*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: 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)) Weak DP Rules: Weak TRS Rules: 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 basic terms: {foldr#3,main,rev_l#2,step_x_f#1}/{Cons,Nil,fleft_op_e_xs_1,rev_l,step_x_f} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: 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 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: 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 basic terms: {foldr#3,main,rev_l#2,step_x_f#1}/{Cons,Nil,fleft_op_e_xs_1,rev_l,step_x_f} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).