8.00/3.55	YES
9.71/4.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.71/4.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.71/4.02	
9.71/4.02	
9.71/4.02	H-Termination with start terms of the given HASKELL could be proven:
9.71/4.02	
9.71/4.02	(0) HASKELL
9.71/4.02	(1) BR [EQUIVALENT, 0 ms]
9.71/4.02	(2) HASKELL
9.71/4.02	(3) COR [EQUIVALENT, 0 ms]
9.71/4.02	(4) HASKELL
9.71/4.02	(5) Narrow [SOUND, 0 ms]
9.71/4.02	(6) QDP
9.71/4.02	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.71/4.02	(8) YES
9.71/4.02	
9.71/4.02	
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(0)
9.71/4.02	Obligation:
9.71/4.02	mainModule Main 
9.71/4.02	module Main where {
9.71/4.02	import qualified Prelude;
9.71/4.02	}
9.71/4.02	
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(1) BR (EQUIVALENT)
9.71/4.02	Replaced joker patterns by fresh variables and removed binding patterns.
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(2)
9.71/4.02	Obligation:
9.71/4.02	mainModule Main 
9.71/4.02	module Main where {
9.71/4.02	import qualified Prelude;
9.71/4.02	}
9.71/4.02	
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(3) COR (EQUIVALENT)
9.71/4.02	Cond Reductions:
9.71/4.02	The following Function with conditions
9.71/4.02	"undefined |Falseundefined;
9.71/4.02	"
9.71/4.02	is transformed to
9.71/4.02	"undefined  = undefined1;
9.71/4.02	"
9.71/4.02	"undefined0 True = undefined;
9.71/4.02	"
9.71/4.02	"undefined1  = undefined0 False;
9.71/4.02	"
9.71/4.02	
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(4)
9.71/4.02	Obligation:
9.71/4.02	mainModule Main 
9.71/4.02	module Main where {
9.71/4.02	import qualified Prelude;
9.71/4.02	}
9.71/4.02	
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(5) Narrow (SOUND)
9.71/4.02	Haskell To QDPs
9.71/4.02	
9.71/4.02	digraph dp_graph {
9.71/4.02	node [outthreshold=100, inthreshold=100];1[label="fmap",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.71/4.02	3[label="fmap vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.71/4.02	4[label="fmap vx3 vx4",fontsize=16,color="blue",shape="box"];38[label="fmap :: (a -> b) -> (IO a) -> IO b",fontsize=10,color="white",style="solid",shape="box"];4 -> 38[label="",style="solid", color="blue", weight=9];
9.71/4.02	38 -> 5[label="",style="solid", color="blue", weight=3];
9.71/4.02	39[label="fmap :: (a -> b) -> (Maybe a) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];4 -> 39[label="",style="solid", color="blue", weight=9];
9.71/4.02	39 -> 6[label="",style="solid", color="blue", weight=3];
9.71/4.02	40[label="fmap :: (a -> b) -> ([] a) -> [] b",fontsize=10,color="white",style="solid",shape="box"];4 -> 40[label="",style="solid", color="blue", weight=9];
9.71/4.02	40 -> 7[label="",style="solid", color="blue", weight=3];
9.71/4.02	5[label="fmap vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 8[label="",style="solid", color="black", weight=3];
9.71/4.02	6[label="fmap vx3 vx4",fontsize=16,color="burlywood",shape="box"];41[label="vx4/Nothing",fontsize=10,color="white",style="solid",shape="box"];6 -> 41[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	41 -> 9[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	42[label="vx4/Just vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 42[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	42 -> 10[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	7[label="fmap vx3 vx4",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
9.71/4.02	8[label="vx4 >>= return . vx3",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9.71/4.02	9[label="fmap vx3 Nothing",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.71/4.02	10[label="fmap vx3 (Just vx40)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.71/4.02	11[label="map vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];43[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];11 -> 43[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	43 -> 15[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	44[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];11 -> 44[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	44 -> 16[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	12[label="primbindIO vx4 (return . vx3)",fontsize=16,color="burlywood",shape="box"];45[label="vx4/IO vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 45[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	45 -> 17[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	46[label="vx4/AProVE_IO vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 46[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	46 -> 18[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	47[label="vx4/AProVE_Exception vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 47[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	47 -> 19[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	48[label="vx4/AProVE_Error vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 48[label="",style="solid", color="burlywood", weight=9];
