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) :|: 1+X₀ ≤ X₁
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, X₁, X₂, X₃)
t₅: 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 [X₂; X₃] that do not contribute to the problem

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant 0 ≤ X₀ for location eval_foo_bb1_in

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

Found invariant X₁ ≤ X₀ ∧ 0 ≤ 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:
t₁₁: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(0, X₁)
t₁₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₁₅: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁) :|: 0 ≤ X₀ ∧ X₁ ≤ X₀
t₁₆: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₁₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

• eval_foo_bb1_in: [X₁-X₀]
• eval_foo_bb2_in: [X₁-1-X₀]

MPRF for transition t₁₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

• eval_foo_bb1_in: [X₁-X₀]
• eval_foo_bb2_in: [X₁-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: 0 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: X₁ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₄, X₀: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: X₁ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}