7.64/3.50 YES 9.84/4.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.84/4.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.84/4.08 9.84/4.08 9.84/4.08 H-Termination with start terms of the given HASKELL could be proven: 9.84/4.08 9.84/4.08 (0) HASKELL 9.84/4.08 (1) IFR [EQUIVALENT, 0 ms] 9.84/4.08 (2) HASKELL 9.84/4.08 (3) BR [EQUIVALENT, 0 ms] 9.84/4.08 (4) HASKELL 9.84/4.08 (5) COR [EQUIVALENT, 0 ms] 9.84/4.08 (6) HASKELL 9.84/4.08 (7) NumRed [SOUND, 0 ms] 9.84/4.08 (8) HASKELL 9.84/4.08 (9) Narrow [EQUIVALENT, 33 ms] 9.84/4.08 (10) YES 9.84/4.08 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (0) 9.84/4.08 Obligation: 9.84/4.08 mainModule Main 9.84/4.08 module Main where { 9.84/4.08 import qualified Prelude; 9.84/4.08 } 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (1) IFR (EQUIVALENT) 9.84/4.08 If Reductions: 9.84/4.08 The following If expression 9.84/4.08 "if b then (showChar '(') . p . showChar ')' else p" 9.84/4.08 is transformed to 9.84/4.08 "showParen0 p True = (showChar '(') . p . showChar ')'; 9.84/4.08 showParen0 p False = p; 9.84/4.08 " 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (2) 9.84/4.08 Obligation: 9.84/4.08 mainModule Main 9.84/4.08 module Main where { 9.84/4.08 import qualified Prelude; 9.84/4.08 } 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (3) BR (EQUIVALENT) 9.84/4.08 Replaced joker patterns by fresh variables and removed binding patterns. 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (4) 9.84/4.08 Obligation: 9.84/4.08 mainModule Main 9.84/4.08 module Main where { 9.84/4.08 import qualified Prelude; 9.84/4.08 } 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (5) COR (EQUIVALENT) 9.84/4.08 Cond Reductions: 9.84/4.08 The following Function with conditions 9.84/4.08 "undefined |Falseundefined; 9.84/4.08 " 9.84/4.08 is transformed to 9.84/4.08 "undefined = undefined1; 9.84/4.08 " 9.84/4.08 "undefined0 True = undefined; 9.84/4.08 " 9.84/4.08 "undefined1 = undefined0 False; 9.84/4.08 " 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (6) 9.84/4.08 Obligation: 9.84/4.08 mainModule Main 9.84/4.08 module Main where { 9.84/4.08 import qualified Prelude; 9.84/4.08 } 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (7) NumRed (SOUND) 9.84/4.08 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (8) 9.84/4.08 Obligation: 9.84/4.08 mainModule Main 9.84/4.08 module Main where { 9.84/4.08 import qualified Prelude; 9.84/4.08 } 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (9) Narrow (EQUIVALENT) 9.84/4.08 Haskell To QDPs 9.84/4.08 9.84/4.08 digraph dp_graph { 9.84/4.08 node [outthreshold=100, inthreshold=100];1[label="showParen",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.84/4.08 3[label="showParen vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.84/4.08 4[label="showParen vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 9.84/4.08 5[label="showParen vx3 vx4 vx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.84/4.08 6[label="showParen0 vx4 vx3 vx5",fontsize=16,color="burlywood",shape="box"];31[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];6 -> 31[label="",style="solid", color="burlywood", weight=9]; 9.84/4.08 31 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.84/4.08 32[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];6 -> 32[label="",style="solid", color="burlywood", weight=9]; 9.84/4.08 32 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.84/4.08 7[label="showParen0 vx4 False vx5",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 9.84/4.08 8[label="showParen0 vx4 True vx5",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9.84/4.08 9[label="vx4 vx5",fontsize=16,color="green",shape="box"];9 -> 11[label="",style="dashed", color="green", weight=3]; 9.84/4.08 10 -> 16[label="",style="dashed", color="red", weight=0]; 9.84/4.08 10[label="(showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))) . vx4 . showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="magenta"];10 -> 17[label="",style="dashed", color="magenta", weight=3]; 9.84/4.08 10 -> 18[label="",style="dashed", color="magenta", weight=3]; 9.84/4.08 10 -> 19[label="",style="dashed", color="magenta", weight=3]; 9.84/4.08 10 -> 20[label="",style="dashed", color="magenta", weight=3]; 9.84/4.08 11[label="vx5",fontsize=16,color="green",shape="box"];17[label="vx5",fontsize=16,color="green",shape="box"];18[label="vx4",fontsize=16,color="green",shape="box"];19[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];20[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];16[label="(showChar (Char (Succ vx11))) . vx12 . showChar (Char (Succ vx13))",fontsize=16,color="black",shape="triangle"];16 -> 25[label="",style="solid", color="black", weight=3]; 9.84/4.08 25[label="showChar (Char (Succ vx11)) (vx12 . showChar (Char (Succ vx13)))",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3]; 9.84/4.08 26[label="(:) Char (Succ vx11) vx12 . showChar (Char (Succ vx13))",fontsize=16,color="green",shape="box"];26 -> 27[label="",style="dashed", color="green", weight=3]; 9.84/4.08 27[label="vx12 . showChar (Char (Succ vx13))",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3]; 9.84/4.08 28[label="vx12 (showChar (Char (Succ vx13)) vx14)",fontsize=16,color="green",shape="box"];28 -> 29[label="",style="dashed", color="green", weight=3]; 9.84/4.08 29[label="showChar (Char (Succ vx13)) vx14",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3]; 9.84/4.08 30[label="(:) Char (Succ vx13) vx14",fontsize=16,color="green",shape="box"];} 9.84/4.08 9.84/4.08 ---------------------------------------- 9.84/4.08 9.84/4.08 (10) 9.84/4.08 YES 9.84/4.12 EOF