9.71/4.02	48 -> 20[label="",style="solid", color="burlywood", weight=3];
9.71/4.02	13[label="Nothing",fontsize=16,color="green",shape="box"];14[label="Just (vx3 vx40)",fontsize=16,color="green",shape="box"];14 -> 21[label="",style="dashed", color="green", weight=3];
9.71/4.02	15[label="map vx3 (vx40 : vx41)",fontsize=16,color="black",shape="box"];15 -> 22[label="",style="solid", color="black", weight=3];
9.71/4.02	16[label="map vx3 []",fontsize=16,color="black",shape="box"];16 -> 23[label="",style="solid", color="black", weight=3];
9.71/4.02	17[label="primbindIO (IO vx40) (return . vx3)",fontsize=16,color="black",shape="box"];17 -> 24[label="",style="solid", color="black", weight=3];
9.71/4.02	18[label="primbindIO (AProVE_IO vx40) (return . vx3)",fontsize=16,color="black",shape="box"];18 -> 25[label="",style="solid", color="black", weight=3];
9.71/4.02	19[label="primbindIO (AProVE_Exception vx40) (return . vx3)",fontsize=16,color="black",shape="box"];19 -> 26[label="",style="solid", color="black", weight=3];
9.71/4.02	20[label="primbindIO (AProVE_Error vx40) (return . vx3)",fontsize=16,color="black",shape="box"];20 -> 27[label="",style="solid", color="black", weight=3];
9.71/4.02	21[label="vx3 vx40",fontsize=16,color="green",shape="box"];21 -> 28[label="",style="dashed", color="green", weight=3];
9.71/4.02	22[label="vx3 vx40 : map vx3 vx41",fontsize=16,color="green",shape="box"];22 -> 29[label="",style="dashed", color="green", weight=3];
9.71/4.02	22 -> 30[label="",style="dashed", color="green", weight=3];
9.71/4.02	23[label="[]",fontsize=16,color="green",shape="box"];24[label="error []",fontsize=16,color="red",shape="box"];25[label="return . vx3",fontsize=16,color="black",shape="box"];25 -> 31[label="",style="solid", color="black", weight=3];
9.71/4.02	26[label="AProVE_Exception vx40",fontsize=16,color="green",shape="box"];27[label="AProVE_Error vx40",fontsize=16,color="green",shape="box"];28[label="vx40",fontsize=16,color="green",shape="box"];29[label="vx3 vx40",fontsize=16,color="green",shape="box"];29 -> 32[label="",style="dashed", color="green", weight=3];
9.71/4.02	30 -> 11[label="",style="dashed", color="red", weight=0];
9.71/4.02	30[label="map vx3 vx41",fontsize=16,color="magenta"];30 -> 33[label="",style="dashed", color="magenta", weight=3];
9.71/4.02	31[label="return (vx3 vx40)",fontsize=16,color="black",shape="box"];31 -> 34[label="",style="solid", color="black", weight=3];
9.71/4.02	32[label="vx40",fontsize=16,color="green",shape="box"];33[label="vx41",fontsize=16,color="green",shape="box"];34[label="primretIO (vx3 vx40)",fontsize=16,color="black",shape="box"];34 -> 35[label="",style="solid", color="black", weight=3];
9.71/4.02	35[label="AProVE_IO (vx3 vx40)",fontsize=16,color="green",shape="box"];35 -> 36[label="",style="dashed", color="green", weight=3];
9.71/4.02	36[label="vx3 vx40",fontsize=16,color="green",shape="box"];36 -> 37[label="",style="dashed", color="green", weight=3];
9.71/4.02	37[label="vx40",fontsize=16,color="green",shape="box"];}
9.71/4.02	
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(6)
9.71/4.02	Obligation:
9.71/4.02	Q DP problem:
9.71/4.02	The TRS P consists of the following rules:
9.71/4.02	
9.71/4.02	   new_map(vx3, :(vx40, vx41), h, ba) -> new_map(vx3, vx41, h, ba)
9.71/4.02	
9.71/4.02	R is empty.
9.71/4.02	Q is empty.
9.71/4.02	We have to consider all minimal (P,Q,R)-chains.
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(7) QDPSizeChangeProof (EQUIVALENT)
9.71/4.02	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. 
9.71/4.02	
9.71/4.02	From the DPs we obtained the following set of size-change graphs:
9.71/4.02	*new_map(vx3, :(vx40, vx41), h, ba) -> new_map(vx3, vx41, h, ba)
9.71/4.02	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
9.71/4.02	
9.71/4.02	
9.71/4.02	----------------------------------------
9.71/4.02	
9.71/4.02	(8)
9.71/4.02	YES
9.91/4.08	EOF