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


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YES

Problem 1: 

(VAR @l @l1 @l2 @ls @x @xs)
(RULES
append(@l1,@l2) -> append#1(@l1,@l2)
append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
append#1(nil,@l2) -> @l2
appendAll(@l) -> appendAll#1(@l)
appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
appendAll#1(nil) -> nil
appendAll2(@l) -> appendAll2#1(@l)
appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
appendAll2#1(nil) -> nil
appendAll3(@l) -> appendAll3#1(@l)
appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
appendAll3#1(nil) -> nil
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 APPEND(@l1,@l2) -> APPEND#1(@l1,@l2)
 APPEND#1(::(@x,@xs),@l2) -> APPEND(@xs,@l2)
 APPENDALL(@l) -> APPENDALL#1(@l)
 APPENDALL#1(::(@l1,@ls)) -> APPEND(@l1,appendAll(@ls))
 APPENDALL#1(::(@l1,@ls)) -> APPENDALL(@ls)
 APPENDALL2(@l) -> APPENDALL2#1(@l)
 APPENDALL2#1(::(@l1,@ls)) -> APPEND(appendAll(@l1),appendAll2(@ls))
 APPENDALL2#1(::(@l1,@ls)) -> APPENDALL(@l1)
 APPENDALL2#1(::(@l1,@ls)) -> APPENDALL2(@ls)
 APPENDALL3(@l) -> APPENDALL3#1(@l)
 APPENDALL3#1(::(@l1,@ls)) -> APPEND(appendAll2(@l1),appendAll3(@ls))
 APPENDALL3#1(::(@l1,@ls)) -> APPENDALL2(@l1)
 APPENDALL3#1(::(@l1,@ls)) -> APPENDALL3(@ls)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil

Problem 1: 

SCC Processor:
-> Pairs:
 APPEND(@l1,@l2) -> APPEND#1(@l1,@l2)
 APPEND#1(::(@x,@xs),@l2) -> APPEND(@xs,@l2)
 APPENDALL(@l) -> APPENDALL#1(@l)
 APPENDALL#1(::(@l1,@ls)) -> APPEND(@l1,appendAll(@ls))
 APPENDALL#1(::(@l1,@ls)) -> APPENDALL(@ls)
 APPENDALL2(@l) -> APPENDALL2#1(@l)
 APPENDALL2#1(::(@l1,@ls)) -> APPEND(appendAll(@l1),appendAll2(@ls))
 APPENDALL2#1(::(@l1,@ls)) -> APPENDALL(@l1)
 APPENDALL2#1(::(@l1,@ls)) -> APPENDALL2(@ls)
 APPENDALL3(@l) -> APPENDALL3#1(@l)
 APPENDALL3#1(::(@l1,@ls)) -> APPEND(appendAll2(@l1),appendAll3(@ls))
 APPENDALL3#1(::(@l1,@ls)) -> APPENDALL2(@l1)
 APPENDALL3#1(::(@l1,@ls)) -> APPENDALL3(@ls)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->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
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->->Cycle:
->->-> Pairs:
 APPENDALL(@l) -> APPENDALL#1(@l)
 APPENDALL#1(::(@l1,@ls)) -> APPENDALL(@ls)
->->-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->->Cycle:
->->-> Pairs:
 APPENDALL2(@l) -> APPENDALL2#1(@l)
 APPENDALL2#1(::(@l1,@ls)) -> APPENDALL2(@ls)
->->-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->->Cycle:
->->-> Pairs:
 APPENDALL3(@l) -> APPENDALL3#1(@l)
 APPENDALL3#1(::(@l1,@ls)) -> APPENDALL3(@ls)
->->-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil


The problem is decomposed in 4 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
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->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
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 APPENDALL(@l) -> APPENDALL#1(@l)
 APPENDALL#1(::(@l1,@ls)) -> APPENDALL(@ls)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->Projection:
 pi(APPENDALL) = 1
 pi(APPENDALL#1) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 APPENDALL(@l) -> APPENDALL#1(@l)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 APPENDALL2(@l) -> APPENDALL2#1(@l)
 APPENDALL2#1(::(@l1,@ls)) -> APPENDALL2(@ls)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->Projection:
 pi(APPENDALL2) = 1
 pi(APPENDALL2#1) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 APPENDALL2(@l) -> APPENDALL2#1(@l)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 APPENDALL3(@l) -> APPENDALL3#1(@l)
 APPENDALL3#1(::(@l1,@ls)) -> APPENDALL3(@ls)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->Projection:
 pi(APPENDALL3) = 1
 pi(APPENDALL3#1) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 APPENDALL3(@l) -> APPENDALL3#1(@l)
-> Rules:
 append(@l1,@l2) -> append#1(@l1,@l2)
 append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
 append#1(nil,@l2) -> @l2
 appendAll(@l) -> appendAll#1(@l)
 appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls))
 appendAll#1(nil) -> nil
 appendAll2(@l) -> appendAll2#1(@l)
 appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls))
 appendAll2#1(nil) -> nil
 appendAll3(@l) -> appendAll3#1(@l)
 appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls))
 appendAll3#1(nil) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.