Certificate for #8088 ⟨a, b | aaa=1, babb=bba⟩

Completion settings:

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1

[1] aaa=1

Axiom: aaa=1.

Defines rule #3.

Referenced by [3].

[2] bba=babb

Axiom: babb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] babababb=bb

Overlap of [2] bba=babb with [1] aaa=1:

bb a aaa

Critical pair: bb=babbaa.

Reduce RHS:

[2]	ba(bba)a
[2]	⇒ baba(bba)
	⇒ babababb

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] bbbbbbbbbb=bbb

Overlap of [2] bba=babb with [3] babababb=bb:

b ba babababb

Critical pair: bbb=babbbababb.

Reduce RHS:

[2]	bab(bba)babb
[2]	⇒ ba(bba)bbbabb
[2]	⇒ bababbb(bba)bb
[2]	⇒ bababb(bba)bbbb
[2]	⇒ babab(bba)bbbbbb
[2]	⇒ baba(bba)bbbbbbbb
[3]	⇒ (babababb)bbbbbbbb
	⇒ bbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.