* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: h(x,c(y,z)) -> h(c(s(y),x),z) h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z))) - Signature: {h/2} / {0/0,c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {0,c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: h(x,c(y,z)) -> h(c(s(y),x),z) h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z))) - Signature: {h/2} / {0/0,c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {0,c,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: h(x,z){z -> c(y,z)} = h(x,c(y,z)) ->^+ h(c(s(y),x),z) = C[h(c(s(y),x),z) = h(x,z){x -> c(s(y),x)}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: h(x,c(y,z)) -> h(c(s(y),x),z) h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z))) - Signature: {h/2} / {0/0,c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {0,c,s} + 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() -> 8 c_0(2,2) -> 2 c_1(2,2) -> 7 c_1(2,5) -> 7 c_1(4,2) -> 3 c_1(4,3) -> 3 c_1(4,11) -> 3 c_1(6,5) -> 5 c_1(6,7) -> 5 c_2(10,2) -> 9 c_2(10,3) -> 9 c_2(10,9) -> 9 c_2(10,11) -> 9 c_2(12,9) -> 11 h_0(2,2) -> 1 h_1(2,5) -> 1 h_1(3,2) -> 1 h_1(3,5) -> 1 h_1(9,5) -> 1 h_1(11,5) -> 1 h_2(9,5) -> 1 h_2(9,7) -> 1 h_2(11,2) -> 1 h_2(11,5) -> 1 s_0(2) -> 2 s_1(2) -> 4 s_1(8) -> 6 s_2(2) -> 12 s_2(6) -> 10 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: h(x,c(y,z)) -> h(c(s(y),x),z) h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z))) - Signature: {h/2} / {0/0,c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {0,c,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))