Certificate for #1770 ⟨a, b, c | aab=cc, aac=1⟩

Back:⟨a, b, c | aab=cc, aac=1⟩

Completion settings:

[1] cc=aab

Axiom: aab=cc.

Flip LHS and RHS.

Referenced by [3], [4].

[2] aac=1

Axiom: aac=1.

Referenced by [4], [6].

[3] caab=aabc

Overlap of [1] cc=aab with [1] cc=aab:

c c cc

Critical pair: caab=aabc.

Referenced by [5].

[4] c=aaaab

Overlap of [2] aac=1 with [1] cc=aab:

aa c cc

Critical pair: aaaab=c.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[5] aabaaaab=aaaabaab

Simplify [3] caab=aabc.

Reduce LHS:

[4](c)aab
⇒ aaaabaab

Reduce RHS:

[4]aab(c)
⇒ aabaaaab

Flip LHS and RHS.

Defines rule #2.

[6] aaaaaab=1

Overlap of [2] aac=1 with [4] c=aaaab:

aa c c

Critical pair: aaaaaab=1.

Defines rule #1.