YES

Problem 1: 

(VAR v_NonEmpty:S x1:S)
(RULES
a(c(x1:S)) -> c(a(x1:S))
a(l(x1:S)) -> l(a(x1:S))
c(a(r(x1:S))) -> r(a(x1:S))
l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(c(x1:S)) -> C(a(x1:S))
 A(l(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 C(a(r(x1:S))) -> A(x1:S)
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))

Problem 1: 

SCC Processor:
-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(c(x1:S)) -> C(a(x1:S))
 A(l(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 C(a(r(x1:S))) -> A(x1:S)
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(c(x1:S)) -> C(a(x1:S))
 A(l(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 C(a(r(x1:S))) -> A(x1:S)
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
->->-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(c(x1:S)) -> C(a(x1:S))
 A(l(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 C(a(r(x1:S))) -> A(x1:S)
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
-> Usable rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 1
[c](X) = X
[l](X) = 2.X + 1
[r](X) = 2.X + 1
[A](X) = 2.X + 2
[C](X) = X
[L](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 C(a(r(x1:S))) -> A(x1:S)
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
->->-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
-> Usable rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[c](X) = X
[l](X) = 2.X + 2
[r](X) = 2.X + 2
[A](X) = 2.X + 2
[L](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
->->-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(c(x1:S)) -> A(x1:S)
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
-> Usable rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X
[c](X) = 2.X + 2
[l](X) = 0
[r](X) = 2.X
[A](X) = 2.X + 2
[L](X) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
->->-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
-> Usable rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[c](X) = X
[l](X) = 2.X + 2
[r](X) = 2.X + 2
[A](X) = 2.X
[L](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
->->-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(l(x1:S)) -> L(a(x1:S))
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
-> Usable rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X
[c](X) = 1/2.X
[l](X) = 2.X + 1/2
[r](X) = 2
[A](X) = X
[L](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
-> Rules:
 a(c(x1:S)) -> c(a(x1:S))
 a(l(x1:S)) -> l(a(x1:S))
 c(a(r(x1:S))) -> r(a(x1:S))
 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.