Certificate for #16443 ⟨a, b | aba=bb, aaab=bb⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(a) = 0; deg(b) = 1

Axiom: aba=bb.

Flip LHS and RHS.

Referenced by [2], [3].

Axiom: aaab=bb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [5], [6], [7], [8], [9].

Simplify [1] bb=aba.

Reduce RHS:

Defines rule #3.

Referenced by [4], [5], [6], [7], [9].

Overlap of [3] bb=aaab with [3] bb=aaab:

Critical pair: baaab=aaabb.

Reduce RHS:

Defines rule #4.

Referenced by [6], [7], [8].

Overlap of [2] aba=aaab with [2] aba=aaab:

Critical pair: abaaab=aaabba.

Reduce LHS:

Reduce RHS:

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

Overlap of [3] bb=aaab with [4] baaab=aaaaaab:

Critical pair: baaaaaab=aaabaaab.

Reduce RHS:

Referenced by [10].

Overlap of [2] aba=aaab with [4] baaab=aaaaaab:

Critical pair: aaaaaaab=aaabaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

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

Overlap of [4] baaab=aaaaaab with [2] aba=aaab:

Critical pair: baaaaab=aaaaaaba.

Reduce RHS:

Defines rule #5.

Referenced by [9].

Overlap of [3] bb=aaab with [8] baaaaab=aaaaaaab:

Critical pair: baaaaaaab=aaabaaaaab.

Reduce RHS:

Defines rule #7.

Simplify [6] baaaaaab=aaaaaaaab.

Reduce RHS:

Defines rule #6.