7.79/3.55 YES 9.62/4.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.62/4.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.62/4.10 9.62/4.10 9.62/4.10 H-Termination with start terms of the given HASKELL could be proven: 9.62/4.10 9.62/4.10 (0) HASKELL 9.62/4.10 (1) LR [EQUIVALENT, 0 ms] 9.62/4.10 (2) HASKELL 9.62/4.10 (3) IPR [EQUIVALENT, 0 ms] 9.62/4.10 (4) HASKELL 9.62/4.10 (5) BR [EQUIVALENT, 0 ms] 9.62/4.10 (6) HASKELL 9.62/4.10 (7) COR [EQUIVALENT, 0 ms] 9.62/4.10 (8) HASKELL 9.62/4.10 (9) Narrow [SOUND, 0 ms] 9.62/4.10 (10) QDP 9.62/4.10 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.62/4.10 (12) YES 9.62/4.10 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (0) 9.62/4.10 Obligation: 9.62/4.10 mainModule Main 9.62/4.10 module Main where { 9.62/4.10 import qualified Prelude; 9.62/4.10 } 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (1) LR (EQUIVALENT) 9.62/4.10 Lambda Reductions: 9.62/4.10 The following Lambda expression 9.62/4.10 "\(a,b,c)~(as,bs,cs)->(a : as,b : bs,c : cs)" 9.62/4.10 is transformed to 9.62/4.10 "unzip30 (a,b,c) ~(as,bs,cs) = (a : as,b : bs,c : cs); 9.62/4.10 " 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (2) 9.62/4.10 Obligation: 9.62/4.10 mainModule Main 9.62/4.10 module Main where { 9.62/4.10 import qualified Prelude; 9.62/4.10 } 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (3) IPR (EQUIVALENT) 9.62/4.10 IrrPat Reductions: 9.62/4.10 The variables of the following irrefutable Pattern 9.62/4.10 "~(as,bs,cs)" 9.62/4.10 are replaced by calls to these functions 9.62/4.10 "unzip300 (as,bs,cs) = as; 9.62/4.10 " 9.62/4.10 "unzip301 (as,bs,cs) = bs; 9.62/4.10 " 9.62/4.10 "unzip302 (as,bs,cs) = cs; 9.62/4.10 " 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (4) 9.62/4.10 Obligation: 9.62/4.10 mainModule Main 9.62/4.10 module Main where { 9.62/4.10 import qualified Prelude; 9.62/4.10 } 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (5) BR (EQUIVALENT) 9.62/4.10 Replaced joker patterns by fresh variables and removed binding patterns. 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (6) 9.62/4.10 Obligation: 9.62/4.10 mainModule Main 9.62/4.10 module Main where { 9.62/4.10 import qualified Prelude; 9.62/4.10 } 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (7) COR (EQUIVALENT) 9.62/4.10 Cond Reductions: 9.62/4.10 The following Function with conditions 9.62/4.10 "undefined |Falseundefined; 9.62/4.10 " 9.62/4.10 is transformed to 9.62/4.10 "undefined = undefined1; 9.62/4.10 " 9.62/4.10 "undefined0 True = undefined; 9.62/4.10 " 9.62/4.10 "undefined1 = undefined0 False; 9.62/4.10 " 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (8) 9.62/4.10 Obligation: 9.62/4.10 mainModule Main 9.62/4.10 module Main where { 9.62/4.10 import qualified Prelude; 9.62/4.10 } 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (9) Narrow (SOUND) 9.62/4.10 Haskell To QDPs 9.62/4.10 9.62/4.10 digraph dp_graph { 9.62/4.10 node [outthreshold=100, inthreshold=100];1[label="unzip3",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.62/4.10 3[label="unzip3 vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.62/4.10 4[label="foldr unzip30 ([],[],[]) vy3",fontsize=16,color="burlywood",shape="triangle"];23[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 23[label="",style="solid", color="burlywood", weight=9]; 9.62/4.10 23 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.62/4.10 24[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 24[label="",style="solid", color="burlywood", weight=9]; 9.62/4.10 24 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.62/4.10 5[label="foldr unzip30 ([],[],[]) (vy30 : vy31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 9.62/4.10 6[label="foldr unzip30 ([],[],[]) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.62/4.10 7 -> 9[label="",style="dashed", color="red", weight=0]; 9.62/4.10 7[label="unzip30 vy30 (foldr unzip30 ([],[],[]) vy31)",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 9.62/4.10 8[label="([],[],[])",fontsize=16,color="green",shape="box"];10 -> 4[label="",style="dashed", color="red", weight=0]; 9.62/4.10 10[label="foldr unzip30 ([],[],[]) vy31",fontsize=16,color="magenta"];10 -> 11[label="",style="dashed", color="magenta", weight=3]; 9.62/4.10 9[label="unzip30 vy30 vy4",fontsize=16,color="burlywood",shape="triangle"];25[label="vy30/(vy300,vy301,vy302)",fontsize=10,color="white",style="solid",shape="box"];9 -> 25[label="",style="solid", color="burlywood", weight=9]; 9.62/4.10 25 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.62/4.10 11[label="vy31",fontsize=16,color="green",shape="box"];12[label="unzip30 (vy300,vy301,vy302) vy4",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 9.62/4.10 13[label="(vy300 : unzip300 vy4,vy301 : unzip301 vy4,vy302 : unzip302 vy4)",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3]; 9.62/4.10 13 -> 15[label="",style="dashed", color="green", weight=3]; 9.62/4.10 13 -> 16[label="",style="dashed", color="green", weight=3]; 9.62/4.10 14[label="unzip300 vy4",fontsize=16,color="burlywood",shape="box"];26[label="vy4/(vy40,vy41,vy42)",fontsize=10,color="white",style="solid",shape="box"];14 -> 26[label="",style="solid", color="burlywood", weight=9]; 9.62/4.10 26 -> 17[label="",style="solid", color="burlywood", weight=3]; 9.62/4.10 15[label="unzip301 vy4",fontsize=16,color="burlywood",shape="box"];27[label="vy4/(vy40,vy41,vy42)",fontsize=10,color="white",style="solid",shape="box"];15 -> 27[label="",style="solid", color="burlywood", weight=9]; 9.62/4.10 27 -> 18[label="",style="solid", color="burlywood", weight=3]; 9.62/4.10 16[label="unzip302 vy4",fontsize=16,color="burlywood",shape="box"];28[label="vy4/(vy40,vy41,vy42)",fontsize=10,color="white",style="solid",shape="box"];16 -> 28[label="",style="solid", color="burlywood", weight=9]; 9.62/4.10 28 -> 19[label="",style="solid", color="burlywood", weight=3]; 9.62/4.10 17[label="unzip300 (vy40,vy41,vy42)",fontsize=16,color="black",shape="box"];17 -> 20[label="",style="solid", color="black", weight=3]; 9.62/4.10 18[label="unzip301 (vy40,vy41,vy42)",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3]; 9.62/4.10 19[label="unzip302 (vy40,vy41,vy42)",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3]; 9.62/4.10 20[label="vy40",fontsize=16,color="green",shape="box"];21[label="vy41",fontsize=16,color="green",shape="box"];22[label="vy42",fontsize=16,color="green",shape="box"];} 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (10) 9.62/4.10 Obligation: 9.62/4.10 Q DP problem: 9.62/4.10 The TRS P consists of the following rules: 9.62/4.10 9.62/4.10 new_foldr(:(vy30, vy31), h, ba, bb) -> new_foldr(vy31, h, ba, bb) 9.62/4.10 9.62/4.10 R is empty. 9.62/4.10 Q is empty. 9.62/4.10 We have to consider all minimal (P,Q,R)-chains. 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (11) QDPSizeChangeProof (EQUIVALENT) 9.62/4.10 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. 9.62/4.10 9.62/4.10 From the DPs we obtained the following set of size-change graphs: 9.62/4.10 *new_foldr(:(vy30, vy31), h, ba, bb) -> new_foldr(vy31, h, ba, bb) 9.62/4.10 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 9.62/4.10 9.62/4.10 9.62/4.10 ---------------------------------------- 9.62/4.10 9.62/4.10 (12) 9.62/4.10 YES 9.87/4.14 EOF