10.85/4.41 MAYBE 13.12/5.07 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 13.12/5.07 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.12/5.07 13.12/5.07 13.12/5.07 H-Termination with start terms of the given HASKELL could not be shown: 13.12/5.07 13.12/5.07 (0) HASKELL 13.12/5.07 (1) LR [EQUIVALENT, 0 ms] 13.12/5.07 (2) HASKELL 13.12/5.07 (3) IPR [EQUIVALENT, 0 ms] 13.12/5.07 (4) HASKELL 13.12/5.07 (5) BR [EQUIVALENT, 0 ms] 13.12/5.07 (6) HASKELL 13.12/5.07 (7) COR [EQUIVALENT, 0 ms] 13.12/5.07 (8) HASKELL 13.12/5.07 (9) Narrow [SOUND, 0 ms] 13.12/5.07 (10) AND 13.12/5.07 (11) QDP 13.12/5.07 (12) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (13) QDP 13.12/5.07 (14) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (15) QDP 13.12/5.07 (16) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (17) QDP 13.12/5.07 (18) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (19) QDP 13.12/5.07 (20) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (21) QDP 13.12/5.07 (22) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (23) QDP 13.12/5.07 (24) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (25) QDP 13.12/5.07 (26) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (27) QDP 13.12/5.07 (28) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (29) QDP 13.12/5.07 (30) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (31) QDP 13.12/5.07 (32) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (33) QDP 13.12/5.07 (34) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.12/5.07 (35) YES 13.12/5.07 (36) QDP 13.12/5.07 (37) DependencyGraphProof [EQUIVALENT, 0 ms] 13.12/5.07 (38) QDP 13.12/5.07 (39) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.12/5.07 (40) YES 13.12/5.07 (41) QDP 13.12/5.07 (42) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.12/5.07 (43) YES 13.12/5.07 (44) QDP 13.12/5.07 (45) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.12/5.07 (46) YES 13.12/5.07 (47) QDP 13.12/5.07 (48) MRRProof [EQUIVALENT, 55 ms] 13.12/5.07 (49) QDP 13.12/5.07 (50) DependencyGraphProof [EQUIVALENT, 0 ms] 13.12/5.07 (51) AND 13.12/5.07 (52) QDP 13.12/5.07 (53) MRRProof [EQUIVALENT, 0 ms] 13.12/5.07 (54) QDP 13.12/5.07 (55) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (56) QDP 13.12/5.07 (57) NonTerminationLoopProof [COMPLETE, 0 ms] 13.12/5.07 (58) NO 13.12/5.07 (59) QDP 13.12/5.07 (60) MRRProof [EQUIVALENT, 7 ms] 13.12/5.07 (61) QDP 13.12/5.07 (62) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (63) QDP 13.12/5.07 (64) NonTerminationLoopProof [COMPLETE, 0 ms] 13.12/5.07 (65) NO 13.12/5.07 (66) QDP 13.12/5.07 (67) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (68) QDP 13.12/5.07 (69) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (70) QDP 13.12/5.07 (71) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (72) QDP 13.12/5.07 (73) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (74) QDP 13.12/5.07 (75) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (76) QDP 13.12/5.07 (77) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (78) QDP 13.12/5.07 (79) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.12/5.07 (80) YES 13.12/5.07 (81) QDP 13.12/5.07 (82) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (83) QDP 13.12/5.07 (84) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (85) QDP 13.12/5.07 (86) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (87) QDP 13.12/5.07 (88) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (89) QDP 13.12/5.07 (90) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (91) QDP 13.12/5.07 (92) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (93) QDP 13.12/5.07 (94) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (95) QDP 13.12/5.07 (96) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (97) QDP 13.12/5.07 (98) UsableRulesProof [EQUIVALENT, 0 ms] 13.12/5.07 (99) QDP 13.12/5.07 (100) QReductionProof [EQUIVALENT, 0 ms] 13.12/5.07 (101) QDP 13.12/5.07 (102) TransformationProof [EQUIVALENT, 0 ms] 13.12/5.07 (103) QDP 13.12/5.07 (104) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.12/5.07 (105) YES 13.12/5.07 (106) QDP 13.12/5.07 (107) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.12/5.07 (108) YES 13.12/5.07 (109) Narrow [COMPLETE, 0 ms] 13.12/5.07 (110) TRUE 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (0) 13.12/5.07 Obligation: 13.12/5.07 mainModule Main 13.12/5.07 module Maybe where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Main where { 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Monad where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Prelude; 13.12/5.07 mapAndUnzipM :: Monad b => (c -> b (d,a)) -> [c] -> b ([d],[a]); 13.12/5.07 mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip; 13.12/5.07 13.12/5.07 } 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (1) LR (EQUIVALENT) 13.12/5.07 Lambda Reductions: 13.12/5.07 The following Lambda expression 13.12/5.07 "\(a,b)~(as,bs)->(a : as,b : bs)" 13.12/5.07 is transformed to 13.12/5.07 "unzip0 (a,b) ~(as,bs) = (a : as,b : bs); 13.12/5.07 " 13.12/5.07 The following Lambda expression 13.12/5.07 "\xs->return (x : xs)" 13.12/5.07 is transformed to 13.12/5.07 "sequence0 x xs = return (x : xs); 13.12/5.07 " 13.12/5.07 The following Lambda expression 13.12/5.07 "\x->sequence cs >>= sequence0 x" 13.12/5.07 is transformed to 13.12/5.07 "sequence1 cs x = sequence cs >>= sequence0 x; 13.12/5.07 " 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (2) 13.12/5.07 Obligation: 13.12/5.07 mainModule Main 13.12/5.07 module Maybe where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Main where { 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Monad where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Prelude; 13.12/5.07 mapAndUnzipM :: Monad d => (b -> d (c,a)) -> [b] -> d ([c],[a]); 13.12/5.07 mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip; 13.12/5.07 13.12/5.07 } 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (3) IPR (EQUIVALENT) 13.12/5.07 IrrPat Reductions: 13.12/5.07 The variables of the following irrefutable Pattern 13.12/5.07 "~(as,bs)" 13.12/5.07 are replaced by calls to these functions 13.12/5.07 "unzip00 (as,bs) = as; 13.12/5.07 " 13.12/5.07 "unzip01 (as,bs) = bs; 13.12/5.07 " 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (4) 13.12/5.07 Obligation: 13.12/5.07 mainModule Main 13.12/5.07 module Maybe where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Main where { 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Monad where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Prelude; 13.12/5.07 mapAndUnzipM :: Monad d => (b -> d (a,c)) -> [b] -> d ([a],[c]); 13.12/5.07 mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip; 13.12/5.07 13.12/5.07 } 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (5) BR (EQUIVALENT) 13.12/5.07 Replaced joker patterns by fresh variables and removed binding patterns. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (6) 13.12/5.07 Obligation: 13.12/5.07 mainModule Main 13.12/5.07 module Maybe where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Main where { 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Monad where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Prelude; 13.12/5.07 mapAndUnzipM :: Monad b => (a -> b (c,d)) -> [a] -> b ([c],[d]); 13.12/5.07 mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip; 13.12/5.07 13.12/5.07 } 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (7) COR (EQUIVALENT) 13.12/5.07 Cond Reductions: 13.12/5.07 The following Function with conditions 13.12/5.07 "undefined |Falseundefined; 13.12/5.07 " 13.12/5.07 is transformed to 13.12/5.07 "undefined = undefined1; 13.12/5.07 " 13.12/5.07 "undefined0 True = undefined; 13.12/5.07 " 13.12/5.07 "undefined1 = undefined0 False; 13.12/5.07 " 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (8) 13.12/5.07 Obligation: 13.12/5.07 mainModule Main 13.12/5.07 module Maybe where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Main where { 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Monad; 13.12/5.07 import qualified Prelude; 13.12/5.07 } 13.12/5.07 module Monad where { 13.12/5.07 import qualified Main; 13.12/5.07 import qualified Maybe; 13.12/5.07 import qualified Prelude; 13.12/5.07 mapAndUnzipM :: Monad c => (d -> c (a,b)) -> [d] -> c ([a],[b]); 13.12/5.07 mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip; 13.12/5.07 13.12/5.07 } 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (9) Narrow (SOUND) 13.12/5.07 Haskell To QDPs 13.12/5.07 13.12/5.07 digraph dp_graph { 13.12/5.07 node [outthreshold=100, inthreshold=100];1[label="Monad.mapAndUnzipM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 13.12/5.07 3[label="Monad.mapAndUnzipM vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 13.12/5.07 4[label="Monad.mapAndUnzipM vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 13.12/5.07 5[label="sequence (map vz3 vz4) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];314[label="vz4/vz40 : vz41",fontsize=10,color="white",style="solid",shape="box"];5 -> 314[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 314 -> 6[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 315[label="vz4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 315[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 315 -> 7[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 6[label="sequence (map vz3 (vz40 : vz41)) >>= return . unzip",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 13.12/5.07 7[label="sequence (map vz3 []) >>= return . unzip",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 13.12/5.07 8[label="sequence (vz3 vz40 : map vz3 vz41) >>= return . unzip",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 13.12/5.07 9[label="sequence [] >>= return . unzip",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 13.12/5.07 10 -> 12[label="",style="dashed", color="red", weight=0]; 13.12/5.07 10[label="vz3 vz40 >>= sequence1 (map vz3 vz41) >>= return . unzip",fontsize=16,color="magenta"];10 -> 13[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 11[label="return [] >>= return . unzip",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3]; 13.12/5.07 13[label="vz3 vz40",fontsize=16,color="green",shape="box"];13 -> 18[label="",style="dashed", color="green", weight=3]; 13.12/5.07 12[label="vz5 >>= sequence1 (map vz3 vz41) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];316[label="vz5/vz50 : vz51",fontsize=10,color="white",style="solid",shape="box"];12 -> 316[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 316 -> 16[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 317[label="vz5/[]",fontsize=10,color="white",style="solid",shape="box"];12 -> 317[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 317 -> 17[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 14[label="[] : [] >>= return . unzip",fontsize=16,color="black",shape="box"];14 -> 19[label="",style="solid", color="black", weight=3]; 13.12/5.07 18[label="vz40",fontsize=16,color="green",shape="box"];16[label="vz50 : vz51 >>= sequence1 (map vz3 vz41) >>= return . unzip",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 13.12/5.07 17[label="[] >>= sequence1 (map vz3 vz41) >>= return . unzip",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 13.12/5.07 19 -> 129[label="",style="dashed", color="red", weight=0]; 13.12/5.07 19[label="return . unzip ++ ([] >>= return . unzip)",fontsize=16,color="magenta"];19 -> 130[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 19 -> 131[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 20[label="sequence1 (map vz3 vz41) vz50 ++ (vz51 >>= sequence1 (map vz3 vz41)) >>= return . unzip",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3]; 13.12/5.07 21[label="[] >>= return . unzip",fontsize=16,color="black",shape="triangle"];21 -> 24[label="",style="solid", color="black", weight=3]; 13.12/5.07 130[label="[]",fontsize=16,color="green",shape="box"];131 -> 21[label="",style="dashed", color="red", weight=0]; 13.12/5.07 131[label="[] >>= return . unzip",fontsize=16,color="magenta"];129[label="return . unzip ++ vz22",fontsize=16,color="black",shape="triangle"];129 -> 135[label="",style="solid", color="black", weight=3]; 13.12/5.07 23[label="(sequence (map vz3 vz41) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (map vz3 vz41)) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];318[label="vz41/vz410 : vz411",fontsize=10,color="white",style="solid",shape="box"];23 -> 318[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 318 -> 27[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 319[label="vz41/[]",fontsize=10,color="white",style="solid",shape="box"];23 -> 319[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 319 -> 28[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 24[label="[]",fontsize=16,color="green",shape="box"];135[label="return (unzip vz90) ++ vz22",fontsize=16,color="black",shape="box"];135 -> 145[label="",style="solid", color="black", weight=3]; 13.12/5.07 27[label="(sequence (map vz3 (vz410 : vz411)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (map vz3 (vz410 : vz411))) >>= return . unzip",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3]; 13.12/5.07 28[label="(sequence (map vz3 []) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (map vz3 [])) >>= return . unzip",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3]; 13.12/5.07 145[label="(unzip vz90 : []) ++ vz22",fontsize=16,color="black",shape="box"];145 -> 156[label="",style="solid", color="black", weight=3]; 13.12/5.07 30[label="(sequence (vz3 vz410 : map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (vz3 vz410 : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];30 -> 33[label="",style="solid", color="black", weight=3]; 13.12/5.07 31[label="(sequence [] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="triangle"];31 -> 34[label="",style="solid", color="black", weight=3]; 13.12/5.07 156[label="unzip vz90 : [] ++ vz22",fontsize=16,color="green",shape="box"];156 -> 168[label="",style="dashed", color="green", weight=3]; 13.12/5.07 156 -> 169[label="",style="dashed", color="green", weight=3]; 13.12/5.07 33 -> 37[label="",style="dashed", color="red", weight=0]; 13.12/5.07 33[label="(vz3 vz410 >>= sequence1 (map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (vz3 vz410 : map vz3 vz411)) >>= return . unzip",fontsize=16,color="magenta"];33 -> 38[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 34[label="(return [] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];34 -> 39[label="",style="solid", color="black", weight=3]; 13.12/5.07 168[label="unzip vz90",fontsize=16,color="black",shape="box"];168 -> 179[label="",style="solid", color="black", weight=3]; 13.12/5.07 169[label="[] ++ vz22",fontsize=16,color="black",shape="box"];169 -> 180[label="",style="solid", color="black", weight=3]; 13.12/5.07 38[label="vz3 vz410",fontsize=16,color="green",shape="box"];38 -> 45[label="",style="dashed", color="green", weight=3]; 13.12/5.07 37[label="(vz7 >>= sequence1 (map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (vz7 : map vz3 vz411)) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];320[label="vz7/vz70 : vz71",fontsize=10,color="white",style="solid",shape="box"];37 -> 320[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 320 -> 43[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 321[label="vz7/[]",fontsize=10,color="white",style="solid",shape="box"];37 -> 321[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 321 -> 44[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 39[label="([] : [] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3]; 13.12/5.07 179[label="foldr unzip0 ([],[]) vz90",fontsize=16,color="burlywood",shape="triangle"];322[label="vz90/vz900 : vz901",fontsize=10,color="white",style="solid",shape="box"];179 -> 322[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 322 -> 187[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 323[label="vz90/[]",fontsize=10,color="white",style="solid",shape="box"];179 -> 323[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 323 -> 188[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 180[label="vz22",fontsize=16,color="green",shape="box"];45[label="vz410",fontsize=16,color="green",shape="box"];43[label="(vz70 : vz71 >>= sequence1 (map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];43 -> 48[label="",style="solid", color="black", weight=3]; 13.12/5.07 44[label="([] >>= sequence1 (map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];44 -> 49[label="",style="solid", color="black", weight=3]; 13.12/5.07 46[label="(sequence0 vz50 [] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3]; 13.12/5.07 187[label="foldr unzip0 ([],[]) (vz900 : vz901)",fontsize=16,color="black",shape="box"];187 -> 207[label="",style="solid", color="black", weight=3]; 13.12/5.07 188[label="foldr unzip0 ([],[]) []",fontsize=16,color="black",shape="box"];188 -> 208[label="",style="solid", color="black", weight=3]; 13.12/5.07 48[label="(sequence1 (map vz3 vz411) vz70 ++ (vz71 >>= sequence1 (map vz3 vz411)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];48 -> 51[label="",style="solid", color="black", weight=3]; 13.12/5.07 49[label="([] >>= sequence0 vz50) ++ (vz51 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];49 -> 52[label="",style="solid", color="black", weight=3]; 13.12/5.07 50[label="(return (vz50 : []) ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];50 -> 53[label="",style="solid", color="black", weight=3]; 13.12/5.07 207 -> 220[label="",style="dashed", color="red", weight=0]; 13.12/5.07 207[label="unzip0 vz900 (foldr unzip0 ([],[]) vz901)",fontsize=16,color="magenta"];207 -> 221[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 208[label="([],[])",fontsize=16,color="green",shape="box"];51[label="((sequence (map vz3 vz411) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 vz411)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 vz411)) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];324[label="vz411/vz4110 : vz4111",fontsize=10,color="white",style="solid",shape="box"];51 -> 324[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 324 -> 54[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 325[label="vz411/[]",fontsize=10,color="white",style="solid",shape="box"];51 -> 325[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 325 -> 55[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 52[label="[] ++ (vz51 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 13.12/5.07 53[label="(((vz50 : []) : []) ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3]; 13.12/5.07 221 -> 179[label="",style="dashed", color="red", weight=0]; 13.12/5.07 221[label="foldr unzip0 ([],[]) vz901",fontsize=16,color="magenta"];221 -> 222[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 220[label="unzip0 vz900 vz25",fontsize=16,color="burlywood",shape="triangle"];326[label="vz900/(vz9000,vz9001)",fontsize=10,color="white",style="solid",shape="box"];220 -> 326[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 326 -> 223[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 54[label="((sequence (map vz3 (vz4110 : vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 (vz4110 : vz4111))) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 (vz4110 : vz4111))) >>= return . unzip",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 13.12/5.07 55[label="((sequence (map vz3 []) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 [])) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 [])) >>= return . unzip",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 13.12/5.07 56[label="vz51 >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];327[label="vz51/vz510 : vz511",fontsize=10,color="white",style="solid",shape="box"];56 -> 327[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 327 -> 60[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 328[label="vz51/[]",fontsize=10,color="white",style="solid",shape="box"];56 -> 328[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 328 -> 61[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 57[label="((vz50 : []) : [] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];57 -> 62[label="",style="solid", color="black", weight=3]; 13.12/5.07 222[label="vz901",fontsize=16,color="green",shape="box"];223[label="unzip0 (vz9000,vz9001) vz25",fontsize=16,color="black",shape="box"];223 -> 226[label="",style="solid", color="black", weight=3]; 13.12/5.07 58 -> 68[label="",style="dashed", color="red", weight=0]; 13.12/5.07 58[label="((sequence (vz3 vz4110 : map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : vz3 vz4110 : map vz3 vz4111)) >>= return . unzip",fontsize=16,color="magenta"];58 -> 69[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 58 -> 70[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 58 -> 71[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 58 -> 72[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 58 -> 73[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 58 -> 74[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 58 -> 75[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 59 -> 103[label="",style="dashed", color="red", weight=0]; 13.12/5.07 59[label="((sequence [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : [])) >>= return . unzip",fontsize=16,color="magenta"];59 -> 104[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 59 -> 105[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 59 -> 106[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 59 -> 107[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 60[label="vz510 : vz511 >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="black",shape="box"];60 -> 65[label="",style="solid", color="black", weight=3]; 13.12/5.07 61[label="[] >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="black",shape="box"];61 -> 66[label="",style="solid", color="black", weight=3]; 13.12/5.07 62[label="(vz50 : []) : ([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];62 -> 67[label="",style="solid", color="black", weight=3]; 13.12/5.07 226[label="(vz9000 : unzip00 vz25,vz9001 : unzip01 vz25)",fontsize=16,color="green",shape="box"];226 -> 243[label="",style="dashed", color="green", weight=3]; 13.12/5.07 226 -> 244[label="",style="dashed", color="green", weight=3]; 13.12/5.07 69[label="vz3",fontsize=16,color="green",shape="box"];70[label="vz4110",fontsize=16,color="green",shape="box"];71[label="vz4111",fontsize=16,color="green",shape="box"];72[label="(sequence (vz3 vz4110 : map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];72 -> 83[label="",style="solid", color="black", weight=3]; 13.12/5.07 73[label="vz71",fontsize=16,color="green",shape="box"];74[label="vz70",fontsize=16,color="green",shape="box"];75[label="vz51",fontsize=16,color="green",shape="box"];68[label="vz9 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];329[label="vz9/vz90 : vz91",fontsize=10,color="white",style="solid",shape="box"];68 -> 329[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 329 -> 84[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 330[label="vz9/[]",fontsize=10,color="white",style="solid",shape="box"];68 -> 330[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 330 -> 85[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 104[label="vz71",fontsize=16,color="green",shape="box"];105[label="vz51",fontsize=16,color="green",shape="box"];106[label="vz70",fontsize=16,color="green",shape="box"];107[label="(sequence [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];107 -> 120[label="",style="solid", color="black", weight=3]; 13.12/5.07 103[label="vz18 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];331[label="vz18/vz180 : vz181",fontsize=10,color="white",style="solid",shape="box"];103 -> 331[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 331 -> 121[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 332[label="vz18/[]",fontsize=10,color="white",style="solid",shape="box"];103 -> 332[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 332 -> 122[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 65[label="sequence1 ([] : map vz3 vz411) vz510 ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];65 -> 87[label="",style="solid", color="black", weight=3]; 13.12/5.07 66 -> 21[label="",style="dashed", color="red", weight=0]; 13.12/5.07 66[label="[] >>= return . unzip",fontsize=16,color="magenta"];67 -> 129[label="",style="dashed", color="red", weight=0]; 13.12/5.07 67[label="return . unzip ++ (([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip)",fontsize=16,color="magenta"];67 -> 132[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 67 -> 133[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 243[label="unzip00 vz25",fontsize=16,color="burlywood",shape="box"];333[label="vz25/(vz250,vz251)",fontsize=10,color="white",style="solid",shape="box"];243 -> 333[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 333 -> 260[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 244[label="unzip01 vz25",fontsize=16,color="burlywood",shape="box"];334[label="vz25/(vz250,vz251)",fontsize=10,color="white",style="solid",shape="box"];244 -> 334[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 334 -> 261[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 83 -> 89[label="",style="dashed", color="red", weight=0]; 13.12/5.07 83[label="(vz3 vz4110 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="magenta"];83 -> 90[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 84[label="(vz90 : vz91) ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];84 -> 91[label="",style="solid", color="black", weight=3]; 13.12/5.07 85[label="[] ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];85 -> 92[label="",style="solid", color="black", weight=3]; 13.12/5.07 120[label="(return [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];120 -> 136[label="",style="solid", color="black", weight=3]; 13.12/5.07 121[label="(vz180 : vz181) ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];121 -> 137[label="",style="solid", color="black", weight=3]; 13.12/5.07 122[label="[] ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];122 -> 138[label="",style="solid", color="black", weight=3]; 13.12/5.07 87[label="(sequence ([] : map vz3 vz411) >>= sequence0 vz510) ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];87 -> 94[label="",style="solid", color="black", weight=3]; 13.12/5.07 132[label="vz50 : []",fontsize=16,color="green",shape="box"];133[label="([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3]; 13.12/5.07 260[label="unzip00 (vz250,vz251)",fontsize=16,color="black",shape="box"];260 -> 264[label="",style="solid", color="black", weight=3]; 13.12/5.07 261[label="unzip01 (vz250,vz251)",fontsize=16,color="black",shape="box"];261 -> 265[label="",style="solid", color="black", weight=3]; 13.12/5.07 90[label="vz3 vz4110",fontsize=16,color="green",shape="box"];90 -> 99[label="",style="dashed", color="green", weight=3]; 13.12/5.07 89[label="(vz16 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz16 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];335[label="vz16/vz160 : vz161",fontsize=10,color="white",style="solid",shape="box"];89 -> 335[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 335 -> 97[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 336[label="vz16/[]",fontsize=10,color="white",style="solid",shape="box"];89 -> 336[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 336 -> 98[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 91[label="vz90 : vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];91 -> 100[label="",style="solid", color="black", weight=3]; 13.12/5.07 92[label="vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];337[label="vz10/vz100 : vz101",fontsize=10,color="white",style="solid",shape="box"];92 -> 337[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 337 -> 101[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 338[label="vz10/[]",fontsize=10,color="white",style="solid",shape="box"];92 -> 338[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 338 -> 102[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 136[label="([] : [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];136 -> 146[label="",style="solid", color="black", weight=3]; 13.12/5.07 137[label="vz180 : vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];137 -> 147[label="",style="solid", color="black", weight=3]; 13.12/5.07 138[label="vz19 >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];339[label="vz19/vz190 : vz191",fontsize=10,color="white",style="solid",shape="box"];138 -> 339[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 339 -> 148[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 340[label="vz19/[]",fontsize=10,color="white",style="solid",shape="box"];138 -> 340[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 340 -> 149[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 94 -> 37[label="",style="dashed", color="red", weight=0]; 13.12/5.07 94[label="([] >>= sequence1 (map vz3 vz411) >>= sequence0 vz510) ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="magenta"];94 -> 123[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 94 -> 124[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 94 -> 125[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 139[label="([] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];139 -> 150[label="",style="solid", color="black", weight=3]; 13.12/5.07 264[label="vz250",fontsize=16,color="green",shape="box"];265[label="vz251",fontsize=16,color="green",shape="box"];99[label="vz4110",fontsize=16,color="green",shape="box"];97[label="(vz160 : vz161 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];97 -> 127[label="",style="solid", color="black", weight=3]; 13.12/5.07 98[label="([] >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];98 -> 128[label="",style="solid", color="black", weight=3]; 13.12/5.07 100 -> 129[label="",style="dashed", color="red", weight=0]; 13.12/5.07 100[label="return . unzip ++ (vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip)",fontsize=16,color="magenta"];100 -> 134[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 101[label="vz100 : vz101 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="black",shape="box"];101 -> 140[label="",style="solid", color="black", weight=3]; 13.12/5.07 102[label="[] >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="black",shape="box"];102 -> 141[label="",style="solid", color="black", weight=3]; 13.12/5.07 146[label="(sequence0 vz70 [] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];146 -> 157[label="",style="solid", color="black", weight=3]; 13.12/5.07 147 -> 129[label="",style="dashed", color="red", weight=0]; 13.12/5.07 147[label="return . unzip ++ (vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip)",fontsize=16,color="magenta"];147 -> 158[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 147 -> 159[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 148[label="vz190 : vz191 >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="black",shape="box"];148 -> 160[label="",style="solid", color="black", weight=3]; 13.12/5.07 149[label="[] >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="black",shape="box"];149 -> 161[label="",style="solid", color="black", weight=3]; 13.12/5.07 123[label="[]",fontsize=16,color="green",shape="box"];124[label="vz510",fontsize=16,color="green",shape="box"];125[label="vz511",fontsize=16,color="green",shape="box"];150[label="[] ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];150 -> 162[label="",style="solid", color="black", weight=3]; 13.12/5.07 127[label="(sequence1 (map vz3 vz4111) vz160 ++ (vz161 >>= sequence1 (map vz3 vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];127 -> 142[label="",style="solid", color="black", weight=3]; 13.12/5.07 128[label="([] >>= sequence0 vz70) ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];128 -> 143[label="",style="solid", color="black", weight=3]; 13.12/5.07 134 -> 68[label="",style="dashed", color="red", weight=0]; 13.12/5.07 134[label="vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="magenta"];134 -> 144[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 140 -> 68[label="",style="dashed", color="red", weight=0]; 13.12/5.07 140[label="sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) vz100 ++ (vz101 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="magenta"];140 -> 151[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 140 -> 152[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 141 -> 21[label="",style="dashed", color="red", weight=0]; 13.12/5.07 141[label="[] >>= return . unzip",fontsize=16,color="magenta"];157[label="(return (vz70 : []) ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];157 -> 170[label="",style="solid", color="black", weight=3]; 13.12/5.07 158[label="vz180",fontsize=16,color="green",shape="box"];159 -> 103[label="",style="dashed", color="red", weight=0]; 13.12/5.07 159[label="vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="magenta"];159 -> 171[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 160 -> 103[label="",style="dashed", color="red", weight=0]; 13.12/5.07 160[label="sequence1 ((vz20 : vz21) : []) vz190 ++ (vz191 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="magenta"];160 -> 172[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 160 -> 173[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 161 -> 21[label="",style="dashed", color="red", weight=0]; 13.12/5.07 161[label="[] >>= return . unzip",fontsize=16,color="magenta"];162[label="vz51 >>= sequence1 [] >>= return . unzip",fontsize=16,color="burlywood",shape="box"];341[label="vz51/vz510 : vz511",fontsize=10,color="white",style="solid",shape="box"];162 -> 341[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 341 -> 174[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 342[label="vz51/[]",fontsize=10,color="white",style="solid",shape="box"];162 -> 342[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 342 -> 175[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 142[label="((sequence (map vz3 vz4111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];343[label="vz4111/vz41110 : vz41111",fontsize=10,color="white",style="solid",shape="box"];142 -> 343[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 343 -> 153[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 344[label="vz4111/[]",fontsize=10,color="white",style="solid",shape="box"];142 -> 344[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 344 -> 154[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 143[label="[] ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];143 -> 155[label="",style="solid", color="black", weight=3]; 13.12/5.07 144[label="vz91",fontsize=16,color="green",shape="box"];151[label="sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) vz100",fontsize=16,color="black",shape="triangle"];151 -> 163[label="",style="solid", color="black", weight=3]; 13.12/5.07 152[label="vz101",fontsize=16,color="green",shape="box"];170[label="(((vz70 : []) : []) ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];170 -> 181[label="",style="solid", color="black", weight=3]; 13.12/5.07 171[label="vz181",fontsize=16,color="green",shape="box"];172[label="vz191",fontsize=16,color="green",shape="box"];173[label="sequence1 ((vz20 : vz21) : []) vz190",fontsize=16,color="black",shape="triangle"];173 -> 182[label="",style="solid", color="black", weight=3]; 13.12/5.07 174[label="vz510 : vz511 >>= sequence1 [] >>= return . unzip",fontsize=16,color="black",shape="box"];174 -> 183[label="",style="solid", color="black", weight=3]; 13.12/5.07 175[label="[] >>= sequence1 [] >>= return . unzip",fontsize=16,color="black",shape="box"];175 -> 184[label="",style="solid", color="black", weight=3]; 13.12/5.07 153[label="((sequence (map vz3 (vz41110 : vz41111)) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 (vz41110 : vz41111))) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 (vz41110 : vz41111))) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];153 -> 164[label="",style="solid", color="black", weight=3]; 13.12/5.07 154[label="((sequence (map vz3 []) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 [])) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];154 -> 165[label="",style="solid", color="black", weight=3]; 13.12/5.07 155[label="vz71 >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];345[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];155 -> 345[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 345 -> 166[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 346[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];155 -> 346[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 346 -> 167[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 163[label="sequence ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];163 -> 176[label="",style="solid", color="black", weight=3]; 13.12/5.07 181[label="((vz70 : []) : [] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];181 -> 189[label="",style="solid", color="black", weight=3]; 13.12/5.07 182[label="sequence ((vz20 : vz21) : []) >>= sequence0 vz190",fontsize=16,color="black",shape="box"];182 -> 190[label="",style="solid", color="black", weight=3]; 13.12/5.07 183[label="sequence1 [] vz510 ++ (vz511 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];183 -> 191[label="",style="solid", color="black", weight=3]; 13.12/5.07 184 -> 21[label="",style="dashed", color="red", weight=0]; 13.12/5.07 184[label="[] >>= return . unzip",fontsize=16,color="magenta"];164 -> 177[label="",style="dashed", color="red", weight=0]; 13.12/5.07 164[label="((sequence (vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];164 -> 178[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 165 -> 185[label="",style="dashed", color="red", weight=0]; 13.12/5.07 165[label="((sequence [] >>= sequence0 vz160) ++ (vz161 >>= sequence1 []) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];165 -> 186[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 166[label="vz710 : vz711 >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];166 -> 192[label="",style="solid", color="black", weight=3]; 13.12/5.07 167[label="[] >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];167 -> 193[label="",style="solid", color="black", weight=3]; 13.12/5.07 176[label="vz11 : vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];176 -> 194[label="",style="solid", color="black", weight=3]; 13.12/5.07 189[label="(vz70 : []) : ([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];189 -> 209[label="",style="solid", color="black", weight=3]; 13.12/5.07 190[label="vz20 : vz21 >>= sequence1 [] >>= sequence0 vz190",fontsize=16,color="black",shape="box"];190 -> 210[label="",style="solid", color="black", weight=3]; 13.12/5.07 191 -> 31[label="",style="dashed", color="red", weight=0]; 13.12/5.07 191[label="(sequence [] >>= sequence0 vz510) ++ (vz511 >>= sequence1 []) >>= return . unzip",fontsize=16,color="magenta"];191 -> 211[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 191 -> 212[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 178 -> 72[label="",style="dashed", color="red", weight=0]; 13.12/5.07 178[label="(sequence (vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz70",fontsize=16,color="magenta"];178 -> 195[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 178 -> 196[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 178 -> 197[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 178 -> 198[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 178 -> 199[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 177[label="vz23 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];347[label="vz23/vz230 : vz231",fontsize=10,color="white",style="solid",shape="box"];177 -> 347[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 347 -> 200[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 348[label="vz23/[]",fontsize=10,color="white",style="solid",shape="box"];177 -> 348[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 348 -> 201[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 186 -> 107[label="",style="dashed", color="red", weight=0]; 13.12/5.07 186[label="(sequence [] >>= sequence0 vz160) ++ (vz161 >>= sequence1 []) >>= sequence0 vz70",fontsize=16,color="magenta"];186 -> 202[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 186 -> 203[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 186 -> 204[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 185[label="vz24 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];349[label="vz24/vz240 : vz241",fontsize=10,color="white",style="solid",shape="box"];185 -> 349[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 349 -> 205[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 350[label="vz24/[]",fontsize=10,color="white",style="solid",shape="box"];185 -> 350[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 350 -> 206[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 192[label="sequence1 ([] : map vz3 vz4111) vz710 ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];192 -> 213[label="",style="solid", color="black", weight=3]; 13.12/5.07 193[label="[] >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];193 -> 214[label="",style="solid", color="black", weight=3]; 13.12/5.07 194[label="sequence1 (vz13 vz14 : map vz13 vz15) vz11 ++ (vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15)) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];194 -> 215[label="",style="solid", color="black", weight=3]; 13.12/5.07 209 -> 252[label="",style="dashed", color="red", weight=0]; 13.12/5.07 209[label="sequence0 vz50 (vz70 : []) ++ (([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50)",fontsize=16,color="magenta"];209 -> 253[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 209 -> 254[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 210[label="sequence1 [] vz20 ++ (vz21 >>= sequence1 []) >>= sequence0 vz190",fontsize=16,color="black",shape="box"];210 -> 227[label="",style="solid", color="black", weight=3]; 13.12/5.07 211[label="vz510",fontsize=16,color="green",shape="box"];212[label="vz511",fontsize=16,color="green",shape="box"];195[label="vz160",fontsize=16,color="green",shape="box"];196[label="vz161",fontsize=16,color="green",shape="box"];197[label="vz70",fontsize=16,color="green",shape="box"];198[label="vz41110",fontsize=16,color="green",shape="box"];199[label="vz41111",fontsize=16,color="green",shape="box"];200[label="(vz230 : vz231) ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];200 -> 216[label="",style="solid", color="black", weight=3]; 13.12/5.07 201[label="[] ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];201 -> 217[label="",style="solid", color="black", weight=3]; 13.12/5.07 202[label="vz160",fontsize=16,color="green",shape="box"];203[label="vz161",fontsize=16,color="green",shape="box"];204[label="vz70",fontsize=16,color="green",shape="box"];205[label="(vz240 : vz241) ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];205 -> 218[label="",style="solid", color="black", weight=3]; 13.12/5.07 206[label="[] ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];206 -> 219[label="",style="solid", color="black", weight=3]; 13.12/5.07 213[label="(sequence ([] : map vz3 vz4111) >>= sequence0 vz710) ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];213 -> 228[label="",style="solid", color="black", weight=3]; 13.12/5.07 214[label="[]",fontsize=16,color="green",shape="box"];215 -> 72[label="",style="dashed", color="red", weight=0]; 13.12/5.07 215[label="(sequence (vz13 vz14 : map vz13 vz15) >>= sequence0 vz11) ++ (vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15)) >>= sequence0 vz100",fontsize=16,color="magenta"];215 -> 229[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 215 -> 230[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 215 -> 231[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 215 -> 232[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 215 -> 233[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 215 -> 234[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 253[label="vz70 : []",fontsize=16,color="green",shape="box"];254 -> 262[label="",style="dashed", color="red", weight=0]; 13.12/5.07 254[label="([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];254 -> 263[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 252[label="sequence0 vz50 vz230 ++ vz27",fontsize=16,color="black",shape="triangle"];252 -> 266[label="",style="solid", color="black", weight=3]; 13.12/5.07 227 -> 107[label="",style="dashed", color="red", weight=0]; 13.12/5.07 227[label="(sequence [] >>= sequence0 vz20) ++ (vz21 >>= sequence1 []) >>= sequence0 vz190",fontsize=16,color="magenta"];227 -> 245[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 227 -> 246[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 227 -> 247[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 216[label="vz230 : vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];216 -> 237[label="",style="solid", color="black", weight=3]; 13.12/5.07 217[label="vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];351[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];217 -> 351[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 351 -> 238[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 352[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];217 -> 352[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 352 -> 239[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 218[label="vz240 : vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];218 -> 240[label="",style="solid", color="black", weight=3]; 13.12/5.07 219[label="vz71 >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];353[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];219 -> 353[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 353 -> 241[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 354[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];219 -> 354[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 354 -> 242[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 228 -> 89[label="",style="dashed", color="red", weight=0]; 13.12/5.07 228[label="([] >>= sequence1 (map vz3 vz4111) >>= sequence0 vz710) ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="magenta"];228 -> 248[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 228 -> 249[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 228 -> 250[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 229[label="vz13",fontsize=16,color="green",shape="box"];230[label="vz11",fontsize=16,color="green",shape="box"];231[label="vz12",fontsize=16,color="green",shape="box"];232[label="vz100",fontsize=16,color="green",shape="box"];233[label="vz14",fontsize=16,color="green",shape="box"];234[label="vz15",fontsize=16,color="green",shape="box"];263 -> 193[label="",style="dashed", color="red", weight=0]; 13.12/5.07 263[label="[] >>= sequence0 vz70",fontsize=16,color="magenta"];263 -> 267[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 262[label="([] ++ vz28) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];262 -> 268[label="",style="solid", color="black", weight=3]; 13.12/5.07 266[label="return (vz50 : vz230) ++ vz27",fontsize=16,color="black",shape="box"];266 -> 275[label="",style="solid", color="black", weight=3]; 13.12/5.07 245[label="vz20",fontsize=16,color="green",shape="box"];246[label="vz21",fontsize=16,color="green",shape="box"];247[label="vz190",fontsize=16,color="green",shape="box"];237 -> 252[label="",style="dashed", color="red", weight=0]; 13.12/5.07 237[label="sequence0 vz50 vz230 ++ (vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50)",fontsize=16,color="magenta"];237 -> 257[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 238[label="vz710 : vz711 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];238 -> 269[label="",style="solid", color="black", weight=3]; 13.12/5.07 239[label="[] >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];239 -> 270[label="",style="solid", color="black", weight=3]; 13.12/5.07 240 -> 252[label="",style="dashed", color="red", weight=0]; 13.12/5.07 240[label="sequence0 vz50 vz240 ++ (vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50)",fontsize=16,color="magenta"];240 -> 258[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 240 -> 259[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 241[label="vz710 : vz711 >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];241 -> 271[label="",style="solid", color="black", weight=3]; 13.12/5.07 242[label="[] >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];242 -> 272[label="",style="solid", color="black", weight=3]; 13.12/5.07 248[label="vz710",fontsize=16,color="green",shape="box"];249[label="vz711",fontsize=16,color="green",shape="box"];250[label="[]",fontsize=16,color="green",shape="box"];267[label="vz70",fontsize=16,color="green",shape="box"];268[label="vz28 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];355[label="vz28/vz280 : vz281",fontsize=10,color="white",style="solid",shape="box"];268 -> 355[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 355 -> 276[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 356[label="vz28/[]",fontsize=10,color="white",style="solid",shape="box"];268 -> 356[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 356 -> 277[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 275[label="((vz50 : vz230) : []) ++ vz27",fontsize=16,color="black",shape="box"];275 -> 282[label="",style="solid", color="black", weight=3]; 13.12/5.07 257 -> 177[label="",style="dashed", color="red", weight=0]; 13.12/5.07 257[label="vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];257 -> 273[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 269 -> 177[label="",style="dashed", color="red", weight=0]; 13.12/5.07 269[label="sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) vz710 ++ (vz711 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];269 -> 278[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 269 -> 279[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 270 -> 193[label="",style="dashed", color="red", weight=0]; 13.12/5.07 270[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];258[label="vz240",fontsize=16,color="green",shape="box"];259 -> 185[label="",style="dashed", color="red", weight=0]; 13.12/5.07 259[label="vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];259 -> 274[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 271 -> 185[label="",style="dashed", color="red", weight=0]; 13.12/5.07 271[label="sequence1 ((vz160 : vz161) : []) vz710 ++ (vz711 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];271 -> 280[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 271 -> 281[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 272 -> 193[label="",style="dashed", color="red", weight=0]; 13.12/5.07 272[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];276[label="(vz280 : vz281) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];276 -> 283[label="",style="solid", color="black", weight=3]; 13.12/5.07 277[label="[] ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];277 -> 284[label="",style="solid", color="black", weight=3]; 