Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
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, X₄) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(1+X₀, 2+X₁, X₂, X₃, X₄)
t₅: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

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

Found invariant X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location eval_foo_bb2_in

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_stop

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_bb3_in

Problem after Preprocessing

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:
t₁₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₁₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₁₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₁₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, 2+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₁₅: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁
t₁₆: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₁₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

X₂+X₃ {O(n)}

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

MPRF for transition t₁₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, 2+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

X₂+X₃ {O(n)}

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

All Bounds

Timebounds

Overall timebound:2⋅X₂+2⋅X₃+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₂+X₃ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₃ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂+2⋅X₃+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₂+X₃ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₃ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₂ {O(n)}
t₁₁, X₁: X₃ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₀: 2⋅X₂+X₃ {O(n)}
t₁₂, X₁: 2⋅X₂+3⋅X₃ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: 3⋅X₂+X₃ {O(n)}
t₁₃, X₁: 2⋅X₂+4⋅X₃ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}
t₁₄, X₀: 2⋅X₂+X₃ {O(n)}
t₁₄, X₁: 2⋅X₂+3⋅X₃ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: 3⋅X₂+X₃ {O(n)}
t₁₅, X₁: 2⋅X₂+4⋅X₃ {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}