/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) Narrow [SOUND, 0 ms] (6) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data Main.Maybe a = Nothing | Just a ; data Tup0 = Tup0 ; foldr :: (a -> b -> b) -> b -> List a -> b; foldr f z Nil = z; foldr f z (Cons x xs) = f x (foldr f z xs); gtGt0 q vv = q; gtGtEsMaybe :: Main.Maybe a -> (a -> Main.Maybe b) -> Main.Maybe b; gtGtEsMaybe (Main.Just x) k = k x; gtGtEsMaybe Main.Nothing k = Main.Nothing; gtGtMaybe :: Main.Maybe b -> Main.Maybe a -> Main.Maybe a; gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q); returnMaybe :: a -> Main.Maybe a; returnMaybe = Main.Just; sequence_ = foldr gtGtMaybe (returnMaybe Tup0); } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data Main.Maybe a = Nothing | Just a ; data Tup0 = Tup0 ; foldr :: (b -> a -> a) -> a -> List b -> a; foldr f z Nil = z; foldr f z (Cons x xs) = f x (foldr f z xs); gtGt0 q vv = q; gtGtEsMaybe :: Main.Maybe b -> (b -> Main.Maybe a) -> Main.Maybe a; gtGtEsMaybe (Main.Just x) k = k x; gtGtEsMaybe Main.Nothing k = Main.Nothing; gtGtMaybe :: Main.Maybe b -> Main.Maybe a -> Main.Maybe a; gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q); returnMaybe :: a -> Main.Maybe a; returnMaybe = Main.Just; sequence_ = foldr gtGtMaybe (returnMaybe Tup0); } ---------------------------------------- (3) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data Main.Maybe a = Nothing | Just a ; data Tup0 = Tup0 ; foldr :: (b -> a -> a) -> a -> List b -> a; foldr f z Nil = z; foldr f z (Cons x xs) = f x (foldr f z xs); gtGt0 q vv = q; gtGtEsMaybe :: Main.Maybe b -> (b -> Main.Maybe a) -> Main.Maybe a; gtGtEsMaybe (Main.Just x) k = k x; gtGtEsMaybe Main.Nothing k = Main.Nothing; gtGtMaybe :: Main.Maybe a -> Main.Maybe b -> Main.Maybe b; gtGtMaybe p q = gtGtEsMaybe p (gtGt0 q); returnMaybe :: a -> Main.Maybe a; returnMaybe = Main.Just; sequence_ = foldr gtGtMaybe (returnMaybe Tup0); } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="sequence_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="sequence_ vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="foldr gtGtMaybe (returnMaybe Tup0) vy3",fontsize=16,color="burlywood",shape="triangle"];19[label="vy3/Cons vy30 vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 19[label="",style="solid", color="burlywood", weight=9]; 19 -> 5[label="",style="solid", color="burlywood", weight=3]; 20[label="vy3/Nil",fontsize=10,color="white",style="solid",shape="box"];4 -> 20[label="",style="solid", color="burlywood", weight=9]; 20 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="foldr gtGtMaybe (returnMaybe Tup0) (Cons vy30 vy31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="foldr gtGtMaybe (returnMaybe Tup0) Nil",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7 -> 9[label="",style="dashed", color="red", weight=0]; 7[label="gtGtMaybe vy30 (foldr gtGtMaybe (returnMaybe Tup0) vy31)",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 8[label="returnMaybe Tup0",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 10 -> 4[label="",style="dashed", color="red", weight=0]; 10[label="foldr gtGtMaybe (returnMaybe Tup0) vy31",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3]; 9[label="gtGtMaybe vy30 vy4",fontsize=16,color="black",shape="triangle"];9 -> 13[label="",style="solid", color="black", weight=3]; 11[label="Just Tup0",fontsize=16,color="green",shape="box"];12[label="vy31",fontsize=16,color="green",shape="box"];13[label="gtGtEsMaybe vy30 (gtGt0 vy4)",fontsize=16,color="burlywood",shape="box"];21[label="vy30/Nothing",fontsize=10,color="white",style="solid",shape="box"];13 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 14[label="",style="solid", color="burlywood", weight=3]; 22[label="vy30/Just vy300",fontsize=10,color="white",style="solid",shape="box"];13 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 15[label="",style="solid", color="burlywood", weight=3]; 14[label="gtGtEsMaybe Nothing (gtGt0 vy4)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="gtGtEsMaybe (Just vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="Nothing",fontsize=16,color="green",shape="box"];17[label="gtGt0 vy4 vy300",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 18[label="vy4",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(Cons(vy30, vy31), h) -> new_foldr(vy31, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_foldr(Cons(vy30, vy31), h) -> new_foldr(vy31, h) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (8) YES