8.03/3.62 YES 9.93/4.14 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 9.93/4.14 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.93/4.14 9.93/4.14 9.93/4.14 H-Termination with start terms of the given HASKELL could be proven: 9.93/4.14 9.93/4.14 (0) HASKELL 9.93/4.14 (1) BR [EQUIVALENT, 0 ms] 9.93/4.14 (2) HASKELL 9.93/4.14 (3) COR [EQUIVALENT, 0 ms] 9.93/4.14 (4) HASKELL 9.93/4.14 (5) NumRed [SOUND, 0 ms] 9.93/4.14 (6) HASKELL 9.93/4.14 (7) Narrow [EQUIVALENT, 9 ms] 9.93/4.14 (8) YES 9.93/4.14 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (0) 9.93/4.14 Obligation: 9.93/4.14 mainModule Main 9.93/4.14 module Main where { 9.93/4.14 import qualified Prelude; 9.93/4.14 } 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (1) BR (EQUIVALENT) 9.93/4.14 Replaced joker patterns by fresh variables and removed binding patterns. 9.93/4.14 9.93/4.14 Binding Reductions: 9.93/4.14 The bind variable of the following binding Pattern 9.93/4.14 "r@(vv,vw)" 9.93/4.14 is replaced by the following term 9.93/4.14 "(vv,vw)" 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (2) 9.93/4.14 Obligation: 9.93/4.14 mainModule Main 9.93/4.14 module Main where { 9.93/4.14 import qualified Prelude; 9.93/4.14 } 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (3) COR (EQUIVALENT) 9.93/4.14 Cond Reductions: 9.93/4.14 The following Function with conditions 9.93/4.14 "rangeSize (vv,vw)|null (range (vv,vw))0|otherwiseindex (vv,vw) vw + 1; 9.93/4.14 " 9.93/4.14 is transformed to 9.93/4.14 "rangeSize (vv,vw) = rangeSize2 (vv,vw); 9.93/4.14 " 9.93/4.14 "rangeSize1 vv vw True = 0; 9.93/4.14 rangeSize1 vv vw False = rangeSize0 vv vw otherwise; 9.93/4.14 " 9.93/4.14 "rangeSize0 vv vw True = index (vv,vw) vw + 1; 9.93/4.14 " 9.93/4.14 "rangeSize2 (vv,vw) = rangeSize1 vv vw (null (range (vv,vw))); 9.93/4.14 " 9.93/4.14 The following Function with conditions 9.93/4.14 "undefined |Falseundefined; 9.93/4.14 " 9.93/4.14 is transformed to 9.93/4.14 "undefined = undefined1; 9.93/4.14 " 9.93/4.14 "undefined0 True = undefined; 9.93/4.14 " 9.93/4.14 "undefined1 = undefined0 False; 9.93/4.14 " 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (4) 9.93/4.14 Obligation: 9.93/4.14 mainModule Main 9.93/4.14 module Main where { 9.93/4.14 import qualified Prelude; 9.93/4.14 } 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (5) NumRed (SOUND) 9.93/4.14 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (6) 9.93/4.14 Obligation: 9.93/4.14 mainModule Main 9.93/4.14 module Main where { 9.93/4.14 import qualified Prelude; 9.93/4.14 } 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (7) Narrow (EQUIVALENT) 9.93/4.14 Haskell To QDPs 9.93/4.14 9.93/4.14 digraph dp_graph { 9.93/4.14 node [outthreshold=100, inthreshold=100];1[label="rangeSize",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.93/4.14 3[label="rangeSize ww3",fontsize=16,color="burlywood",shape="triangle"];19[label="ww3/(ww30,ww31)",fontsize=10,color="white",style="solid",shape="box"];3 -> 19[label="",style="solid", color="burlywood", weight=9]; 9.93/4.14 19 -> 4[label="",style="solid", color="burlywood", weight=3]; 9.93/4.14 4[label="rangeSize (ww30,ww31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.93/4.14 5[label="rangeSize2 (ww30,ww31)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.93/4.14 6[label="rangeSize1 ww30 ww31 (null (range (ww30,ww31)))",fontsize=16,color="burlywood",shape="box"];20[label="ww30/()",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9]; 9.93/4.14 20 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.93/4.14 7[label="rangeSize1 () ww31 (null (range ((),ww31)))",fontsize=16,color="burlywood",shape="box"];21[label="ww31/()",fontsize=10,color="white",style="solid",shape="box"];7 -> 21[label="",style="solid", color="burlywood", weight=9]; 9.93/4.14 21 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.93/4.14 8[label="rangeSize1 () () (null (range ((),())))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9.93/4.14 9[label="rangeSize1 () () (null (() : []))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 9.93/4.14 10[label="rangeSize1 () () False",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 9.93/4.14 11[label="rangeSize0 () () otherwise",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 9.93/4.14 12[label="rangeSize0 () () True",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 9.93/4.14 13[label="index ((),()) () + Pos (Succ Zero)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 9.93/4.14 14[label="primPlusInt (index ((),()) ()) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 9.93/4.14 15[label="primPlusInt (Pos Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 9.93/4.14 16[label="Pos (primPlusNat Zero (Succ Zero))",fontsize=16,color="green",shape="box"];16 -> 17[label="",style="dashed", color="green", weight=3]; 9.93/4.14 17[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 9.93/4.14 18[label="Succ Zero",fontsize=16,color="green",shape="box"];} 9.93/4.14 9.93/4.14 ---------------------------------------- 9.93/4.14 9.93/4.14 (8) 9.93/4.14 YES 9.93/4.20 EOF