8.92/3.84 YES 10.49/4.30 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 10.49/4.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.49/4.30 10.49/4.30 10.49/4.30 H-Termination with start terms of the given HASKELL could be proven: 10.49/4.30 10.49/4.30 (0) HASKELL 10.49/4.30 (1) BR [EQUIVALENT, 0 ms] 10.49/4.30 (2) HASKELL 10.49/4.30 (3) COR [EQUIVALENT, 0 ms] 10.49/4.30 (4) HASKELL 10.49/4.30 (5) Narrow [EQUIVALENT, 20 ms] 10.49/4.30 (6) YES 10.49/4.30 10.49/4.30 10.49/4.30 ---------------------------------------- 10.49/4.30 10.49/4.30 (0) 10.49/4.30 Obligation: 10.49/4.30 mainModule Main 10.49/4.30 module Maybe where { 10.49/4.30 import qualified Main; 10.49/4.30 import qualified Monad; 10.49/4.30 import qualified Prelude; 10.49/4.30 } 10.49/4.30 module Main where { 10.49/4.30 import qualified Maybe; 10.49/4.30 import qualified Monad; 10.49/4.30 import qualified Prelude; 10.49/4.30 } 10.49/4.30 module Monad where { 10.49/4.30 import qualified Main; 10.49/4.30 import qualified Maybe; 10.49/4.30 import qualified Prelude; 10.49/4.30 class Monad a => MonadPlus a where { 10.49/4.30 mzero :: MonadPlus a => a b; 10.49/4.30 } 10.49/4.30 instance MonadPlus Maybe where { 10.49/4.30 mzero = Nothing; 10.49/4.30 } 10.49/4.30 instance MonadPlus [] where { 10.49/4.30 } 10.49/4.30 guard :: MonadPlus a => Bool -> a (); 10.49/4.30 guard True = return (); 10.49/4.30 guard False = mzero; 10.49/4.30 10.49/4.30 } 10.49/4.30 10.49/4.30 ---------------------------------------- 10.49/4.30 10.49/4.30 (1) BR (EQUIVALENT) 10.49/4.30 Replaced joker patterns by fresh variables and removed binding patterns. 10.49/4.30 ---------------------------------------- 10.49/4.30 10.49/4.30 (2) 10.49/4.30 Obligation: 10.49/4.30 mainModule Main 10.49/4.30 module Maybe where { 10.49/4.30 import qualified Main; 10.49/4.30 import qualified Monad; 10.49/4.30 import qualified Prelude; 10.49/4.30 } 10.49/4.30 module Main where { 10.49/4.30 import qualified Maybe; 10.49/4.30 import qualified Monad; 10.49/4.30 import qualified Prelude; 10.49/4.30 } 10.49/4.30 module Monad where { 10.49/4.30 import qualified Main; 10.49/4.30 import qualified Maybe; 10.49/4.30 import qualified Prelude; 10.49/4.30 class Monad a => MonadPlus a where { 10.49/4.30 mzero :: MonadPlus a => a b; 10.49/4.30 } 10.49/4.30 instance MonadPlus Maybe where { 10.49/4.30 mzero = Nothing; 10.49/4.30 } 10.49/4.30 instance MonadPlus [] where { 10.49/4.30 } 10.49/4.30 guard :: MonadPlus a => Bool -> a (); 10.49/4.30 guard True = return (); 10.49/4.30 guard False = mzero; 10.49/4.30 10.49/4.30 } 10.49/4.30 10.49/4.30 ---------------------------------------- 10.49/4.30 10.49/4.30 (3) COR (EQUIVALENT) 10.49/4.30 Cond Reductions: 10.49/4.30 The following Function with conditions 10.49/4.30 "undefined |Falseundefined; 10.49/4.30 " 10.49/4.30 is transformed to 10.49/4.30 "undefined = undefined1; 10.49/4.30 " 10.49/4.30 "undefined0 True = undefined; 10.49/4.30 " 10.49/4.30 "undefined1 = undefined0 False; 10.49/4.30 " 10.49/4.30 10.49/4.30 ---------------------------------------- 10.49/4.30 10.49/4.30 (4) 10.49/4.30 Obligation: 10.49/4.30 mainModule Main 10.49/4.30 module Maybe where { 10.49/4.30 import qualified Main; 10.49/4.30 import qualified Monad; 10.49/4.30 import qualified Prelude; 10.49/4.30 } 10.49/4.30 module Main where { 10.49/4.30 import qualified Maybe; 10.49/4.30 import qualified Monad; 10.49/4.30 import qualified Prelude; 10.49/4.30 } 10.49/4.30 module Monad where { 10.49/4.30 import qualified Main; 10.49/4.30 import qualified Maybe; 10.49/4.30 import qualified Prelude; 10.49/4.30 class Monad a => MonadPlus a where { 10.49/4.30 mzero :: MonadPlus a => a b; 10.49/4.30 } 10.49/4.30 instance MonadPlus Maybe where { 10.49/4.30 mzero = Nothing; 10.49/4.30 } 10.49/4.30 instance MonadPlus [] where { 10.49/4.30 } 10.49/4.30 guard :: MonadPlus a => Bool -> a (); 10.49/4.30 guard True = return (); 10.49/4.30 guard False = mzero; 10.49/4.30 10.49/4.30 } 10.49/4.30 10.49/4.30 ---------------------------------------- 10.49/4.30 10.49/4.30 (5) Narrow (EQUIVALENT) 10.49/4.30 Haskell To QDPs 10.49/4.30 10.49/4.30 digraph dp_graph { 10.49/4.30 node [outthreshold=100, inthreshold=100];1[label="Monad.guard",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.49/4.30 3[label="Monad.guard vy3",fontsize=16,color="burlywood",shape="triangle"];10[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];3 -> 10[label="",style="solid", color="burlywood", weight=9]; 10.49/4.30 10 -> 4[label="",style="solid", color="burlywood", weight=3]; 10.49/4.30 11[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];3 -> 11[label="",style="solid", color="burlywood", weight=9]; 10.49/4.30 11 -> 5[label="",style="solid", color="burlywood", weight=3]; 10.49/4.30 4[label="Monad.guard False",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 10.49/4.30 5[label="Monad.guard True",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 10.49/4.30 6[label="Monad.mzero",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 10.49/4.30 7[label="return ()",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 10.49/4.30 8[label="Nothing",fontsize=16,color="green",shape="box"];9[label="Just ()",fontsize=16,color="green",shape="box"];} 10.49/4.30 10.49/4.30 ---------------------------------------- 10.49/4.30 10.49/4.30 (6) 10.49/4.30 YES 10.58/4.35 EOF