YES

Problem 1: 

(VAR v_NonEmpty:S)
(RULES
f(g(h(a,b),c),d) -> if(e,f(.(b,g(h(a,b),c)),d),f(c,d'))
f(g(i(a,b,b'),c),d) -> if(e,f(.(b,c),d'),f(.(b',c),d'))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(g(h(a,b),c),d) -> if(e,f(.(b,g(h(a,b),c)),d),f(c,d'))
 f(g(i(a,b,b'),c),d) -> if(e,f(.(b,c),d'),f(.(b',c),d'))
-> 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:
 f(g(h(a,b),c),d) -> if(e,f(.(b,g(h(a,b),c)),d),f(c,d'))
 f(g(i(a,b,b'),c),d) -> if(e,f(.(b,c),d'),f(.(b',c),d'))

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(g(h(a,b),c),d) -> if(e,f(.(b,g(h(a,b),c)),d),f(c,d'))
 f(g(i(a,b,b'),c),d) -> if(e,f(.(b,c),d'),f(.(b',c),d'))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.