8.26/3.57	YES
10.38/4.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.38/4.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.38/4.13	
10.38/4.13	
10.38/4.13	H-Termination with start terms of the given HASKELL could be proven:
10.38/4.13	
10.38/4.13	(0) HASKELL
10.38/4.13	(1) LR [EQUIVALENT, 0 ms]
10.38/4.13	(2) HASKELL
10.38/4.13	(3) BR [EQUIVALENT, 0 ms]
10.38/4.13	(4) HASKELL
10.38/4.13	(5) COR [EQUIVALENT, 0 ms]
10.38/4.13	(6) HASKELL
10.38/4.13	(7) Narrow [SOUND, 0 ms]
10.38/4.13	(8) QDP
10.38/4.13	(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.38/4.13	(10) YES
10.38/4.13	
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(0)
10.38/4.13	Obligation:
10.38/4.13	mainModule Main 
10.38/4.13	module Main where {
10.38/4.13	import qualified Prelude;
10.38/4.13	}
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(1) LR (EQUIVALENT)
10.38/4.13	Lambda Reductions:
10.38/4.13	The following Lambda expression
10.38/4.13	"\_->q"
10.38/4.13	is transformed to
10.38/4.13	"gtGt0 q _ = q;
10.38/4.13	"
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(2)
10.38/4.13	Obligation:
10.38/4.13	mainModule Main 
10.38/4.13	module Main where {
10.38/4.13	import qualified Prelude;
10.38/4.13	}
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(3) BR (EQUIVALENT)
10.38/4.13	Replaced joker patterns by fresh variables and removed binding patterns.
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(4)
10.38/4.13	Obligation:
10.38/4.13	mainModule Main 
10.38/4.13	module Main where {
10.38/4.13	import qualified Prelude;
10.38/4.13	}
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(5) COR (EQUIVALENT)
10.38/4.13	Cond Reductions:
10.38/4.13	The following Function with conditions
10.38/4.13	"randomSelect (x : []) = x;
10.38/4.13	randomSelect (x : xs)|terminatorrandomSelect xs|otherwisex;
10.38/4.13	"
10.38/4.13	is transformed to
10.38/4.13	"randomSelect (x : []) = randomSelect3 (x : []);
10.38/4.13	randomSelect (x : xs) = randomSelect2 (x : xs);
10.38/4.13	"
10.38/4.13	"randomSelect0 x xs True = x;
10.38/4.13	"
10.38/4.13	"randomSelect1 x xs True = randomSelect xs;
10.38/4.13	randomSelect1 x xs False = randomSelect0 x xs otherwise;
10.38/4.13	"
10.38/4.13	"randomSelect2 (x : xs) = randomSelect1 x xs terminator;
10.38/4.13	"
10.38/4.13	"randomSelect3 (x : []) = x;
10.38/4.13	randomSelect3 wv = randomSelect2 wv;
10.38/4.13	"
10.38/4.13	The following Function with conditions
10.38/4.13	"undefined |Falseundefined;
10.38/4.13	"
10.38/4.13	is transformed to
10.38/4.13	"undefined  = undefined1;
10.38/4.13	"
10.38/4.13	"undefined0 True = undefined;
10.38/4.13	"
10.38/4.13	"undefined1  = undefined0 False;
10.38/4.13	"
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(6)
10.38/4.13	Obligation:
10.38/4.13	mainModule Main 
10.38/4.13	module Main where {
10.38/4.13	import qualified Prelude;
10.38/4.13	}
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(7) Narrow (SOUND)
10.38/4.13	Haskell To QDPs
10.38/4.13	
10.38/4.13	digraph dp_graph {
10.38/4.13	node [outthreshold=100, inthreshold=100];1[label="writeFile",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.38/4.13	3[label="writeFile ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.38/4.13	4[label="writeFile ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.38/4.13	5[label="putStr ww3 >> putStr ww4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.38/4.13	6[label="putStr ww3 >>= gtGt0 (putStr ww4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.38/4.13	7 -> 38[label="",style="dashed", color="red", weight=0];
10.38/4.13	7[label="primbindIO (putStr ww3) (gtGt0 (putStr ww4))",fontsize=16,color="magenta"];7 -> 39[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	7 -> 40[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	39[label="putStr ww4",fontsize=16,color="burlywood",shape="triangle"];91[label="ww4/ww40 : ww41",fontsize=10,color="white",style="solid",shape="box"];39 -> 91[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	91 -> 42[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	92[label="ww4/[]",fontsize=10,color="white",style="solid",shape="box"];39 -> 92[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	92 -> 43[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	40 -> 39[label="",style="dashed", color="red", weight=0];
