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(X₃, X₁, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ 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 [X₁] that do not contribute to the problem

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

Found invariant X₂ ≤ X₀ for location eval_foo_bb1_in

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

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

Problem after Preprocessing

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

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

new bound:

X₁+X₂ {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, X₂) → eval_foo_bb1_in(1+X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₁+X₂ {O(n)}

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

All Bounds

Timebounds

Overall timebound:2⋅X₁+2⋅X₂+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁+X₂ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁+X₂ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+2⋅X₂+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁+X₂ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁+X₂ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

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