YES

Problem 1: 

(VAR v_NonEmpty:S x1:S)
(RULES
0(1(2(3(4(x1:S))))) -> 0(2(1(3(4(x1:S)))))
0(5(1(2(4(3(x1:S)))))) -> 0(5(2(1(4(3(x1:S))))))
0(5(2(4(1(3(x1:S)))))) -> 0(1(5(2(4(3(x1:S))))))
0(5(3(1(2(4(x1:S)))))) -> 0(1(5(3(2(4(x1:S))))))
0(5(4(1(3(2(x1:S)))))) -> 0(5(4(3(1(2(x1:S))))))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 0(1(2(3(4(x1:S))))) -> 0(2(1(3(4(x1:S)))))
 0(5(1(2(4(3(x1:S)))))) -> 0(5(2(1(4(3(x1:S))))))
 0(5(2(4(1(3(x1:S)))))) -> 0(1(5(2(4(3(x1:S))))))
 0(5(3(1(2(4(x1:S)))))) -> 0(1(5(3(2(4(x1:S))))))
 0(5(4(1(3(2(x1:S)))))) -> 0(5(4(3(1(2(x1:S))))))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 0(1(2(3(4(x1:S))))) -> 0(2(1(3(4(x1:S)))))
 0(5(1(2(4(3(x1:S)))))) -> 0(5(2(1(4(3(x1:S))))))
 0(5(2(4(1(3(x1:S)))))) -> 0(1(5(2(4(3(x1:S))))))
 0(5(3(1(2(4(x1:S)))))) -> 0(1(5(3(2(4(x1:S))))))
 0(5(4(1(3(2(x1:S)))))) -> 0(5(4(3(1(2(x1:S))))))

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0(1(2(3(4(x1:S))))) -> 0(2(1(3(4(x1:S)))))
 0(5(1(2(4(3(x1:S)))))) -> 0(5(2(1(4(3(x1:S))))))
 0(5(2(4(1(3(x1:S)))))) -> 0(1(5(2(4(3(x1:S))))))
 0(5(3(1(2(4(x1:S)))))) -> 0(1(5(3(2(4(x1:S))))))
 0(5(4(1(3(2(x1:S)))))) -> 0(5(4(3(1(2(x1:S))))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.