Let c$,$ a and b be constants, with a $<=$ b and a $+$ b $<1.$ Find, and prove a good bound on T$($n$)$ for the recurrence:

T$($n$)<=$ c for n $<$ max$\{$a$^-1,(1-$b$-$a$)^-1\}$ and

T$($n$)<=$ c $+$ T$($floor$($a n$))+$ T$($floor$($b n$))+$ T$($floor$((1-$a$-$b$)$n$))$ otherwise.