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