Consider the TRS R consisting of the rewrite rules 1: f(g(i(a,b,b'),c),d) -> if(e,f(b . c,d'),f(b' . c,d')) 2: f(g(h(a,b),c),d) -> if(e,f(b . g(h(a,b),c),d),f(c,d')) There are 4 dependency pairs: 3: F(g(i(a,b,b'),c),d) -> F(b . c,d') 4: F(g(i(a,b,b'),c),d) -> F(b' . c,d') 5: F(g(h(a,b),c),d) -> F(b . g(h(a,b),c),d) 6: F(g(h(a,b),c),d) -> F(c,d') The approximated dependency graph contains no SCCs and hence the TRS is trivially terminating.