Certificate for #4136 ⟨a, b | aababbaba=ab⟩

Completion settings:

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

Axiom: aababbaba=ab.

Referenced by [3].

Axiom: bbaba=c.

Defines rule #12.

Referenced by [3], [4], [7], [8], [9], [10], [11], [12], [13], [14].

Overlap of [1] aababbaba=ab with [2] bbaba=c:

Critical pair: aabac=ab.

Defines rule #3.

Referenced by [4], [5].

Overlap of [2] bbaba=c with [3] aabac=ab:

Critical pair: bbabab=cabac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [3] aabac=ab with [4] cabac=cb:

Critical pair: aabacb=ababac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [7], [8].

Overlap of [4] cabac=cb with [4] cabac=cb:

Critical pair: cabacb=cbabac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [2] bbaba=c with [5] ababac=abb:

Critical pair: bbabb=cbac.

Defines rule #13.

Referenced by [14].

Overlap of [5] ababac=abb with [4] cabac=cb:

Critical pair: ababacb=abbabac.

Reduce LHS:

Reduce RHS:

Defines rule #10.

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

Overlap of [2] bbaba=c with [8] abbb=acc:

Critical pair: bbabacc=cbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [12], [13].

Overlap of [8] abbb=acc with [2] bbaba=c:

Critical pair: abc=accaba.

Defines rule #1.

Overlap of [8] abbb=acc with [2] bbaba=c:

Critical pair: abbc=accbaba.

Defines rule #5.

Overlap of [9] cbbb=ccc with [2] bbaba=c:

Critical pair: cbc=cccaba.

Defines rule #2.

Overlap of [9] cbbb=ccc with [2] bbaba=c:

Critical pair: cbbc=cccbaba.

Defines rule #6.

Overlap of [7] bbabb=cbac with [2] bbaba=c:

Critical pair: bbac=cbacaba.

Defines rule #7.