13.12/5.07 282[label="(vz50 : vz230) : [] ++ vz27",fontsize=16,color="green",shape="box"];282 -> 294[label="",style="dashed", color="green", weight=3]; 13.12/5.07 273[label="vz231",fontsize=16,color="green",shape="box"];278[label="vz711",fontsize=16,color="green",shape="box"];279 -> 151[label="",style="dashed", color="red", weight=0]; 13.12/5.07 279[label="sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) vz710",fontsize=16,color="magenta"];279 -> 285[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 279 -> 286[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 279 -> 287[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 279 -> 288[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 279 -> 289[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 279 -> 290[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 274[label="vz241",fontsize=16,color="green",shape="box"];280[label="vz711",fontsize=16,color="green",shape="box"];281 -> 173[label="",style="dashed", color="red", weight=0]; 13.12/5.07 281[label="sequence1 ((vz160 : vz161) : []) vz710",fontsize=16,color="magenta"];281 -> 291[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 281 -> 292[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 281 -> 293[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 283[label="vz280 : vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];283 -> 295[label="",style="solid", color="black", weight=3]; 13.12/5.07 284[label="vz71 >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];357[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];284 -> 357[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 357 -> 296[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 358[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];284 -> 358[label="",style="solid", color="burlywood", weight=9]; 13.12/5.07 358 -> 297[label="",style="solid", color="burlywood", weight=3]; 13.12/5.07 294[label="[] ++ vz27",fontsize=16,color="black",shape="box"];294 -> 298[label="",style="solid", color="black", weight=3]; 13.12/5.07 285[label="vz3",fontsize=16,color="green",shape="box"];286[label="vz41110",fontsize=16,color="green",shape="box"];287[label="vz41111",fontsize=16,color="green",shape="box"];288[label="vz161",fontsize=16,color="green",shape="box"];289[label="vz160",fontsize=16,color="green",shape="box"];290[label="vz710",fontsize=16,color="green",shape="box"];291[label="vz161",fontsize=16,color="green",shape="box"];292[label="vz160",fontsize=16,color="green",shape="box"];293[label="vz710",fontsize=16,color="green",shape="box"];295 -> 252[label="",style="dashed", color="red", weight=0]; 13.12/5.07 295[label="sequence0 vz50 vz280 ++ (vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50)",fontsize=16,color="magenta"];295 -> 299[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 295 -> 300[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 296[label="vz710 : vz711 >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="black",shape="box"];296 -> 301[label="",style="solid", color="black", weight=3]; 13.12/5.07 297[label="[] >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="black",shape="box"];297 -> 302[label="",style="solid", color="black", weight=3]; 13.12/5.07 298[label="vz27",fontsize=16,color="green",shape="box"];299[label="vz280",fontsize=16,color="green",shape="box"];300 -> 268[label="",style="dashed", color="red", weight=0]; 13.12/5.07 300[label="vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];300 -> 303[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 301 -> 268[label="",style="dashed", color="red", weight=0]; 13.12/5.07 301[label="sequence1 [] vz710 ++ (vz711 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];301 -> 304[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 301 -> 305[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 302 -> 193[label="",style="dashed", color="red", weight=0]; 13.12/5.07 302[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];303[label="vz281",fontsize=16,color="green",shape="box"];304[label="sequence1 [] vz710",fontsize=16,color="black",shape="box"];304 -> 306[label="",style="solid", color="black", weight=3]; 13.12/5.07 305[label="vz711",fontsize=16,color="green",shape="box"];306[label="sequence [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];306 -> 307[label="",style="solid", color="black", weight=3]; 13.12/5.07 307[label="return [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];307 -> 308[label="",style="solid", color="black", weight=3]; 13.12/5.07 308[label="[] : [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];308 -> 309[label="",style="solid", color="black", weight=3]; 13.12/5.07 309 -> 252[label="",style="dashed", color="red", weight=0]; 13.12/5.07 309[label="sequence0 vz710 [] ++ ([] >>= sequence0 vz710)",fontsize=16,color="magenta"];309 -> 310[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 309 -> 311[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 309 -> 312[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 310[label="vz710",fontsize=16,color="green",shape="box"];311[label="[]",fontsize=16,color="green",shape="box"];312 -> 193[label="",style="dashed", color="red", weight=0]; 13.12/5.07 312[label="[] >>= sequence0 vz710",fontsize=16,color="magenta"];312 -> 313[label="",style="dashed", color="magenta", weight=3]; 13.12/5.07 313[label="vz710",fontsize=16,color="green",shape="box"];} 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (10) 13.12/5.07 Complex Obligation (AND) 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (11) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_sequence1(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_sequence1(vz20, vz21, vz190, bb, bc) -> new_gtGtEs2(vz20, vz21, vz190, bb, bc) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 new_gtGtEs2(vz70, vz71, vz50, h, ba) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, h, ba), vz71, vz50, h, ba), h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_gtGtEs2(x0, x1, x2, x3, x4) 13.12/5.07 new_sequence1(x0, x1, x2, x3, x4) 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (12) TransformationProof (EQUIVALENT) 13.12/5.07 By rewriting [LPAR04] the rule new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_sequence1(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba) at position [0] we obtained the following new rules [LPAR04]: 13.12/5.07 13.12/5.07 (new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_gtGtEs2(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba),new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_gtGtEs2(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba)) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (13) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_gtGtEs2(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_sequence1(vz20, vz21, vz190, bb, bc) -> new_gtGtEs2(vz20, vz21, vz190, bb, bc) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 new_gtGtEs2(vz70, vz71, vz50, h, ba) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, h, ba), vz71, vz50, h, ba), h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_gtGtEs2(x0, x1, x2, x3, x4) 13.12/5.07 new_sequence1(x0, x1, x2, x3, x4) 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (14) UsableRulesProof (EQUIVALENT) 13.12/5.07 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (15) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_gtGtEs2(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs2(vz70, vz71, vz50, h, ba) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, h, ba), vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_gtGtEs2(x0, x1, x2, x3, x4) 13.12/5.07 new_sequence1(x0, x1, x2, x3, x4) 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (16) QReductionProof (EQUIVALENT) 13.12/5.07 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.12/5.07 13.12/5.07 new_sequence1(x0, x1, x2, x3, x4) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (17) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_gtGtEs2(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs2(vz70, vz71, vz50, h, ba) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, h, ba), vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_gtGtEs2(x0, x1, x2, x3, x4) 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (18) TransformationProof (EQUIVALENT) 13.12/5.07 By rewriting [LPAR04] the rule new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_gtGtEs2(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba) at position [0] we obtained the following new rules [LPAR04]: 13.12/5.07 13.12/5.07 (new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_psPs(vz710, :(vz160, []), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba), h, ba), vz711, vz160, vz161, vz50, h, ba),new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_psPs(vz710, :(vz160, []), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba), h, ba), vz711, vz160, vz161, vz50, h, ba)) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (19) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_psPs(vz710, :(vz160, []), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba), h, ba), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs2(vz70, vz71, vz50, h, ba) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, h, ba), vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_gtGtEs2(x0, x1, x2, x3, x4) 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (20) UsableRulesProof (EQUIVALENT) 13.12/5.07 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (21) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_psPs(vz710, :(vz160, []), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba), h, ba), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_gtGtEs2(x0, x1, x2, x3, x4) 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (22) QReductionProof (EQUIVALENT) 13.12/5.07 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.12/5.07 13.12/5.07 new_gtGtEs2(x0, x1, x2, x3, x4) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (23) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_psPs(vz710, :(vz160, []), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba), h, ba), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (24) TransformationProof (EQUIVALENT) 13.12/5.07 By rewriting [LPAR04] the rule new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(new_psPs(vz710, :(vz160, []), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba), h, ba), vz711, vz160, vz161, vz50, h, ba) at position [0] we obtained the following new rules [LPAR04]: 13.12/5.07 13.12/5.07 (new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba),new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba)) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (25) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (26) TransformationProof (EQUIVALENT) 13.12/5.07 By rewriting [LPAR04] the rule new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs3(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) at position [0,1] we obtained the following new rules [LPAR04]: 13.12/5.07 13.12/5.07 (new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba),new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba)) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (27) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs3(vz28, vz71, vz50, h, ba) -> new_gtGtEs4(vz28, vz71, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (28) UsableRulesProof (EQUIVALENT) 13.12/5.07 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (29) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (30) QReductionProof (EQUIVALENT) 13.12/5.07 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.12/5.07 13.12/5.07 new_gtGtEs3(x0, x1, x2, x3, x4) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (31) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (32) TransformationProof (EQUIVALENT) 13.12/5.07 By rewriting [LPAR04] the rule new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4(new_gtGtEs0(vz160, h, ba), vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) at position [0,1,0] we obtained the following new rules [LPAR04]: 13.12/5.07 13.12/5.07 (new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4([], vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba),new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4([], vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba)) 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (33) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4([], vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs0(vz50, h, ba) -> [] 13.12/5.07 new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba) 13.12/5.07 new_gtGtEs4([], [], vz50, h, ba) -> new_gtGtEs0(vz50, h, ba) 13.12/5.07 new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.12/5.07 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_psPs(x0, x1, x2, x3, x4) 13.12/5.07 new_gtGtEs4([], [], x0, x1, x2) 13.12/5.07 new_gtGtEs0(x0, x1, x2) 13.12/5.07 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.12/5.07 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (34) QDPSizeChangeProof (EQUIVALENT) 13.12/5.07 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 13.12/5.07 13.12/5.07 From the DPs we obtained the following set of size-change graphs: 13.12/5.07 *new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) -> new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba) 13.12/5.07 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7 13.12/5.07 13.12/5.07 13.12/5.07 *new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) -> new_gtGtEs1(:(:(vz710, :(vz160, [])), new_gtGtEs4([], vz161, vz710, h, ba)), vz711, vz160, vz161, vz50, h, ba) 13.12/5.07 The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (35) 13.12/5.07 YES 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (36) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) -> new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) 13.12/5.07 new_gtGtEs11([], :(vz100, vz101), vz11, vz12, vz13, vz14, vz15, h, ba, bb) -> new_gtGtEs11(new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, h, ba, bb), vz101, vz11, vz12, vz13, vz14, vz15, h, ba, bb) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, h, ba, bb) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, h, ba, bb) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (37) DependencyGraphProof (EQUIVALENT) 13.12/5.07 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (38) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) -> new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) 13.12/5.07 13.12/5.07 The TRS R consists of the following rules: 13.12/5.07 13.12/5.07 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, h, ba, bb) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, h, ba, bb) 13.12/5.07 13.12/5.07 The set Q consists of the following terms: 13.12/5.07 13.12/5.07 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.12/5.07 13.12/5.07 We have to consider all minimal (P,Q,R)-chains. 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (39) QDPSizeChangeProof (EQUIVALENT) 13.12/5.07 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 13.12/5.07 13.12/5.07 From the DPs we obtained the following set of size-change graphs: 13.12/5.07 *new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) -> new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) 13.12/5.07 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 13.12/5.07 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (40) 13.12/5.07 YES 13.12/5.07 13.12/5.07 ---------------------------------------- 13.12/5.07 13.12/5.07 (41) 13.12/5.07 Obligation: 13.12/5.07 Q DP problem: 13.12/5.07 The TRS P consists of the following rules: 13.12/5.07 13.12/5.07 new_foldr(:(vz900, vz901), h, ba) -> new_foldr(vz901, h, ba) 13.39/5.07 13.39/5.07 R is empty. 13.39/5.07 Q is empty. 13.39/5.07 We have to consider all minimal (P,Q,R)-chains. 13.39/5.07 ---------------------------------------- 13.39/5.07 13.39/5.07 (42) QDPSizeChangeProof (EQUIVALENT) 13.39/5.07 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 13.39/5.07 13.39/5.07 From the DPs we obtained the following set of size-change graphs: 13.39/5.07 *new_foldr(:(vz900, vz901), h, ba) -> new_foldr(vz901, h, ba) 13.39/5.07 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 13.39/5.07 13.39/5.07 13.39/5.07 ---------------------------------------- 13.39/5.07 13.39/5.07 (43) 13.39/5.07 YES 13.39/5.07 13.39/5.07 ---------------------------------------- 13.39/5.07 13.39/5.07 (44) 13.39/5.07 Obligation: 13.39/5.07 Q DP problem: 13.39/5.07 The TRS P consists of the following rules: 13.39/5.07 13.39/5.07 new_gtGtEs9(vz50, :(vz510, vz511), h, ba) -> new_gtGtEs9(vz510, vz511, h, ba) 13.39/5.07 13.39/5.07 R is empty. 13.39/5.07 Q is empty. 13.39/5.07 We have to consider all minimal (P,Q,R)-chains. 