Certificate for #1105 ⟨a, b | abaaab=aba⟩

Completion settings:

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

Axiom: abaaab=aba.

Referenced by [3].

Axiom: abaa=c.

Referenced by [3], [4].

Overlap of [1] abaaab=aba with [2] abaa=c:

Critical pair: cab=aba.

Flip LHS and RHS.

Referenced by [4], [5], [6], [7], [8], [10].

Overlap of [2] abaa=c with [3] aba=cab:

Critical pair: caba=c.

Reduce LHS:

Referenced by [6], [7], [11].

Overlap of [3] aba=cab with [3] aba=cab:

Critical pair: abcab=cabba.

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] ccab=c with [3] aba=cab:

Critical pair: cccab=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [9], [10], [11].

Overlap of [6] ca=cc with [3] aba=cab:

Critical pair: ccab=ccba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [7] ccba=c with [3] aba=cab:

Critical pair: ccbcab=cba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [5] cabba=abcab.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Simplify [3] aba=cab.

Reduce RHS:

Defines rule #5.

Overlap of [4] ccab=c with [6] ca=cc:

Critical pair: cccb=c.

Defines rule #1.