WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: compS_f#1(compS_f(x2),x1) -> compS_f#1(x2,S(x1)) compS_f#1(id(),x3) -> S(x3) iter#3(0()) -> id() iter#3(S(x6)) -> compS_f(iter#3(x6)) main(0()) -> 0() main(S(x9)) -> compS_f#1(iter#3(x9),0()) - Signature: {compS_f#1/2,iter#3/1,main/1} / {0/0,S/1,compS_f/1,id/0} - Obligation: innermost runtime complexity wrt. defined symbols {compS_f#1,iter#3,main} and constructors {0,S,compS_f,id} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 1 S_0(2) -> 2 S_1(1) -> 1 S_1(2) -> 1 S_1(2) -> 3 S_1(3) -> 1 S_2(1) -> 1 S_2(1) -> 5 S_2(5) -> 1 compS_f_0(2) -> 2 compS_f_1(4) -> 1 compS_f_1(4) -> 4 compS_f#1_0(2,2) -> 1 compS_f#1_1(2,1) -> 1 compS_f#1_1(2,3) -> 1 compS_f#1_1(4,1) -> 1 compS_f#1_2(4,1) -> 1 compS_f#1_2(4,5) -> 1 id_0() -> 2 id_1() -> 1 id_1() -> 4 iter#3_0(2) -> 1 iter#3_1(2) -> 4 main_0(2) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: compS_f#1(compS_f(x2),x1) -> compS_f#1(x2,S(x1)) compS_f#1(id(),x3) -> S(x3) iter#3(0()) -> id() iter#3(S(x6)) -> compS_f(iter#3(x6)) main(0()) -> 0() main(S(x9)) -> compS_f#1(iter#3(x9),0()) - Signature: {compS_f#1/2,iter#3/1,main/1} / {0/0,S/1,compS_f/1,id/0} - Obligation: innermost runtime complexity wrt. defined symbols {compS_f#1,iter#3,main} and constructors {0,S,compS_f,id} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))