Initial Problem

Start: eval_size01_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_size01_bb0_in, eval_size01_bb1_in, eval_size01_bb2_in, eval_size01_bb3_in, eval_size01_start, eval_size01_stop
Transitions:
t₁: eval_size01_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_size01_bb1_in(X₁, X₁, X₂, X₃, X₄)
t₂: eval_size01_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_size01_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀
t₃: eval_size01_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_size01_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₄: eval_size01_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_size01_bb1_in(X₀-1, X₁, X₂, X₃, X₄)
t₅: eval_size01_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_size01_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_size01_start(X₀, X₁, X₂, X₃, X₄) → eval_size01_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables [X₂; X₃; X₄] that do not contribute to the problem

Found invariant X₀ ≤ X₁ for location eval_size01_bb1_in

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_size01_bb2_in

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_size01_bb3_in

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_size01_stop

Problem after Preprocessing

Start: eval_size01_start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval_size01_bb0_in, eval_size01_bb1_in, eval_size01_bb2_in, eval_size01_bb3_in, eval_size01_start, eval_size01_stop
Transitions:
t₁₁: eval_size01_bb0_in(X₀, X₁) → eval_size01_bb1_in(X₁, X₁)
t₁₂: eval_size01_bb1_in(X₀, X₁) → eval_size01_bb2_in(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁
t₁₃: eval_size01_bb1_in(X₀, X₁) → eval_size01_bb3_in(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ X₁
t₁₄: eval_size01_bb2_in(X₀, X₁) → eval_size01_bb1_in(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₁₅: eval_size01_bb3_in(X₀, X₁) → eval_size01_stop(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ X₁
t₁₆: eval_size01_start(X₀, X₁) → eval_size01_bb0_in(X₀, X₁)

MPRF for transition t₁₂: eval_size01_bb1_in(X₀, X₁) → eval_size01_bb2_in(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

• eval_size01_bb1_in: [X₀]
• eval_size01_bb2_in: [X₀-1]

MPRF for transition t₁₄: eval_size01_bb2_in(X₀, X₁) → eval_size01_bb1_in(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

• eval_size01_bb1_in: [X₀]
• eval_size01_bb2_in: [X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₁+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 2⋅X₁ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₄, X₀: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: 2⋅X₁ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}