YES
0 QTRS
↳1 QTRSRRRProof (⇔, 0 ms)
↳2 QTRS
↳3 RisEmptyProof (⇔, 0 ms)
↳4 YES
.(1, x) → x
.(x, 1) → x
.(i(x), x) → 1
.(x, i(x)) → 1
i(1) → 1
i(i(x)) → x
.(i(y), .(y, z)) → z
.(y, .(i(y), z)) → z
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
POL(.(x1, x2)) = 2 + 2·x1 + 2·x2
POL(1) = 2
POL(i(x1)) = 2 + x1
.(1, x) → x
.(x, 1) → x
.(i(x), x) → 1
.(x, i(x)) → 1
i(1) → 1
i(i(x)) → x
.(i(y), .(y, z)) → z
.(y, .(i(y), z)) → z