* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(x,s(y)) -> g(f(x,y),0()) g(0(),f(x,x)) -> x g(f(x,y),0()) -> f(g(x,0()),g(y,0())) g(s(x),y) -> g(f(x,y),0()) - Signature: {g/2} / {0/0,f/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {0,f,s} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 3 0_1() -> 6 0_2() -> 11 0_2() -> 12 f_0(1,1) -> 2 f_0(1,1) -> 3 f_0(1,2) -> 2 f_0(1,2) -> 3 f_0(1,4) -> 2 f_0(1,4) -> 3 f_0(2,1) -> 2 f_0(2,1) -> 3 f_0(2,2) -> 2 f_0(2,2) -> 3 f_0(2,4) -> 2 f_0(2,4) -> 3 f_0(4,1) -> 2 f_0(4,1) -> 3 f_0(4,2) -> 2 f_0(4,2) -> 3 f_0(4,4) -> 2 f_0(4,4) -> 3 f_1(1,1) -> 5 f_1(1,2) -> 5 f_1(1,4) -> 5 f_1(1,6) -> 1 f_1(1,6) -> 3 f_1(1,12) -> 13 f_1(2,1) -> 5 f_1(2,2) -> 5 f_1(2,4) -> 5 f_1(2,6) -> 1 f_1(2,6) -> 3 f_1(2,12) -> 13 f_1(4,1) -> 5 f_1(4,2) -> 5 f_1(4,4) -> 5 f_1(4,6) -> 1 f_1(4,6) -> 3 f_1(4,12) -> 13 f_1(7,8) -> 3 f_1(8,8) -> 3 f_1(8,8) -> 8 f_1(8,8) -> 10 f_2(9,10) -> 3 f_2(10,10) -> 3 f_2(10,14) -> 7 f_2(10,14) -> 8 f_2(10,14) -> 9 f_2(10,14) -> 10 g_0(1,1) -> 3 g_0(1,2) -> 3 g_0(1,4) -> 3 g_0(2,1) -> 3 g_0(2,2) -> 3 g_0(2,4) -> 3 g_0(4,1) -> 3 g_0(4,2) -> 3 g_0(4,4) -> 3 g_1(1,6) -> 7 g_1(1,6) -> 8 g_1(2,6) -> 8 g_1(4,6) -> 8 g_1(5,6) -> 3 g_1(6,6) -> 8 g_1(13,6) -> 10 g_2(1,11) -> 9 g_2(1,12) -> 10 g_2(2,12) -> 10 g_2(4,12) -> 10 g_2(6,12) -> 14 g_2(12,12) -> 14 s_0(1) -> 3 s_0(1) -> 4 s_0(2) -> 3 s_0(2) -> 4 s_0(4) -> 3 s_0(4) -> 4 1 -> 3 2 -> 3 4 -> 3 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: g(x,s(y)) -> g(f(x,y),0()) g(0(),f(x,x)) -> x g(f(x,y),0()) -> f(g(x,0()),g(y,0())) g(s(x),y) -> g(f(x,y),0()) - Signature: {g/2} / {0/0,f/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {0,f,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))