Certificate for #4813 ⟨a, b | ababaaab=aba⟩

Completion settings:

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

Axiom: ababaaab=aba.

Referenced by [3].

Axiom: abaa=c.

Defines rule #9.

Referenced by [3], [4], [5], [6], [7].

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

Critical pair: abcab=aba.

Referenced by [5], [6], [7], [11].

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

Critical pair: abac=cbaa.

Flip LHS and RHS.

Defines rule #8.

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

Critical pair: abaaba=cbcab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: abcc=abaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

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

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

Critical pair: abcaba=abacab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [10], [12].

Overlap of [7] cbccb=c with [7] cbccb=c:

Critical pair: cbcc=cccb.

Flip LHS and RHS.

Defines rule #1.

Simplify [5] cbcab=cba.

Reduce LHS:

Defines rule #5.

Referenced by [10].

Overlap of [9] cbabccb=cba with [7] cbccb=c:

Critical pair: cbabcc=cbaccb.

Flip LHS and RHS.

Defines rule #4.

Overlap of [3] abcab=aba with [6] ca=abcc:

Critical pair: ababccb=aba.

Defines rule #7.

Referenced by [12].

Overlap of [11] ababccb=aba with [7] cbccb=c:

Critical pair: ababcc=abaccb.

Flip LHS and RHS.

Defines rule #6.