Initial Problem

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:
t₁: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(0, X₁, X₂)
t₂: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: X₀ ≤ 10
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 11 ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, X₁, X₂)
t₅: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂)
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

Preprocessing

Eliminate variables [X₁; X₂] that do not contribute to the problem

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant 0 ≤ X₀ for location eval_foo_bb1_in

Found invariant 11 ≤ X₀ for location eval_foo_stop

Found invariant 11 ≤ 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) :|: X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₃: eval_foo_bb1_in(X₀) → eval_foo_bb3_in(X₀) :|: 11 ≤ X₀ ∧ 0 ≤ X₀
t₁₄: eval_foo_bb2_in(X₀) → eval_foo_bb1_in(1+X₀) :|: X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₅: eval_foo_bb3_in(X₀) → eval_foo_stop(X₀) :|: 11 ≤ X₀
t₁₆: eval_foo_start(X₀) → eval_foo_bb0_in(X₀)

MPRF for transition t₁₂: eval_foo_bb1_in(X₀) → eval_foo_bb2_in(X₀) :|: X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

• eval_foo_bb1_in: [11-X₀]
• eval_foo_bb2_in: [10-X₀]

MPRF for transition t₁₄: eval_foo_bb2_in(X₀) → eval_foo_bb1_in(1+X₀) :|: X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

• eval_foo_bb1_in: [11-X₀]
• eval_foo_bb2_in: [11-X₀]

All Bounds

Timebounds

Overall timebound:26 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 11 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 11 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 26 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 11 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 11 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₂, X₀: 10 {O(1)}
t₁₃, X₀: 11 {O(1)}
t₁₄, X₀: 11 {O(1)}
t₁₅, X₀: 11 {O(1)}
t₁₆, X₀: X₀ {O(n)}