Initial Problem

Start: f30
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: f3, f30, f4, f5
Transitions:
t₂: f30(X₀, X₁, X₂, X₃, X₄) → f4(2, X₁, 2, F, X₄)
t₀: f4(X₀, X₁, X₂, X₃, X₄) → f5(X₀, 1, X₂, X₃, X₄) :|: 2 ≤ X₀
t₁: f4(X₀, X₁, X₂, X₃, X₄) → f5(X₀, 0, X₂, X₃, X₄) :|: X₀ ≤ 1
t₅: f5(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, X₂, X₃, 0) :|: X₁ ≤ 0
t₃: f5(X₀, X₁, X₂, X₃, X₄) → f4(X₀-1, X₁, X₂, F, X₄) :|: 1 ≤ F ∧ F ≤ 0
t₄: f5(X₀, X₁, X₂, X₃, X₄) → f4(1+X₀, X₁, X₂, F, X₄) :|: 1 ≤ F

Preprocessing

Cut unsatisfiable transition [t₃: f5→f4]

Eliminate variables [X₂; X₃; X₄] that do not contribute to the problem

Found invariant 1 ≤ 0 for location f3

Found invariant 2 ≤ X₀ for location f4

Found invariant X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f5

Cut unsatisfiable transition [t₁₄: f4→f5; t₁₅: f5→f3]

Cut unreachable locations [f3] from the program graph

Problem after Preprocessing

Start: f30
Program_Vars: X₀, X₁
Temp_Vars: F
Locations: f30, f4, f5
Transitions:
t₁₂: f30(X₀, X₁) → f4(2, X₁)
t₁₃: f4(X₀, X₁) → f5(X₀, 1) :|: 2 ≤ X₀
t₁₆: f5(X₀, X₁) → f4(1+X₀, X₁) :|: 1 ≤ F ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 3 ≤ X₀+X₁

Found invariant X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f5_v1

Found invariant X₀ ≤ 2 ∧ 2 ≤ X₀ for location f4

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location f4_v1

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location f5_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}
t₁₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}
t₁₆: inf {Infinity}

Sizebounds

t₁₂, X₀: 2 {O(1)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₁: 1 {O(1)}
t₁₆, X₁: 1 {O(1)}