8.91/3.93 YES 11.02/4.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 11.02/4.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.02/4.49 11.02/4.49 11.02/4.49 H-Termination with start terms of the given HASKELL could be proven: 11.02/4.49 11.02/4.49 (0) HASKELL 11.02/4.49 (1) LR [EQUIVALENT, 0 ms] 11.02/4.49 (2) HASKELL 11.02/4.49 (3) BR [EQUIVALENT, 0 ms] 11.02/4.49 (4) HASKELL 11.02/4.49 (5) COR [EQUIVALENT, 0 ms] 11.02/4.49 (6) HASKELL 11.02/4.49 (7) Narrow [SOUND, 0 ms] 11.02/4.49 (8) AND 11.02/4.49 (9) QDP 11.02/4.49 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.02/4.49 (11) YES 11.02/4.49 (12) QDP 11.02/4.49 (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.02/4.49 (14) YES 11.02/4.49 (15) QDP 11.02/4.49 (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.02/4.49 (17) YES 11.02/4.49 (18) QDP 11.02/4.49 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 11.02/4.49 (20) YES 11.02/4.49 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (0) 11.02/4.49 Obligation: 11.02/4.49 mainModule Main 11.02/4.49 module Maybe where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Main where { 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Monad where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Prelude; 11.02/4.49 liftM3 :: Monad a => (b -> c -> e -> d) -> a b -> a c -> a e -> a d; 11.02/4.49 liftM3 f m1 m2 m3 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->return (f x1 x2 x3)))); 11.02/4.49 11.02/4.49 } 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (1) LR (EQUIVALENT) 11.02/4.49 Lambda Reductions: 11.02/4.49 The following Lambda expression 11.02/4.49 "\x3->return (f x1 x2 x3)" 11.02/4.49 is transformed to 11.02/4.49 "liftM30 f x1 x2 x3 = return (f x1 x2 x3); 11.02/4.49 " 11.02/4.49 The following Lambda expression 11.02/4.49 "\x2->m3 >>= liftM30 f x1 x2" 11.02/4.49 is transformed to 11.02/4.49 "liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; 11.02/4.49 " 11.02/4.49 The following Lambda expression 11.02/4.49 "\x1->m2 >>= liftM31 m3 f x1" 11.02/4.49 is transformed to 11.02/4.49 "liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1; 11.02/4.49 " 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (2) 11.02/4.49 Obligation: 11.02/4.49 mainModule Main 11.02/4.49 module Maybe where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Main where { 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Monad where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Prelude; 11.02/4.49 liftM3 :: Monad a => (e -> b -> d -> c) -> a e -> a b -> a d -> a c; 11.02/4.49 liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f; 11.02/4.49 11.02/4.49 liftM30 f x1 x2 x3 = return (f x1 x2 x3); 11.02/4.49 11.02/4.49 liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; 11.02/4.49 11.02/4.49 liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1; 11.02/4.49 11.02/4.49 } 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (3) BR (EQUIVALENT) 11.02/4.49 Replaced joker patterns by fresh variables and removed binding patterns. 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (4) 11.02/4.49 Obligation: 11.02/4.49 mainModule Main 11.02/4.49 module Maybe where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Main where { 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Monad where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Prelude; 11.02/4.49 liftM3 :: Monad e => (c -> b -> a -> d) -> e c -> e b -> e a -> e d; 11.02/4.49 liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f; 11.02/4.49 11.02/4.49 liftM30 f x1 x2 x3 = return (f x1 x2 x3); 11.02/4.49 11.02/4.49 liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; 11.02/4.49 11.02/4.49 liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1; 11.02/4.49 11.02/4.49 } 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (5) COR (EQUIVALENT) 11.02/4.49 Cond Reductions: 11.02/4.49 The following Function with conditions 11.02/4.49 "undefined |Falseundefined; 11.02/4.49 " 11.02/4.49 is transformed to 11.02/4.49 "undefined = undefined1; 11.02/4.49 " 11.02/4.49 "undefined0 True = undefined; 11.02/4.49 " 11.02/4.49 "undefined1 = undefined0 False; 11.02/4.49 " 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (6) 11.02/4.49 Obligation: 11.02/4.49 mainModule Main 11.02/4.49 module Maybe where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Main where { 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Monad; 11.02/4.49 import qualified Prelude; 11.02/4.49 } 11.02/4.49 module Monad where { 11.02/4.49 import qualified Main; 11.02/4.49 import qualified Maybe; 11.02/4.49 import qualified Prelude; 11.02/4.49 liftM3 :: Monad e => (c -> a -> d -> b) -> e c -> e a -> e d -> e b; 11.02/4.49 liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f; 11.02/4.49 11.02/4.49 liftM30 f x1 x2 x3 = return (f x1 x2 x3); 11.02/4.49 11.02/4.49 liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; 11.02/4.49 11.02/4.49 liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1; 11.02/4.49 11.02/4.49 } 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (7) Narrow (SOUND) 11.02/4.49 Haskell To QDPs 11.02/4.49 11.02/4.49 digraph dp_graph { 11.02/4.49 node [outthreshold=100, inthreshold=100];1[label="Monad.liftM3",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 11.02/4.49 3[label="Monad.liftM3 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 11.02/4.49 