Certificate for #1119 ⟨a, b | ababab=aba⟩

Completion settings:

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

Axiom: ababab=aba.

Referenced by [3].

Axiom: aba=c.

Defines rule #7.

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

Simplify [1] ababab=aba.

Reduce RHS:

Referenced by [4].

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

Critical pair: cbab=c.

Referenced by [6].

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

Critical pair: abc=cba.

Flip LHS and RHS.

Referenced by [6], [8].

Simplify [4] cbab=c.

Reduce LHS:

Referenced by [7], [9], [10].

Overlap of [2] aba=c with [6] abcb=c:

Critical pair: abc=cbcb.

Defines rule #4.

Referenced by [8], [9], [10], [11].

Simplify [5] cba=abc.

Reduce RHS:

Defines rule #6.

Referenced by [9], [11].

Overlap of [6] abcb=c with [8] cba=cbcb:

Critical pair: abcbcb=ca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [6] abcb=c with [7] abc=cbcb:

Critical pair: cbcbb=c.

Defines rule #2.

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

Overlap of [8] cba=cbcb with [7] abc=cbcb:

Critical pair: cbcbcb=cbcbbc.

Reduce RHS:

Defines rule #3.

Referenced by [12].

Overlap of [11] cbcbcb=cc with [10] cbcbb=c:

Critical pair: cbc=ccb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [13].

Simplify [9] ca=cbcbbcb.

Reduce RHS:

Defines rule #5.