WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: @'(Cons(z0,z1),z2) -> c(@'(z1,z2)) @'(Nil(),z0) -> c1() BINOM(Cons(z0,z1),Cons(z2,z3)) -> c2(@'(binom(z1,z3),binom(z1,Cons(z2,z3))),BINOM(z1,z3)) BINOM(Cons(z0,z1),Cons(z2,z3)) -> c3(@'(binom(z1,z3),binom(z1,Cons(z2,z3))),BINOM(z1,Cons(z2,z3))) BINOM(Cons(z0,z1),Nil()) -> c4() BINOM(Nil(),z0) -> c5() GOAL(z0,z1) -> c6(BINOM(z0,z1)) - Weak TRS: @(Cons(z0,z1),z2) -> Cons(z0,@(z1,z2)) @(Nil(),z0) -> z0 binom(Cons(z0,z1),Cons(z2,z3)) -> @(binom(z1,z3),binom(z1,Cons(z2,z3))) binom(Cons(z0,z1),Nil()) -> Cons(Nil(),Nil()) binom(Nil(),z0) -> Cons(Nil(),Nil()) goal(z0,z1) -> binom(z0,z1) - Signature: {@/2,@'/2,BINOM/2,GOAL/2,binom/2,goal/2} / {Cons/2,Nil/0,c/1,c1/0,c2/2,c3/2,c4/0,c5/0,c6/1} - Obligation: innermost runtime complexity wrt. defined symbols {@,@',BINOM,GOAL,binom,goal} and constructors {Cons,Nil,c ,c1,c2,c3,c4,c5,c6} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: @'(Cons(z0,z1),z2) -> c(@'(z1,z2)) @'(Nil(),z0) -> c1() BINOM(Cons(z0,z1),Cons(z2,z3)) -> c2(@'(binom(z1,z3),binom(z1,Cons(z2,z3))),BINOM(z1,z3)) BINOM(Cons(z0,z1),Cons(z2,z3)) -> c3(@'(binom(z1,z3),binom(z1,Cons(z2,z3))),BINOM(z1,Cons(z2,z3))) BINOM(Cons(z0,z1),Nil()) -> c4() BINOM(Nil(),z0) -> c5() GOAL(z0,z1) -> c6(BINOM(z0,z1)) - Weak TRS: @(Cons(z0,z1),z2) -> Cons(z0,@(z1,z2)) @(Nil(),z0) -> z0 binom(Cons(z0,z1),Cons(z2,z3)) -> @(binom(z1,z3),binom(z1,Cons(z2,z3))) binom(Cons(z0,z1),Nil()) -> Cons(Nil(),Nil()) binom(Nil(),z0) -> Cons(Nil(),Nil()) goal(z0,z1) -> binom(z0,z1) - Signature: {@/2,@'/2,BINOM/2,GOAL/2,binom/2,goal/2} / {Cons/2,Nil/0,c/1,c1/0,c2/2,c3/2,c4/0,c5/0,c6/1} - Obligation: innermost runtime complexity wrt. defined symbols {@,@',BINOM,GOAL,binom,goal} and constructors {Cons,Nil,c ,c1,c2,c3,c4,c5,c6} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: @'(Cons(z0,z1),z2) -> c(@'(z1,z2)) @'(Nil(),z0) -> c1() BINOM(Cons(z0,z1),Cons(z2,z3)) -> c2(@'(binom(z1,z3),binom(z1,Cons(z2,z3))),BINOM(z1,z3)) BINOM(Cons(z0,z1),Cons(z2,z3)) -> c3(@'(binom(z1,z3),binom(z1,Cons(z2,z3))),BINOM(z1,Cons(z2,z3))) BINOM(Cons(z0,z1),Nil()) -> c4() BINOM(Nil(),z0) -> c5() GOAL(z0,z1) -> c6(BINOM(z0,z1)) - Weak TRS: @(Cons(z0,z1),z2) -> Cons(z0,@(z1,z2)) @(Nil(),z0) -> z0 binom(Cons(z0,z1),Cons(z2,z3)) -> @(binom(z1,z3),binom(z1,Cons(z2,z3))) binom(Cons(z0,z1),Nil()) -> Cons(Nil(),Nil()) binom(Nil(),z0) -> Cons(Nil(),Nil()) goal(z0,z1) -> binom(z0,z1) - Signature: {@/2,@'/2,BINOM/2,GOAL/2,binom/2,goal/2} / {Cons/2,Nil/0,c/1,c1/0,c2/2,c3/2,c4/0,c5/0,c6/1} - Obligation: innermost runtime complexity wrt. defined symbols {@,@',BINOM,GOAL,binom,goal} and constructors {Cons,Nil,c ,c1,c2,c3,c4,c5,c6} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: @'(y,z){y -> Cons(x,y)} = @'(Cons(x,y),z) ->^+ c(@'(y,z)) = C[@'(y,z) = @'(y,z){}] WORST_CASE(Omega(n^1),?)