4[label="Monad.liftM3 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 11.02/4.49 5[label="Monad.liftM3 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3]; 11.02/4.49 6[label="Monad.liftM3 vy3 vy4 vy5 vy6",fontsize=16,color="black",shape="triangle"];6 -> 7[label="",style="solid", color="black", weight=3]; 11.02/4.49 7[label="vy4 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="blue",shape="box"];126[label=">>= :: (IO a) -> (a -> IO b) -> IO b",fontsize=10,color="white",style="solid",shape="box"];7 -> 126[label="",style="solid", color="blue", weight=9]; 11.02/4.49 126 -> 8[label="",style="solid", color="blue", weight=3]; 11.02/4.49 127[label=">>= :: ([] a) -> (a -> [] b) -> [] b",fontsize=10,color="white",style="solid",shape="box"];7 -> 127[label="",style="solid", color="blue", weight=9]; 11.02/4.49 127 -> 9[label="",style="solid", color="blue", weight=3]; 11.02/4.49 128[label=">>= :: (Maybe a) -> (a -> Maybe b) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];7 -> 128[label="",style="solid", color="blue", weight=9]; 11.02/4.49 128 -> 10[label="",style="solid", color="blue", weight=3]; 11.02/4.49 8[label="vy4 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 11.02/4.49 9[label="vy4 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="burlywood",shape="triangle"];129[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];9 -> 129[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 129 -> 12[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 130[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 130[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 130 -> 13[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 10[label="vy4 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="burlywood",shape="box"];131[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];10 -> 131[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 131 -> 14[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 132[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];10 -> 132[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 132 -> 15[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 11[label="primbindIO vy4 (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="burlywood",shape="box"];133[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];11 -> 133[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 133 -> 16[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 134[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];11 -> 134[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 134 -> 17[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 135[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];11 -> 135[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 135 -> 18[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 136[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];11 -> 136[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 136 -> 19[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 12[label="vy40 : vy41 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];12 -> 20[label="",style="solid", color="black", weight=3]; 11.02/4.49 13[label="[] >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];13 -> 21[label="",style="solid", color="black", weight=3]; 11.02/4.49 14[label="Nothing >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];14 -> 22[label="",style="solid", color="black", weight=3]; 11.02/4.49 15[label="Just vy40 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];15 -> 23[label="",style="solid", color="black", weight=3]; 11.02/4.49 16[label="primbindIO (IO vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];16 -> 24[label="",style="solid", color="black", weight=3]; 11.02/4.49 17[label="primbindIO (AProVE_IO vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];17 -> 25[label="",style="solid", color="black", weight=3]; 11.02/4.49 18[label="primbindIO (AProVE_Exception vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];18 -> 26[label="",style="solid", color="black", weight=3]; 11.02/4.49 19[label="primbindIO (AProVE_Error vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];19 -> 27[label="",style="solid", color="black", weight=3]; 11.02/4.49 20 -> 70[label="",style="dashed", color="red", weight=0]; 11.02/4.49 20[label="Monad.liftM32 vy5 vy6 vy3 vy40 ++ (vy41 >>= Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="magenta"];20 -> 71[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 20 -> 72[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 21[label="[]",fontsize=16,color="green",shape="box"];22[label="Nothing",fontsize=16,color="green",shape="box"];23[label="Monad.liftM32 vy5 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];23 -> 30[label="",style="solid", color="black", weight=3]; 11.02/4.49 24[label="error []",fontsize=16,color="red",shape="box"];25[label="Monad.liftM32 vy5 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];25 -> 31[label="",style="solid", color="black", weight=3]; 11.02/4.49 26[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];27[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];71 -> 9[label="",style="dashed", color="red", weight=0]; 11.02/4.49 71[label="vy41 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="magenta"];71 -> 81[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 72[label="Monad.liftM32 