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_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀, X₁, X₁)
t₂: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀, X₁, X₂-1) :|: 3 ≤ X₂
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: X₂ ≤ 2
t₄: eval_foo_bb2_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 [X₀] that do not contribute to the problem

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ for location eval_foo_bb2_in

Found invariant X₁ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ for location eval_foo_stop

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_start, eval_foo_stop
Transitions:
t₁₀: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₀)
t₁₁: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₁-1) :|: 3 ≤ X₁ ∧ X₁ ≤ X₀
t₁₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₁ ≤ 2 ∧ X₁ ≤ X₀
t₁₃: eval_foo_bb2_in(X₀, X₁) → eval_foo_stop(X₀, X₁) :|: X₁ ≤ 2 ∧ X₁ ≤ X₀
t₁₄: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₁₁: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₁-1) :|: 3 ≤ X₁ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• eval_foo_bb1_in: [X₁]

All Bounds

Timebounds

Overall timebound:X₀+4 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: X₀+4 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}

Sizebounds

t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₀ {O(n)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 2⋅X₀ {O(n)}
t₁₃, X₀: 2⋅X₀ {O(n)}
t₁₃, X₁: 2⋅X₀ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}