9.54/3.92 YES 11.71/4.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 11.71/4.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.71/4.53 11.71/4.53 11.71/4.53 H-Termination with start terms of the given HASKELL could be proven: 11.71/4.53 11.71/4.53 (0) HASKELL 11.71/4.53 (1) LR [EQUIVALENT, 0 ms] 11.71/4.53 (2) HASKELL 11.71/4.53 (3) BR [EQUIVALENT, 0 ms] 11.71/4.53 (4) HASKELL 11.71/4.53 (5) COR [EQUIVALENT, 0 ms] 11.71/4.53 (6) HASKELL 11.71/4.53 (7) Narrow [SOUND, 0 ms] 11.71/4.53 (8) AND 11.71/4.53 (9) QDP 11.71/4.53 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.71/4.53 (11) YES 11.71/4.53 (12) QDP 11.71/4.53 (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.71/4.53 (14) YES 11.71/4.53 (15) QDP 11.71/4.53 (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.71/4.53 (17) YES 11.71/4.53 (18) QDP 11.71/4.53 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.71/4.53 (20) YES 11.71/4.53 (21) QDP 11.71/4.53 (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.71/4.53 (23) YES 11.71/4.53 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (0) 11.71/4.53 Obligation: 11.71/4.53 mainModule Main 11.71/4.53 module Maybe where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Main where { 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Monad where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Prelude; 11.71/4.53 liftM4 :: Monad c => (b -> d -> e -> f -> a) -> c b -> c d -> c e -> c f -> c a; 11.71/4.53 liftM4 f m1 m2 m3 m4 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->return (f x1 x2 x3 x4))))); 11.71/4.53 11.71/4.53 } 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (1) LR (EQUIVALENT) 11.71/4.53 Lambda Reductions: 11.71/4.53 The following Lambda expression 11.71/4.53 "\x4->return (f x1 x2 x3 x4)" 11.71/4.53 is transformed to 11.71/4.53 "liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4); 11.71/4.53 " 11.71/4.53 The following Lambda expression 11.71/4.53 "\x3->m4 >>= liftM40 f x1 x2 x3" 11.71/4.53 is transformed to 11.71/4.53 "liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3; 11.71/4.53 " 11.71/4.53 The following Lambda expression 11.71/4.53 "\x2->m3 >>= liftM41 m4 f x1 x2" 11.71/4.53 is transformed to 11.71/4.53 "liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2; 11.71/4.53 " 11.71/4.53 The following Lambda expression 11.71/4.53 "\x1->m2 >>= liftM42 m3 m4 f x1" 11.71/4.53 is transformed to 11.71/4.53 "liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1; 11.71/4.53 " 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (2) 11.71/4.53 Obligation: 11.71/4.53 mainModule Main 11.71/4.53 module Maybe where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Main where { 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Monad where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Prelude; 11.71/4.53 liftM4 :: Monad b => (e -> c -> f -> a -> d) -> b e -> b c -> b f -> b a -> b d; 11.71/4.53 liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f; 11.71/4.53 11.71/4.53 liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4); 11.71/4.53 11.71/4.53 liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3; 11.71/4.53 11.71/4.53 liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2; 11.71/4.53 11.71/4.53 liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1; 11.71/4.53 11.71/4.53 } 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (3) BR (EQUIVALENT) 11.71/4.53 Replaced joker patterns by fresh variables and removed binding patterns. 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (4) 11.71/4.53 Obligation: 11.71/4.53 mainModule Main 11.71/4.53 module Maybe where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Main where { 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Monad where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Prelude; 11.71/4.53 liftM4 :: Monad c => (e -> f -> b -> a -> d) -> c e -> c f -> c b -> c a -> c d; 11.71/4.53 liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f; 11.71/4.53 11.71/4.53 liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4); 11.71/4.53 11.71/4.53 liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3; 11.71/4.53 11.71/4.53 liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2; 11.71/4.53 11.71/4.53 liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1; 11.71/4.53 11.71/4.53 } 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (5) COR (EQUIVALENT) 11.71/4.53 Cond Reductions: 11.71/4.53 The following Function with conditions 11.71/4.53 "undefined |Falseundefined; 11.71/4.53 " 11.71/4.53 is transformed to 11.71/4.53 "undefined = undefined1; 11.71/4.53 " 11.71/4.53 "undefined0 True = undefined; 11.71/4.53 " 11.71/4.53 "undefined1 = undefined0 False; 11.71/4.53 " 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (6) 11.71/4.53 Obligation: 11.71/4.53 mainModule Main 11.71/4.53 module Maybe