Certificate for #20188 ⟨a, b | aba=a, aaab=bba⟩

Back:⟨a, b | aba=a, aaab=bba⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #2.

Referenced by [3], [4].

[2] bba=aaab

Axiom: aaab=bba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] aaaaaab=aaab

Overlap of [2] bba=aaab with [1] aba=a:

bb a aba

Critical pair: bba=aaabba.

Reduce LHS:

[2](bba)
⇒ aaab

Reduce RHS:

[2]aaa(bba)
⇒ aaaaaab

Flip LHS and RHS.

Referenced by [4].

[4] aaaaaa=aaa

Overlap of [3] aaaaaab=aaab with [1] aba=a:

aaaaa ab aba

Critical pair: aaaaaa=aaaba.

Reduce RHS:

[1]aa(aba)
⇒ aaa

Defines rule #1.