8.19/3.75	YES
10.18/4.28	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.18/4.28	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.18/4.28	
10.18/4.28	
10.18/4.28	H-Termination with start terms of the given HASKELL could be proven:
10.18/4.28	
10.18/4.28	(0) HASKELL
10.18/4.28	(1) LR [EQUIVALENT, 0 ms]
10.18/4.28	(2) HASKELL
10.18/4.28	(3) BR [EQUIVALENT, 0 ms]
10.18/4.28	(4) HASKELL
10.18/4.28	(5) COR [EQUIVALENT, 0 ms]
10.18/4.28	(6) HASKELL
10.18/4.28	(7) Narrow [SOUND, 0 ms]
10.18/4.28	(8) QDP
10.18/4.28	(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.18/4.28	(10) YES
10.18/4.28	
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(0)
10.18/4.28	Obligation:
10.18/4.28	mainModule Main 
10.18/4.28	module Main where {
10.18/4.28	import qualified Prelude;
10.18/4.28	}
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(1) LR (EQUIVALENT)
10.18/4.28	Lambda Reductions:
10.18/4.28	The following Lambda expression
10.18/4.28	"\_->q"
10.18/4.28	is transformed to
10.18/4.28	"gtGt0 q _ = q;
10.18/4.28	"
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(2)
10.18/4.28	Obligation:
10.18/4.28	mainModule Main 
10.18/4.28	module Main where {
10.18/4.28	import qualified Prelude;
10.18/4.28	}
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(3) BR (EQUIVALENT)
10.18/4.28	Replaced joker patterns by fresh variables and removed binding patterns.
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(4)
10.18/4.28	Obligation:
10.18/4.28	mainModule Main 
10.18/4.28	module Main where {
10.18/4.28	import qualified Prelude;
10.18/4.28	}
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(5) COR (EQUIVALENT)
10.18/4.28	Cond Reductions:
10.18/4.28	The following Function with conditions
10.18/4.28	"undefined |Falseundefined;
10.18/4.28	"
10.18/4.28	is transformed to
10.18/4.28	"undefined  = undefined1;
10.18/4.28	"
10.18/4.28	"undefined0 True = undefined;
10.18/4.28	"
10.18/4.28	"undefined1  = undefined0 False;
10.18/4.28	"
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(6)
10.18/4.28	Obligation:
10.18/4.28	mainModule Main 
10.18/4.28	module Main where {
10.18/4.28	import qualified Prelude;
10.18/4.28	}
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(7) Narrow (SOUND)
10.18/4.28	Haskell To QDPs
10.18/4.28	
10.18/4.28	digraph dp_graph {
10.18/4.28	node [outthreshold=100, inthreshold=100];1[label="mapM_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.18/4.28	3[label="mapM_ vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.18/4.28	4[label="mapM_ vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.18/4.28	5[label="sequence_ . map vy3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.18/4.28	6[label="sequence_ (map vy3 vy4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.18/4.28	7[label="foldr (>>) (return ()) (map vy3 vy4)",fontsize=16,color="burlywood",shape="triangle"];34[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];7 -> 34[label="",style="solid", color="burlywood", weight=9];
10.18/4.28	34 -> 8[label="",style="solid", color="burlywood", weight=3];
10.18/4.28	35[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 35[label="",style="solid", color="burlywood", weight=9];
10.18/4.28	35 -> 9[label="",style="solid", color="burlywood", weight=3];
10.18/4.28	8[label="foldr (>>) (return ()) (map vy3 (vy40 : vy41))",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
10.18/4.28	9[label="foldr (>>) (return ()) (map vy3 [])",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10.18/4.28	10[label="foldr (>>) (return ()) (vy3 vy40 : map vy3 vy41)",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
10.18/4.28	11[label="foldr (>>) (return ()) []",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
10.18/4.28	12 -> 14[label="",style="dashed", color="red", weight=0];
10.18/4.28	12[label="(>>) vy3 vy40 foldr (>>) (return ()) (map vy3 vy41)",fontsize=16,color="magenta"];12 -> 15[label="",style="dashed", color="magenta", weight=3];
10.18/4.28	13[label="return ()",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3];