13.39/5.07 ---------------------------------------- 13.39/5.07 13.39/5.07 (45) QDPSizeChangeProof (EQUIVALENT) 13.39/5.07 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 13.39/5.07 13.39/5.07 From the DPs we obtained the following set of size-change graphs: 13.39/5.07 *new_gtGtEs9(vz50, :(vz510, vz511), h, ba) -> new_gtGtEs9(vz510, vz511, h, ba) 13.39/5.07 The graph contains the following edges 2 > 1, 2 > 2, 3 >= 3, 4 >= 4 13.39/5.07 13.39/5.07 13.39/5.07 ---------------------------------------- 13.39/5.07 13.39/5.07 (46) 13.39/5.07 YES 13.39/5.07 13.39/5.07 ---------------------------------------- 13.39/5.07 13.39/5.07 (47) 13.39/5.07 Obligation: 13.39/5.07 Q DP problem: 13.39/5.07 The TRS P consists of the following rules: 13.39/5.07 13.39/5.07 new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) -> new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.07 new_gtGtEs6(vz3, vz4111, h, ba, bb) -> new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.07 new_gtGtEs5(vz3, vz4110, vz4111, h, ba, bb) -> new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.07 new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) -> new_sequence11(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.07 new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) -> new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.07 new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) -> new_gtGtEs5(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.07 new_sequence11(vz13, vz14, vz15, bc, bd, be) -> new_gtGtEs5(vz13, vz14, vz15, bc, bd, be) 13.39/5.07 13.39/5.07 The TRS R consists of the following rules: 13.39/5.07 13.39/5.07 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, bc, bd, be) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, bc, bd, be) 13.39/5.07 13.39/5.07 The set Q consists of the following terms: 13.39/5.07 13.39/5.07 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.07 13.39/5.07 We have to consider all minimal (P,Q,R)-chains. 13.39/5.07 ---------------------------------------- 13.39/5.07 13.39/5.07 (48) MRRProof (EQUIVALENT) 13.39/5.07 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 13.39/5.07 13.39/5.07 Strictly oriented dependency pairs: 13.39/5.07 13.39/5.07 new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) -> new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.07 new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) -> new_gtGtEs5(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.07 new_sequence11(vz13, vz14, vz15, bc, bd, be) -> new_gtGtEs5(vz13, vz14, vz15, bc, bd, be) 13.39/5.08 13.39/5.08 13.39/5.08 Used ordering: Polynomial interpretation [POLO]: 13.39/5.08 13.39/5.08 POL(:(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 13.39/5.08 POL(new_gtGtEs5(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_1 + 2*x_2 + 2*x_3 + x_4 + x_5 + x_6 13.39/5.08 POL(new_gtGtEs6(x_1, x_2, x_3, x_4, x_5)) = 1 + x_1 + 2*x_2 + x_3 + x_4 + x_5 13.39/5.08 POL(new_gtGtEs7(x_1, x_2, x_3, x_4, x_5, x_6)) = 2 + x_1 + 2*x_2 + 2*x_3 + x_4 + x_5 + x_6 13.39/5.08 POL(new_gtGtEs8(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9)) = 2 + x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 13.39/5.08 POL(new_sequence10(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 + 2*x_4 + 2*x_5 + 2*x_6 + 2*x_7 + 2*x_8 + 2*x_9 13.39/5.08 POL(new_sequence11(x_1, x_2, x_3, x_4, x_5, x_6)) = 2 + x_1 + 2*x_2 + 2*x_3 + x_4 + x_5 + x_6 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (49) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) -> new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.08 new_gtGtEs6(vz3, vz4111, h, ba, bb) -> new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.08 new_gtGtEs5(vz3, vz4110, vz4111, h, ba, bb) -> new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.08 new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) -> new_sequence11(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, bc, bd, be) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, bc, bd, be) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (50) DependencyGraphProof (EQUIVALENT) 13.39/5.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (51) 13.39/5.08 Complex Obligation (AND) 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (52) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs6(vz3, vz4111, h, ba, bb) -> new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, bc, bd, be) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, bc, bd, be) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (53) MRRProof (EQUIVALENT) 13.39/5.08 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 13.39/5.08 13.39/5.08 13.39/5.08 Strictly oriented rules of the TRS R: 13.39/5.08 13.39/5.08 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, bc, bd, be) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, bc, bd, be) 13.39/5.08 13.39/5.08 Used ordering: Polynomial interpretation [POLO]: 13.39/5.08 13.39/5.08 POL(new_gtGtEs6(x_1, x_2, x_3, x_4, x_5)) = x_1 + x_2 + x_3 + x_4 + x_5 13.39/5.08 POL(new_gtGtEs8(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9)) = 1 + x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 13.39/5.08 POL(new_sequence10(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 + 2*x_4 + 2*x_5 + 2*x_6 + 2*x_7 + 2*x_8 + 2*x_9 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (54) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs6(vz3, vz4111, h, ba, bb) -> new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.08 13.39/5.08 R is empty. 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (55) QReductionProof (EQUIVALENT) 13.39/5.08 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.39/5.08 13.39/5.08 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (56) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs6(vz3, vz4111, h, ba, bb) -> new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.08 13.39/5.08 R is empty. 13.39/5.08 Q is empty. 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (57) NonTerminationLoopProof (COMPLETE) 13.39/5.08 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 13.39/5.08 Found a loop by semiunifying a rule from P directly. 13.39/5.08 13.39/5.08 s = new_gtGtEs6(vz3, vz4111, h, ba, bb) evaluates to t =new_gtGtEs6(vz3, vz4111, h, ba, bb) 13.39/5.08 13.39/5.08 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 13.39/5.08 * Matcher: [ ] 13.39/5.08 * Semiunifier: [ ] 13.39/5.08 13.39/5.08 -------------------------------------------------------------------------------- 13.39/5.08 Rewriting sequence 13.39/5.08 13.39/5.08 The DP semiunifies directly so there is only one rewrite step from new_gtGtEs6(vz3, vz4111, h, ba, bb) to new_gtGtEs6(vz3, vz4111, h, ba, bb). 13.39/5.08 13.39/5.08 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (58) 13.39/5.08 NO 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (59) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) -> new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, bc, bd, be) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, bc, bd, be) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (60) MRRProof (EQUIVALENT) 13.39/5.08 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 13.39/5.08 13.39/5.08 13.39/5.08 Strictly oriented rules of the TRS R: 13.39/5.08 13.39/5.08 new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, bc, bd, be) -> new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, bc, bd, be) 13.39/5.08 13.39/5.08 Used ordering: Polynomial interpretation [POLO]: 13.39/5.08 13.39/5.08 POL(new_gtGtEs7(x_1, x_2, x_3, x_4, x_5, x_6)) = x_1 + x_2 + x_3 + x_4 + x_5 + x_6 13.39/5.08 POL(new_gtGtEs8(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9)) = 1 + x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 13.39/5.08 POL(new_sequence10(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 + 2*x_4 + 2*x_5 + 2*x_6 + 2*x_7 + 2*x_8 + 2*x_9 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (61) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) -> new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.08 13.39/5.08 R is empty. 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (62) QReductionProof (EQUIVALENT) 13.39/5.08 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.39/5.08 13.39/5.08 new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (63) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) -> new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.08 13.39/5.08 R is empty. 13.39/5.08 Q is empty. 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (64) NonTerminationLoopProof (COMPLETE) 13.39/5.08 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 13.39/5.08 Found a loop by semiunifying a rule from P directly. 13.39/5.08 13.39/5.08 s = new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) evaluates to t =new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) 13.39/5.08 13.39/5.08 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 13.39/5.08 * Matcher: [ ] 13.39/5.08 * Semiunifier: [ ] 13.39/5.08 13.39/5.08 -------------------------------------------------------------------------------- 13.39/5.08 Rewriting sequence 13.39/5.08 13.39/5.08 The DP semiunifies directly so there is only one rewrite step from new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) to new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb). 13.39/5.08 13.39/5.08 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (65) 13.39/5.08 NO 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (66) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) 13.39/5.08 new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, h, ba) -> [] 13.39/5.08 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (67) TransformationProof (EQUIVALENT) 13.39/5.08 By rewriting [LPAR04] the rule new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba) at position [0] we obtained the following new rules [LPAR04]: 13.39/5.08 13.39/5.08 (new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), new_gtGtEs0(vz710, h, ba)), vz711, vz50, h, ba),new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), new_gtGtEs0(vz710, h, ba)), vz711, vz50, h, ba)) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (68) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), new_gtGtEs0(vz710, h, ba)), vz711, vz50, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, h, ba) -> [] 13.39/5.08 new_psPs(vz50, vz230, vz27, h, ba) -> :(:(vz50, vz230), vz27) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (69) UsableRulesProof (EQUIVALENT) 13.39/5.08 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (70) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), new_gtGtEs0(vz710, h, ba)), vz711, vz50, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, h, ba) -> [] 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (71) QReductionProof (EQUIVALENT) 13.39/5.08 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.39/5.08 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (72) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), new_gtGtEs0(vz710, h, ba)), vz711, vz50, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, h, ba) -> [] 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (73) TransformationProof (EQUIVALENT) 13.39/5.08 By rewriting [LPAR04] the rule new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), new_gtGtEs0(vz710, h, ba)), vz711, vz50, h, ba) at position [0,1] we obtained the following new rules [LPAR04]: 13.39/5.08 13.39/5.08 (new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), []), vz711, vz50, h, ba),new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), []), vz711, vz50, h, ba)) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (74) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), []), vz711, vz50, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, h, ba) -> [] 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (75) UsableRulesProof (EQUIVALENT) 13.39/5.08 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (76) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), []), vz711, vz50, h, ba) 13.39/5.08 13.39/5.08 R is empty. 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (77) QReductionProof (EQUIVALENT) 13.39/5.08 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.39/5.08 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (78) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), []), vz711, vz50, h, ba) 13.39/5.08 13.39/5.08 R is empty. 13.39/5.08 Q is empty. 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (79) QDPSizeChangeProof (EQUIVALENT) 13.39/5.08 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 13.39/5.08 13.39/5.08 From the DPs we obtained the following set of size-change graphs: 13.39/5.08 *new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) -> new_gtGtEs(vz281, vz71, vz50, h, ba) 13.39/5.08 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5 13.39/5.08 13.39/5.08 13.39/5.08 *new_gtGtEs([], :(vz710, vz711), vz50, h, ba) -> new_gtGtEs(:(:(vz710, []), []), vz711, vz50, h, ba) 13.39/5.08 The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (80) 13.39/5.08 YES 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (81) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_sequence1(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_sequence1(vz20, vz21, vz190, h, ba) -> new_gtGtEs2(vz20, vz21, vz190, h, ba) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 new_gtGtEs2(vz70, vz71, vz50, bb, bc) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, bb, bc), vz71, vz50, bb, bc), bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence1(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs2(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (82) TransformationProof (EQUIVALENT) 13.39/5.08 By rewriting [LPAR04] the rule new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_sequence1(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba) at position [0] we obtained the following new rules [LPAR04]: 13.39/5.08 13.39/5.08 (new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_gtGtEs2(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba),new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_gtGtEs2(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba)) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (83) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_gtGtEs2(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_sequence1(vz20, vz21, vz190, h, ba) -> new_gtGtEs2(vz20, vz21, vz190, h, ba) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 new_gtGtEs2(vz70, vz71, vz50, bb, bc) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, bb, bc), vz71, vz50, bb, bc), bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence1(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs2(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (84) UsableRulesProof (EQUIVALENT) 13.39/5.08 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (85) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_gtGtEs2(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs2(vz70, vz71, vz50, bb, bc) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, bb, bc), vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_sequence1(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs2(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (86) QReductionProof (EQUIVALENT) 13.39/5.08 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.39/5.08 13.39/5.08 new_sequence1(x0, x1, x2, x3, x4) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (87) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_gtGtEs2(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs2(vz70, vz71, vz50, bb, bc) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, bb, bc), vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs2(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (88) TransformationProof (EQUIVALENT) 13.39/5.08 By rewriting [LPAR04] the rule new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_gtGtEs2(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba) at position [0] we obtained the following new rules [LPAR04]: 13.39/5.08 13.39/5.08 (new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_psPs(vz190, :(vz20, []), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba), h, ba), vz191, vz20, vz21, h, ba),new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_psPs(vz190, :(vz20, []), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba), h, ba), vz191, vz20, vz21, h, ba)) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (89) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_psPs(vz190, :(vz20, []), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba), h, ba), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs2(vz70, vz71, vz50, bb, bc) -> new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, bb, bc), vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs2(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (90) UsableRulesProof (EQUIVALENT) 13.39/5.08 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (91) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_psPs(vz190, :(vz20, []), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba), h, ba), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs2(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (92) QReductionProof (EQUIVALENT) 13.39/5.08 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.39/5.08 