Certificate for #1902 ⟨a, b | aaababba=ab⟩

Completion settings:

• Auxiliary generators:
  1. c = ab
• Reduction order:
  • Right-to-left recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b

Axiom: aaababba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #1.

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

Simplify [1] aaababba=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaababba=c with [2] ab=c:

Critical pair: aacabba=c.

Reduce LHS:

Defines rule #7.

Referenced by [5], [6], [8], [10].

Overlap of [4] aaccba=c with [2] ab=c:

Critical pair: aaccbc=cb.

Defines rule #4.

Referenced by [6], [9], [12].

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

Critical pair: aaccbc=caccba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8], [9], [11].

Overlap of [6] caccba=cb with [2] ab=c:

Critical pair: caccbc=cbb.

Flip LHS and RHS.

Defines rule #2.

Overlap of [6] caccba=cb with [4] aaccba=c:

Critical pair: caccbc=cbaccba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [10], [11], [12], [13].

Overlap of [6] caccba=cb with [5] aaccbc=cb:

Critical pair: caccbcb=cbaccbc.

Defines rule #6.

Overlap of [4] aaccba=c with [8] cbaccba=caccbc:

Critical pair: aaccaccbc=cccba.

Defines rule #9.

Overlap of [6] caccba=cb with [8] cbaccba=caccbc:

Critical pair: caccaccbc=cbccba.

Defines rule #5.

Overlap of [8] cbaccba=caccbc with [5] aaccbc=cb:

Critical pair: cbaccbcb=caccbcaccbc.

Defines rule #11.

Overlap of [8] cbaccba=caccbc with [8] cbaccba=caccbc:

Critical pair: cbaccaccbc=caccbcccba.

Defines rule #10.