Initial Problem

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:
t₁: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(0, X₁)
t₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: 0 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 1+X₀ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(X₀-1, X₁)
t₅: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁)
t₀: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

Preprocessing

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

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

Found invariant X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location eval_foo_bb1_in

Found invariant 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location eval_foo_stop

Found invariant 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location eval_foo_bb3_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀
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) → eval_foo_bb1_in(0)
t₁₂: eval_foo_bb1_in(X₀) → eval_foo_bb2_in(X₀) :|: 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 0
t₁₃: eval_foo_bb1_in(X₀) → eval_foo_bb3_in(X₀) :|: 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 0
t₁₄: eval_foo_bb2_in(X₀) → eval_foo_bb1_in(X₀-1) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₁₅: eval_foo_bb3_in(X₀) → eval_foo_stop(X₀) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ 0
t₁₆: eval_foo_start(X₀) → eval_foo_bb0_in(X₀)

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₂: eval_foo_bb1_in(X₀) → eval_foo_bb2_in(X₀) :|: 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 0

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₄: eval_foo_bb2_in(X₀) → eval_foo_bb1_in(X₀-1) :|: 0 ≤ X₀ ∧ X₀ ≤ 0

All Bounds

Timebounds

Overall timebound:6 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 6 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₂, X₀: 0 {O(1)}
t₁₃, X₀: 1 {O(1)}
t₁₄, X₀: 1 {O(1)}
t₁₅, X₀: 1 {O(1)}
t₁₆, X₀: X₀ {O(n)}