13.39/5.08 new_gtGtEs2(x0, x1, x2, x3, x4) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (93) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_psPs(vz190, :(vz20, []), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba), h, ba), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (94) TransformationProof (EQUIVALENT) 13.39/5.08 By rewriting [LPAR04] the rule new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(new_psPs(vz190, :(vz20, []), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba), h, ba), vz191, vz20, vz21, h, ba) at position [0] we obtained the following new rules [LPAR04]: 13.39/5.08 13.39/5.08 (new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba),new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba)) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (95) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (96) TransformationProof (EQUIVALENT) 13.39/5.08 By rewriting [LPAR04] the rule new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs3(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) at position [0,1] we obtained the following new rules [LPAR04]: 13.39/5.08 13.39/5.08 (new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba),new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba)) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (97) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs3(vz28, vz71, vz50, bb, bc) -> new_gtGtEs4(vz28, vz71, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (98) UsableRulesProof (EQUIVALENT) 13.39/5.08 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (99) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (100) QReductionProof (EQUIVALENT) 13.39/5.08 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 13.39/5.08 13.39/5.08 new_gtGtEs3(x0, x1, x2, x3, x4) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (101) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (102) TransformationProof (EQUIVALENT) 13.39/5.08 By rewriting [LPAR04] the rule new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4(new_gtGtEs0(vz20, h, ba), vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) at position [0,1,0] we obtained the following new rules [LPAR04]: 13.39/5.08 13.39/5.08 (new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4([], vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba),new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4([], vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba)) 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (103) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4([], vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) 13.39/5.08 13.39/5.08 The TRS R consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs0(vz50, bb, bc) -> [] 13.39/5.08 new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) -> new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc) 13.39/5.08 new_gtGtEs4([], [], vz50, bb, bc) -> new_gtGtEs0(vz50, bb, bc) 13.39/5.08 new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) -> new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc) 13.39/5.08 new_psPs(vz50, vz230, vz27, bb, bc) -> :(:(vz50, vz230), vz27) 13.39/5.08 13.39/5.08 The set Q consists of the following terms: 13.39/5.08 13.39/5.08 new_gtGtEs4([], :(x0, x1), x2, x3, x4) 13.39/5.08 new_psPs(x0, x1, x2, x3, x4) 13.39/5.08 new_gtGtEs4(:(x0, x1), x2, x3, x4, x5) 13.39/5.08 new_gtGtEs4([], [], x0, x1, x2) 13.39/5.08 new_gtGtEs0(x0, x1, x2) 13.39/5.08 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (104) QDPSizeChangeProof (EQUIVALENT) 13.39/5.08 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 13.39/5.08 13.39/5.08 From the DPs we obtained the following set of size-change graphs: 13.39/5.08 *new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) -> new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba) 13.39/5.08 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6 13.39/5.08 13.39/5.08 13.39/5.08 *new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) -> new_gtGtEs10(:(:(vz190, :(vz20, [])), new_gtGtEs4([], vz21, vz190, h, ba)), vz191, vz20, vz21, h, ba) 13.39/5.08 The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (105) 13.39/5.08 YES 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (106) 13.39/5.08 Obligation: 13.39/5.08 Q DP problem: 13.39/5.08 The TRS P consists of the following rules: 13.39/5.08 13.39/5.08 new_gtGtEs12([], vz3, vz411, vz50, :(vz510, vz511), h, ba, bb) -> new_gtGtEs12([], vz3, vz411, vz510, vz511, h, ba, bb) 13.39/5.08 13.39/5.08 R is empty. 13.39/5.08 Q is empty. 13.39/5.08 We have to consider all minimal (P,Q,R)-chains. 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (107) QDPSizeChangeProof (EQUIVALENT) 13.39/5.08 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 13.39/5.08 13.39/5.08 From the DPs we obtained the following set of size-change graphs: 13.39/5.08 *new_gtGtEs12([], vz3, vz411, vz50, :(vz510, vz511), h, ba, bb) -> new_gtGtEs12([], vz3, vz411, vz510, vz511, h, ba, bb) 13.39/5.08 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7, 8 >= 8 13.39/5.08 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (108) 13.39/5.08 YES 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (109) Narrow (COMPLETE) 13.39/5.08 Haskell To QDPs 13.39/5.08 13.39/5.08 digraph dp_graph { 13.39/5.08 node [outthreshold=100, inthreshold=100];1[label="Monad.mapAndUnzipM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 13.39/5.08 3[label="Monad.mapAndUnzipM vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 13.39/5.08 4[label="Monad.mapAndUnzipM vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 13.39/5.08 5[label="sequence (map vz3 vz4) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];314[label="vz4/vz40 : vz41",fontsize=10,color="white",style="solid",shape="box"];5 -> 314[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 314 -> 6[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 315[label="vz4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 315[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 315 -> 7[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 6[label="sequence (map vz3 (vz40 : vz41)) >>= return . unzip",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 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13.39/5.08 12[label="vz5 >>= sequence1 (map vz3 vz41) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];316[label="vz5/vz50 : vz51",fontsize=10,color="white",style="solid",shape="box"];12 -> 316[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 316 -> 16[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 317[label="vz5/[]",fontsize=10,color="white",style="solid",shape="box"];12 -> 317[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 317 -> 17[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 14[label="[] : [] >>= return . unzip",fontsize=16,color="black",shape="box"];14 -> 19[label="",style="solid", color="black", weight=3]; 13.39/5.08 18[label="vz40",fontsize=16,color="green",shape="box"];16[label="vz50 : vz51 >>= sequence1 (map vz3 vz41) >>= return . unzip",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 13.39/5.08 17[label="[] >>= sequence1 (map vz3 vz41) >>= return . unzip",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 13.39/5.08 19 -> 129[label="",style="dashed", color="red", weight=0]; 13.39/5.08 19[label="return . unzip ++ ([] >>= return . unzip)",fontsize=16,color="magenta"];19 -> 130[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 19 -> 131[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 20[label="sequence1 (map vz3 vz41) vz50 ++ (vz51 >>= sequence1 (map vz3 vz41)) >>= return . unzip",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3]; 13.39/5.08 21[label="[] >>= return . unzip",fontsize=16,color="black",shape="triangle"];21 -> 24[label="",style="solid", color="black", weight=3]; 13.39/5.08 130[label="[]",fontsize=16,color="green",shape="box"];131 -> 21[label="",style="dashed", color="red", weight=0]; 13.39/5.08 131[label="[] >>= return . unzip",fontsize=16,color="magenta"];129[label="return . unzip ++ vz22",fontsize=16,color="black",shape="triangle"];129 -> 135[label="",style="solid", color="black", weight=3]; 13.39/5.08 23[label="(sequence (map vz3 vz41) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (map vz3 vz41)) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];318[label="vz41/vz410 : vz411",fontsize=10,color="white",style="solid",shape="box"];23 -> 318[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 318 -> 27[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 319[label="vz41/[]",fontsize=10,color="white",style="solid",shape="box"];23 -> 319[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 319 -> 28[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 24[label="[]",fontsize=16,color="green",shape="box"];135[label="return (unzip vz90) ++ vz22",fontsize=16,color="black",shape="box"];135 -> 145[label="",style="solid", color="black", weight=3]; 13.39/5.08 27[label="(sequence (map vz3 (vz410 : vz411)) >>= sequence0 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13.39/5.08 156[label="unzip vz90 : [] ++ vz22",fontsize=16,color="green",shape="box"];156 -> 168[label="",style="dashed", color="green", weight=3]; 13.39/5.08 156 -> 169[label="",style="dashed", color="green", weight=3]; 13.39/5.08 33 -> 37[label="",style="dashed", color="red", weight=0]; 13.39/5.08 33[label="(vz3 vz410 >>= sequence1 (map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (vz3 vz410 : map vz3 vz411)) >>= return . unzip",fontsize=16,color="magenta"];33 -> 38[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 34[label="(return [] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];34 -> 39[label="",style="solid", color="black", weight=3]; 13.39/5.08 168[label="unzip vz90",fontsize=16,color="black",shape="box"];168 -> 179[label="",style="solid", color="black", weight=3]; 13.39/5.08 169[label="[] ++ vz22",fontsize=16,color="black",shape="box"];169 -> 180[label="",style="solid", color="black", weight=3]; 13.39/5.08 38[label="vz3 vz410",fontsize=16,color="green",shape="box"];38 -> 45[label="",style="dashed", color="green", weight=3]; 13.39/5.08 37[label="(vz7 >>= sequence1 (map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (vz7 : map vz3 vz411)) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];320[label="vz7/vz70 : vz71",fontsize=10,color="white",style="solid",shape="box"];37 -> 320[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 320 -> 43[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 321[label="vz7/[]",fontsize=10,color="white",style="solid",shape="box"];37 -> 321[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 321 -> 44[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 39[label="([] : [] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3]; 13.39/5.08 179[label="foldr unzip0 ([],[]) 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return . unzip",fontsize=16,color="black",shape="box"];44 -> 49[label="",style="solid", color="black", weight=3]; 13.39/5.08 46[label="(sequence0 vz50 [] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3]; 13.39/5.08 187[label="foldr unzip0 ([],[]) (vz900 : vz901)",fontsize=16,color="black",shape="box"];187 -> 207[label="",style="solid", color="black", weight=3]; 13.39/5.08 188[label="foldr unzip0 ([],[]) []",fontsize=16,color="black",shape="box"];188 -> 208[label="",style="solid", color="black", weight=3]; 13.39/5.08 48[label="(sequence1 (map vz3 vz411) vz70 ++ (vz71 >>= sequence1 (map vz3 vz411)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];48 -> 51[label="",style="solid", color="black", weight=3]; 13.39/5.08 49[label="([] >>= sequence0 vz50) ++ (vz51 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];49 -> 52[label="",style="solid", color="black", weight=3]; 13.39/5.08 50[label="(return (vz50 : []) ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];50 -> 53[label="",style="solid", color="black", weight=3]; 13.39/5.08 207 -> 220[label="",style="dashed", color="red", weight=0]; 13.39/5.08 207[label="unzip0 vz900 (foldr unzip0 ([],[]) vz901)",fontsize=16,color="magenta"];207 -> 221[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 208[label="([],[])",fontsize=16,color="green",shape="box"];51[label="((sequence (map vz3 vz411) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 vz411)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 vz411)) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];324[label="vz411/vz4110 : vz4111",fontsize=10,color="white",style="solid",shape="box"];51 -> 324[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 324 -> 54[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 325[label="vz411/[]",fontsize=10,color="white",style="solid",shape="box"];51 -> 325[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 325 -> 55[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 52[label="[] ++ (vz51 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 13.39/5.08 53[label="(((vz50 : []) : []) ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3]; 13.39/5.08 221 -> 179[label="",style="dashed", color="red", weight=0]; 13.39/5.08 221[label="foldr unzip0 ([],[]) vz901",fontsize=16,color="magenta"];221 -> 222[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 220[label="unzip0 vz900 vz25",fontsize=16,color="burlywood",shape="triangle"];326[label="vz900/(vz9000,vz9001)",fontsize=10,color="white",style="solid",shape="box"];220 -> 326[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 326 -> 223[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 54[label="((sequence (map vz3 (vz4110 : vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 (vz4110 : vz4111))) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 (vz4110 : vz4111))) >>= return . unzip",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3]; 13.39/5.08 55[label="((sequence (map vz3 []) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 [])) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 [])) >>= return . unzip",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3]; 13.39/5.08 56[label="vz51 >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];327[label="vz51/vz510 : vz511",fontsize=10,color="white",style="solid",shape="box"];56 -> 327[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 327 -> 60[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 328[label="vz51/[]",fontsize=10,color="white",style="solid",shape="box"];56 -> 328[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 328 -> 61[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 57[label="((vz50 : []) : [] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];57 -> 62[label="",style="solid", color="black", weight=3]; 13.39/5.08 222[label="vz901",fontsize=16,color="green",shape="box"];223[label="unzip0 (vz9000,vz9001) vz25",fontsize=16,color="black",shape="box"];223 -> 226[label="",style="solid", color="black", weight=3]; 13.39/5.08 58 -> 68[label="",style="dashed", color="red", weight=0]; 13.39/5.08 58[label="((sequence (vz3 vz4110 : map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : vz3 vz4110 : map vz3 vz4111)) >>= return . unzip",fontsize=16,color="magenta"];58 -> 69[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 58 -> 70[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 58 -> 71[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 58 -> 72[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 58 -> 73[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 58 -> 74[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 58 -> 75[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 59 -> 103[label="",style="dashed", color="red", weight=0]; 13.39/5.08 59[label="((sequence [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : [])) >>= return . unzip",fontsize=16,color="magenta"];59 -> 104[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 59 -> 105[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 59 -> 106[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 59 -> 107[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 60[label="vz510 : vz511 >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="black",shape="box"];60 -> 65[label="",style="solid", color="black", weight=3]; 13.39/5.08 61[label="[] >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="black",shape="box"];61 -> 66[label="",style="solid", color="black", weight=3]; 13.39/5.08 62[label="(vz50 : []) : ([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];62 -> 67[label="",style="solid", color="black", weight=3]; 13.39/5.08 226[label="(vz9000 : unzip00 vz25,vz9001 : unzip01 vz25)",fontsize=16,color="green",shape="box"];226 -> 243[label="",style="dashed", color="green", weight=3]; 13.39/5.08 226 -> 244[label="",style="dashed", color="green", weight=3]; 13.39/5.08 69[label="vz3",fontsize=16,color="green",shape="box"];70[label="vz4110",fontsize=16,color="green",shape="box"];71[label="vz4111",fontsize=16,color="green",shape="box"];72[label="(sequence (vz3 vz4110 : map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];72 -> 83[label="",style="solid", color="black", weight=3]; 