Certificate for #4833 ⟨a, b | ababbaab=aba⟩

Completion settings:

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

Axiom: ababbaab=aba.

Referenced by [3].

Axiom: aab=c.

Defines rule #6.

Referenced by [3], [4], [5], [6], [8], [9], [11].

Overlap of [1] ababbaab=aba with [2] aab=c:

Critical pair: ababbc=aba.

Defines rule #8.

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

Overlap of [2] aab=c with [3] ababbc=aba:

Critical pair: aaba=cabbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

Overlap of [3] ababbc=aba with [4] cabbc=ca:

Critical pair: ababbca=abaabbc.

Reduce LHS:

Reduce RHS:

Defines rule #9.

Referenced by [7], [11].

Overlap of [4] cabbc=ca with [4] cabbc=ca:

Critical pair: cabbca=caabbc.

Reduce LHS:

Reduce RHS:

Defines rule #5.

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

Overlap of [3] ababbc=aba with [6] caa=ccbc:

Critical pair: ababbccbc=abaaa.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [6] caa=ccbc with [2] aab=c:

Critical pair: cc=ccbcb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [10].

Overlap of [6] caa=ccbc with [2] aab=c:

Critical pair: cac=ccbcab.

Defines rule #2.

Overlap of [3] ababbc=aba with [8] ccbcb=cc:

Critical pair: ababbcc=abacbcb.

Reduce LHS:

Reduce RHS:

Defines rule #7.

Overlap of [5] abaa=abcbc with [2] aab=c:

Critical pair: abc=abcbcb.

Flip LHS and RHS.

Defines rule #4.