* 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)) p(s(0())) -> 0() p(s(s(x))) -> s(p(s(x))) plus(0(),x) -> x plus(s(x),y) -> s(plus(p(s(x)),y)) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(p(s(x)),y)) tower(x,y) -> towerIter(x,y,s(0())) towerIter(0(),y,z) -> z towerIter(s(x),y,z) -> towerIter(p(s(x)),y,exp(y,z)) - Signature: {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {exp,p,plus,times,tower,towerIter} and constructors {0,s} + 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)) p(s(0())) -> 0() p(s(s(x))) -> s(p(s(x))) plus(0(),x) -> x plus(s(x),y) -> s(plus(p(s(x)),y)) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(p(s(x)),y)) tower(x,y) -> towerIter(x,y,s(0())) towerIter(0(),y,z) -> z towerIter(s(x),y,z) -> towerIter(p(s(x)),y,exp(y,z)) - Signature: {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {exp,p,plus,times,tower,towerIter} and constructors {0,s} + 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),?)