* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a(1(),id()) -> 1() a(1(),p(x,y)) -> x a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(t(),id()) -> t() a(t(),p(x,y)) -> y - Signature: {a/2} / {1/0,id/0,lambda/1,p/2,t/0} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {1,id,lambda,p,t} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a(1(),id()) -> 1() a(1(),p(x,y)) -> x a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(t(),id()) -> t() a(t(),p(x,y)) -> y - Signature: {a/2} / {1/0,id/0,lambda/1,p/2,t/0} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {1,id,lambda,p,t} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: a(x,y){x -> lambda(x)} = a(lambda(x),y) ->^+ lambda(a(x,p(1(),a(y,t())))) = C[a(x,p(1(),a(y,t()))) = a(x,y){y -> p(1(),a(y,t()))}] WORST_CASE(Omega(n^1),?)