Certificate for #2322 ⟨a, b | ababaab=aab⟩

Back:⟨a, b | ababaab=aab⟩

Completion settings:

[1] ababaab=aab

Axiom: ababaab=aab.

Referenced by [3].

[2] ababa=c

Axiom: ababa=c.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7].

[3] aab=cab

Overlap of [1] ababaab=aab with [2] ababa=c:

ababaab ababa

Critical pair: cab=aab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6].

[4] abc=cba

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

ab aba ababa

Critical pair: abc=cba.

Defines rule #3.

Referenced by [5], [7].

[5] cbcbcab=cab

Overlap of [2] ababa=c with [3] aab=cab:

abab a aab

Critical pair: ababcab=cab.

Reduce LHS:

[4]ab(abc)ab
[4]⇒ (abc)baab
[3]⇒ cbab(aab)
[4]⇒ cb(abc)ab
[3]⇒ cbcb(aab)
⇒ cbcbcab

Defines rule #6.

[6] ac=cc

Overlap of [3] aab=cab with [2] ababa=c:

a ab ababa

Critical pair: ac=cababa.

Reduce RHS:

[2]c(ababa)
⇒ cc

Defines rule #1.

Referenced by [7].

[7] cbcbcc=cc

Overlap of [2] ababa=c with [6] ac=cc:

abab a ac

Critical pair: ababcc=cc.

Reduce LHS:

[4]ab(abc)c
[4]⇒ (abc)bac
[6]⇒ cbab(ac)
[4]⇒ cb(abc)c
[6]⇒ cbcb(ac)
⇒ cbcbcc

Defines rule #5.