7.77/3.50	YES
9.80/4.02	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.80/4.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.80/4.02	
9.80/4.02	
9.80/4.02	H-Termination with start terms of the given HASKELL could be proven:
9.80/4.02	
9.80/4.02	(0) HASKELL
9.80/4.02	(1) LR [EQUIVALENT, 0 ms]
9.80/4.02	(2) HASKELL
9.80/4.02	(3) BR [EQUIVALENT, 0 ms]
9.80/4.02	(4) HASKELL
9.80/4.02	(5) COR [EQUIVALENT, 0 ms]
9.80/4.02	(6) HASKELL
9.80/4.02	(7) Narrow [SOUND, 0 ms]
9.80/4.02	(8) QDP
9.80/4.02	(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.80/4.02	(10) YES
9.80/4.02	
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(0)
9.80/4.02	Obligation:
9.80/4.02	mainModule Main 
9.80/4.02	module Main where {
9.80/4.02	import qualified Prelude;
9.80/4.02	}
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(1) LR (EQUIVALENT)
9.80/4.02	Lambda Reductions:
9.80/4.02	The following Lambda expression
9.80/4.02	"\_->q"
9.80/4.02	is transformed to
9.80/4.02	"gtGt0 q _ = q;
9.80/4.02	"
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(2)
9.80/4.02	Obligation:
9.80/4.02	mainModule Main 
9.80/4.02	module Main where {
9.80/4.02	import qualified Prelude;
9.80/4.02	}
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(3) BR (EQUIVALENT)
9.80/4.02	Replaced joker patterns by fresh variables and removed binding patterns.
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(4)
9.80/4.02	Obligation:
9.80/4.02	mainModule Main 
9.80/4.02	module Main where {
9.80/4.02	import qualified Prelude;
9.80/4.02	}
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(5) COR (EQUIVALENT)
9.80/4.02	Cond Reductions:
9.80/4.02	The following Function with conditions
9.80/4.02	"undefined |Falseundefined;
9.80/4.02	"
9.80/4.02	is transformed to
9.80/4.02	"undefined  = undefined1;
9.80/4.02	"
9.80/4.02	"undefined0 True = undefined;
9.80/4.02	"
9.80/4.02	"undefined1  = undefined0 False;
9.80/4.02	"
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(6)
9.80/4.02	Obligation:
9.80/4.02	mainModule Main 
9.80/4.02	module Main where {
9.80/4.02	import qualified Prelude;
9.80/4.02	}
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(7) Narrow (SOUND)
9.80/4.02	Haskell To QDPs
9.80/4.02	
9.80/4.02	digraph dp_graph {
9.80/4.02	node [outthreshold=100, inthreshold=100];1[label="sequence_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.80/4.02	3[label="sequence_ vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.80/4.02	4[label="foldr (>>) (return ()) vy3",fontsize=16,color="burlywood",shape="triangle"];25[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 25[label="",style="solid", color="burlywood", weight=9];
9.80/4.02	25 -> 5[label="",style="solid", color="burlywood", weight=3];
9.80/4.02	26[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 26[label="",style="solid", color="burlywood", weight=9];
9.80/4.02	26 -> 6[label="",style="solid", color="burlywood", weight=3];
9.80/4.02	5[label="foldr (>>) (return ()) (vy30 : vy31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.80/4.02	6[label="foldr (>>) (return ()) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.80/4.02	7 -> 9[label="",style="dashed", color="red", weight=0];
9.80/4.02	7[label="(>>) vy30 foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3];
9.80/4.02	8[label="return ()",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.80/4.02	10 -> 4[label="",style="dashed", color="red", weight=0];
9.80/4.02	10[label="foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3];
9.80/4.02	9[label="(>>) vy30 vy4",fontsize=16,color="black",shape="triangle"];9 -> 13[label="",style="solid", color="black", weight=3];
9.80/4.02	11[label="primretIO ()",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3];
9.80/4.02	12[label="vy31",fontsize=16,color="green",shape="box"];13[label="vy30 >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
9.80/4.02	14[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];15[label="primbindIO vy30 (gtGt0 vy4)",fontsize=16,color="burlywood",shape="box"];27[label="vy30/IO vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 27[label="",style="solid", color="burlywood", weight=9];
9.80/4.02	27 -> 16[label="",style="solid", color="burlywood", weight=3];
9.80/4.02	28[label="vy30/AProVE_IO vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 28[label="",style="solid", color="burlywood", weight=9];
9.80/4.02	28 -> 17[label="",style="solid", color="burlywood", weight=3];
9.80/4.02	29[label="vy30/AProVE_Exception vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 29[label="",style="solid", color="burlywood", weight=9];
9.80/4.02	29 -> 18[label="",style="solid", color="burlywood", weight=3];
9.80/4.02	30[label="vy30/AProVE_Error vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 30[label="",style="solid", color="burlywood", weight=9];
9.80/4.02	30 -> 19[label="",style="solid", color="burlywood", weight=3];
9.80/4.02	16[label="primbindIO (IO vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.80/4.02	17[label="primbindIO (AProVE_IO vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
9.80/4.02	18[label="primbindIO (AProVE_Exception vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
9.80/4.02	19[label="primbindIO (AProVE_Error vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
9.80/4.02	20[label="error []",fontsize=16,color="red",shape="box"];21[label="gtGt0 vy4 vy300",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
9.80/4.02	22[label="AProVE_Exception vy300",fontsize=16,color="green",shape="box"];23[label="AProVE_Error vy300",fontsize=16,color="green",shape="box"];24[label="vy4",fontsize=16,color="green",shape="box"];}
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(8)
9.80/4.02	Obligation:
9.80/4.02	Q DP problem:
9.80/4.02	The TRS P consists of the following rules:
9.80/4.02	
9.80/4.02	   new_foldr(:(vy30, vy31), h) -> new_foldr(vy31, h)
9.80/4.02	
9.80/4.02	R is empty.
9.80/4.02	Q is empty.
9.80/4.02	We have to consider all minimal (P,Q,R)-chains.
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(9) QDPSizeChangeProof (EQUIVALENT)
9.80/4.02	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. 
9.80/4.02	
9.80/4.02	From the DPs we obtained the following set of size-change graphs:
9.80/4.02	*new_foldr(:(vy30, vy31), h) -> new_foldr(vy31, h)
9.80/4.02	The graph contains the following edges 1 > 1, 2 >= 2
9.80/4.02	
9.80/4.02	
9.80/4.02	----------------------------------------
9.80/4.02	
9.80/4.02	(10)
9.80/4.02	YES
9.83/4.07	EOF