* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_f} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_f} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: foldr#3(y){y -> Cons(x,y)} = foldr#3(Cons(x,y)) ->^+ step_x_f(rev_l(),x,foldr#3(y)) = C[foldr#3(y) = foldr#3(y){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_f} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. Cons_0(2,2) -> 2 Cons_1(2,2) -> 1 Cons_2(2,1) -> 1 Cons_2(2,2) -> 1 Cons_3(2,1) -> 1 Cons_3(2,5) -> 1 Nil_0() -> 2 Nil_1() -> 1 Nil_1() -> 5 fleft_op_e_xs_1_0() -> 2 fleft_op_e_xs_1_1() -> 1 fleft_op_e_xs_1_1() -> 4 foldr#3_0(2) -> 1 foldr#3_1(2) -> 4 main_0(2) -> 1 rev_l_0() -> 2 rev_l_1() -> 3 rev_l#2_0(2,2) -> 1 rev_l#2_1(1,2) -> 1 rev_l#2_1(2,2) -> 1 rev_l#2_2(1,2) -> 1 rev_l#2_2(5,2) -> 1 step_x_f_0(2,2,2) -> 2 step_x_f_1(3,2,4) -> 1 step_x_f_1(3,2,4) -> 4 step_x_f#1_0(2,2,2,2) -> 1 step_x_f#1_1(2,2,2,1) -> 1 step_x_f#1_1(3,2,4,5) -> 1 step_x_f#1_2(3,2,4,1) -> 1 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))