13.39/5.08 73[label="vz71",fontsize=16,color="green",shape="box"];74[label="vz70",fontsize=16,color="green",shape="box"];75[label="vz51",fontsize=16,color="green",shape="box"];68[label="vz9 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];329[label="vz9/vz90 : vz91",fontsize=10,color="white",style="solid",shape="box"];68 -> 329[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 329 -> 84[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 330[label="vz9/[]",fontsize=10,color="white",style="solid",shape="box"];68 -> 330[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 330 -> 85[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 104[label="vz71",fontsize=16,color="green",shape="box"];105[label="vz51",fontsize=16,color="green",shape="box"];106[label="vz70",fontsize=16,color="green",shape="box"];107[label="(sequence [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];107 -> 120[label="",style="solid", color="black", weight=3]; 13.39/5.08 103[label="vz18 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];331[label="vz18/vz180 : vz181",fontsize=10,color="white",style="solid",shape="box"];103 -> 331[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 331 -> 121[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 332[label="vz18/[]",fontsize=10,color="white",style="solid",shape="box"];103 -> 332[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 332 -> 122[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 65[label="sequence1 ([] : map vz3 vz411) vz510 ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];65 -> 87[label="",style="solid", color="black", weight=3]; 13.39/5.08 66 -> 21[label="",style="dashed", color="red", weight=0]; 13.39/5.08 66[label="[] >>= return . unzip",fontsize=16,color="magenta"];67 -> 129[label="",style="dashed", color="red", weight=0]; 13.39/5.08 67[label="return . unzip ++ (([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip)",fontsize=16,color="magenta"];67 -> 132[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 67 -> 133[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 243[label="unzip00 vz25",fontsize=16,color="burlywood",shape="box"];333[label="vz25/(vz250,vz251)",fontsize=10,color="white",style="solid",shape="box"];243 -> 333[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 333 -> 260[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 244[label="unzip01 vz25",fontsize=16,color="burlywood",shape="box"];334[label="vz25/(vz250,vz251)",fontsize=10,color="white",style="solid",shape="box"];244 -> 334[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 334 -> 261[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 83 -> 89[label="",style="dashed", color="red", weight=0]; 13.39/5.08 83[label="(vz3 vz4110 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="magenta"];83 -> 90[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 84[label="(vz90 : vz91) ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];84 -> 91[label="",style="solid", color="black", weight=3]; 13.39/5.08 85[label="[] ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];85 -> 92[label="",style="solid", color="black", weight=3]; 13.39/5.08 120[label="(return [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];120 -> 136[label="",style="solid", color="black", weight=3]; 13.39/5.08 121[label="(vz180 : vz181) ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];121 -> 137[label="",style="solid", color="black", weight=3]; 13.39/5.08 122[label="[] ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];122 -> 138[label="",style="solid", color="black", weight=3]; 13.39/5.08 87[label="(sequence ([] : map vz3 vz411) >>= sequence0 vz510) ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];87 -> 94[label="",style="solid", color="black", weight=3]; 13.39/5.08 132[label="vz50 : []",fontsize=16,color="green",shape="box"];133[label="([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3]; 13.39/5.08 260[label="unzip00 (vz250,vz251)",fontsize=16,color="black",shape="box"];260 -> 264[label="",style="solid", color="black", weight=3]; 13.39/5.08 261[label="unzip01 (vz250,vz251)",fontsize=16,color="black",shape="box"];261 -> 265[label="",style="solid", color="black", weight=3]; 13.39/5.08 90[label="vz3 vz4110",fontsize=16,color="green",shape="box"];90 -> 99[label="",style="dashed", color="green", weight=3]; 13.39/5.08 89[label="(vz16 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz16 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];335[label="vz16/vz160 : vz161",fontsize=10,color="white",style="solid",shape="box"];89 -> 335[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 335 -> 97[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 336[label="vz16/[]",fontsize=10,color="white",style="solid",shape="box"];89 -> 336[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 336 -> 98[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 91[label="vz90 : vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];91 -> 100[label="",style="solid", color="black", weight=3]; 13.39/5.08 92[label="vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];337[label="vz10/vz100 : vz101",fontsize=10,color="white",style="solid",shape="box"];92 -> 337[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 337 -> 101[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 338[label="vz10/[]",fontsize=10,color="white",style="solid",shape="box"];92 -> 338[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 338 -> 102[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 136[label="([] : [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];136 -> 146[label="",style="solid", color="black", weight=3]; 13.39/5.08 137[label="vz180 : vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];137 -> 147[label="",style="solid", color="black", weight=3]; 13.39/5.08 138[label="vz19 >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];339[label="vz19/vz190 : vz191",fontsize=10,color="white",style="solid",shape="box"];138 -> 339[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 339 -> 148[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 340[label="vz19/[]",fontsize=10,color="white",style="solid",shape="box"];138 -> 340[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 340 -> 149[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 94 -> 37[label="",style="dashed", color="red", weight=0]; 13.39/5.08 94[label="([] >>= sequence1 (map vz3 vz411) >>= sequence0 vz510) ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="magenta"];94 -> 123[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 94 -> 124[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 94 -> 125[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 139[label="([] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];139 -> 150[label="",style="solid", color="black", weight=3]; 13.39/5.08 264[label="vz250",fontsize=16,color="green",shape="box"];265[label="vz251",fontsize=16,color="green",shape="box"];99[label="vz4110",fontsize=16,color="green",shape="box"];97[label="(vz160 : vz161 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];97 -> 127[label="",style="solid", color="black", weight=3]; 13.39/5.08 98[label="([] >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];98 -> 128[label="",style="solid", color="black", weight=3]; 13.39/5.08 100 -> 129[label="",style="dashed", color="red", weight=0]; 13.39/5.08 100[label="return . unzip ++ (vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip)",fontsize=16,color="magenta"];100 -> 134[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 101[label="vz100 : vz101 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="black",shape="box"];101 -> 140[label="",style="solid", color="black", weight=3]; 13.39/5.08 102[label="[] >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="black",shape="box"];102 -> 141[label="",style="solid", color="black", weight=3]; 13.39/5.08 146[label="(sequence0 vz70 [] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];146 -> 157[label="",style="solid", color="black", weight=3]; 13.39/5.08 147 -> 129[label="",style="dashed", color="red", weight=0]; 13.39/5.08 147[label="return . unzip ++ (vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip)",fontsize=16,color="magenta"];147 -> 158[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 147 -> 159[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 148[label="vz190 : vz191 >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="black",shape="box"];148 -> 160[label="",style="solid", color="black", weight=3]; 13.39/5.08 149[label="[] >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="black",shape="box"];149 -> 161[label="",style="solid", color="black", weight=3]; 13.39/5.08 123[label="[]",fontsize=16,color="green",shape="box"];124[label="vz510",fontsize=16,color="green",shape="box"];125[label="vz511",fontsize=16,color="green",shape="box"];150[label="[] ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];150 -> 162[label="",style="solid", color="black", weight=3]; 13.39/5.08 127[label="(sequence1 (map vz3 vz4111) vz160 ++ (vz161 >>= sequence1 (map vz3 vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];127 -> 142[label="",style="solid", color="black", weight=3]; 13.39/5.08 128[label="([] >>= sequence0 vz70) ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];128 -> 143[label="",style="solid", color="black", weight=3]; 13.39/5.08 134 -> 68[label="",style="dashed", color="red", weight=0]; 13.39/5.08 134[label="vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="magenta"];134 -> 144[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 140 -> 68[label="",style="dashed", color="red", weight=0]; 13.39/5.08 140[label="sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) vz100 ++ (vz101 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="magenta"];140 -> 151[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 140 -> 152[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 141 -> 21[label="",style="dashed", color="red", weight=0]; 13.39/5.08 141[label="[] >>= return . unzip",fontsize=16,color="magenta"];157[label="(return (vz70 : []) ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];157 -> 170[label="",style="solid", color="black", weight=3]; 13.39/5.08 158[label="vz180",fontsize=16,color="green",shape="box"];159 -> 103[label="",style="dashed", color="red", weight=0]; 13.39/5.08 159[label="vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="magenta"];159 -> 171[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 160 -> 103[label="",style="dashed", color="red", weight=0]; 13.39/5.08 160[label="sequence1 ((vz20 : vz21) : []) vz190 ++ (vz191 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="magenta"];160 -> 172[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 160 -> 173[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 161 -> 21[label="",style="dashed", color="red", weight=0]; 13.39/5.08 161[label="[] >>= return . unzip",fontsize=16,color="magenta"];162[label="vz51 >>= sequence1 [] >>= return . unzip",fontsize=16,color="burlywood",shape="box"];341[label="vz51/vz510 : vz511",fontsize=10,color="white",style="solid",shape="box"];162 -> 341[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 341 -> 174[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 342[label="vz51/[]",fontsize=10,color="white",style="solid",shape="box"];162 -> 342[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 342 -> 175[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 142[label="((sequence (map vz3 vz4111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];343[label="vz4111/vz41110 : vz41111",fontsize=10,color="white",style="solid",shape="box"];142 -> 343[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 343 -> 153[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 344[label="vz4111/[]",fontsize=10,color="white",style="solid",shape="box"];142 -> 344[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 344 -> 154[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 143[label="[] ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];143 -> 155[label="",style="solid", color="black", weight=3]; 13.39/5.08 144[label="vz91",fontsize=16,color="green",shape="box"];151[label="sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) vz100",fontsize=16,color="black",shape="triangle"];151 -> 163[label="",style="solid", color="black", weight=3]; 13.39/5.08 152[label="vz101",fontsize=16,color="green",shape="box"];170[label="(((vz70 : []) : []) ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];170 -> 181[label="",style="solid", color="black", weight=3]; 13.39/5.08 171[label="vz181",fontsize=16,color="green",shape="box"];172[label="vz191",fontsize=16,color="green",shape="box"];173[label="sequence1 ((vz20 : vz21) : []) vz190",fontsize=16,color="black",shape="triangle"];173 -> 182[label="",style="solid", color="black", weight=3]; 13.39/5.08 174[label="vz510 : vz511 >>= sequence1 [] >>= return . unzip",fontsize=16,color="black",shape="box"];174 -> 183[label="",style="solid", color="black", weight=3]; 13.39/5.08 175[label="[] >>= sequence1 [] >>= return . unzip",fontsize=16,color="black",shape="box"];175 -> 184[label="",style="solid", color="black", weight=3]; 13.39/5.08 153[label="((sequence (map vz3 (vz41110 : vz41111)) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 (vz41110 : vz41111))) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 (vz41110 : vz41111))) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];153 -> 164[label="",style="solid", color="black", weight=3]; 13.39/5.08 154[label="((sequence (map vz3 []) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 [])) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];154 -> 165[label="",style="solid", color="black", weight=3]; 13.39/5.08 155[label="vz71 >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];345[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];155 -> 345[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 345 -> 166[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 346[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];155 -> 346[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 346 -> 167[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 163[label="sequence ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];163 -> 176[label="",style="solid", color="black", weight=3]; 13.39/5.08 181[label="((vz70 : []) : [] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];181 -> 189[label="",style="solid", color="black", weight=3]; 13.39/5.08 182[label="sequence ((vz20 : vz21) : []) >>= sequence0 vz190",fontsize=16,color="black",shape="box"];182 -> 190[label="",style="solid", color="black", weight=3]; 13.39/5.08 183[label="sequence1 [] vz510 ++ (vz511 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];183 -> 191[label="",style="solid", color="black", weight=3]; 13.39/5.08 184 -> 21[label="",style="dashed", color="red", weight=0]; 13.39/5.08 184[label="[] >>= return . unzip",fontsize=16,color="magenta"];164 -> 177[label="",style="dashed", color="red", weight=0]; 13.39/5.08 164[label="((sequence (vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];164 -> 178[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 165 -> 185[label="",style="dashed", color="red", weight=0]; 13.39/5.08 165[label="((sequence [] >>= sequence0 vz160) ++ (vz161 >>= sequence1 []) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];165 -> 186[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 166[label="vz710 : vz711 >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];166 -> 192[label="",style="solid", color="black", weight=3]; 13.39/5.08 167[label="[] >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];167 -> 193[label="",style="solid", color="black", weight=3]; 13.39/5.08 176[label="vz11 : vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];176 -> 194[label="",style="solid", color="black", weight=3]; 13.39/5.08 189[label="(vz70 : []) : ([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];189 -> 209[label="",style="solid", color="black", weight=3]; 13.39/5.08 190[label="vz20 : vz21 >>= sequence1 [] >>= sequence0 vz190",fontsize=16,color="black",shape="box"];190 -> 210[label="",style="solid", color="black", weight=3]; 13.39/5.08 191 -> 31[label="",style="dashed", color="red", weight=0]; 13.39/5.08 191[label="(sequence [] >>= sequence0 vz510) ++ (vz511 >>= sequence1 []) >>= return . unzip",fontsize=16,color="magenta"];191 -> 211[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 191 -> 212[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 178 -> 72[label="",style="dashed", color="red", weight=0]; 13.39/5.08 178[label="(sequence (vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz70",fontsize=16,color="magenta"];178 -> 195[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 178 -> 196[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 178 -> 197[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 178 -> 198[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 178 -> 199[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 177[label="vz23 