* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: gt(0(),y) -> false() gt(s(x),0()) -> true() gt(s(x),s(y)) -> gt(x,y) if(false(),x,y) -> 0() if(true(),x,y) -> s(minus(x,y)) if1(false(),x,y) -> mod(minus(x,y),y) if1(true(),x,y) -> x lt(x,0()) -> false() lt(0(),s(x)) -> true() lt(s(x),s(y)) -> lt(x,y) minus(0(),y) -> 0() minus(s(x),y) -> if(gt(s(x),y),x,y) mod(x,0()) -> 0() mod(x,s(y)) -> if1(lt(x,s(y)),x,s(y)) - Signature: {gt/2,if/3,if1/3,lt/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {gt,if,if1,lt,minus,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: gt(0(),y) -> false() gt(s(x),0()) -> true() gt(s(x),s(y)) -> gt(x,y) if(false(),x,y) -> 0() if(true(),x,y) -> s(minus(x,y)) if1(false(),x,y) -> mod(minus(x,y),y) if1(true(),x,y) -> x lt(x,0()) -> false() lt(0(),s(x)) -> true() lt(s(x),s(y)) -> lt(x,y) minus(0(),y) -> 0() minus(s(x),y) -> if(gt(s(x),y),x,y) mod(x,0()) -> 0() mod(x,s(y)) -> if1(lt(x,s(y)),x,s(y)) - Signature: {gt/2,if/3,if1/3,lt/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {gt,if,if1,lt,minus,mod} and constructors {0,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: gt(x,y){x -> s(x),y -> s(y)} = gt(s(x),s(y)) ->^+ gt(x,y) = C[gt(x,y) = gt(x,y){}] WORST_CASE(Omega(n^1),?)