Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H, I
Locations: f0, f1, f2, f3, f4
Transitions:
t₁: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f0(X₀-1, X₂, X₂-1, X₀, X₄, X₅, X₆) :|: 1 ≤ X₀
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₂: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f0(X₀-1, X₁, X₂-1, X₃, X₂, X₀, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₂
t₄: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f0(H, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ H ∧ 1 ≤ X₂
t₃: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f4(X₀, X₁, X₂, X₃, X₄, X₅, H) :|: X₂ ≤ 0
t₅: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f2(H, X₁, I, X₃, X₄, X₅, X₆)

Preprocessing

Cut unreachable locations [f1] from the program graph

Eliminate variables [X₁; X₃; X₄; X₅; X₆] that do not contribute to the problem

Found invariant 0 ≤ X₀ for location f0

Found invariant X₁ ≤ 0 for location f4

Problem after Preprocessing

Start: f3
Program_Vars: X₀, X₁
Temp_Vars: H, I
Locations: f0, f2, f3, f4
Transitions:
t₁₁: f0(X₀, X₁) → f0(X₀-1, X₁-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
t₁₂: f0(X₀, X₁) → f2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₃: f2(X₀, X₁) → f0(H, X₁) :|: 1 ≤ H ∧ 1 ≤ X₁
t₁₄: f2(X₀, X₁) → f4(X₀, X₁) :|: X₁ ≤ 0
t₁₅: f3(X₀, X₁) → f2(H, I)

Found invariant 0 ≤ X₀ for location f0_v2

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f0_v1

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f2_v1

Found invariant X₁ ≤ 0 for location f4

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Sizebounds

t₁₂, X₀: 0 {O(1)}