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];347[label="vz23/vz230 : vz231",fontsize=10,color="white",style="solid",shape="box"];177 -> 347[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 347 -> 200[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 348[label="vz23/[]",fontsize=10,color="white",style="solid",shape="box"];177 -> 348[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 348 -> 201[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 186 -> 107[label="",style="dashed", color="red", weight=0]; 13.39/5.08 186[label="(sequence [] >>= sequence0 vz160) ++ (vz161 >>= sequence1 []) >>= sequence0 vz70",fontsize=16,color="magenta"];186 -> 202[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 186 -> 203[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 186 -> 204[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 185[label="vz24 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];349[label="vz24/vz240 : vz241",fontsize=10,color="white",style="solid",shape="box"];185 -> 349[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 349 -> 205[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 350[label="vz24/[]",fontsize=10,color="white",style="solid",shape="box"];185 -> 350[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 350 -> 206[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 192[label="sequence1 ([] : map vz3 vz4111) vz710 ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];192 -> 213[label="",style="solid", color="black", weight=3]; 13.39/5.08 193[label="[] >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];193 -> 214[label="",style="solid", color="black", weight=3]; 13.39/5.08 194[label="sequence1 (vz13 vz14 : map vz13 vz15) vz11 ++ (vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15)) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];194 -> 215[label="",style="solid", color="black", weight=3]; 13.39/5.08 209 -> 252[label="",style="dashed", color="red", weight=0]; 13.39/5.08 209[label="sequence0 vz50 (vz70 : []) ++ (([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50)",fontsize=16,color="magenta"];209 -> 253[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 209 -> 254[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 210[label="sequence1 [] vz20 ++ (vz21 >>= sequence1 []) >>= sequence0 vz190",fontsize=16,color="black",shape="box"];210 -> 227[label="",style="solid", color="black", weight=3]; 13.39/5.08 211[label="vz510",fontsize=16,color="green",shape="box"];212[label="vz511",fontsize=16,color="green",shape="box"];195[label="vz160",fontsize=16,color="green",shape="box"];196[label="vz161",fontsize=16,color="green",shape="box"];197[label="vz70",fontsize=16,color="green",shape="box"];198[label="vz41110",fontsize=16,color="green",shape="box"];199[label="vz41111",fontsize=16,color="green",shape="box"];200[label="(vz230 : vz231) ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];200 -> 216[label="",style="solid", color="black", weight=3]; 13.39/5.08 201[label="[] ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];201 -> 217[label="",style="solid", color="black", weight=3]; 13.39/5.08 202[label="vz160",fontsize=16,color="green",shape="box"];203[label="vz161",fontsize=16,color="green",shape="box"];204[label="vz70",fontsize=16,color="green",shape="box"];205[label="(vz240 : vz241) ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];205 -> 218[label="",style="solid", color="black", weight=3]; 13.39/5.08 206[label="[] ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];206 -> 219[label="",style="solid", color="black", weight=3]; 13.39/5.08 213[label="(sequence ([] : map vz3 vz4111) >>= sequence0 vz710) ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];213 -> 228[label="",style="solid", color="black", weight=3]; 13.39/5.08 214[label="[]",fontsize=16,color="green",shape="box"];215 -> 72[label="",style="dashed", color="red", weight=0]; 13.39/5.08 215[label="(sequence (vz13 vz14 : map vz13 vz15) >>= sequence0 vz11) ++ (vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15)) >>= sequence0 vz100",fontsize=16,color="magenta"];215 -> 229[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 215 -> 230[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 215 -> 231[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 215 -> 232[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 215 -> 233[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 215 -> 234[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 253[label="vz70 : []",fontsize=16,color="green",shape="box"];254 -> 262[label="",style="dashed", color="red", weight=0]; 13.39/5.08 254[label="([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];254 -> 263[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 252[label="sequence0 vz50 vz230 ++ vz27",fontsize=16,color="black",shape="triangle"];252 -> 266[label="",style="solid", color="black", weight=3]; 13.39/5.08 227 -> 107[label="",style="dashed", color="red", weight=0]; 13.39/5.08 227[label="(sequence [] >>= sequence0 vz20) ++ (vz21 >>= sequence1 []) >>= sequence0 vz190",fontsize=16,color="magenta"];227 -> 245[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 227 -> 246[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 227 -> 247[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 216[label="vz230 : vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];216 -> 237[label="",style="solid", color="black", weight=3]; 13.39/5.08 217[label="vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];351[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];217 -> 351[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 351 -> 238[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 352[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];217 -> 352[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 352 -> 239[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 218[label="vz240 : vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];218 -> 240[label="",style="solid", color="black", weight=3]; 13.39/5.08 219[label="vz71 >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];353[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];219 -> 353[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 353 -> 241[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 354[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];219 -> 354[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 354 -> 242[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 228 -> 89[label="",style="dashed", color="red", weight=0]; 13.39/5.08 228[label="([] >>= sequence1 (map vz3 vz4111) >>= sequence0 vz710) ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="magenta"];228 -> 248[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 228 -> 249[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 228 -> 250[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 229[label="vz13",fontsize=16,color="green",shape="box"];230[label="vz11",fontsize=16,color="green",shape="box"];231[label="vz12",fontsize=16,color="green",shape="box"];232[label="vz100",fontsize=16,color="green",shape="box"];233[label="vz14",fontsize=16,color="green",shape="box"];234[label="vz15",fontsize=16,color="green",shape="box"];263 -> 193[label="",style="dashed", color="red", weight=0]; 13.39/5.08 263[label="[] >>= sequence0 vz70",fontsize=16,color="magenta"];263 -> 267[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 262[label="([] ++ vz28) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];262 -> 268[label="",style="solid", color="black", weight=3]; 13.39/5.08 266[label="return (vz50 : vz230) ++ vz27",fontsize=16,color="black",shape="box"];266 -> 275[label="",style="solid", color="black", weight=3]; 13.39/5.08 245[label="vz20",fontsize=16,color="green",shape="box"];246[label="vz21",fontsize=16,color="green",shape="box"];247[label="vz190",fontsize=16,color="green",shape="box"];237 -> 252[label="",style="dashed", color="red", weight=0]; 13.39/5.08 237[label="sequence0 vz50 vz230 ++ (vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50)",fontsize=16,color="magenta"];237 -> 257[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 238[label="vz710 : vz711 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];238 -> 269[label="",style="solid", color="black", weight=3]; 13.39/5.08 239[label="[] >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];239 -> 270[label="",style="solid", color="black", weight=3]; 13.39/5.08 240 -> 252[label="",style="dashed", color="red", weight=0]; 13.39/5.08 240[label="sequence0 vz50 vz240 ++ (vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50)",fontsize=16,color="magenta"];240 -> 258[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 240 -> 259[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 241[label="vz710 : vz711 >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];241 -> 271[label="",style="solid", color="black", weight=3]; 13.39/5.08 242[label="[] >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];242 -> 272[label="",style="solid", color="black", weight=3]; 13.39/5.08 248[label="vz710",fontsize=16,color="green",shape="box"];249[label="vz711",fontsize=16,color="green",shape="box"];250[label="[]",fontsize=16,color="green",shape="box"];267[label="vz70",fontsize=16,color="green",shape="box"];268[label="vz28 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];355[label="vz28/vz280 : vz281",fontsize=10,color="white",style="solid",shape="box"];268 -> 355[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 355 -> 276[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 356[label="vz28/[]",fontsize=10,color="white",style="solid",shape="box"];268 -> 356[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 356 -> 277[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 275[label="((vz50 : vz230) : []) ++ vz27",fontsize=16,color="black",shape="box"];275 -> 282[label="",style="solid", color="black", weight=3]; 13.39/5.08 257 -> 177[label="",style="dashed", color="red", weight=0]; 13.39/5.08 257[label="vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];257 -> 273[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 269 -> 177[label="",style="dashed", color="red", weight=0]; 13.39/5.08 269[label="sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) vz710 ++ (vz711 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];269 -> 278[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 269 -> 279[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 270 -> 193[label="",style="dashed", color="red", weight=0]; 13.39/5.08 270[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];258[label="vz240",fontsize=16,color="green",shape="box"];259 -> 185[label="",style="dashed", color="red", weight=0]; 13.39/5.08 259[label="vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];259 -> 274[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 271 -> 185[label="",style="dashed", color="red", weight=0]; 13.39/5.08 271[label="sequence1 ((vz160 : vz161) : []) vz710 ++ (vz711 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];271 -> 280[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 271 -> 281[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 272 -> 193[label="",style="dashed", color="red", weight=0]; 13.39/5.08 272[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];276[label="(vz280 : vz281) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];276 -> 283[label="",style="solid", color="black", weight=3]; 13.39/5.08 277[label="[] ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];277 -> 284[label="",style="solid", color="black", weight=3]; 13.39/5.08 282[label="(vz50 : vz230) : [] ++ vz27",fontsize=16,color="green",shape="box"];282 -> 294[label="",style="dashed", color="green", weight=3]; 13.39/5.08 273[label="vz231",fontsize=16,color="green",shape="box"];278[label="vz711",fontsize=16,color="green",shape="box"];279 -> 151[label="",style="dashed", color="red", weight=0]; 13.39/5.08 279[label="sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) vz710",fontsize=16,color="magenta"];279 -> 285[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 279 -> 286[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 279 -> 287[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 279 -> 288[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 279 -> 289[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 279 -> 290[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 274[label="vz241",fontsize=16,color="green",shape="box"];280[label="vz711",fontsize=16,color="green",shape="box"];281 -> 173[label="",style="dashed", color="red", weight=0]; 13.39/5.08 281[label="sequence1 ((vz160 : vz161) : []) vz710",fontsize=16,color="magenta"];281 -> 291[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 281 -> 292[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 281 -> 293[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 283[label="vz280 : vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];283 -> 295[label="",style="solid", color="black", weight=3]; 13.39/5.08 284[label="vz71 >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];357[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];284 -> 357[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 357 -> 296[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 358[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];284 -> 358[label="",style="solid", color="burlywood", weight=9]; 13.39/5.08 358 -> 297[label="",style="solid", color="burlywood", weight=3]; 13.39/5.08 294[label="[] ++ vz27",fontsize=16,color="black",shape="box"];294 -> 298[label="",style="solid", color="black", weight=3]; 13.39/5.08 285[label="vz3",fontsize=16,color="green",shape="box"];286[label="vz41110",fontsize=16,color="green",shape="box"];287[label="vz41111",fontsize=16,color="green",shape="box"];288[label="vz161",fontsize=16,color="green",shape="box"];289[label="vz160",fontsize=16,color="green",shape="box"];290[label="vz710",fontsize=16,color="green",shape="box"];291[label="vz161",fontsize=16,color="green",shape="box"];292[label="vz160",fontsize=16,color="green",shape="box"];293[label="vz710",fontsize=16,color="green",shape="box"];295 -> 252[label="",style="dashed", color="red", weight=0]; 13.39/5.08 295[label="sequence0 vz50 vz280 ++ (vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50)",fontsize=16,color="magenta"];295 -> 299[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 295 -> 300[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 296[label="vz710 : vz711 >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="black",shape="box"];296 -> 301[label="",style="solid", color="black", weight=3]; 13.39/5.08 297[label="[] >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="black",shape="box"];297 -> 302[label="",style="solid", color="black", weight=3]; 13.39/5.08 298[label="vz27",fontsize=16,color="green",shape="box"];299[label="vz280",fontsize=16,color="green",shape="box"];300 -> 268[label="",style="dashed", color="red", weight=0]; 13.39/5.08 300[label="vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];300 -> 303[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 301 -> 268[label="",style="dashed", color="red", weight=0]; 13.39/5.08 301[label="sequence1 [] vz710 ++ (vz711 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];301 -> 304[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 301 -> 305[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 302 -> 193[label="",style="dashed", color="red", weight=0]; 13.39/5.08 302[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];303[label="vz281",fontsize=16,color="green",shape="box"];304[label="sequence1 [] vz710",fontsize=16,color="black",shape="box"];304 -> 306[label="",style="solid", color="black", weight=3]; 13.39/5.08 305[label="vz711",fontsize=16,color="green",shape="box"];306[label="sequence [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];306 -> 307[label="",style="solid", color="black", weight=3]; 13.39/5.08 307[label="return [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];307 -> 308[label="",style="solid", color="black", weight=3]; 13.39/5.08 308[label="[] : [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];308 -> 309[label="",style="solid", color="black", weight=3]; 13.39/5.08 309 -> 252[label="",style="dashed", color="red", weight=0]; 13.39/5.08 309[label="sequence0 vz710 [] ++ ([] >>= sequence0 vz710)",fontsize=16,color="magenta"];309 -> 310[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 309 -> 311[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 309 -> 312[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 310[label="vz710",fontsize=16,color="green",shape="box"];311[label="[]",fontsize=16,color="green",shape="box"];312 -> 193[label="",style="dashed", color="red", weight=0]; 13.39/5.08 312[label="[] >>= sequence0 vz710",fontsize=16,color="magenta"];312 -> 313[label="",style="dashed", color="magenta", weight=3]; 13.39/5.08 313[label="vz710",fontsize=16,color="green",shape="box"];} 13.39/5.08 13.39/5.08 ---------------------------------------- 13.39/5.08 13.39/5.08 (110) 13.39/5.08 TRUE 13.39/5.12 EOF