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