Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
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, X₃) → eval_foo_bb1_in(0, X₁, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 39
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 40 ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₃ ≤ 0
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(2+X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ 0
t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(2+X₀, X₁, X₂, X₃) :|: 1 ≤ X₃
t₇: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃)
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Eliminate variables [X₁; X₂] that do not contribute to the problem

Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant 0 ≤ X₀ for location eval_foo_bb1_in

Found invariant 40 ≤ X₀ for location eval_foo_stop

Found invariant 40 ≤ X₀ for location eval_foo_bb3_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:
t₁₅: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(0, X₁)
t₁₆: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀
t₁₇: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 40 ≤ X₀ ∧ 0 ≤ X₀
t₁₈: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₁₉: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(2+X₀, X₁) :|: 1+X₁ ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₀: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(2+X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₁: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁) :|: 40 ≤ X₀
t₂₂: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₁₆: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

• eval_foo_bb1_in: [40-X₀]
• eval_foo_bb2_in: [39-X₀]

MPRF for transition t₁₈: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

• eval_foo_bb1_in: [40-X₀]
• eval_foo_bb2_in: [40-X₀]

MPRF for transition t₁₉: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(2+X₀, X₁) :|: 1+X₁ ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

1522 {O(1)}

• eval_foo_bb1_in: [1522-39⋅X₀]
• eval_foo_bb2_in: [1483-38⋅X₀]

MPRF for transition t₂₀: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(2+X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

1522 {O(1)}

• eval_foo_bb1_in: [1522-39⋅X₀]
• eval_foo_bb2_in: [1483-38⋅X₀]

All Bounds

Timebounds

Overall timebound:3128 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 40 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 40 {O(1)}
t₁₉: 1522 {O(1)}
t₂₀: 1522 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: 3128 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 40 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 40 {O(1)}
t₁₉: 1522 {O(1)}
t₂₀: 1522 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}

Sizebounds

t₁₅, X₀: 0 {O(1)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: 39 {O(1)}
t₁₆, X₁: X₁ {O(n)}
t₁₇, X₀: 122 {O(1)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₈, X₀: 40 {O(1)}
t₁₈, X₁: 0 {O(1)}
t₁₉, X₀: 41 {O(1)}
t₁₉, X₁: X₁ {O(n)}
t₂₀, X₀: 41 {O(1)}
t₂₀, X₁: X₁ {O(n)}
t₂₁, X₀: 122 {O(1)}
t₂₁, X₁: 2⋅X₁ {O(n)}
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}