vy5 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];72 -> 82[label="",style="solid", color="black", weight=3]; 11.02/4.49 70[label="vy8 ++ vy7",fontsize=16,color="burlywood",shape="triangle"];137[label="vy8/vy80 : vy81",fontsize=10,color="white",style="solid",shape="box"];70 -> 137[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 137 -> 83[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 138[label="vy8/[]",fontsize=10,color="white",style="solid",shape="box"];70 -> 138[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 138 -> 84[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 30[label="vy5 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="burlywood",shape="box"];139[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];30 -> 139[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 139 -> 34[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 140[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];30 -> 140[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 140 -> 35[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 31[label="vy5 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];31 -> 36[label="",style="solid", color="black", weight=3]; 11.02/4.49 81[label="vy41",fontsize=16,color="green",shape="box"];82[label="vy5 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];141[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];82 -> 141[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 141 -> 90[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 142[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];82 -> 142[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 142 -> 91[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 83[label="(vy80 : vy81) ++ vy7",fontsize=16,color="black",shape="box"];83 -> 92[label="",style="solid", color="black", weight=3]; 11.02/4.49 84[label="[] ++ vy7",fontsize=16,color="black",shape="box"];84 -> 93[label="",style="solid", color="black", weight=3]; 11.02/4.49 34[label="Nothing >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];34 -> 39[label="",style="solid", color="black", weight=3]; 11.02/4.49 35[label="Just vy50 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3]; 11.02/4.49 36[label="primbindIO vy5 (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];143[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];36 -> 143[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 143 -> 41[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 144[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];36 -> 144[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 144 -> 42[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 145[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];36 -> 145[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 145 -> 43[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 146[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];36 -> 146[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 146 -> 44[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 90[label="vy50 : vy51 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];90 -> 96[label="",style="solid", color="black", weight=3]; 11.02/4.49 91[label="[] >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];91 -> 97[label="",style="solid", color="black", weight=3]; 11.02/4.49 92[label="vy80 : vy81 ++ vy7",fontsize=16,color="green",shape="box"];92 -> 98[label="",style="dashed", color="green", weight=3]; 11.02/4.49 93[label="vy7",fontsize=16,color="green",shape="box"];39[label="Nothing",fontsize=16,color="green",shape="box"];40[label="Monad.liftM31 vy6 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3]; 11.02/4.49 41[label="primbindIO (IO vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3]; 11.02/4.49 42[label="primbindIO (AProVE_IO vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3]; 11.02/4.49 43[label="primbindIO (AProVE_Exception vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3]; 11.02/4.49 44[label="primbindIO (AProVE_Error vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3]; 11.02/4.49 96 -> 70[label="",style="dashed", color="red", weight=0]; 11.02/4.49 96[label="Monad.liftM31 vy6 vy3 vy40 vy50 ++ (vy51 >>= Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="magenta"];96 -> 103[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 96 -> 104[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 97[label="[]",fontsize=16,color="green",shape="box"];98 -> 70[label="",style="dashed", color="red", weight=0]; 11.02/4.49 98[label="vy81 ++ vy7",fontsize=16,color="magenta"];98 -> 105[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 47[label="vy6 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];147[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];47 -> 147[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 147 -> 54[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 148[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];47 -> 148[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 148 -> 55[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 48[label="error []",fontsize=16,color="red",shape="box"];49[label="Monad.liftM31 vy6 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];49 -> 56[label="",style="solid", color="black", weight=3]; 11.02/4.49 