A graph $H$H is a clique graph if $H$H is a vertex-disjoin union of cliques. Abu-Khzam (2017) introduced the $(a,d)$(a,d)-{Cluster Editing} problem, where for fixed natural numbers $a,d$a,d, given a graph $G$G and vertex-weights $a^:\ V(G)\rightarrow {0,1,\dots, a}$a: V(G)→0,1,…,a and $d^{}:\ V(G)\rightarrow {0,1,\dots, d}$d: V(G)→0,1,…,d, we are to decide whether $G$G can be turned into a cluster graph by deleting at most $d^(v)$d(v) edges incident to every $v\in V(G)$v∈V(G) and adding at most $a^(v)$a(v) edges incident to every $v\in V(G)$v∈V(G). Results by Komusiewicz and Uhlmann (2012) and Abu-Khzam (2017) provided a dichotomy of complexity (in P or NP-complete) of $(a,d)$(a,d)-{Cluster Editing} for all pairs $a,d$a,d apart from $a=d=1.$a=d=1. Abu-Khzam (2017) conjectured that $(1,1)$(1,1)-{Cluster Editing} is in P. We resolve Abu-Khzam's conjecture in affirmative by (i) providing a serious of five polynomial-time reductions to $C_3$C3​-free and $C_4$C4​-free graphs of maximum degree at most 3, and (ii) designing a polynomial-time algorithm for solving $(1,1)$(1,1)-{Cluster Editing} on $C_3$C3​-free and $C_4$C4​-free graphs of maximum degree at most 3.