8.98/3.94 YES 10.36/4.39 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 10.36/4.39 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.36/4.39 10.36/4.39 10.36/4.39 H-Termination with start terms of the given HASKELL could be proven: 10.36/4.39 10.36/4.39 (0) HASKELL 10.36/4.39 (1) BR [EQUIVALENT, 0 ms] 10.36/4.39 (2) HASKELL 10.36/4.39 (3) COR [EQUIVALENT, 0 ms] 10.36/4.39 (4) HASKELL 10.36/4.39 (5) Narrow [EQUIVALENT, 11 ms] 10.36/4.39 (6) YES 10.36/4.39 10.36/4.39 10.36/4.39 ---------------------------------------- 10.36/4.39 10.36/4.39 (0) 10.36/4.39 Obligation: 10.36/4.39 mainModule Main 10.36/4.39 module Maybe where { 10.36/4.39 import qualified Main; 10.36/4.39 import qualified Monad; 10.36/4.39 import qualified Prelude; 10.36/4.39 } 10.36/4.39 module Main where { 10.36/4.39 import qualified Maybe; 10.36/4.39 import qualified Monad; 10.36/4.39 import qualified Prelude; 10.36/4.39 } 10.36/4.39 module Monad where { 10.36/4.39 import qualified Main; 10.36/4.39 import qualified Maybe; 10.36/4.39 import qualified Prelude; 10.36/4.39 join :: Monad a => a (a b) -> a b; 10.36/4.39 join x = x >>= id; 10.36/4.39 10.36/4.39 } 10.36/4.39 10.36/4.39 ---------------------------------------- 10.36/4.39 10.36/4.39 (1) BR (EQUIVALENT) 10.36/4.39 Replaced joker patterns by fresh variables and removed binding patterns. 10.36/4.39 ---------------------------------------- 10.36/4.39 10.36/4.39 (2) 10.36/4.39 Obligation: 10.36/4.39 mainModule Main 10.36/4.39 module Maybe where { 10.36/4.39 import qualified Main; 10.36/4.39 import qualified Monad; 10.36/4.39 import qualified Prelude; 10.36/4.39 } 10.36/4.39 module Main where { 10.36/4.39 import qualified Maybe; 10.36/4.39 import qualified Monad; 10.36/4.39 import qualified Prelude; 10.36/4.39 } 10.36/4.39 module Monad where { 10.36/4.39 import qualified Main; 10.36/4.39 import qualified Maybe; 10.36/4.39 import qualified Prelude; 10.36/4.39 join :: Monad b => b (b a) -> b a; 10.36/4.39 join x = x >>= id; 10.36/4.39 10.36/4.39 } 10.36/4.39 10.36/4.39 ---------------------------------------- 10.36/4.39 10.36/4.39 (3) COR (EQUIVALENT) 10.36/4.39 Cond Reductions: 10.36/4.39 The following Function with conditions 10.36/4.39 "undefined |Falseundefined; 10.36/4.39 " 10.36/4.39 is transformed to 10.36/4.39 "undefined = undefined1; 10.36/4.39 " 10.36/4.39 "undefined0 True = undefined; 10.36/4.39 " 10.36/4.39 "undefined1 = undefined0 False; 10.36/4.39 " 10.36/4.39 10.36/4.39 ---------------------------------------- 10.36/4.39 10.36/4.39 (4) 10.36/4.39 Obligation: 10.36/4.39 mainModule Main 10.36/4.39 module Maybe where { 10.36/4.39 import qualified Main; 10.36/4.39 import qualified Monad; 10.36/4.39 import qualified Prelude; 10.36/4.39 } 10.36/4.39 module Main where { 10.36/4.39 import qualified Maybe; 10.36/4.39 import qualified Monad; 10.36/4.39 import qualified Prelude; 10.36/4.39 } 10.36/4.39 module Monad where { 10.36/4.39 import qualified Main; 10.36/4.39 import qualified Maybe; 10.36/4.39 import qualified Prelude; 10.36/4.39 join :: Monad b => b (b a) -> b a; 10.36/4.39 join x = x >>= id; 10.36/4.39 10.36/4.39 } 10.36/4.39 10.36/4.39 ---------------------------------------- 10.36/4.39 10.36/4.39 (5) Narrow (EQUIVALENT) 10.36/4.39 Haskell To QDPs 10.36/4.39 10.36/4.39 digraph dp_graph { 10.36/4.39 node [outthreshold=100, inthreshold=100];1[label="Monad.join",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.36/4.39 3[label="Monad.join vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 10.36/4.39 4[label="vy3 >>= id",fontsize=16,color="burlywood",shape="box"];10[label="vy3/Nothing",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9]; 10.36/4.39 10 -> 5[label="",style="solid", color="burlywood", weight=3]; 10.36/4.39 11[label="vy3/Just vy30",fontsize=10,color="white",style="solid",shape="box"];4 -> 11[label="",style="solid", color="burlywood", weight=9]; 10.36/4.39 11 -> 6[label="",style="solid", color="burlywood", weight=3]; 10.36/4.39 5[label="Nothing >>= id",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 10.36/4.39 6[label="Just vy30 >>= id",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 10.36/4.39 7[label="Nothing",fontsize=16,color="green",shape="box"];8[label="id vy30",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 10.36/4.39 9[label="vy30",fontsize=16,color="green",shape="box"];} 10.36/4.39 10.36/4.39 ---------------------------------------- 10.36/4.39 10.36/4.39 (6) 10.36/4.39 YES 10.64/4.43 EOF