| Back: | ⟨a, b | aaba=b, bbbbbb=1⟩ |
|---|
Completion settings:
Axiom: aaba=b.
Referenced by [3], [5], [9], [12], [13], [14], [15], [16], [18], [19].
Axiom: bbbbbb=1.
Defines rule #3.
Referenced by [4], [6], [8], [9], [10], [11], [17], [22], [23].
Overlap of [1] aaba=b with [1] aaba=b:
Critical pair: aabb=baba.
Referenced by [4], [7], [9], [12], [19], [20].
Overlap of [3] aabb=baba with [2] bbbbbb=1:
Critical pair: aa=bababbbb.
Flip LHS and RHS.
Referenced by [5].
Overlap of [1] aaba=b with [4] bababbbb=aa:
Critical pair: aaaa=bbabbbb.
Flip LHS and RHS.
Referenced by [6].
Overlap of [2] bbbbbb=1 with [5] bbabbbb=aaaa:
Critical pair: bbbbaaaa=abbbb.
Flip LHS and RHS.
Overlap of [3] aabb=baba with [6] abbbb=bbbbaaaa:
Critical pair: abbbbaaaa=bababb.
Reduce LHS:
| [6] | (abbbb)aaaa |
| ⇒ bbbbaaaaaaaa |
Flip LHS and RHS.
Overlap of [2] bbbbbb=1 with [7] bababb=bbbbaaaaaaaa:
Critical pair: bbbbbbbbbaaaaaaaa=ababb.
Reduce LHS:
| [2] | (bbbbbb)bbbaaaaaaaa |
| ⇒ bbbaaaaaaaa |
Flip LHS and RHS.
Referenced by [11].
Overlap of [6] abbbb=bbbbaaaa with [7] bababb=bbbbaaaaaaaa:
Critical pair: abbbbbbbaaaaaaaa=bbbbaaaaababb.
Reduce LHS:
| [2] | a(bbbbbb)baaaaaaaa |
| ⇒ abaaaaaaaa |
Reduce RHS:
| [1] | bbbbaaa(aaba)bb |
| [3] | ⇒ bbbba(aabb)b |
| ⇒ bbbbababab |
Flip LHS and RHS.
Overlap of [2] bbbbbb=1 with [9] bbbbababab=abaaaaaaaa:
Critical pair: bbabaaaaaaaa=ababab.
Flip LHS and RHS.
Referenced by [12].
Overlap of [9] bbbbababab=abaaaaaaaa with [8] ababb=bbbaaaaaaaa:
Critical pair: bbbbabbbbaaaaaaaa=abaaaaaaaab.
Reduce LHS:
| [6] | bbbb(abbbb)aaaaaaaa |
| [2] | ⇒ (bbbbbb)bbaaaaaaaaaaaa |
| ⇒ bbaaaaaaaaaaaa |
Flip LHS and RHS.
Referenced by [13].
Overlap of [1] aaba=b with [10] ababab=bbabaaaaaaaa:
Critical pair: aabbbabaaaaaaaa=bbabab.
Reduce LHS:
| [3] | (aabb)babaaaaaaaa |
| [10] | ⇒ b(ababab)aaaaaaaa |
| ⇒ bbbabaaaaaaaaaaaaaaaa |
Flip LHS and RHS.
Referenced by [17].
Overlap of [11] abaaaaaaaab=bbaaaaaaaaaaaa with [1] aaba=b:
Critical pair: abaaaaaab=bbaaaaaaaaaaaaa.
Referenced by [14].
Overlap of [13] abaaaaaab=bbaaaaaaaaaaaaa with [1] aaba=b:
Critical pair: abaaaab=bbaaaaaaaaaaaaaa.
Referenced by [15].
Overlap of [14] abaaaab=bbaaaaaaaaaaaaaa with [1] aaba=b:
Critical pair: abaab=bbaaaaaaaaaaaaaaa.
Referenced by [16].
Overlap of [15] abaab=bbaaaaaaaaaaaaaaa with [1] aaba=b:
Critical pair: abb=bbaaaaaaaaaaaaaaaa.
Overlap of [2] bbbbbb=1 with [12] bbabab=bbbabaaaaaaaaaaaaaaaa:
Critical pair: bbbbbbbabaaaaaaaaaaaaaaaa=abab.
Reduce LHS:
| [2] | (bbbbbb)babaaaaaaaaaaaaaaaa |
| ⇒ babaaaaaaaaaaaaaaaa |
Flip LHS and RHS.
Overlap of [1] aaba=b with [17] abab=babaaaaaaaaaaaaaaaa:
Critical pair: ababaaaaaaaaaaaaaaaa=bb.
Reduce LHS:
| [17] | (abab)aaaaaaaaaaaaaaaa |
| ⇒ babaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa |
Referenced by [21].
Overlap of [1] aaba=b with [17] abab=babaaaaaaaaaaaaaaaa:
Critical pair: aabbabaaaaaaaaaaaaaaaa=bbab.
Reduce LHS:
| [3] | (aabb)abaaaaaaaaaaaaaaaa |
| [1] | ⇒ bab(aaba)aaaaaaaaaaaaaaa |
| [16] | ⇒ b(abb)aaaaaaaaaaaaaaa |
| ⇒ bbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa |
Flip LHS and RHS.
Referenced by [22].
Overlap of [3] aabb=baba with [16] abb=bbaaaaaaaaaaaaaaaa:
Critical pair: abbaaaaaaaaaaaaaaaa=baba.
Reduce LHS:
| [16] | (abb)aaaaaaaaaaaaaaaa |
| ⇒ bbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa |
Flip LHS and RHS.
Referenced by [21].
Overlap of [18] babaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=bb with [20] baba=bbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa:
Critical pair: bbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=bb.
Referenced by [23].
Overlap of [2] bbbbbb=1 with [19] bbab=bbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa:
Critical pair: bbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=ab.
Reduce LHS:
| [2] | (bbbbbb)baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa |
| ⇒ baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa |
Flip LHS and RHS.
Defines rule #2.
Overlap of [2] bbbbbb=1 with [21] bbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=bb:
Critical pair: bbbbbb=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.
Reduce LHS:
| [2] | (bbbbbb) |
| ⇒ 1 |
Flip LHS and RHS.
Defines rule #1.