Certificate for #5149 ⟨a, b, c | aa=a, bbcb=a⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Referenced by [3].

[2] a=bbcb

Axiom: bbcb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aa=bbcb

Simplify [1] aa=a.

Reduce RHS:

[2](a)
⇒ bbcb

Referenced by [4].

[4] bbcbbbcb=bbcb

Overlap of [3] aa=bbcb with [2] a=bbcb:

aa a

Critical pair: bbcba=bbcb.

Reduce LHS:

[2]bbcb(a)
⇒ bbcbbbcb

Defines rule #1.