YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
a(c(x:S)) -> x:S
a(d(x:S)) -> d(c(b(a(x:S))))
b(c(x:S)) -> c(d(a(b(x:S))))
b(d(x:S)) -> x:S
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(d(x:S)) -> A(x:S)
 A(d(x:S)) -> B(a(x:S))
 B(c(x:S)) -> A(b(x:S))
 B(c(x:S)) -> B(x:S)
-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 A(d(x:S)) -> A(x:S)
 A(d(x:S)) -> B(a(x:S))
 B(c(x:S)) -> A(b(x:S))
 B(c(x:S)) -> B(x:S)
-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(d(x:S)) -> A(x:S)
 A(d(x:S)) -> B(a(x:S))
 B(c(x:S)) -> A(b(x:S))
 B(c(x:S)) -> B(x:S)
->->-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S

Problem 1: 

Narrowing Processor:
-> Pairs:
 A(d(x:S)) -> A(x:S)
 A(d(x:S)) -> B(a(x:S))
 B(c(x:S)) -> A(b(x:S))
 B(c(x:S)) -> B(x:S)
-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S
->Narrowed Pairs:
->->Original Pair:
 A(d(x:S)) -> B(a(x:S))
->-> Narrowed pairs:
 A(d(c(x:S))) -> B(x:S)
 A(d(d(x:S))) -> B(d(c(b(a(x:S)))))
->->Original Pair:
 B(c(x:S)) -> A(b(x:S))
->-> Narrowed pairs:
 B(c(c(x:S))) -> A(c(d(a(b(x:S)))))
 B(c(d(x:S))) -> A(x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 A(d(c(x:S))) -> B(x:S)
 A(d(d(x:S))) -> B(d(c(b(a(x:S)))))
 A(d(x:S)) -> A(x:S)
 B(c(c(x:S))) -> A(c(d(a(b(x:S)))))
 B(c(d(x:S))) -> A(x:S)
 B(c(x:S)) -> B(x:S)
-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(d(c(x:S))) -> B(x:S)
 A(d(x:S)) -> A(x:S)
 B(c(d(x:S))) -> A(x:S)
 B(c(x:S)) -> B(x:S)
->->-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S

Problem 1: 

Subterm Processor:
-> Pairs:
 A(d(c(x:S))) -> B(x:S)
 A(d(x:S)) -> A(x:S)
 B(c(d(x:S))) -> A(x:S)
 B(c(x:S)) -> B(x:S)
-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S
->Projection:
 pi(A) = 1
 pi(B) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a(c(x:S)) -> x:S
 a(d(x:S)) -> d(c(b(a(x:S))))
 b(c(x:S)) -> c(d(a(b(x:S))))
 b(d(x:S)) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.