/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 x y z)
(RULES
++(.(x,y),z) -> .(x,++(y,z))
++(nil,y) -> y
++(x,++(y,z)) -> ++(++(x,y),z)
++(x,nil) -> x
make(x) -> .(x,nil)
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(rev(x)) -> x
rev(nil) -> nil
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 ++#(x,++(y,z)) -> ++#(++(x,y),z)
 ++#(x,++(y,z)) -> ++#(x,y)
 REV(++(x,y)) -> ++#(rev(y),rev(x))
 REV(++(x,y)) -> REV(x)
 REV(++(x,y)) -> REV(y)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 ++(x,++(y,z)) -> ++(++(x,y),z)
 ++(x,nil) -> x
 make(x) -> .(x,nil)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 rev(nil) -> nil

Problem 1: 

SCC Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 ++#(x,++(y,z)) -> ++#(++(x,y),z)
 ++#(x,++(y,z)) -> ++#(x,y)
 REV(++(x,y)) -> ++#(rev(y),rev(x))
 REV(++(x,y)) -> REV(x)
 REV(++(x,y)) -> REV(y)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 ++(x,++(y,z)) -> ++(++(x,y),z)
 ++(x,nil) -> x
 make(x) -> .(x,nil)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 rev(nil) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 ++#(x,++(y,z)) -> ++#(++(x,y),z)
 ++#(x,++(y,z)) -> ++#(x,y)
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 ++(x,++(y,z)) -> ++(++(x,y),z)
 ++(x,nil) -> x
 make(x) -> .(x,nil)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 rev(nil) -> nil
->->Cycle:
->->-> Pairs:
 REV(++(x,y)) -> REV(x)
 REV(++(x,y)) -> REV(y)
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 ++(x,++(y,z)) -> ++(++(x,y),z)
 ++(x,nil) -> x
 make(x) -> .(x,nil)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 rev(nil) -> nil


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 ++#(x,++(y,z)) -> ++#(++(x,y),z)
 ++#(x,++(y,z)) -> ++#(x,y)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 ++(x,++(y,z)) -> ++(++(x,y),z)
 ++(x,nil) -> x
 make(x) -> .(x,nil)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 rev(nil) -> nil
->Projection:
 pi(++#) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 ++(x,++(y,z)) -> ++(++(x,y),z)
 ++(x,nil) -> x
 make(x) -> .(x,nil)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 rev(nil) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 ++(x,++(y,z)) -> ++(++(x,y),z)
 ++(x,nil) -> x
 make(x) -> .(x,nil)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 rev(nil) -> nil

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.