Certificate for #1645 ⟨a, b | aab=ba, bbb=b⟩

Completion settings:

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

[1] ba=aab

Axiom: aab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[2] bbb=b

Axiom: bbb=b.

Defines rule #3.

Referenced by [3].

[3] aaaaaaaab=aab

Overlap of [2] bbb=b with [1] ba=aab:

bb b ba

Critical pair: bbaab=ba.

Reduce LHS:

[1]	b(ba)ab
[1]	⇒ (ba)abab
[1]	⇒ aa(ba)bab
[1]	⇒ aaaab(ba)b
[1]	⇒ aaaa(ba)abb
[1]	⇒ aaaaaa(ba)bb
[2]	⇒ aaaaaaaa(bbb)
	⇒ aaaaaaaab

Reduce RHS:

[1]	(ba)
	⇒ aab

Defines rule #1.