* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: exp(x,0()) -> s(0()) exp(x,s(y)) -> times(x,exp(x,y)) ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z)) help(true(),c,x,y,z) -> z plus(0(),x) -> x plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(x,y)) tower(x,y) -> towerIter(0(),x,y,s(0())) towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z) - Signature: {exp/2,ge/2,help/5,plus/2,times/2,tower/2,towerIter/4} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {exp,ge,help,plus,times,tower ,towerIter} 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: exp(x,0()) -> s(0()) exp(x,s(y)) -> times(x,exp(x,y)) ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z)) help(true(),c,x,y,z) -> z plus(0(),x) -> x plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(x,y)) tower(x,y) -> towerIter(0(),x,y,s(0())) towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z) - Signature: {exp/2,ge/2,help/5,plus/2,times/2,tower/2,towerIter/4} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {exp,ge,help,plus,times,tower ,towerIter} and constructors {0,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: exp(x,y){y -> s(y)} = exp(x,s(y)) ->^+ times(x,exp(x,y)) = C[exp(x,y) = exp(x,y){}] WORST_CASE(Omega(n^1),?)