/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
car(.(x,y)) -> x
cdr(.(x,y)) -> y
null(.(x,y)) -> false
null(nil) -> true
rev(.(x,y)) -> ++(rev(y),.(x,nil))
rev(nil) -> nil
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 rev(nil) -> nil
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 REV(.(x,y)) -> ++#(rev(y),.(x,nil))
 REV(.(x,y)) -> REV(y)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 rev(nil) -> nil

Problem 1: 

SCC Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 REV(.(x,y)) -> ++#(rev(y),.(x,nil))
 REV(.(x,y)) -> REV(y)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 rev(nil) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 rev(nil) -> nil
->->Cycle:
->->-> Pairs:
 REV(.(x,y)) -> REV(y)
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 rev(nil) -> nil


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 rev(nil) -> nil
->Projection:
 pi(++#) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 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(y)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(.(x,y)) -> false
 null(nil) -> true
 rev(.(x,y)) -> ++(rev(y),.(x,nil))
 rev(nil) -> nil
->Projection:
 pi(REV) = 1

Problem 1.2: 

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

The problem is finite.