Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_start
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(X₁, X₁)
t₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀-1, X₁) :|: 1 ≤ X₀
t₄: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ 0
t₅: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₀: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

Preprocessing

Cut unsatisfiable transition [t₂: eval_foo_bb1_in→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_start
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(X₁, X₁)
t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀-1, X₁) :|: 1 ≤ X₀
t₄: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ 0
t₅: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₀: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(X₀-1, X₁) :|: 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

• eval_foo_bb1_in: [X₀]

MPRF for transition t₄: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ 0 of depth 1:

new bound:

X₁+1 {O(n)}

• eval_foo_bb1_in: [1-X₀]

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v3

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location eval_foo_bb1_in_v2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_bb1_in

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: X₁ {O(n)}
t₄: X₁+1 {O(n)}
t₅: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: X₁ {O(n)}
t₄: X₁+1 {O(n)}
t₅: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₁: 3⋅X₁ {O(n)}