Certificate for #4821 ⟨a, b | abababab=aba⟩

Back:⟨a, b | abababab=aba⟩

Completion settings:

[1] abababab=aba

Axiom: abababab=aba.

Referenced by [3].

[2] aba=c

Axiom: aba=c.

Defines rule #5.

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

[3] abababab=c

Simplify [1] abababab=aba.

Reduce RHS:

[2](aba)
⇒ c

Referenced by [4].

[4] cbcb=c

Overlap of [3] abababab=c with [2] aba=c:

abababab aba

Critical pair: cbabab=c.

Reduce LHS:

[2]cb(aba)b
⇒ cbcb

Defines rule #2.

Referenced by [6], [7].

[5] cba=abc

Overlap of [2] aba=c with [2] aba=c:

ab a aba

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

[6] ccb=cbc

Overlap of [4] cbcb=c with [4] cbcb=c:

cb cb cbcb

Critical pair: cbc=ccb.

Flip LHS and RHS.

Defines rule #1.

[7] ca=abcbc

Overlap of [4] cbcb=c with [5] cba=abc:

cb cb cba

Critical pair: cbabc=ca.

Reduce LHS:

[5](cba)bc
⇒ abcbc

Flip LHS and RHS.

Defines rule #3.