Initial Problem

Start: f3
Program_Vars: X₀, X₁
Temp_Vars: C, D
Locations: f2, f3, f300
Transitions:
t₀: f2(X₀, X₁) → f2(D-1, X₁) :|: 1+X₀ ≤ 0 ∧ C ≤ 0
t₁: f2(X₀, X₁) → f2(1+D, X₁) :|: 1+X₀ ≤ 0 ∧ 2 ≤ C
t₂: f2(X₀, X₁) → f2(D-1, X₁) :|: 1 ≤ X₀ ∧ 2+C ≤ 0
t₃: f2(X₀, X₁) → f2(1+D, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ C
t₅: f2(X₀, X₁) → f300(0, D) :|: 1+X₀ ≤ 0
t₆: f2(X₀, X₁) → f300(0, D) :|: 1 ≤ X₀
t₇: f2(X₀, X₁) → f300(X₀, D) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₄: f3(X₀, X₁) → f2(X₀, X₁)

Preprocessing

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

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f300

Problem after Preprocessing

Start: f3
Program_Vars: X₀
Temp_Vars: C, D
Locations: f2, f3, f300
Transitions:
t₁₅: f2(X₀) → f2(D-1) :|: 1+X₀ ≤ 0 ∧ C ≤ 0
t₁₆: f2(X₀) → f2(1+D) :|: 1+X₀ ≤ 0 ∧ 2 ≤ C
t₁₇: f2(X₀) → f2(D-1) :|: 1 ≤ X₀ ∧ 2+C ≤ 0
t₁₈: f2(X₀) → f2(1+D) :|: 1 ≤ X₀ ∧ 0 ≤ C
t₁₉: f2(X₀) → f300(0) :|: 1+X₀ ≤ 0
t₂₀: f2(X₀) → f300(0) :|: 1 ≤ X₀
t₂₁: f2(X₀) → f300(X₀) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₂₂: f3(X₀) → f2(X₀)

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f300

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}

Sizebounds

t₁₉, X₀: 0 {O(1)}
t₂₀, X₀: 0 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₂, X₀: X₀ {O(n)}