Certificate for #2323 ⟨a, b | ababaab=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: ababaab=aba.

Referenced by [3].

Axiom: aba=c.

Defines rule #5.

Referenced by [3], [4], [5], [7], [8], [10], [12].

Simplify [1] ababaab=aba.

Reduce RHS:

Referenced by [4].

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

Critical pair: cbaab=c.

Referenced by [6].

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

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [9].

Simplify [4] cbaab=c.

Reduce LHS:

Referenced by [7], [8], [12].

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

Critical pair: abc=cbcab.

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: abcc=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [9], [12].

Simplify [7] cbcab=abc.

Reduce LHS:

Referenced by [10].

Overlap of [2] aba=c with [9] abcbccb=abc:

Critical pair: ababc=cbcbccb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [10] cbcbccb=cbc with [10] cbcbccb=cbc:

Critical pair: cbcbccbc=cbccbccb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [6] abcab=c with [8] ca=abcc:

Critical pair: ababccb=c.

Reduce LHS:

Defines rule #2.

Referenced by [13].

Overlap of [11] cbccbccb=cbcc with [12] cbccb=c:

Critical pair: cccb=cbcc.

Defines rule #1.