10.38/4.13	40[label="putStr ww3",fontsize=16,color="magenta"];40 -> 44[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	38[label="primbindIO ww5 (gtGt0 ww6)",fontsize=16,color="burlywood",shape="triangle"];93[label="ww5/IO ww50",fontsize=10,color="white",style="solid",shape="box"];38 -> 93[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	93 -> 45[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	94[label="ww5/AProVE_IO ww50",fontsize=10,color="white",style="solid",shape="box"];38 -> 94[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	94 -> 46[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	95[label="ww5/AProVE_Exception ww50",fontsize=10,color="white",style="solid",shape="box"];38 -> 95[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	95 -> 47[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	96[label="ww5/AProVE_Error ww50",fontsize=10,color="white",style="solid",shape="box"];38 -> 96[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	96 -> 48[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	42[label="putStr (ww40 : ww41)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
10.38/4.13	43[label="putStr []",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3];
10.38/4.13	44[label="ww3",fontsize=16,color="green",shape="box"];45[label="primbindIO (IO ww50) (gtGt0 ww6)",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3];
10.38/4.13	46[label="primbindIO (AProVE_IO ww50) (gtGt0 ww6)",fontsize=16,color="black",shape="box"];46 -> 52[label="",style="solid", color="black", weight=3];
10.38/4.13	47[label="primbindIO (AProVE_Exception ww50) (gtGt0 ww6)",fontsize=16,color="black",shape="box"];47 -> 53[label="",style="solid", color="black", weight=3];
10.38/4.13	48[label="primbindIO (AProVE_Error ww50) (gtGt0 ww6)",fontsize=16,color="black",shape="box"];48 -> 54[label="",style="solid", color="black", weight=3];
10.38/4.13	49 -> 55[label="",style="dashed", color="red", weight=0];
10.38/4.13	49[label="putChar ww40 >> putStr ww41",fontsize=16,color="magenta"];49 -> 56[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	50[label="output",fontsize=16,color="black",shape="triangle"];50 -> 57[label="",style="solid", color="black", weight=3];
10.38/4.13	51[label="error []",fontsize=16,color="red",shape="box"];52[label="gtGt0 ww6 ww50",fontsize=16,color="black",shape="box"];52 -> 58[label="",style="solid", color="black", weight=3];
10.38/4.13	53[label="AProVE_Exception ww50",fontsize=16,color="green",shape="box"];54[label="AProVE_Error ww50",fontsize=16,color="green",shape="box"];56 -> 39[label="",style="dashed", color="red", weight=0];
10.38/4.13	56[label="putStr ww41",fontsize=16,color="magenta"];56 -> 59[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	55[label="putChar ww40 >> ww7",fontsize=16,color="black",shape="triangle"];55 -> 60[label="",style="solid", color="black", weight=3];
10.38/4.13	57[label="randomSelect (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];57 -> 61[label="",style="solid", color="black", weight=3];
10.38/4.13	58[label="ww6",fontsize=16,color="green",shape="box"];59[label="ww41",fontsize=16,color="green",shape="box"];60[label="putChar ww40 >>= gtGt0 ww7",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
10.38/4.13	61[label="randomSelect2 (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];61 -> 63[label="",style="solid", color="black", weight=3];
10.38/4.13	62 -> 38[label="",style="dashed", color="red", weight=0];
10.38/4.13	62[label="primbindIO (putChar ww40) (gtGt0 ww7)",fontsize=16,color="magenta"];62 -> 64[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	62 -> 65[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	63[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];63 -> 66[label="",style="solid", color="black", weight=3];
10.38/4.13	64[label="ww7",fontsize=16,color="green",shape="box"];65[label="putChar ww40",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3];
10.38/4.13	66[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) ter1m",fontsize=16,color="burlywood",shape="box"];97[label="ter1m/False",fontsize=10,color="white",style="solid",shape="box"];66 -> 97[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	97 -> 68[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	98[label="ter1m/True",fontsize=10,color="white",style="solid",shape="box"];66 -> 98[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	98 -> 69[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	67 -> 70[label="",style="dashed", color="red", weight=0];
