* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,y,z,u,v) -> if2(le(y,s(u)),x,y,s(z),s(u),v) if(true(),x,y,z,u,v) -> v if2(false(),x,y,z,u,v) -> quotIter(x,y,z,u,v) if2(true(),x,y,z,u,v) -> quotIter(x,y,z,0(),s(v)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) quot(x,0()) -> quotZeroErro() quot(x,s(y)) -> quotIter(x,s(y),0(),0(),0()) quotIter(x,s(y),z,u,v) -> if(le(x,z),x,s(y),z,u,v) - Signature: {if/6,if2/6,le/2,quot/2,quotIter/5} / {0/0,false/0,quotZeroErro/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,if2,le,quot,quotIter} and constructors {0,false ,quotZeroErro,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,y,z,u,v) -> if2(le(y,s(u)),x,y,s(z),s(u),v) if(true(),x,y,z,u,v) -> v if2(false(),x,y,z,u,v) -> quotIter(x,y,z,u,v) if2(true(),x,y,z,u,v) -> quotIter(x,y,z,0(),s(v)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) quot(x,0()) -> quotZeroErro() quot(x,s(y)) -> quotIter(x,s(y),0(),0(),0()) quotIter(x,s(y),z,u,v) -> if(le(x,z),x,s(y),z,u,v) - Signature: {if/6,if2/6,le/2,quot/2,quotIter/5} / {0/0,false/0,quotZeroErro/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,if2,le,quot,quotIter} and constructors {0,false ,quotZeroErro,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),?)