31 new_eltsFM_LE0(x0, x1, x2) 12.71/5.31 new_foldFM_LE7(x0, EmptyFM, x1) 12.71/5.31 new_foldFM_LE7(x0, Branch(x1, x2, x3, x4, x5), x6) 12.71/5.31 12.71/5.31 We have to consider all minimal (P,Q,R)-chains. 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (28) QDPSizeChangeProof (EQUIVALENT) 12.71/5.31 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. 12.71/5.31 12.71/5.31 From the DPs we obtained the following set of size-change graphs: 12.71/5.31 *new_foldFM_LE8(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE11(wz8, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h) 12.71/5.31 The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE11(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz8, wz343, h) 12.71/5.31 The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3 12.71/5.31 12.71/5.31 12.71/5.31 *new_foldFM_LE11(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h) 12.71/5.31 The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4 12.71/5.31 12.71/5.31 12.71/5.31 ---------------------------------------- 12.71/5.31 12.71/5.31 (29) 12.71/5.31 YES 12.71/5.34 EOF