Certificate for #4726 ⟨a, b | aabbbaba=abb⟩

Completion settings:

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

Axiom: aabbbaba=abb.

Referenced by [3].

Axiom: abb=c.

Defines rule #1.

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

Simplify [1] aabbbaba=abb.

Reduce RHS:

Referenced by [4].

Overlap of [3] aabbbaba=c with [2] abb=c:

Critical pair: acbaba=c.

Defines rule #2.

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

Overlap of [4] acbaba=c with [2] abb=c:

Critical pair: acbabc=cbb.

Defines rule #4.

Referenced by [6], [9].

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

Critical pair: acbabc=ccbaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [6] ccbaba=cbb with [2] abb=c:

Critical pair: ccbabc=cbbbb.

Flip LHS and RHS.

Defines rule #5.

Overlap of [6] ccbaba=cbb with [4] acbaba=c:

Critical pair: ccbabc=cbbcbaba.

Flip LHS and RHS.

Defines rule #6.

Overlap of [6] ccbaba=cbb with [5] acbabc=cbb:

Critical pair: ccbabcbb=cbbcbabc.

Flip LHS and RHS.

Defines rule #7.