/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) Narrow [EQUIVALENT, 18 ms] (8) YES ---------------------------------------- (0) Obligation: mainModule Main module Maybe where { import qualified Main; import qualified Monad; import qualified Prelude; } module Main where { import qualified Maybe; import qualified Monad; import qualified Prelude; } module Monad where { import qualified Main; import qualified Maybe; import qualified Prelude; liftM2 :: Monad d => (b -> a -> c) -> d b -> d a -> d c; liftM2 f m1 m2 = m1 >>= (\x1 ->m2 >>= (\x2 ->return (f x1 x2))); } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\x2->return (f x1 x2)" is transformed to "liftM20 f x1 x2 = return (f x1 x2); " The following Lambda expression "\x1->m2 >>= liftM20 f x1" is transformed to "liftM21 m2 f x1 = m2 >>= liftM20 f x1; " ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified Main; import qualified Monad; import qualified Prelude; } module Main where { import qualified Maybe; import qualified Monad; import qualified Prelude; } module Monad where { import qualified Main; import qualified Maybe; import qualified Prelude; liftM2 :: Monad a => (c -> d -> b) -> a c -> a d -> a b; liftM2 f m1 m2 = m1 >>= liftM21 m2 f; liftM20 f x1 x2 = return (f x1 x2); liftM21 m2 f x1 = m2 >>= liftM20 f x1; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Maybe where { import qualified Main; import qualified Monad; import qualified Prelude; } module Main where { import qualified Maybe; import qualified Monad; import qualified Prelude; } module Monad where { import qualified Main; import qualified Maybe; import qualified Prelude; liftM2 :: Monad a => (c -> b -> d) -> a c -> a b -> a d; liftM2 f m1 m2 = m1 >>= liftM21 m2 f; liftM20 f x1 x2 = return (f x1 x2); liftM21 m2 f x1 = m2 >>= liftM20 f x1; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (6) Obligation: mainModule Main module Maybe where { import qualified Main; import qualified Monad; import qualified Prelude; } module Main where { import qualified Maybe; import qualified Monad; import qualified Prelude; } module Monad where { import qualified Main; import qualified Maybe; import qualified Prelude; liftM2 :: Monad d => (c -> b -> a) -> d c -> d b -> d a; liftM2 f m1 m2 = m1 >>= liftM21 m2 f; liftM20 f x1 x2 = return (f x1 x2); liftM21 m2 f x1 = m2 >>= liftM20 f x1; } ---------------------------------------- (7) Narrow (EQUIVALENT) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="Monad.liftM2",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="Monad.liftM2 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="Monad.liftM2 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="Monad.liftM2 vy3 vy4 vy5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="vy4 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="burlywood",shape="box"];21[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 7[label="",style="solid", color="burlywood", weight=3]; 22[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 8[label="",style="solid", color="burlywood", weight=3]; 7[label="Nothing >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8[label="Just vy40 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9[label="Nothing",fontsize=16,color="green",shape="box"];10[label="Monad.liftM21 vy5 vy3 vy40",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11[label="vy5 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="burlywood",shape="box"];23[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];11 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 12[label="",style="solid", color="burlywood", weight=3]; 24[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];11 -> 24[label="",style="solid", color="burlywood", weight=9]; 24 -> 13[label="",style="solid", color="burlywood", weight=3]; 12[label="Nothing >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="Just vy50 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="Nothing",fontsize=16,color="green",shape="box"];15[label="Monad.liftM20 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 16[label="return (vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 17[label="Just (vy3 vy40 vy50)",fontsize=16,color="green",shape="box"];17 -> 18[label="",style="dashed", color="green", weight=3]; 18[label="vy3 vy40 vy50",fontsize=16,color="green",shape="box"];18 -> 19[label="",style="dashed", color="green", weight=3]; 18 -> 20[label="",style="dashed", color="green", weight=3]; 19[label="vy40",fontsize=16,color="green",shape="box"];20[label="vy50",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) YES