0.00/0.01	YES
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	(VAR v_NonEmpty:S @l1:S @l2:S @t:S @t1:S @t2:S @x:S @xs:S)
0.00/0.01	(RULES
0.00/0.01	append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	append#1(nil,@l2:S) -> @l2:S
0.00/0.01	subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	subtrees#1(leaf) -> nil
0.00/0.01	subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	) 
0.00/0.01	(STRATEGY INNERMOST)
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Dependency Pairs Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S)
0.00/0.01	 APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S)
0.00/0.01	 SUBTREES(@t:S) -> SUBTREES#1(@t:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES(@t1:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S)
0.00/0.01	 SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 SUBTREES#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> APPEND(@l1:S,@l2:S)
0.00/0.01	-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S)
0.00/0.01	 APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S)
0.00/0.01	 SUBTREES(@t:S) -> SUBTREES#1(@t:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES(@t1:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S)
0.00/0.01	 SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 SUBTREES#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> APPEND(@l1:S,@l2:S)
0.00/0.01	-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S)
0.00/0.01	 APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S)
0.00/0.01	->->-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 SUBTREES(@t:S) -> SUBTREES#1(@t:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES(@t1:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S)
0.00/0.01	->->-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	
0.00/0.01	
0.00/0.01	The problem is decomposed in 2 subproblems.
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S)
0.00/0.01	 APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S)
0.00/0.01	-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	->Projection:
0.00/0.01	 pi(APPEND) = 1
0.00/0.01	 pi(APPEND#1) = 1
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S)
0.00/0.01	-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 SUBTREES(@t:S) -> SUBTREES#1(@t:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES(@t1:S)
0.00/0.01	 SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S)
0.00/0.01	-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	->Projection:
0.00/0.01	 pi(SUBTREES) = 1
0.00/0.01	 pi(SUBTREES#1) = 1
0.00/0.01	 pi(SUBTREES#2) = 3
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 SUBTREES(@t:S) -> SUBTREES#1(@t:S)
0.00/0.01	 SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S)
0.00/0.01	-> Rules:
0.00/0.01	 append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S)
0.00/0.01	 append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S))
0.00/0.01	 append#1(nil,@l2:S) -> @l2:S
0.00/0.01	 subtrees(@t:S) -> subtrees#1(@t:S)
0.00/0.01	 subtrees#1(leaf) -> nil
0.00/0.01	 subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S)
0.00/0.01	 subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	EOF