8.30/3.67	YES
9.77/4.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.77/4.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.77/4.11	
9.77/4.11	
9.77/4.11	H-Termination with start terms of the given HASKELL could be proven:
9.77/4.11	
9.77/4.11	(0) HASKELL
9.77/4.11	(1) BR [EQUIVALENT, 0 ms]
9.77/4.11	(2) HASKELL
9.77/4.11	(3) COR [EQUIVALENT, 0 ms]
9.77/4.11	(4) HASKELL
9.77/4.11	(5) Narrow [SOUND, 0 ms]
9.77/4.11	(6) QDP
9.77/4.11	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.77/4.11	(8) YES
9.77/4.11	
9.77/4.11	
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(0)
9.77/4.11	Obligation:
9.77/4.11	mainModule Main 
9.77/4.11	module Main where {
9.77/4.11	import qualified Prelude;
9.77/4.11	}
9.77/4.11	
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(1) BR (EQUIVALENT)
9.77/4.11	Replaced joker patterns by fresh variables and removed binding patterns.
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(2)
9.77/4.11	Obligation:
9.77/4.11	mainModule Main 
9.77/4.11	module Main where {
9.77/4.11	import qualified Prelude;
9.77/4.11	}
9.77/4.11	
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(3) COR (EQUIVALENT)
9.77/4.11	Cond Reductions:
9.77/4.11	The following Function with conditions
9.77/4.11	"undefined |Falseundefined;
9.77/4.11	"
9.77/4.11	is transformed to
9.77/4.11	"undefined  = undefined1;
9.77/4.11	"
9.77/4.11	"undefined0 True = undefined;
9.77/4.11	"
9.77/4.11	"undefined1  = undefined0 False;
9.77/4.11	"
9.77/4.11	
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(4)
9.77/4.11	Obligation:
9.77/4.11	mainModule Main 
9.77/4.11	module Main where {
9.77/4.11	import qualified Prelude;
9.77/4.11	}
9.77/4.11	
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(5) Narrow (SOUND)
9.77/4.11	Haskell To QDPs
9.77/4.11	
9.77/4.11	digraph dp_graph {
9.77/4.11	node [outthreshold=100, inthreshold=100];1[label="fmap",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.77/4.11	3[label="fmap vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.77/4.11	4[label="fmap vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.77/4.11	5[label="map vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];14[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];5 -> 14[label="",style="solid", color="burlywood", weight=9];
9.77/4.11	14 -> 6[label="",style="solid", color="burlywood", weight=3];
9.77/4.11	15[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 15[label="",style="solid", color="burlywood", weight=9];
9.77/4.11	15 -> 7[label="",style="solid", color="burlywood", weight=3];
9.77/4.11	6[label="map vx3 (vx40 : vx41)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.77/4.11	7[label="map vx3 []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.77/4.11	8[label="vx3 vx40 : map vx3 vx41",fontsize=16,color="green",shape="box"];8 -> 10[label="",style="dashed", color="green", weight=3];
9.77/4.11	8 -> 11[label="",style="dashed", color="green", weight=3];
9.77/4.11	9[label="[]",fontsize=16,color="green",shape="box"];10[label="vx3 vx40",fontsize=16,color="green",shape="box"];10 -> 12[label="",style="dashed", color="green", weight=3];
9.77/4.11	11 -> 5[label="",style="dashed", color="red", weight=0];
9.77/4.11	11[label="map vx3 vx41",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3];
9.77/4.11	12[label="vx40",fontsize=16,color="green",shape="box"];13[label="vx41",fontsize=16,color="green",shape="box"];}
9.77/4.11	
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(6)
9.77/4.11	Obligation:
9.77/4.11	Q DP problem:
9.77/4.11	The TRS P consists of the following rules:
9.77/4.11	
9.77/4.11	   new_map(vx3, :(vx40, vx41), h, ba) -> new_map(vx3, vx41, h, ba)
9.77/4.11	
9.77/4.11	R is empty.
9.77/4.11	Q is empty.
9.77/4.11	We have to consider all minimal (P,Q,R)-chains.
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(7) QDPSizeChangeProof (EQUIVALENT)
9.77/4.11	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. 
9.77/4.11	
9.77/4.11	From the DPs we obtained the following set of size-change graphs:
9.77/4.11	*new_map(vx3, :(vx40, vx41), h, ba) -> new_map(vx3, vx41, h, ba)
9.77/4.11	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
9.77/4.11	
9.77/4.11	
9.77/4.11	----------------------------------------
9.77/4.11	
9.77/4.11	(8)
9.77/4.11	YES
10.09/4.26	EOF