9.36/3.97 YES 11.46/4.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 11.46/4.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.46/4.50 11.46/4.50 11.46/4.50 H-Termination with start terms of the given HASKELL could be proven: 11.46/4.50 11.46/4.50 (0) HASKELL 11.46/4.50 (1) IFR [EQUIVALENT, 0 ms] 11.46/4.50 (2) HASKELL 11.46/4.50 (3) BR [EQUIVALENT, 0 ms] 11.46/4.50 (4) HASKELL 11.46/4.50 (5) COR [EQUIVALENT, 0 ms] 11.46/4.50 (6) HASKELL 11.46/4.50 (7) Narrow [EQUIVALENT, 11 ms] 11.46/4.50 (8) YES 11.46/4.50 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (0) 11.46/4.50 Obligation: 11.46/4.50 mainModule Main 11.46/4.50 module Maybe where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Main where { 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Monad where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Prelude; 11.46/4.50 unless :: Monad a => Bool -> a () -> a (); 11.46/4.50 unless p s = if p then return () else s; 11.46/4.50 11.46/4.50 } 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (1) IFR (EQUIVALENT) 11.46/4.50 If Reductions: 11.46/4.50 The following If expression 11.46/4.50 "if p then return () else s" 11.46/4.50 is transformed to 11.46/4.50 "unless0 s True = return (); 11.46/4.50 unless0 s False = s; 11.46/4.50 " 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (2) 11.46/4.50 Obligation: 11.46/4.50 mainModule Main 11.46/4.50 module Maybe where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Main where { 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Monad where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Prelude; 11.46/4.50 unless :: Monad a => Bool -> a () -> a (); 11.46/4.50 unless p s = unless0 s p; 11.46/4.50 11.46/4.50 unless0 s True = return (); 11.46/4.50 unless0 s False = s; 11.46/4.50 11.46/4.50 } 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (3) BR (EQUIVALENT) 11.46/4.50 Replaced joker patterns by fresh variables and removed binding patterns. 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (4) 11.46/4.50 Obligation: 11.46/4.50 mainModule Main 11.46/4.50 module Maybe where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Main where { 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Monad where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Prelude; 11.46/4.50 unless :: Monad a => Bool -> a () -> a (); 11.46/4.50 unless p s = unless0 s p; 11.46/4.50 11.46/4.50 unless0 s True = return (); 11.46/4.50 unless0 s False = s; 11.46/4.50 11.46/4.50 } 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (5) COR (EQUIVALENT) 11.46/4.50 Cond Reductions: 11.46/4.50 The following Function with conditions 11.46/4.50 "undefined |Falseundefined; 11.46/4.50 " 11.46/4.50 is transformed to 11.46/4.50 "undefined = undefined1; 11.46/4.50 " 11.46/4.50 "undefined0 True = undefined; 11.46/4.50 " 11.46/4.50 "undefined1 = undefined0 False; 11.46/4.50 " 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (6) 11.46/4.50 Obligation: 11.46/4.50 mainModule Main 11.46/4.50 module Maybe where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Main where { 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Monad; 11.46/4.50 import qualified Prelude; 11.46/4.50 } 11.46/4.50 module Monad where { 11.46/4.50 import qualified Main; 11.46/4.50 import qualified Maybe; 11.46/4.50 import qualified Prelude; 11.46/4.50 unless :: Monad a => Bool -> a () -> a (); 11.46/4.50 unless p s = unless0 s p; 11.46/4.50 11.46/4.50 unless0 s True = return (); 11.46/4.50 unless0 s False = s; 11.46/4.50 11.46/4.50 } 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (7) Narrow (EQUIVALENT) 11.46/4.50 Haskell To QDPs 11.46/4.50 11.46/4.50 digraph dp_graph { 11.46/4.50 node [outthreshold=100, inthreshold=100];1[label="Monad.unless",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 11.46/4.50 3[label="Monad.unless vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 11.46/4.50 4[label="Monad.unless vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 11.46/4.50 5[label="Monad.unless0 vy4 vy3",fontsize=16,color="burlywood",shape="box"];12[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];5 -> 12[label="",style="solid", color="burlywood", weight=9]; 11.46/4.50 12 -> 6[label="",style="solid", color="burlywood", weight=3]; 11.46/4.50 13[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];5 -> 13[label="",style="solid", color="burlywood", weight=9]; 11.46/4.50 13 -> 7[label="",style="solid", color="burlywood", weight=3]; 11.46/4.50 6[label="Monad.unless0 vy4 False",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 11.46/4.50 7[label="Monad.unless0 vy4 True",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 11.46/4.50 8[label="vy4",fontsize=16,color="green",shape="box"];9[label="return ()",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 11.46/4.50 10[label="primretIO ()",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11.46/4.50 11[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];} 11.46/4.50 11.46/4.50 ---------------------------------------- 11.46/4.50 11.46/4.50 (8) 11.46/4.50 YES 11.54/4.55 EOF