Certificate for #4769 ⟨a, b | abaaabab=aba⟩

Completion settings:

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

Axiom: abaaabab=aba.

Referenced by [3].

Axiom: abaaa=c.

Referenced by [3], [4].

Overlap of [1] abaaabab=aba with [2] abaaa=c:

Critical pair: cbab=aba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5], [6], [7], [11].

Overlap of [2] abaaa=c with [3] aba=cbab:

Critical pair: cbabaa=c.

Reduce LHS:

Referenced by [6], [9].

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

Critical pair: abcbab=cbabba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8], [12].

Overlap of [4] cbcbcbab=c with [3] aba=cbab:

Critical pair: cbcbcbcbab=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [12].

Overlap of [6] ca=cbc with [3] aba=cbab:

Critical pair: ccbab=cbcba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9], [10], [11], [12].

Overlap of [7] cbcba=ccbab with [5] cbabba=abcbab:

Critical pair: cbabcbab=ccbabbba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [10].

Overlap of [4] cbcbcbab=c with [7] cbcba=ccbab:

Critical pair: cbccbabb=c.

Defines rule #5.

Referenced by [10], [12].

Overlap of [9] cbccbabb=c with [8] ccbabbba=cbabcbab:

Critical pair: cbcbabcbab=cba.

Reduce LHS:

Referenced by [11], [13], [14].

Overlap of [10] ccbabbcbab=cba with [3] aba=cbab:

Critical pair: ccbabbcbcbab=cbaa.

Reduce LHS:

Defines rule #10.

Referenced by [12], [13].

Overlap of [11] ccbabbccbabb=cbaa with [5] cbabba=abcbab:

Critical pair: ccbabbcabcbab=cbaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [11] ccbabbccbabb=cbaa with [10] ccbabbcbab=cba:

Critical pair: ccbabbcba=cbaacbab.

Defines rule #8.

Referenced by [14].

Overlap of [10] ccbabbcbab=cba with [13] ccbabbcba=cbaacbab:

Critical pair: cbaacbabb=cba.

Defines rule #9.