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