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