/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 v_NonEmpty:S x:S y:S z:S)
(RULES
++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
++(nil,y:S) -> y:S
++(x:S,nil) -> x:S
flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
flatten(flatten(x:S)) -> flatten(x:S)
flatten(nil) -> nil
flatten(unit(x:S)) -> flatten(x:S)
rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
rev(rev(x:S)) -> x:S
rev(nil) -> nil
rev(unit(x:S)) -> unit(x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ++#(++(x:S,y:S),z:S) -> ++#(x:S,++(y:S,z:S))
 ++#(++(x:S,y:S),z:S) -> ++#(y:S,z:S)
 FLATTEN(++(unit(x:S),y:S)) -> ++#(flatten(x:S),flatten(y:S))
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(x:S)
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(y:S)
 FLATTEN(++(x:S,y:S)) -> ++#(flatten(x:S),flatten(y:S))
 FLATTEN(++(x:S,y:S)) -> FLATTEN(x:S)
 FLATTEN(++(x:S,y:S)) -> FLATTEN(y:S)
 FLATTEN(unit(x:S)) -> FLATTEN(x:S)
 REV(++(x:S,y:S)) -> ++#(rev(y:S),rev(x:S))
 REV(++(x:S,y:S)) -> REV(x:S)
 REV(++(x:S,y:S)) -> REV(y:S)
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 ++#(++(x:S,y:S),z:S) -> ++#(x:S,++(y:S,z:S))
 ++#(++(x:S,y:S),z:S) -> ++#(y:S,z:S)
 FLATTEN(++(unit(x:S),y:S)) -> ++#(flatten(x:S),flatten(y:S))
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(x:S)
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(y:S)
 FLATTEN(++(x:S,y:S)) -> ++#(flatten(x:S),flatten(y:S))
 FLATTEN(++(x:S,y:S)) -> FLATTEN(x:S)
 FLATTEN(++(x:S,y:S)) -> FLATTEN(y:S)
 FLATTEN(unit(x:S)) -> FLATTEN(x:S)
 REV(++(x:S,y:S)) -> ++#(rev(y:S),rev(x:S))
 REV(++(x:S,y:S)) -> REV(x:S)
 REV(++(x:S,y:S)) -> REV(y:S)
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ++#(++(x:S,y:S),z:S) -> ++#(x:S,++(y:S,z:S))
 ++#(++(x:S,y:S),z:S) -> ++#(y:S,z:S)
->->-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->->Cycle:
->->-> Pairs:
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(x:S)
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(y:S)
 FLATTEN(++(x:S,y:S)) -> FLATTEN(x:S)
 FLATTEN(++(x:S,y:S)) -> FLATTEN(y:S)
 FLATTEN(unit(x:S)) -> FLATTEN(x:S)
->->-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->->Cycle:
->->-> Pairs:
 REV(++(x:S,y:S)) -> REV(x:S)
 REV(++(x:S,y:S)) -> REV(y:S)
->->-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ++#(++(x:S,y:S),z:S) -> ++#(x:S,++(y:S,z:S))
 ++#(++(x:S,y:S),z:S) -> ++#(y:S,z:S)
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->Projection:
 pi(++#) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(x:S)
 FLATTEN(++(unit(x:S),y:S)) -> FLATTEN(y:S)
 FLATTEN(++(x:S,y:S)) -> FLATTEN(x:S)
 FLATTEN(++(x:S,y:S)) -> FLATTEN(y:S)
 FLATTEN(unit(x:S)) -> FLATTEN(x:S)
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->Projection:
 pi(FLATTEN) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 REV(++(x:S,y:S)) -> REV(x:S)
 REV(++(x:S,y:S)) -> REV(y:S)
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->Projection:
 pi(REV) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(++(x:S,y:S),z:S) -> ++(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 ++(x:S,nil) -> x:S
 flatten(++(unit(x:S),y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(++(x:S,y:S)) -> ++(flatten(x:S),flatten(y:S))
 flatten(flatten(x:S)) -> flatten(x:S)
 flatten(nil) -> nil
 flatten(unit(x:S)) -> flatten(x:S)
 rev(++(x:S,y:S)) -> ++(rev(y:S),rev(x:S))
 rev(rev(x:S)) -> x:S
 rev(nil) -> nil
 rev(unit(x:S)) -> unit(x:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.