* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: ack_in(0(),n) -> ack_out(s(n)) ack_in(s(m),0()) -> u11(ack_in(m,s(0()))) ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m) u11(ack_out(n)) -> ack_out(n) u21(ack_out(n),m) -> u22(ack_in(m,n)) u22(ack_out(n)) -> ack_out(n) - Signature: {ack_in/2,u11/1,u21/2,u22/1} / {0/0,ack_out/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {ack_in,u11,u21,u22} and constructors {0,ack_out,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: ack_in(0(),n) -> ack_out(s(n)) ack_in(s(m),0()) -> u11(ack_in(m,s(0()))) ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m) u11(ack_out(n)) -> ack_out(n) u21(ack_out(n),m) -> u22(ack_in(m,n)) u22(ack_out(n)) -> ack_out(n) - Signature: {ack_in/2,u11/1,u21/2,u22/1} / {0/0,ack_out/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {ack_in,u11,u21,u22} and constructors {0,ack_out,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ack_in(s(x),y){y -> s(y)} = ack_in(s(x),s(y)) ->^+ u21(ack_in(s(x),y),x) = C[ack_in(s(x),y) = ack_in(s(x),y){}] WORST_CASE(Omega(n^1),?)