where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Main where { 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Monad; 11.71/4.53 import qualified Prelude; 11.71/4.53 } 11.71/4.53 module Monad where { 11.71/4.53 import qualified Main; 11.71/4.53 import qualified Maybe; 11.71/4.53 import qualified Prelude; 11.71/4.53 liftM4 :: Monad f => (b -> e -> c -> a -> d) -> f b -> f e -> f c -> f a -> f d; 11.71/4.53 liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f; 11.71/4.53 11.71/4.53 liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4); 11.71/4.53 11.71/4.53 liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3; 11.71/4.53 11.71/4.53 liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2; 11.71/4.53 11.71/4.53 liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1; 11.71/4.53 11.71/4.53 } 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (7) Narrow (SOUND) 11.71/4.53 Haskell To QDPs 11.71/4.53 11.71/4.53 digraph dp_graph { 11.71/4.53 node [outthreshold=100, inthreshold=100];1[label="Monad.liftM4",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 11.71/4.53 3[label="Monad.liftM4 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 11.71/4.53 4[label="Monad.liftM4 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 11.71/4.53 5[label="Monad.liftM4 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3]; 11.71/4.53 6[label="Monad.liftM4 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3]; 11.71/4.53 7[label="Monad.liftM4 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="black",shape="triangle"];7 -> 8[label="",style="solid", color="black", weight=3]; 11.71/4.53 8[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="burlywood",shape="triangle"];77[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];8 -> 77[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 77 -> 9[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 78[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];8 -> 78[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 78 -> 10[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 9[label="vy40 : vy41 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 11.71/4.53 10[label="[] >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11.71/4.53 11 -> 28[label="",style="dashed", color="red", weight=0]; 11.71/4.53 11[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40 ++ (vy41 >>= Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="magenta"];11 -> 29[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 11 -> 30[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 12[label="[]",fontsize=16,color="green",shape="box"];29[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];29 -> 39[label="",style="solid", color="black", weight=3]; 11.71/4.53 30 -> 8[label="",style="dashed", color="red", weight=0]; 11.71/4.53 30[label="vy41 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="magenta"];30 -> 40[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 28[label="vy9 ++ vy8",fontsize=16,color="burlywood",shape="triangle"];79[label="vy9/vy90 : vy91",fontsize=10,color="white",style="solid",shape="box"];28 -> 79[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 79 -> 41[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 80[label="vy9/[]",fontsize=10,color="white",style="solid",shape="box"];28 -> 80[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 80 -> 42[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 39[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];81[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];39 -> 81[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 81 -> 43[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 82[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];39 -> 82[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 82 -> 44[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 40[label="vy41",fontsize=16,color="green",shape="box"];41[label="(vy90 : vy91) ++ vy8",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3]; 11.71/4.53 42[label="[] ++ vy8",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3]; 11.71/4.53 43[label="vy50 : vy51 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3]; 11.71/4.53 44[label="[] >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];44 -> 48[label="",style="solid", color="black", weight=3]; 11.71/4.53 45[label="vy90 : vy91 ++ vy8",fontsize=16,color="green",shape="box"];45 -> 49[label="",style="dashed", color="green", weight=3]; 11.71/4.53 46[label="vy8",fontsize=16,color="green",shape="box"];47 -> 28[label="",style="dashed", color="red", weight=0]; 11.71/4.53 47[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50 ++ (vy51 >>= Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="magenta"];47 -> 50[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 47 -> 