10.38/4.13	67[label="(seq ww40 output)",fontsize=16,color="magenta"];67 -> 71[label="",style="dashed", color="magenta", weight=3];
10.38/4.13	68[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];68 -> 72[label="",style="solid", color="black", weight=3];
10.38/4.13	69[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];69 -> 73[label="",style="solid", color="black", weight=3];
10.38/4.13	71 -> 50[label="",style="dashed", color="red", weight=0];
10.38/4.13	71[label="output",fontsize=16,color="magenta"];70[label="(seq ww40 ww8)",fontsize=16,color="black",shape="triangle"];70 -> 74[label="",style="solid", color="black", weight=3];
10.38/4.13	72[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];72 -> 75[label="",style="solid", color="black", weight=3];
10.38/4.13	73[label="randomSelect (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];73 -> 76[label="",style="solid", color="black", weight=3];
10.38/4.13	74[label="enforceWHNF (WHNF ww40) ww8",fontsize=16,color="black",shape="box"];74 -> 77[label="",style="solid", color="black", weight=3];
10.38/4.13	75[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];75 -> 78[label="",style="solid", color="black", weight=3];
10.38/4.13	76[label="randomSelect2 (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];76 -> 79[label="",style="solid", color="black", weight=3];
10.38/4.13	77[label="ww8",fontsize=16,color="green",shape="box"];78[label="aIOE IOError_FullError",fontsize=16,color="black",shape="box"];78 -> 80[label="",style="solid", color="black", weight=3];
10.38/4.13	79[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];79 -> 81[label="",style="solid", color="black", weight=3];
10.38/4.13	80[label="AProVE_Exception (AET_IOError (IOError IOError_FullError [] [] Nothing))",fontsize=16,color="green",shape="box"];81[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) ter2m",fontsize=16,color="burlywood",shape="box"];99[label="ter2m/False",fontsize=10,color="white",style="solid",shape="box"];81 -> 99[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	99 -> 82[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	100[label="ter2m/True",fontsize=10,color="white",style="solid",shape="box"];81 -> 100[label="",style="solid", color="burlywood", weight=9];
10.38/4.13	100 -> 83[label="",style="solid", color="burlywood", weight=3];
10.38/4.13	82[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];82 -> 84[label="",style="solid", color="black", weight=3];
10.38/4.13	83[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];83 -> 85[label="",style="solid", color="black", weight=3];
10.38/4.13	84[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];84 -> 86[label="",style="solid", color="black", weight=3];
10.38/4.13	85[label="randomSelect (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];85 -> 87[label="",style="solid", color="black", weight=3];
10.38/4.13	86[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];86 -> 88[label="",style="solid", color="black", weight=3];
10.38/4.13	87[label="randomSelect3 (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];87 -> 89[label="",style="solid", color="black", weight=3];
10.38/4.13	88[label="aIOE IOError_PermDenied",fontsize=16,color="black",shape="box"];88 -> 90[label="",style="solid", color="black", weight=3];
10.38/4.13	89[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];90[label="AProVE_Exception (AET_IOError (IOError IOError_PermDenied [] [] Nothing))",fontsize=16,color="green",shape="box"];}
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(8)
10.38/4.13	Obligation:
10.38/4.13	Q DP problem:
10.38/4.13	The TRS P consists of the following rules:
10.38/4.13	
10.38/4.13	   new_putStr(:(ww40, ww41)) -> new_putStr(ww41)
10.38/4.13	
10.38/4.13	R is empty.
10.38/4.13	Q is empty.
10.38/4.13	We have to consider all minimal (P,Q,R)-chains.
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(9) QDPSizeChangeProof (EQUIVALENT)
10.38/4.13	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. 
10.38/4.13	
10.38/4.13	From the DPs we obtained the following set of size-change graphs:
10.38/4.13	*new_putStr(:(ww40, ww41)) -> new_putStr(ww41)
10.38/4.13	The graph contains the following edges 1 > 1
10.38/4.13	
10.38/4.13	
10.38/4.13	----------------------------------------
10.38/4.13	
10.38/4.13	(10)
10.38/4.13	YES
10.63/4.17	EOF