/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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, 10 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 c => (d -> b -> a) -> c d -> c b -> c a; 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 d => (a -> c -> b) -> d a -> d c -> d 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 c => (b -> d -> a) -> c b -> c d -> c 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; } ---------------------------------------- (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 b => (a -> c -> d) -> b a -> b c -> b 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; } ---------------------------------------- (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="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="primbindIO vy4 (Monad.liftM21 vy5 vy3)",fontsize=16,color="burlywood",shape="box"];32[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];7 -> 32[label="",style="solid", color="burlywood", weight=9]; 32 -> 8[label="",style="solid", color="burlywood", weight=3]; 33[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];7 -> 33[label="",style="solid", color="burlywood", weight=9]; 33 -> 9[label="",style="solid", color="burlywood", weight=3]; 34[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];7 -> 34[label="",style="solid", color="burlywood", weight=9]; 34 -> 10[label="",style="solid", color="burlywood", weight=3]; 35[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];7 -> 35[label="",style="solid", color="burlywood", weight=9]; 35 -> 11[label="",style="solid", color="burlywood", weight=3]; 8[label="primbindIO (IO vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3]; 9[label="primbindIO (AProVE_IO vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 10[label="primbindIO (AProVE_Exception vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 11[label="primbindIO (AProVE_Error vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 12[label="error []",fontsize=16,color="red",shape="box"];13[label="Monad.liftM21 vy5 vy3 vy40",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3]; 14[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];15[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];16[label="vy5 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 17[label="primbindIO vy5 (Monad.liftM20 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];36[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];17 -> 36[label="",style="solid", color="burlywood", weight=9]; 36 -> 18[label="",style="solid", color="burlywood", weight=3]; 37[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];17 -> 37[label="",style="solid", color="burlywood", weight=9]; 37 -> 19[label="",style="solid", color="burlywood", weight=3]; 38[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];17 -> 38[label="",style="solid", color="burlywood", weight=9]; 38 -> 20[label="",style="solid", color="burlywood", weight=3]; 39[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];17 -> 39[label="",style="solid", color="burlywood", weight=9]; 39 -> 21[label="",style="solid", color="burlywood", weight=3]; 18[label="primbindIO (IO vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 19[label="primbindIO (AProVE_IO vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="primbindIO (AProVE_Exception vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="primbindIO (AProVE_Error vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22[label="error []",fontsize=16,color="red",shape="box"];23[label="Monad.liftM20 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3]; 24[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];25[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];26[label="return (vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];26 -> 27[label="",style="solid", color="black", weight=3]; 27[label="primretIO (vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3]; 28[label="AProVE_IO (vy3 vy40 vy50)",fontsize=16,color="green",shape="box"];28 -> 29[label="",style="dashed", color="green", weight=3]; 29[label="vy3 vy40 vy50",fontsize=16,color="green",shape="box"];29 -> 30[label="",style="dashed", color="green", weight=3]; 29 -> 31[label="",style="dashed", color="green", weight=3]; 30[label="vy40",fontsize=16,color="green",shape="box"];31[label="vy50",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) YES