51[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 48[label="[]",fontsize=16,color="green",shape="box"];49 -> 28[label="",style="dashed", color="red", weight=0]; 11.71/4.53 49[label="vy91 ++ vy8",fontsize=16,color="magenta"];49 -> 52[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 50[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];50 -> 53[label="",style="solid", color="black", weight=3]; 11.71/4.53 51 -> 39[label="",style="dashed", color="red", weight=0]; 11.71/4.53 51[label="vy51 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="magenta"];51 -> 54[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 52[label="vy91",fontsize=16,color="green",shape="box"];53[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];83[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];53 -> 83[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 83 -> 55[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 84[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];53 -> 84[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 84 -> 56[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 54[label="vy51",fontsize=16,color="green",shape="box"];55[label="vy60 : vy61 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];55 -> 57[label="",style="solid", color="black", weight=3]; 11.71/4.53 56[label="[] >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];56 -> 58[label="",style="solid", color="black", weight=3]; 11.71/4.53 57 -> 28[label="",style="dashed", color="red", weight=0]; 11.71/4.53 57[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60 ++ (vy61 >>= Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="magenta"];57 -> 59[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 57 -> 60[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 58[label="[]",fontsize=16,color="green",shape="box"];59[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];59 -> 61[label="",style="solid", color="black", weight=3]; 11.71/4.53 60 -> 53[label="",style="dashed", color="red", weight=0]; 11.71/4.53 60[label="vy61 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="magenta"];60 -> 62[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 61[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="triangle"];85[label="vy7/vy70 : vy71",fontsize=10,color="white",style="solid",shape="box"];61 -> 85[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 85 -> 63[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 86[label="vy7/[]",fontsize=10,color="white",style="solid",shape="box"];61 -> 86[label="",style="solid", color="burlywood", weight=9]; 11.71/4.53 86 -> 64[label="",style="solid", color="burlywood", weight=3]; 11.71/4.53 62[label="vy61",fontsize=16,color="green",shape="box"];63[label="vy70 : vy71 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];63 -> 65[label="",style="solid", color="black", weight=3]; 11.71/4.53 64[label="[] >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];64 -> 66[label="",style="solid", color="black", weight=3]; 11.71/4.53 65 -> 28[label="",style="dashed", color="red", weight=0]; 11.71/4.53 65[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70 ++ (vy71 >>= Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="magenta"];65 -> 67[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 65 -> 68[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 66[label="[]",fontsize=16,color="green",shape="box"];67[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];67 -> 69[label="",style="solid", color="black", weight=3]; 11.71/4.53 68 -> 61[label="",style="dashed", color="red", weight=0]; 11.71/4.53 68[label="vy71 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="magenta"];68 -> 70[label="",style="dashed", color="magenta", weight=3]; 11.71/4.53 69[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];69 -> 71[label="",style="solid", color="black", weight=3]; 11.71/4.53 70[label="vy71",fontsize=16,color="green",shape="box"];71[label="vy3 vy40 vy50 vy60 vy70 : []",fontsize=16,color="green",shape="box"];71 -> 72[label="",style="dashed", color="green", weight=3]; 11.71/4.53 72[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];72 -> 73[label="",style="dashed", color="green", weight=3]; 11.71/4.53 72 -> 74[label="",style="dashed", color="green", weight=3]; 11.71/4.53 72 -> 75[label="",style="dashed", color="green", weight=3]; 11.71/4.53 72 -> 76[label="",style="dashed", color="green", weight=3]; 11.71/4.53 73[label="vy40",fontsize=16,color="green",shape="box"];74[label="vy50",fontsize=16,color="green",shape="box"];75[label="vy60",fontsize=16,color="green",shape="box"];76[label="vy70",fontsize=16,color="green",shape="box"];} 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (8) 11.71/4.53 Complex Obligation (AND) 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (9) 11.71/4.53 Obligation: 11.71/4.53 Q DP problem: 11.71/4.53 The TRS P consists of the following rules: 11.71/4.53 11.71/4.53 new_gtGtEs0(:(vy60, vy61), vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) -> new_gtGtEs0(vy61, vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) 11.71/4.53 11.71/4.53 R is empty. 