/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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, 20 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; liftM3 :: Monad e => (c -> d -> b -> a) -> e c -> e d -> e b -> e a; liftM3 f m1 m2 m3 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->return (f x1 x2 x3)))); } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\x3->return (f x1 x2 x3)" is transformed to "liftM30 f x1 x2 x3 = return (f x1 x2 x3); " The following Lambda expression "\x2->m3 >>= liftM30 f x1 x2" is transformed to "liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; " The following Lambda expression "\x1->m2 >>= liftM31 m3 f x1" is transformed to "liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 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; liftM3 :: Monad b => (c -> a -> d -> e) -> b c -> b a -> b d -> b e; liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f; liftM30 f x1 x2 x3 = return (f x1 x2 x3); liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 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; liftM3 :: Monad b => (d -> a -> c -> e) -> b d -> b a -> b c -> b e; liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f; liftM30 f x1 x2 x3 = return (f x1 x2 x3); liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 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; liftM3 :: Monad d => (e -> a -> b -> c) -> d e -> d a -> d b -> d c; liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f; liftM30 f x1 x2 x3 = return (f x1 x2 x3); liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2; liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1; } ---------------------------------------- (7) Narrow (EQUIVALENT) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="Monad.liftM3",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="Monad.liftM3 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="Monad.liftM3 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="Monad.liftM3 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3]; 6[label="Monad.liftM3 vy3 vy4 vy5 vy6",fontsize=16,color="black",shape="triangle"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="vy4 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="burlywood",shape="box"];28[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];7 -> 28[label="",style="solid", color="burlywood", weight=9]; 28 -> 8[label="",style="solid", color="burlywood", weight=3]; 29[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];7 -> 29[label="",style="solid", color="burlywood", weight=9]; 29 -> 9[label="",style="solid", color="burlywood", weight=3]; 8[label="Nothing >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9[label="Just vy40 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="Monad.liftM32 vy5 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 12[label="vy5 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="burlywood",shape="box"];30[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];12 -> 30[label="",style="solid", color="burlywood", weight=9]; 30 -> 13[label="",style="solid", color="burlywood", weight=3]; 31[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];12 -> 31[label="",style="solid", color="burlywood", weight=9]; 31 -> 14[label="",style="solid", color="burlywood", weight=3]; 13[label="Nothing >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="Just vy50 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="Nothing",fontsize=16,color="green",shape="box"];16[label="Monad.liftM31 vy6 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 17[label="vy6 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];32[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];17 -> 32[label="",style="solid", color="burlywood", weight=9]; 32 -> 18[label="",style="solid", color="burlywood", weight=3]; 33[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];17 -> 33[label="",style="solid", color="burlywood", weight=9]; 33 -> 19[label="",style="solid", color="burlywood", weight=3]; 18[label="Nothing >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="Just vy60 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="Nothing",fontsize=16,color="green",shape="box"];21[label="Monad.liftM30 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3]; 22[label="return (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3]; 23[label="Just (vy3 vy40 vy50 vy60)",fontsize=16,color="green",shape="box"];23 -> 24[label="",style="dashed", color="green", weight=3]; 24[label="vy3 vy40 vy50 vy60",fontsize=16,color="green",shape="box"];24 -> 25[label="",style="dashed", color="green", weight=3]; 24 -> 26[label="",style="dashed", color="green", weight=3]; 24 -> 27[label="",style="dashed", color="green", weight=3]; 25[label="vy40",fontsize=16,color="green",shape="box"];26[label="vy50",fontsize=16,color="green",shape="box"];27[label="vy60",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) YES