Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, X₁, X₂)
t₂: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: X₀ ≤ 99 ∧ 2 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 1
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 100 ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in((X₀)², X₁, X₂)
t₆: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂)
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

Preprocessing

Eliminate variables [X₁] that do not contribute to the problem

Found invariant X₀ ≤ 99 ∧ 2 ≤ X₀ for location eval_foo_bb2_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₃: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(X₁, X₁)
t₁₄: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 99 ∧ 2 ≤ X₀
t₁₅: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: X₀ ≤ 1
t₁₆: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 100 ≤ X₀
t₁₇: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in((X₀)², X₁) :|: X₀ ≤ 99 ∧ 2 ≤ X₀
t₁₈: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁)
t₁₉: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₁₄: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 99 ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁+100 {O(n)}

• eval_foo_bb1_in: [100-X₀]
• eval_foo_bb2_in: [99-X₀]

MPRF for transition t₁₇: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(Temp_Int₄₉, X₁) :|: 1+X₀ ≤ Temp_Int₄₉ ∧ 4 ≤ Temp_Int₄₉ ∧ X₀ ≤ 99 ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁+100 {O(n)}

• eval_foo_bb1_in: [100-X₀]
• eval_foo_bb2_in: [100-X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₁+205 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁+100 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: X₁+100 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+205 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁+100 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: X₁+100 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₀: X₁ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: 99 {O(1)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: X₁+9801 {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₆, X₀: X₁+9801 {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₇, X₀: 9801 {O(1)}
t₁₇, X₁: X₁ {O(n)}
t₁₈, X₀: 2⋅X₁+19602 {O(n)}
t₁₈, X₁: 4⋅X₁ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}