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:
t₂: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(2, X₁, X₂, X₃) :|: 0 ≤ X₂
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in((X₀)², X₁, X₂, X₃)
t₆: 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; X₃] that do not contribute to the problem

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_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(2, X₁) :|: 0 ≤ X₁
t₁₄: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 1+X₁ ≤ 0
t₁₅: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₁₆: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: X₁ ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₁₇: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in((X₀)², X₁) :|: 1+X₀ ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 0 ≤ 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)

Found invariant 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location eval_foo_bb1_in

Found invariant 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₀: 2 {O(1)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₈, X₁: 3⋅X₁ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}