* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if_quot(x,y,false(),false()) -> 0() if_quot(x,y,false(),true()) -> s(quot(x,y)) if_quot(x,y,true(),z) -> divByZeroError() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,x) -> 0() minus(x,0()) -> x minus(0(),x) -> 0() minus(s(x),s(y)) -> minus(x,y) quot(x,y) -> if_quot(minus(x,y),y,le(y,0()),le(y,x)) - Signature: {if_quot/4,le/2,minus/2,quot/2} / {0/0,divByZeroError/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if_quot,le,minus,quot} and constructors {0,divByZeroError ,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if_quot(x,y,false(),false()) -> 0() if_quot(x,y,false(),true()) -> s(quot(x,y)) if_quot(x,y,true(),z) -> divByZeroError() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,x) -> 0() minus(x,0()) -> x minus(0(),x) -> 0() minus(s(x),s(y)) -> minus(x,y) quot(x,y) -> if_quot(minus(x,y),y,le(y,0()),le(y,x)) - Signature: {if_quot/4,le/2,minus/2,quot/2} / {0/0,divByZeroError/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if_quot,le,minus,quot} and constructors {0,divByZeroError ,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: le(x,y){x -> s(x),y -> s(y)} = le(s(x),s(y)) ->^+ le(x,y) = C[le(x,y) = le(x,y){}] WORST_CASE(Omega(n^1),?)