50[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];51[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];103 -> 82[label="",style="dashed", color="red", weight=0]; 11.02/4.49 103[label="vy51 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="magenta"];103 -> 107[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 104[label="Monad.liftM31 vy6 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];104 -> 108[label="",style="solid", color="black", weight=3]; 11.02/4.49 105[label="vy81",fontsize=16,color="green",shape="box"];54[label="Nothing >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];54 -> 59[label="",style="solid", color="black", weight=3]; 11.02/4.49 55[label="Just vy60 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];55 -> 60[label="",style="solid", color="black", weight=3]; 11.02/4.49 56[label="vy6 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3]; 11.02/4.49 107[label="vy51",fontsize=16,color="green",shape="box"];108[label="vy6 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];149[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];108 -> 149[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 149 -> 110[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 150[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];108 -> 150[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 150 -> 111[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 59[label="Nothing",fontsize=16,color="green",shape="box"];60[label="Monad.liftM30 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3]; 11.02/4.49 61[label="primbindIO vy6 (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="burlywood",shape="box"];151[label="vy6/IO vy60",fontsize=10,color="white",style="solid",shape="box"];61 -> 151[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 151 -> 65[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 152[label="vy6/AProVE_IO vy60",fontsize=10,color="white",style="solid",shape="box"];61 -> 152[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 152 -> 66[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 153[label="vy6/AProVE_Exception vy60",fontsize=10,color="white",style="solid",shape="box"];61 -> 153[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 153 -> 67[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 154[label="vy6/AProVE_Error vy60",fontsize=10,color="white",style="solid",shape="box"];61 -> 154[label="",style="solid", color="burlywood", weight=9]; 11.02/4.49 154 -> 68[label="",style="solid", color="burlywood", weight=3]; 11.02/4.49 110[label="vy60 : vy61 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];110 -> 115[label="",style="solid", color="black", weight=3]; 11.02/4.49 111[label="[] >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];111 -> 116[label="",style="solid", color="black", weight=3]; 11.02/4.49 64[label="return (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];64 -> 85[label="",style="solid", color="black", weight=3]; 11.02/4.49 65[label="primbindIO (IO vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];65 -> 86[label="",style="solid", color="black", weight=3]; 11.02/4.49 66[label="primbindIO (AProVE_IO vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];66 -> 87[label="",style="solid", color="black", weight=3]; 11.02/4.49 67[label="primbindIO (AProVE_Exception vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];67 -> 88[label="",style="solid", color="black", weight=3]; 11.02/4.49 68[label="primbindIO (AProVE_Error vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];68 -> 89[label="",style="solid", color="black", weight=3]; 11.02/4.49 115 -> 70[label="",style="dashed", color="red", weight=0]; 11.02/4.49 115[label="Monad.liftM30 vy3 vy40 vy50 vy60 ++ (vy61 >>= Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="magenta"];115 -> 117[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 115 -> 118[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 116[label="[]",fontsize=16,color="green",shape="box"];85[label="Just (vy3 vy40 vy50 vy60)",fontsize=16,color="green",shape="box"];85 -> 94[label="",style="dashed", color="green", weight=3]; 11.02/4.49 86[label="error []",fontsize=16,color="red",shape="box"];87[label="Monad.liftM30 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];87 -> 95[label="",style="solid", color="black", weight=3]; 11.02/4.49 88[label="AProVE_Exception vy60",fontsize=16,color="green",shape="box"];89[label="AProVE_Error vy60",fontsize=16,color="green",shape="box"];117 -> 108[label="",style="dashed", color="red", weight=0]; 11.02/4.49 117[label="vy61 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="magenta"];117 -> 119[label="",style="dashed", color="magenta", weight=3]; 11.02/4.49 118[label="Monad.liftM30 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];118 -> 120[label="",style="solid", color="black", weight=3]; 11.02/4.49 94[label="vy3 vy40 vy50 vy60",fontsize=16,color="green",shape="box"];94 -> 99[label="",style="dashed", color="green", weight=3]; 11.02/4.49 94 -> 100[label="",style="dashed", color="green", weight=3]; 11.02/4.49 94 -> 101[label="",style="dashed", color="green", weight=3]; 11.02/4.49 95[label="return (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];95 -> 102[label="",style="solid", color="black", weight=3]; 11.02/4.49 119[label="vy61",fontsize=16,color="green",shape="box"];120[label="return (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];120 -> 121[label="",style="solid", color="black", weight=3]; 11.02/4.49 99[label="vy40",fontsize=16,color="green",shape="box"];100[label="vy50",fontsize=16,color="green",shape="box"];101[label="vy60",fontsize=16,color="green",shape="box"];102[label="primretIO (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];102 -> 106[label="",style="solid", color="black", weight=3]; 11.02/4.49 121[label="vy3 vy40 vy50 vy60 : []",fontsize=16,color="green",shape="box"];121 -> 122[label="",style="dashed", color="green", weight=3]; 11.02/4.49 106[label="AProVE_IO (vy3 vy40 vy50 vy60)",fontsize=16,color="green",shape="box"];106 -> 109[label="",style="dashed", color="green", weight=3]; 11.02/4.49 122[label="vy3 vy40 vy50 vy60",fontsize=16,color="green",shape="box"];122 -> 123[label="",style="dashed", color="green", weight=3]; 11.02/4.49 122 -> 124[label="",style="dashed", color="green", weight=3]; 11.02/4.49 122 -> 125[label="",style="dashed", color="green", weight=3]; 11.02/4.49 109[label="vy3 vy40 vy50 vy60",fontsize=16,color="green",shape="box"];109 -> 112[label="",style="dashed", color="green", weight=3]; 11.02/4.49 109 -> 113[label="",style="dashed", color="green", weight=3]; 11.02/4.49 109 -> 114[label="",style="dashed", color="green", weight=3]; 11.02/4.49 123[label="vy40",fontsize=16,color="green",shape="box"];124[label="vy50",fontsize=16,color="green",shape="box"];125[label="vy60",fontsize=16,color="green",shape="box"];112[label="vy40",fontsize=16,color="green",shape="box"];113[label="vy50",fontsize=16,color="green",shape="box"];114[label="vy60",fontsize=16,color="green",shape="box"];} 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (8) 11.02/4.49 Complex Obligation (AND) 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (9) 11.02/4.49 Obligation: 11.02/4.49 Q DP problem: 11.02/4.49 The TRS P consists of the following rules: 11.02/4.49 11.02/4.49 new_gtGtEs(:(vy60, vy61), vy3, vy40, vy50, h, ba, bb, bc) -> new_gtGtEs(vy61, vy3, vy40, vy50, h, ba, bb, bc) 11.02/4.49 11.02/4.49 R is empty. 11.02/4.49 Q is empty. 11.02/4.49 We have to consider all minimal (P,Q,R)-chains. 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (10) QDPSizeChangeProof (EQUIVALENT) 11.02/4.49 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. 11.02/4.49 11.02/4.49 From the DPs we obtained the following set of size-change graphs: 11.02/4.49 *new_gtGtEs(:(vy60, vy61), vy3, vy40, vy50, h, ba, bb, bc) -> new_gtGtEs(vy61, vy3, vy40, vy50, h, ba, bb, bc) 11.02/4.49 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8 11.02/4.49 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (11) 11.02/4.49 YES 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (12) 11.02/4.49 Obligation: 11.02/4.49 Q DP problem: 11.02/4.49 The TRS P consists of the following rules: 11.02/4.49 11.02/4.49 new_gtGtEs1(:(vy40, vy41), vy5, vy6, vy3, h, ba, bb, bc) -> new_gtGtEs1(vy41, vy5, vy6, vy3, h, ba, bb, bc) 11.02/4.49 11.02/4.49 R is empty. 11.02/4.49 Q is empty. 11.02/4.49 We have to consider all minimal (P,Q,R)-chains. 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (13) QDPSizeChangeProof (EQUIVALENT) 11.02/4.49 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. 11.02/4.49 11.02/4.49 From the DPs we obtained the following set of size-change graphs: 11.02/4.49 *new_gtGtEs1(:(vy40, vy41), vy5, vy6, vy3, h, ba, bb, bc) -> new_gtGtEs1(vy41, vy5, vy6, vy3, h, ba, bb, bc) 11.02/4.49 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8 11.02/4.49 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (14) 11.02/4.49 YES 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (15) 11.02/4.49 Obligation: 11.02/4.49 Q DP problem: 11.02/4.49 The TRS P consists of the following rules: 11.02/4.49 11.02/4.49 new_gtGtEs0(:(vy50, vy51), vy6, vy3, vy40, h, ba, bb, bc) -> new_gtGtEs0(vy51, vy6, vy3, vy40, h, ba, bb, bc) 11.02/4.49 11.02/4.49 R is empty. 11.02/4.49 Q is empty. 11.02/4.49 We have to consider all minimal (P,Q,R)-chains. 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (16) QDPSizeChangeProof (EQUIVALENT) 11.02/4.49 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. 11.02/4.49 11.02/4.49 From the DPs we obtained the following set of size-change graphs: 11.02/4.49 *new_gtGtEs0(:(vy50, vy51), vy6, vy3, vy40, h, ba, bb, bc) -> new_gtGtEs0(vy51, vy6, vy3, vy40, h, ba, bb, bc) 11.02/4.49 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8 11.02/4.49 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (17) 11.02/4.49 YES 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (18) 11.02/4.49 Obligation: 11.02/4.49 Q DP problem: 11.02/4.49 The TRS P consists of the following rules: 11.02/4.49 11.02/4.49 new_psPs(:(vy80, vy81), vy7, h) -> new_psPs(vy81, vy7, h) 11.02/4.49 11.02/4.49 R is empty. 11.02/4.49 Q is empty. 11.02/4.49 We have to consider all minimal (P,Q,R)-chains. 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (19) QDPSizeChangeProof (EQUIVALENT) 11.02/4.49 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. 11.02/4.49 11.02/4.49 From the DPs we obtained the following set of size-change graphs: 11.02/4.49 *new_psPs(:(vy80, vy81), vy7, h) -> new_psPs(vy81, vy7, h) 11.02/4.49 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 11.02/4.49 11.02/4.49 11.02/4.49 ---------------------------------------- 11.02/4.49 11.02/4.49 (20) 11.02/4.49 YES 11.02/4.54 EOF