* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) quot(x,0(),s(z)) -> s(quot(x,plus(z,s(0())),s(z))) quot(0(),s(y),s(z)) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {plus/2,quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {plus,quot} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) quot(x,0(),s(z)) -> s(quot(x,plus(z,s(0())),s(z))) quot(0(),s(y),s(z)) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {plus/2,quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {plus,quot} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: plus(x,y){x -> s(x)} = plus(s(x),y) ->^+ s(plus(x,y)) = C[plus(x,y) = plus(x,y){}] WORST_CASE(Omega(n^1),?)