/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR @l1 @l2 @t @t1 @t2 @x @xs)
(RULES
append(@l1,@l2) -> append#1(@l1,@l2)
append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
append#1(nil,@l2) -> @l2
subtrees(@t) -> subtrees#1(@t)
subtrees#1(leaf) -> nil
subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 APPEND(@l1,@l2) -> APPEND#1(@l1,@l2)
 APPEND#1(::(@x,@xs),@l2) -> APPEND(@xs,@l2)
 SUBTREES(@t) -> SUBTREES#1(@t)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES(@t1)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES#2(subtrees(@t1),@t1,@t2,@x)
 SUBTREES#2(@l1,@t1,@t2,@x) -> SUBTREES(@t2)
 SUBTREES#2(@l1,@t1,@t2,@x) -> SUBTREES#3(subtrees(@t2),@l1,@t1,@t2,@x)
 SUBTREES#3(@l2,@l1,@t1,@t2,@x) -> APPEND(@l1,@l2)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))

Problem 1: 

SCC Processor:
-> Pairs:
 APPEND(@l1,@l2) -> APPEND#1(@l1,@l2)
 APPEND#1(::(@x,@xs),@l2) -> APPEND(@xs,@l2)
 SUBTREES(@t) -> SUBTREES#1(@t)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES(@t1)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES#2(subtrees(@t1),@t1,@t2,@x)
 SUBTREES#2(@l1,@t1,@t2,@x) -> SUBTREES(@t2)
 SUBTREES#2(@l1,@t1,@t2,@x) -> SUBTREES#3(subtrees(@t2),@l1,@t1,@t2,@x)
 SUBTREES#3(@l2,@l1,@t1,@t2,@x) -> APPEND(@l1,@l2)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APPEND(@l1,@l2) -> APPEND#1(@l1,@l2)
 APPEND#1(::(@x,@xs),@l2) -> APPEND(@xs,@l2)
->->-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
->->Cycle:
->->-> Pairs:
 SUBTREES(@t) -> SUBTREES#1(@t)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES(@t1)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES#2(subtrees(@t1),@t1,@t2,@x)
 SUBTREES#2(@l1,@t1,@t2,@x) -> SUBTREES(@t2)
->->-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 APPEND(@l1,@l2) -> APPEND#1(@l1,@l2)
 APPEND#1(::(@x,@xs),@l2) -> APPEND(@xs,@l2)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
->Projection:
 pi(APPEND) = 1
 pi(APPEND#1) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 APPEND(@l1,@l2) -> APPEND#1(@l1,@l2)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 SUBTREES(@t) -> SUBTREES#1(@t)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES(@t1)
 SUBTREES#1(node(@x,@t1,@t2)) -> SUBTREES#2(subtrees(@t1),@t1,@t2,@x)
 SUBTREES#2(@l1,@t1,@t2,@x) -> SUBTREES(@t2)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
->Projection:
 pi(SUBTREES) = 1
 pi(SUBTREES#1) = 1
 pi(SUBTREES#2) = 3

Problem 1.2: 

SCC Processor:
-> Pairs:
 SUBTREES(@t) -> SUBTREES#1(@t)
 SUBTREES#2(@l1,@t1,@t2,@x) -> SUBTREES(@t2)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 subtrees(@t) -> subtrees#1(@t)
 subtrees#1(leaf) -> nil
 subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
 subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
 subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.