117.44/30.64 MAYBE 117.44/30.64 117.44/30.64 Proof: 117.44/30.64 ConCon could not decide confluence of the system. 117.44/30.64 \cite{ALS94}, Theorem 4.1 does not apply. 117.44/30.64 This system is of type 3 or smaller. 117.44/30.64 This system is strongly deterministic. 117.44/30.64 This system is of type 3 or smaller. 117.44/30.64 This system is deterministic. 117.44/30.64 ConCon could not decide if this system is quasi-decreasing. 117.44/30.64 \cite{O02}, p. 214, Proposition 7.2.50 does not apply. 117.44/30.64 This system is of type 3 or smaller. 117.44/30.64 This system is deterministic. 117.44/30.64 System R transformed to U(R). 117.44/30.64 The external tool could not decide termination of the system. 117.44/30.64 Call external tool: 117.44/30.64 ./ttt2.sh 117.44/30.64 Input: 117.44/30.64 fstsplit(0, x) -> nil 117.44/30.64 fstsplit(s(n), nil) -> nil 117.44/30.64 fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) 117.44/30.64 sndsplit(0, x) -> x 117.44/30.64 sndsplit(s(n), nil) -> nil 117.44/30.64 sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) 117.44/30.64 empty(nil) -> true 117.44/30.64 empty(cons(h, t)) -> false 117.44/30.64 leq(0, m) -> true 117.44/30.64 leq(s(n), 0) -> false 117.44/30.64 leq(s(n), s(m)) -> leq(n, m) 117.44/30.64 length(nil) -> 0 117.44/30.64 length(cons(h, t)) -> s(length(t)) 117.44/30.64 app(nil, x) -> x 117.44/30.64 app(cons(h, t), x) -> cons(h, app(t, x)) 117.44/30.64 map_f(pid, nil) -> nil 117.44/30.64 map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) 117.44/30.64 head(cons(h, t)) -> h 117.44/30.64 tail(cons(h, t)) -> t 117.44/30.64 ?1(false, st_2, in_2, st_3, m, st_1, in_3) -> ring(sndsplit(m, st_1), cons(fstsplit(m, st_1), in_2), st_2, in_3, st_3, m) 117.44/30.64 ring(st_1, in_2, st_2, in_3, st_3, m) -> ?1(empty(fstsplit(m, st_1)), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ?11(false, st_2, in_2, st_3, m, st_1, in_3) -> ring(st_1, in_2, sndsplit(m, st_2), cons(fstsplit(m, st_2), in_3), st_3, m) 117.44/30.64 ?10(true, st_2, in_2, st_3, m, st_1, in_3) -> ?11(empty(fstsplit(m, st_2)), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ring(st_1, in_2, st_2, in_3, st_3, m) -> ?10(leq(m, length(st_2)), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ?3(false, st_2, in_2, st_3, m, st_1, in_3) -> ring(st_1, tail(in_2), sndsplit(m, app(map_f(two, head(in_2)), st_2)), cons(fstsplit(m, app(map_f(two, head(in_2)), st_2)), in_3), st_3, m) 117.44/30.64 ?2(false, st_2, in_2, st_3, m, st_1, in_3) -> ?3(empty(fstsplit(m, app(map_f(two, head(in_2)), st_2))), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ring(st_1, in_2, st_2, in_3, st_3, m) -> ?2(leq(m, length(st_2)), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ?4(true, st_2, in_2, st_3, m, st_1, in_3) -> ring(st_1, tail(in_2), st_2, in_3, st_3, m) 117.44/30.64 ring(st_1, in_2, st_2, in_3, st_3, m) -> ?4(empty(map_f(two, head(in_2))), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ?6(false, st_2, in_2, st_3, m, st_1, in_3) -> ring(st_1, in_2, st_2, in_3, sndsplit(m, st_3), m) 117.44/30.64 ?5(true, st_2, in_2, st_3, m, st_1, in_3) -> ?6(empty(fstsplit(m, st_3)), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ring(st_1, in_2, st_2, in_3, st_3, m) -> ?5(leq(m, length(st_3)), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ?8(false, st_2, in_2, st_3, m, st_1, in_3) -> ring(st_1, in_2, st_2, tail(in_3), sndsplit(m, app(map_f(three, head(in_3)), st_3)), m) 117.44/30.64 ?7(false, st_2, in_2, st_3, m, st_1, in_3) -> ?8(empty(fstsplit(m, app(map_f(three, head(in_3)), st_3))), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ring(st_1, in_2, st_2, in_3, st_3, m) -> ?7(leq(m, length(st_3)), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 ?9(true, st_2, in_2, st_3, m, st_1, in_3) -> ring(st_1, in_2, st_2, tail(in_3), st_3, m) 117.44/30.64 ring(st_1, in_2, st_2, in_3, st_3, m) -> ?9(empty(map_f(three, head(in_3))), st_2, in_2, st_3, m, st_1, in_3) 117.44/30.64 117.44/30.64 117.44/30.66 EOF