8.32/3.61 YES 10.11/4.18 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 10.11/4.18 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.11/4.18 10.11/4.18 10.11/4.18 H-Termination with start terms of the given HASKELL could be proven: 10.11/4.18 10.11/4.18 (0) HASKELL 10.11/4.18 (1) LR [EQUIVALENT, 0 ms] 10.11/4.18 (2) HASKELL 10.11/4.18 (3) IPR [EQUIVALENT, 0 ms] 10.11/4.18 (4) HASKELL 10.11/4.18 (5) BR [EQUIVALENT, 0 ms] 10.11/4.18 (6) HASKELL 10.11/4.18 (7) COR [EQUIVALENT, 0 ms] 10.11/4.18 (8) HASKELL 10.11/4.18 (9) Narrow [SOUND, 0 ms] 10.11/4.18 (10) QDP 10.11/4.18 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.11/4.18 (12) YES 10.11/4.18 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (0) 10.11/4.18 Obligation: 10.11/4.18 mainModule Main 10.11/4.18 module Main where { 10.11/4.18 import qualified Prelude; 10.11/4.18 } 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (1) LR (EQUIVALENT) 10.11/4.18 Lambda Reductions: 10.11/4.18 The following Lambda expression 10.11/4.18 "\(a,b)~(as,bs)->(a : as,b : bs)" 10.11/4.18 is transformed to 10.11/4.18 "unzip0 (a,b) ~(as,bs) = (a : as,b : bs); 10.11/4.18 " 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (2) 10.11/4.18 Obligation: 10.11/4.18 mainModule Main 10.11/4.18 module Main where { 10.11/4.18 import qualified Prelude; 10.11/4.18 } 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (3) IPR (EQUIVALENT) 10.11/4.18 IrrPat Reductions: 10.11/4.18 The variables of the following irrefutable Pattern 10.11/4.18 "~(as,bs)" 10.11/4.18 are replaced by calls to these functions 10.11/4.18 "unzip00 (as,bs) = as; 10.11/4.18 " 10.11/4.18 "unzip01 (as,bs) = bs; 10.11/4.18 " 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (4) 10.11/4.18 Obligation: 10.11/4.18 mainModule Main 10.11/4.18 module Main where { 10.11/4.18 import qualified Prelude; 10.11/4.18 } 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (5) BR (EQUIVALENT) 10.11/4.18 Replaced joker patterns by fresh variables and removed binding patterns. 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (6) 10.11/4.18 Obligation: 10.11/4.18 mainModule Main 10.11/4.18 module Main where { 10.11/4.18 import qualified Prelude; 10.11/4.18 } 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (7) COR (EQUIVALENT) 10.11/4.18 Cond Reductions: 10.11/4.18 The following Function with conditions 10.11/4.18 "undefined |Falseundefined; 10.11/4.18 " 10.11/4.18 is transformed to 10.11/4.18 "undefined = undefined1; 10.11/4.18 " 10.11/4.18 "undefined0 True = undefined; 10.11/4.18 " 10.11/4.18 "undefined1 = undefined0 False; 10.11/4.18 " 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (8) 10.11/4.18 Obligation: 10.11/4.18 mainModule Main 10.11/4.18 module Main where { 10.11/4.18 import qualified Prelude; 10.11/4.18 } 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (9) Narrow (SOUND) 10.11/4.18 Haskell To QDPs 10.11/4.18 10.11/4.18 digraph dp_graph { 10.11/4.18 node [outthreshold=100, inthreshold=100];1[label="unzip",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.11/4.18 3[label="unzip vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 10.11/4.18 4[label="foldr unzip0 ([],[]) vy3",fontsize=16,color="burlywood",shape="triangle"];20[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 20[label="",style="solid", color="burlywood", weight=9]; 10.11/4.18 20 -> 5[label="",style="solid", color="burlywood", weight=3]; 10.11/4.18 21[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 21[label="",style="solid", color="burlywood", weight=9]; 10.11/4.18 21 -> 6[label="",style="solid", color="burlywood", weight=3]; 10.11/4.18 5[label="foldr unzip0 ([],[]) (vy30 : vy31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 10.11/4.18 6[label="foldr unzip0 ([],[]) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 10.11/4.18 7 -> 9[label="",style="dashed", color="red", weight=0]; 10.11/4.18 7[label="unzip0 vy30 (foldr unzip0 ([],[]) vy31)",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 10.11/4.18 8[label="([],[])",fontsize=16,color="green",shape="box"];10 -> 4[label="",style="dashed", color="red", weight=0]; 10.11/4.18 10[label="foldr unzip0 ([],[]) vy31",fontsize=16,color="magenta"];10 -> 11[label="",style="dashed", color="magenta", weight=3]; 10.11/4.18 9[label="unzip0 vy30 vy4",fontsize=16,color="burlywood",shape="triangle"];22[label="vy30/(vy300,vy301)",fontsize=10,color="white",style="solid",shape="box"];9 -> 22[label="",style="solid", color="burlywood", weight=9]; 10.11/4.18 22 -> 12[label="",style="solid", color="burlywood", weight=3]; 10.11/4.18 11[label="vy31",fontsize=16,color="green",shape="box"];12[label="unzip0 (vy300,vy301) vy4",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 10.11/4.18 13[label="(vy300 : unzip00 vy4,vy301 : unzip01 vy4)",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3]; 10.11/4.18 13 -> 15[label="",style="dashed", color="green", weight=3]; 10.11/4.18 14[label="unzip00 vy4",fontsize=16,color="burlywood",shape="box"];23[label="vy4/(vy40,vy41)",fontsize=10,color="white",style="solid",shape="box"];14 -> 23[label="",style="solid", color="burlywood", weight=9]; 10.11/4.18 23 -> 16[label="",style="solid", color="burlywood", weight=3]; 10.11/4.18 15[label="unzip01 vy4",fontsize=16,color="burlywood",shape="box"];24[label="vy4/(vy40,vy41)",fontsize=10,color="white",style="solid",shape="box"];15 -> 24[label="",style="solid", color="burlywood", weight=9]; 10.11/4.18 24 -> 17[label="",style="solid", color="burlywood", weight=3]; 10.11/4.18 16[label="unzip00 (vy40,vy41)",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 10.11/4.18 17[label="unzip01 (vy40,vy41)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 10.11/4.18 18[label="vy40",fontsize=16,color="green",shape="box"];19[label="vy41",fontsize=16,color="green",shape="box"];} 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (10) 10.11/4.18 Obligation: 10.11/4.18 Q DP problem: 10.11/4.18 The TRS P consists of the following rules: 10.11/4.18 10.11/4.18 new_foldr(:(vy30, vy31), h, ba) -> new_foldr(vy31, h, ba) 10.11/4.18 10.11/4.18 R is empty. 10.11/4.18 Q is empty. 10.11/4.18 We have to consider all minimal (P,Q,R)-chains. 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (11) QDPSizeChangeProof (EQUIVALENT) 10.11/4.18 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. 10.11/4.18 10.11/4.18 From the DPs we obtained the following set of size-change graphs: 10.11/4.18 *new_foldr(:(vy30, vy31), h, ba) -> new_foldr(vy31, h, ba) 10.11/4.18 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 10.11/4.18 10.11/4.18 10.11/4.18 ---------------------------------------- 10.11/4.18 10.11/4.18 (12) 10.11/4.18 YES 10.35/4.22 EOF