* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond(false(),x,y,z) -> 0() cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z))) d(x,s(y),z) -> cond(ge(x,z),x,y,z) div(x,s(y)) -> d(x,s(y),0()) ge(u,0()) -> true() ge(0(),s(v)) -> false() ge(s(u),s(v)) -> ge(u,v) plus(n,0()) -> n plus(n,s(m)) -> s(plus(n,m)) - Signature: {cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond,d,div,ge,plus} and constructors {0,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond(false(),x,y,z) -> 0() cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z))) d(x,s(y),z) -> cond(ge(x,z),x,y,z) div(x,s(y)) -> d(x,s(y),0()) ge(u,0()) -> true() ge(0(),s(v)) -> false() ge(s(u),s(v)) -> ge(u,v) plus(n,0()) -> n plus(n,s(m)) -> s(plus(n,m)) - Signature: {cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond,d,div,ge,plus} and constructors {0,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ge(x,y){x -> s(x),y -> s(y)} = ge(s(x),s(y)) ->^+ ge(x,y) = C[ge(x,y) = ge(x,y){}] WORST_CASE(Omega(n^1),?)