Certificate for #12928 ⟨a, b | aba=aaa, babb=a⟩

Completion settings:

Reduction order:
- Left-to-right shortlex with a < b

[1] aba=aaa

Axiom: aba=aaa.

Defines rule #1.

Referenced by [3], [4], [5].

[2] babb=a

Axiom: babb=a.

Defines rule #4.

Referenced by [3], [4], [5].

[3] baaa=aabb

Overlap of [2] babb=a with [2] babb=a:

bab b babb

Critical pair: baba=aabb.

Reduce LHS:

[1]	b(aba)
	⇒ baaa

Referenced by [7].

[4] aaabb=aa

Overlap of [1] aba=aaa with [2] babb=a:

a ba babb

Critical pair: aa=aaabb.

Flip LHS and RHS.

Referenced by [5], [6], [8].

[5] aaaaa=aa

Overlap of [4] aaabb=aa with [2] babb=a:

aaab b babb

Critical pair: aaaba=aaabb.

Reduce LHS:

[1]	aa(aba)
	⇒ aaaaa

Reduce RHS:

[4]	(aaabb)
	⇒ aa

Defines rule #5.

Referenced by [6].

[6] aabb=aaaa

Overlap of [5] aaaaa=aa with [4] aaabb=aa:

aa aaa aaabb

Critical pair: aaaa=aabb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[7] baaa=aaaa

Simplify [3] baaa=aabb.

Reduce RHS:

[6]	(aabb)
	⇒ aaaa

Referenced by [8].

[8] baa=aaa

Overlap of [7] baaa=aaaa with [4] aaabb=aa:

b aaa aaabb

Critical pair: baa=aaaabb.

Reduce RHS:

[4]	a(aaabb)
	⇒ aaa

Defines rule #2.