8.15/3.67 YES 9.80/4.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.80/4.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.80/4.10 9.80/4.10 9.80/4.10 H-Termination with start terms of the given HASKELL could be proven: 9.80/4.10 9.80/4.10 (0) HASKELL 9.80/4.10 (1) BR [EQUIVALENT, 0 ms] 9.80/4.10 (2) HASKELL 9.80/4.10 (3) COR [EQUIVALENT, 0 ms] 9.80/4.10 (4) HASKELL 9.80/4.10 (5) Narrow [SOUND, 0 ms] 9.80/4.10 (6) AND 9.80/4.10 (7) QDP 9.80/4.10 (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.80/4.10 (9) YES 9.80/4.10 (10) QDP 9.80/4.10 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.80/4.10 (12) YES 9.80/4.10 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (0) 9.80/4.10 Obligation: 9.80/4.10 mainModule Main 9.80/4.10 module Main where { 9.80/4.10 import qualified Prelude; 9.80/4.10 } 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (1) BR (EQUIVALENT) 9.80/4.10 Replaced joker patterns by fresh variables and removed binding patterns. 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (2) 9.80/4.10 Obligation: 9.80/4.10 mainModule Main 9.80/4.10 module Main where { 9.80/4.10 import qualified Prelude; 9.80/4.10 } 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (3) COR (EQUIVALENT) 9.80/4.10 Cond Reductions: 9.80/4.10 The following Function with conditions 9.80/4.10 "undefined |Falseundefined; 9.80/4.10 " 9.80/4.10 is transformed to 9.80/4.10 "undefined = undefined1; 9.80/4.10 " 9.80/4.10 "undefined0 True = undefined; 9.80/4.10 " 9.80/4.10 "undefined1 = undefined0 False; 9.80/4.10 " 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (4) 9.80/4.10 Obligation: 9.80/4.10 mainModule Main 9.80/4.10 module Main where { 9.80/4.10 import qualified Prelude; 9.80/4.10 } 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (5) Narrow (SOUND) 9.80/4.10 Haskell To QDPs 9.80/4.10 9.80/4.10 digraph dp_graph { 9.80/4.10 node [outthreshold=100, inthreshold=100];1[label="(=<<)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.80/4.10 3[label="(=<<) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.80/4.10 4[label="(=<<) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.80/4.10 5[label="vx4 >>= vx3",fontsize=16,color="burlywood",shape="triangle"];26[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];5 -> 26[label="",style="solid", color="burlywood", weight=9]; 9.80/4.10 26 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.80/4.10 27[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 27[label="",style="solid", color="burlywood", weight=9]; 9.80/4.10 27 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.80/4.10 6[label="vx40 : vx41 >>= vx3",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.80/4.10 7[label="[] >>= vx3",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 9.80/4.10 8 -> 13[label="",style="dashed", color="red", weight=0]; 9.80/4.10 8[label="vx3 vx40 ++ (vx41 >>= vx3)",fontsize=16,color="magenta"];8 -> 14[label="",style="dashed", color="magenta", weight=3]; 9.80/4.10 8 -> 15[label="",style="dashed", color="magenta", weight=3]; 9.80/4.10 9[label="[]",fontsize=16,color="green",shape="box"];14 -> 5[label="",style="dashed", color="red", weight=0]; 9.80/4.10 14[label="vx41 >>= vx3",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3]; 9.80/4.10 15[label="vx3 vx40",fontsize=16,color="green",shape="box"];15 -> 18[label="",style="dashed", color="green", weight=3]; 9.80/4.10 13[label="vx6 ++ vx5",fontsize=16,color="burlywood",shape="triangle"];28[label="vx6/vx60 : vx61",fontsize=10,color="white",style="solid",shape="box"];13 -> 28[label="",style="solid", color="burlywood", weight=9]; 9.80/4.10 28 -> 19[label="",style="solid", color="burlywood", weight=3]; 9.80/4.10 29[label="vx6/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 29[label="",style="solid", color="burlywood", weight=9]; 9.80/4.10 29 -> 20[label="",style="solid", color="burlywood", weight=3]; 9.80/4.10 17[label="vx41",fontsize=16,color="green",shape="box"];18[label="vx40",fontsize=16,color="green",shape="box"];19[label="(vx60 : vx61) ++ vx5",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3]; 9.80/4.10 20[label="[] ++ vx5",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3]; 9.80/4.10 22[label="vx60 : vx61 ++ vx5",fontsize=16,color="green",shape="box"];22 -> 24[label="",style="dashed", color="green", weight=3]; 9.80/4.10 23[label="vx5",fontsize=16,color="green",shape="box"];24 -> 13[label="",style="dashed", color="red", weight=0]; 9.80/4.10 24[label="vx61 ++ vx5",fontsize=16,color="magenta"];24 -> 25[label="",style="dashed", color="magenta", weight=3]; 9.80/4.10 25[label="vx61",fontsize=16,color="green",shape="box"];} 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (6) 9.80/4.10 Complex Obligation (AND) 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (7) 9.80/4.10 Obligation: 9.80/4.10 Q DP problem: 9.80/4.10 The TRS P consists of the following rules: 9.80/4.10 9.80/4.10 new_gtGtEs(:(vx40, vx41), vx3, h, ba) -> new_gtGtEs(vx41, vx3, h, ba) 9.80/4.10 9.80/4.10 R is empty. 9.80/4.10 Q is empty. 9.80/4.10 We have to consider all minimal (P,Q,R)-chains. 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (8) QDPSizeChangeProof (EQUIVALENT) 9.80/4.10 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. 9.80/4.10 9.80/4.10 From the DPs we obtained the following set of size-change graphs: 9.80/4.10 *new_gtGtEs(:(vx40, vx41), vx3, h, ba) -> new_gtGtEs(vx41, vx3, h, ba) 9.80/4.10 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 9.80/4.10 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (9) 9.80/4.10 YES 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (10) 9.80/4.10 Obligation: 9.80/4.10 Q DP problem: 9.80/4.10 The TRS P consists of the following rules: 9.80/4.10 9.80/4.10 new_psPs(:(vx60, vx61), vx5, h) -> new_psPs(vx61, vx5, h) 9.80/4.10 9.80/4.10 R is empty. 9.80/4.10 Q is empty. 9.80/4.10 We have to consider all minimal (P,Q,R)-chains. 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (11) QDPSizeChangeProof (EQUIVALENT) 9.80/4.10 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. 9.80/4.10 9.80/4.10 From the DPs we obtained the following set of size-change graphs: 9.80/4.10 *new_psPs(:(vx60, vx61), vx5, h) -> new_psPs(vx61, vx5, h) 9.80/4.10 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 9.80/4.10 9.80/4.10 9.80/4.10 ---------------------------------------- 9.80/4.10 9.80/4.10 (12) 9.80/4.10 YES 9.90/5.60 EOF