Certificate for #4843 ⟨a, b | ababbaba=bab⟩

Completion settings:

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

Axiom: ababbaba=bab.

Referenced by [3].

Axiom: bbaba=c.

Referenced by [3], [4].

Overlap of [1] ababbaba=bab with [2] bbaba=c:

Critical pair: abac=bab.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [2] bbaba=c with [3] bab=abac:

Critical pair: babaca=c.

Reduce LHS:

Defines rule #4.

Referenced by [6], [7], [9], [10], [11].

Overlap of [3] bab=abac with [3] bab=abac:

Critical pair: baabac=abacab.

Defines rule #6.

Referenced by [9].

Overlap of [3] bab=abac with [4] abacaca=c:

Critical pair: bc=abacacaca.

Reduce RHS:

Defines rule #1.

Referenced by [8].

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

Critical pair: abacacc=cbacaca.

Defines rule #7.

Overlap of [3] bab=abac with [6] bc=cca:

Critical pair: bacca=abacc.

Flip LHS and RHS.

Defines rule #3.

Overlap of [5] baabac=abacab with [4] abacaca=c:

Critical pair: bac=abacabaca.

Flip LHS and RHS.

Defines rule #9.

Referenced by [10], [11], [12].

Overlap of [3] bab=abac with [9] abacabaca=bac:

Critical pair: bbac=abacacabaca.

Reduce RHS:

Defines rule #5.

Overlap of [4] abacaca=c with [9] abacabaca=bac:

Critical pair: abacacbac=cbacabaca.

Defines rule #10.

Overlap of [9] abacabaca=bac with [9] abacabaca=bac:

Critical pair: abacbac=bacbaca.

Defines rule #8.