Certificate for #15544 ⟨a, b | aaa=bb, bbbbb=b⟩

Back:⟨a, b | aaa=bb, bbbbb=b⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5].

[2] aaaaaab=b

Axiom: bbbbb=b.

Reduce LHS:

[1](bb)bbb
[1]⇒ aaa(bb)b
⇒ aaaaaab

Referenced by [4].

[3] aaab=baaa

Overlap of [1] bb=aaa with [1] bb=aaa:

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] baaaaaa=b

Simplify [2] aaaaaab=b.

Reduce LHS:

[3]aaa(aaab)
[3]⇒ (aaab)aaa
⇒ baaaaaa

Defines rule #2.

Referenced by [5].

[5] aaaaaaaaa=aaa

Overlap of [1] bb=aaa with [4] baaaaaa=b:

b b baaaaaa

Critical pair: bb=aaaaaaaaa.

Reduce LHS:

[1](bb)
⇒ aaa

Flip LHS and RHS.

Defines rule #1.