11.71/4.53 Q is empty. 11.71/4.53 We have to consider all minimal (P,Q,R)-chains. 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (10) QDPSizeChangeProof (EQUIVALENT) 11.71/4.53 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. 11.71/4.53 11.71/4.53 From the DPs we obtained the following set of size-change graphs: 11.71/4.53 *new_gtGtEs0(:(vy60, vy61), vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) -> new_gtGtEs0(vy61, vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) 11.71/4.53 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10 11.71/4.53 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (11) 11.71/4.53 YES 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (12) 11.71/4.53 Obligation: 11.71/4.53 Q DP problem: 11.71/4.53 The TRS P consists of the following rules: 11.71/4.53 11.71/4.53 new_gtGtEs1(:(vy50, vy51), vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) -> new_gtGtEs1(vy51, vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) 11.71/4.53 11.71/4.53 R is empty. 11.71/4.53 Q is empty. 11.71/4.53 We have to consider all minimal (P,Q,R)-chains. 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (13) QDPSizeChangeProof (EQUIVALENT) 11.71/4.53 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. 11.71/4.53 11.71/4.53 From the DPs we obtained the following set of size-change graphs: 11.71/4.53 *new_gtGtEs1(:(vy50, vy51), vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) -> new_gtGtEs1(vy51, vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) 11.71/4.53 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10 11.71/4.53 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (14) 11.71/4.53 YES 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (15) 11.71/4.53 Obligation: 11.71/4.53 Q DP problem: 11.71/4.53 The TRS P consists of the following rules: 11.71/4.53 11.71/4.53 new_gtGtEs(:(vy70, vy71), vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) -> new_gtGtEs(vy71, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) 11.71/4.53 11.71/4.53 R is empty. 11.71/4.53 Q is empty. 11.71/4.53 We have to consider all minimal (P,Q,R)-chains. 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (16) QDPSizeChangeProof (EQUIVALENT) 11.71/4.53 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. 11.71/4.53 11.71/4.53 From the DPs we obtained the following set of size-change graphs: 11.71/4.53 *new_gtGtEs(:(vy70, vy71), vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) -> new_gtGtEs(vy71, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) 11.71/4.53 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10 11.71/4.53 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (17) 11.71/4.53 YES 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (18) 11.71/4.53 Obligation: 11.71/4.53 Q DP problem: 11.71/4.53 The TRS P consists of the following rules: 11.71/4.53 11.71/4.53 new_psPs(:(vy90, vy91), vy8, h) -> new_psPs(vy91, vy8, h) 11.71/4.53 11.71/4.53 R is empty. 11.71/4.53 Q is empty. 11.71/4.53 We have to consider all minimal (P,Q,R)-chains. 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (19) QDPSizeChangeProof (EQUIVALENT) 11.71/4.53 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. 11.71/4.53 11.71/4.53 From the DPs we obtained the following set of size-change graphs: 11.71/4.53 *new_psPs(:(vy90, vy91), vy8, h) -> new_psPs(vy91, vy8, h) 11.71/4.53 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 11.71/4.53 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (20) 11.71/4.53 YES 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (21) 11.71/4.53 Obligation: 11.71/4.53 Q DP problem: 11.71/4.53 The TRS P consists of the following rules: 11.71/4.53 11.71/4.53 new_gtGtEs2(:(vy40, vy41), vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) -> new_gtGtEs2(vy41, vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) 11.71/4.53 11.71/4.53 R is empty. 11.71/4.53 Q is empty. 11.71/4.53 We have to consider all minimal (P,Q,R)-chains. 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (22) QDPSizeChangeProof (EQUIVALENT) 11.71/4.53 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. 11.71/4.53 11.71/4.53 From the DPs we obtained the following set of size-change graphs: 11.71/4.53 *new_gtGtEs2(:(vy40, vy41), vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) -> new_gtGtEs2(vy41, vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) 11.71/4.53 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10 11.71/4.53 11.71/4.53 11.71/4.53 ---------------------------------------- 11.71/4.53 11.71/4.53 (23) 11.71/4.53 YES 12.06/4.59 EOF