10.18/4.28	15 -> 7[label="",style="dashed", color="red", weight=0];
10.18/4.28	15[label="foldr (>>) (return ()) (map vy3 vy41)",fontsize=16,color="magenta"];15 -> 17[label="",style="dashed", color="magenta", weight=3];
10.18/4.28	14[label="(>>) vy3 vy40 vy5",fontsize=16,color="black",shape="triangle"];14 -> 18[label="",style="solid", color="black", weight=3];
10.18/4.28	16[label="primretIO ()",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
10.18/4.28	17[label="vy41",fontsize=16,color="green",shape="box"];18[label="vy3 vy40 >>= gtGt0 vy5",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
10.18/4.28	19[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];20 -> 21[label="",style="dashed", color="red", weight=0];
10.18/4.28	20[label="primbindIO (vy3 vy40) (gtGt0 vy5)",fontsize=16,color="magenta"];20 -> 22[label="",style="dashed", color="magenta", weight=3];
10.18/4.28	22[label="vy3 vy40",fontsize=16,color="green",shape="box"];22 -> 28[label="",style="dashed", color="green", weight=3];
10.18/4.28	21[label="primbindIO vy6 (gtGt0 vy5)",fontsize=16,color="burlywood",shape="triangle"];36[label="vy6/IO vy60",fontsize=10,color="white",style="solid",shape="box"];21 -> 36[label="",style="solid", color="burlywood", weight=9];
10.18/4.28	36 -> 24[label="",style="solid", color="burlywood", weight=3];
10.18/4.28	37[label="vy6/AProVE_IO vy60",fontsize=10,color="white",style="solid",shape="box"];21 -> 37[label="",style="solid", color="burlywood", weight=9];
10.18/4.28	37 -> 25[label="",style="solid", color="burlywood", weight=3];
10.18/4.28	38[label="vy6/AProVE_Exception vy60",fontsize=10,color="white",style="solid",shape="box"];21 -> 38[label="",style="solid", color="burlywood", weight=9];
10.18/4.28	38 -> 26[label="",style="solid", color="burlywood", weight=3];
10.18/4.28	39[label="vy6/AProVE_Error vy60",fontsize=10,color="white",style="solid",shape="box"];21 -> 39[label="",style="solid", color="burlywood", weight=9];
10.18/4.28	39 -> 27[label="",style="solid", color="burlywood", weight=3];
10.18/4.28	28[label="vy40",fontsize=16,color="green",shape="box"];24[label="primbindIO (IO vy60) (gtGt0 vy5)",fontsize=16,color="black",shape="box"];24 -> 29[label="",style="solid", color="black", weight=3];
10.18/4.28	25[label="primbindIO (AProVE_IO vy60) (gtGt0 vy5)",fontsize=16,color="black",shape="box"];25 -> 30[label="",style="solid", color="black", weight=3];
10.18/4.28	26[label="primbindIO (AProVE_Exception vy60) (gtGt0 vy5)",fontsize=16,color="black",shape="box"];26 -> 31[label="",style="solid", color="black", weight=3];
10.18/4.28	27[label="primbindIO (AProVE_Error vy60) (gtGt0 vy5)",fontsize=16,color="black",shape="box"];27 -> 32[label="",style="solid", color="black", weight=3];
10.18/4.28	29[label="error []",fontsize=16,color="red",shape="box"];30[label="gtGt0 vy5 vy60",fontsize=16,color="black",shape="box"];30 -> 33[label="",style="solid", color="black", weight=3];
10.18/4.28	31[label="AProVE_Exception vy60",fontsize=16,color="green",shape="box"];32[label="AProVE_Error vy60",fontsize=16,color="green",shape="box"];33[label="vy5",fontsize=16,color="green",shape="box"];}
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(8)
10.18/4.28	Obligation:
10.18/4.28	Q DP problem:
10.18/4.28	The TRS P consists of the following rules:
10.18/4.28	
10.18/4.28	   new_foldr(vy3, :(vy40, vy41), h, ba) -> new_foldr(vy3, vy41, h, ba)
10.18/4.28	
10.18/4.28	R is empty.
10.18/4.28	Q is empty.
10.18/4.28	We have to consider all minimal (P,Q,R)-chains.
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(9) QDPSizeChangeProof (EQUIVALENT)
10.18/4.28	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. 
10.18/4.28	
10.18/4.28	From the DPs we obtained the following set of size-change graphs:
10.18/4.28	*new_foldr(vy3, :(vy40, vy41), h, ba) -> new_foldr(vy3, vy41, h, ba)
10.18/4.28	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
10.18/4.28	
10.18/4.28	
10.18/4.28	----------------------------------------
10.18/4.28	
10.18/4.28	(10)
10.18/4.28	YES
10.37/4.32	EOF