MAYBE TRS: { *(x, *(y, z)) -> *(*(x, y), z), *(x, 1()) -> x, *(x, i(x)) -> 1(), *(*(x, y), i(y)) -> x, *(*(x, i(y)), y) -> x, *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)), *(1(), y) -> y, *(i(x), x) -> 1(), *(k(x, y), k(y, x)) -> 1(), i(*(x, y)) -> *(i(y), i(x)), i(1()) -> 1(), i(i(x)) -> x, k(x, x) -> 1(), k(x, 1()) -> 1(), k(*(x, i(y)), *(y, i(x))) -> 1()} DP: Strict: { *#(x, *(y, z)) -> *#(x, y), *#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x)), i#(*(x, y)) -> *#(i(y), i(x)), i#(*(x, y)) -> i#(x), i#(*(x, y)) -> i#(y)} Weak: { *(x, *(y, z)) -> *(*(x, y), z), *(x, 1()) -> x, *(x, i(x)) -> 1(), *(*(x, y), i(y)) -> x, *(*(x, i(y)), y) -> x, *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)), *(1(), y) -> y, *(i(x), x) -> 1(), *(k(x, y), k(y, x)) -> 1(), i(*(x, y)) -> *(i(y), i(x)), i(1()) -> 1(), i(i(x)) -> x, k(x, x) -> 1(), k(x, 1()) -> 1(), k(*(x, i(y)), *(y, i(x))) -> 1()} EDG: {(i#(*(x, y)) -> *#(i(y), i(x)), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x))) (i#(*(x, y)) -> *#(i(y), i(x)), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)) (i#(*(x, y)) -> *#(i(y), i(x)), *#(*(i(x), k(y, z)), x) -> *#(i(x), y)) (i#(*(x, y)) -> *#(i(y), i(x)), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x)) (i#(*(x, y)) -> *#(i(y), i(x)), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x)) (i#(*(x, y)) -> *#(i(y), i(x)), *#(x, *(y, z)) -> *#(*(x, y), z)) (i#(*(x, y)) -> *#(i(y), i(x)), *#(x, *(y, z)) -> *#(x, y)) (*#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x))) (*#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)) (*#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> *#(i(x), y)) (*#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x)) (*#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x)) (*#(x, *(y, z)) -> *#(*(x, y), z), *#(x, *(y, z)) -> *#(*(x, y), z)) (*#(x, *(y, z)) -> *#(*(x, y), z), *#(x, *(y, z)) -> *#(x, y)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x))) (*#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> *#(i(x), y)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(x, *(y, z)) -> *#(*(x, y), z)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(x, *(y, z)) -> *#(x, y)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x))) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> *#(i(x), y)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(x, *(y, z)) -> *#(*(x, y), z)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(x, *(y, z)) -> *#(x, y)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(x, *(y, z)) -> *#(x, y)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(x, *(y, z)) -> *#(*(x, y), z)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> *#(i(x), y)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)) (*#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x))) (*#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(x, *(y, z)) -> *#(x, y)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(x, *(y, z)) -> *#(*(x, y), z)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(*(i(x), k(y, z)), x) -> *#(i(x), y)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)) (*#(*(i(x), k(y, z)), x) -> *#(i(x), z), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x))) (*#(x, *(y, z)) -> *#(x, y), *#(x, *(y, z)) -> *#(x, y)) (*#(x, *(y, z)) -> *#(x, y), *#(x, *(y, z)) -> *#(*(x, y), z)) (*#(x, *(y, z)) -> *#(x, y), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x)) (*#(x, *(y, z)) -> *#(x, y), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x)) (*#(x, *(y, z)) -> *#(x, y), *#(*(i(x), k(y, z)), x) -> *#(i(x), y)) (*#(x, *(y, z)) -> *#(x, y), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)) (*#(x, *(y, z)) -> *#(x, y), *#(*(i(x), k(y, z)), x) -> k#(*(*(i(x), y), x), *(*(i(x), z), x))) (i#(*(x, y)) -> i#(y), i#(*(x, y)) -> *#(i(y), i(x))) (i#(*(x, y)) -> i#(y), i#(*(x, y)) -> i#(x)) (i#(*(x, y)) -> i#(y), i#(*(x, y)) -> i#(y)) (i#(*(x, y)) -> i#(x), i#(*(x, y)) -> *#(i(y), i(x))) (i#(*(x, y)) -> i#(x), i#(*(x, y)) -> i#(x)) (i#(*(x, y)) -> i#(x), i#(*(x, y)) -> i#(y))} SCCS: Scc: {i#(*(x, y)) -> i#(x), i#(*(x, y)) -> i#(y)} Scc: { *#(x, *(y, z)) -> *#(x, y), *#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)} SCC: Strict: {i#(*(x, y)) -> i#(x), i#(*(x, y)) -> i#(y)} Weak: { *(x, *(y, z)) -> *(*(x, y), z), *(x, 1()) -> x, *(x, i(x)) -> 1(), *(*(x, y), i(y)) -> x, *(*(x, i(y)), y) -> x, *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)), *(1(), y) -> y, *(i(x), x) -> 1(), *(k(x, y), k(y, x)) -> 1(), i(*(x, y)) -> *(i(y), i(x)), i(1()) -> 1(), i(i(x)) -> x, k(x, x) -> 1(), k(x, 1()) -> 1(), k(*(x, i(y)), *(y, i(x))) -> 1()} SPSC: Simple Projection: pi(i#) = 0 Strict: {i#(*(x, y)) -> i#(y)} EDG: {(i#(*(x, y)) -> i#(y), i#(*(x, y)) -> i#(y))} SCCS: Scc: {i#(*(x, y)) -> i#(y)} SCC: Strict: {i#(*(x, y)) -> i#(y)} Weak: { *(x, *(y, z)) -> *(*(x, y), z), *(x, 1()) -> x, *(x, i(x)) -> 1(), *(*(x, y), i(y)) -> x, *(*(x, i(y)), y) -> x, *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)), *(1(), y) -> y, *(i(x), x) -> 1(), *(k(x, y), k(y, x)) -> 1(), i(*(x, y)) -> *(i(y), i(x)), i(1()) -> 1(), i(i(x)) -> x, k(x, x) -> 1(), k(x, 1()) -> 1(), k(*(x, i(y)), *(y, i(x))) -> 1()} SPSC: Simple Projection: pi(i#) = 0 Strict: {} Qed SCC: Strict: { *#(x, *(y, z)) -> *#(x, y), *#(x, *(y, z)) -> *#(*(x, y), z), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), y), x), *#(*(i(x), k(y, z)), x) -> *#(*(i(x), z), x), *#(*(i(x), k(y, z)), x) -> *#(i(x), y), *#(*(i(x), k(y, z)), x) -> *#(i(x), z)} Weak: { *(x, *(y, z)) -> *(*(x, y), z), *(x, 1()) -> x, *(x, i(x)) -> 1(), *(*(x, y), i(y)) -> x, *(*(x, i(y)), y) -> x, *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)), *(1(), y) -> y, *(i(x), x) -> 1(), *(k(x, y), k(y, x)) -> 1(), i(*(x, y)) -> *(i(y), i(x)), i(1()) -> 1(), i(i(x)) -> x, k(x, x) -> 1(), k(x, 1()) -> 1(), k(*(x, i(y)), *(y, i(x))) -> 1()} Fail