Initial Problem

Start: f2
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E, F
Locations: f1, f2, f300
Transitions:
t₁: f1(X₀, X₁, X₂, X₃) → f1(1+X₀, X₁, E, X₃) :|: 1 ≤ E ∧ 1+X₀ ≤ X₁
t₂: f1(X₀, X₁, X₂, X₃) → f1(1+X₀, X₁, E, X₃) :|: 1+E ≤ 0 ∧ 1+X₀ ≤ X₁
t₃: f1(X₀, X₁, X₂, X₃) → f1(X₀, X₁, 0, X₃) :|: 1+X₀ ≤ X₁
t₄: f1(X₀, X₁, X₂, X₃) → f1(1+X₀, X₀, E, X₃) :|: 1 ≤ E ∧ F ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₅: f1(X₀, X₁, X₂, X₃) → f1(1+X₀, X₀, E, X₃) :|: 1+E ≤ 0 ∧ F ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₆: f1(X₀, X₁, X₂, X₃) → f1(X₀, X₀, 0, X₃) :|: E ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: f1(X₀, X₁, X₂, X₃) → f300(X₀, X₁, X₂, E) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₈: f1(X₀, X₁, X₂, X₃) → f300(X₀, X₁, X₂, E) :|: 1+X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₀: f2(X₀, X₁, X₂, X₃) → f1(X₀, X₁, X₂, X₃)

Preprocessing

Cut unsatisfiable transition [t₈: f1→f300]

Eliminate variables [X₂; X₃] that do not contribute to the problem

Found invariant 1+X₁ ≤ X₀ for location f300

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁
Temp_Vars: E, F
Locations: f1, f2, f300
Transitions:
t₂₃: f1(X₀, X₁) → f1(1+X₀, X₁) :|: 1 ≤ E ∧ 1+X₀ ≤ X₁
t₂₄: f1(X₀, X₁) → f1(1+X₀, X₁) :|: 1+E ≤ 0 ∧ 1+X₀ ≤ X₁
t₂₅: f1(X₀, X₁) → f1(X₀, X₁) :|: 1+X₀ ≤ X₁
t₂₆: f1(X₀, X₁) → f1(1+X₀, X₀) :|: 1 ≤ E ∧ F ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₇: f1(X₀, X₁) → f1(1+X₀, X₀) :|: 1+E ≤ 0 ∧ F ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₈: f1(X₀, X₁) → f1(X₀, X₀) :|: E ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₉: f1(X₀, X₁) → f300(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₃₀: f2(X₀, X₁) → f1(X₀, X₁)

MPRF for transition t₂₃: f1(X₀, X₁) → f1(1+X₀, X₁) :|: 1 ≤ E ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f1: [X₁-X₀]

MPRF for transition t₂₄: f1(X₀, X₁) → f1(1+X₀, X₁) :|: 1+E ≤ 0 ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f1: [X₁-X₀]

MPRF for transition t₂₆: f1(X₀, X₁) → f1(1+X₀, X₀) :|: 1 ≤ E ∧ F ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f1: [1+X₁-X₀]

MPRF for transition t₂₇: f1(X₀, X₁) → f1(1+X₀, X₀) :|: 1+E ≤ 0 ∧ F ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f1: [1+X₁-X₀]

Found invariant 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ for location f1_v2

Found invariant 1+X₀ ≤ X₁ for location f1_v3

Found invariant 1+X₁ ≤ X₀ for location f300

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location f1_v1

Found invariant X₀ ≤ X₁ for location f1_v4

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₃: X₀+X₁ {O(n)}
t₂₄: X₀+X₁ {O(n)}
t₂₅: inf {Infinity}
t₂₆: X₀+X₁+1 {O(n)}
t₂₇: X₀+X₁+1 {O(n)}
t₂₈: inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₃: X₀+X₁ {O(n)}
t₂₄: X₀+X₁ {O(n)}
t₂₅: inf {Infinity}
t₂₆: X₀+X₁+1 {O(n)}
t₂₇: X₀+X₁+1 {O(n)}
t₂₈: inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}

Sizebounds

t₂₃, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₄, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₅, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₆, X₀: 14⋅X₀+8⋅X₁+4 {O(n)}
t₂₆, X₁: 14⋅X₀+8⋅X₁ {O(n)}
t₂₇, X₀: 14⋅X₀+8⋅X₁+4 {O(n)}
t₂₇, X₁: 14⋅X₀+8⋅X₁ {O(n)}
t₂₈, X₀: 4⋅X₁+7⋅X₀ {O(n)}
t₂₈, X₁: 14⋅X₀+8⋅X₁ {O(n)}
t₂₉, X₀: 16⋅X₁+29⋅X₀+8 {O(n)}
t₂₉, X₁: 17⋅X₁+28⋅X₀ {O(n)}
t₃₀, X₀: X₀ {O(n)}
t₃₀, X₁: X₁ {O(n)}