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