Certificate for #2247 ⟨a, b, c | abab=1, bcbc=1⟩

Back:⟨a, b, c | abab=1, bcbc=1⟩

Completion settings:

[1] abab=1

Axiom: abab=1.

Defines rule #2.

Referenced by [3], [4].

[2] bcbc=1

Axiom: bcbc=1.

Referenced by [3], [5].

[3] cbc=aba

Overlap of [1] abab=1 with [2] bcbc=1:

aba b bcbc

Critical pair: aba=cbc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] cbaba=c

Overlap of [3] cbc=aba with [3] cbc=aba:

cb c cbc

Critical pair: cbaba=ababc.

Reduce RHS:

[1](abab)c
⇒ c

Referenced by [5].

[5] baba=1

Overlap of [2] bcbc=1 with [4] cbaba=c:

bcb c cbaba

Critical pair: bcbc=baba.

Reduce LHS:

[2](bcbc)
⇒ 1

Flip LHS and RHS.

Defines rule #3.