Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E
Locations: f0, f11, f14, f20, f26, f27, f29, f32
Transitions:
t₁₀: f0(X₀, X₁, X₂) → f11(D, E, D)
t₀: f11(X₀, X₁, X₂) → f14(X₀, X₁, X₂) :|: 6 ≤ X₀
t₁: f11(X₀, X₁, X₂) → f14(X₀, X₁, X₂) :|: X₀ ≤ 5 ∧ X₁ ≤ 0
t₉: f11(X₀, X₁, X₂) → f20(X₀, X₁, X₂) :|: X₀ ≤ 5 ∧ 1 ≤ X₁
t₂: f14(X₀, X₁, X₂) → f11(1+X₀, D, X₂) :|: 6 ≤ X₀
t₈: f14(X₀, X₁, X₂) → f11(1+X₀, D, X₂) :|: X₀ ≤ 5
t₇: f20(X₀, X₁, X₂) → f11(X₀, D, X₂) :|: X₀ ≤ 2
t₆: f20(X₀, X₁, X₂) → f20(X₀-1, X₁, X₂) :|: 3 ≤ X₀
t₃: f26(X₀, X₁, X₂) → f27(X₀, X₁, X₂)
t₄: f27(X₀, X₁, X₂) → f27(X₀, X₁, X₂)
t₅: f29(X₀, X₁, X₂) → f32(X₀, X₁, X₂)

Preprocessing

Cut unreachable locations [f26; f27; f29; f32] from the program graph

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

Found invariant 1 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 5 for location f20

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: D, E
Locations: f0, f11, f14, f20
Transitions:
t₂₁: f0(X₀, X₁) → f11(D, E)
t₂₂: f11(X₀, X₁) → f14(X₀, X₁) :|: 6 ≤ X₀
t₂₃: f11(X₀, X₁) → f14(X₀, X₁) :|: X₀ ≤ 5 ∧ X₁ ≤ 0
t₂₄: f11(X₀, X₁) → f20(X₀, X₁) :|: X₀ ≤ 5 ∧ 1 ≤ X₁
t₂₅: f14(X₀, X₁) → f11(1+X₀, D) :|: 6 ≤ X₀
t₂₆: f14(X₀, X₁) → f11(1+X₀, D) :|: X₀ ≤ 5
t₂₇: f20(X₀, X₁) → f11(X₀, D) :|: X₀ ≤ 2 ∧ X₀ ≤ 5 ∧ X₀ ≤ 4+X₁ ∧ 1 ≤ X₁
t₂₈: f20(X₀, X₁) → f20(X₀-1, X₁) :|: 3 ≤ X₀ ∧ X₀ ≤ 5 ∧ X₀ ≤ 4+X₁ ∧ 1 ≤ X₁

Found invariant X₀ ≤ 6 ∧ 6 ≤ X₀ for location f14_v4

Found invariant X₀ ≤ 2 for location f11_v3

Found invariant 1 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 5 for location f20_v1

Found invariant 6 ≤ X₀ for location f14_v2

Found invariant X₀ ≤ 6 for location f11_v2

Found invariant X₀ ≤ 3 for location f11_v4

Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 5 for location f14_v1

Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 2 ∧ X₀ ≤ 2 for location f14_v5

Found invariant 1 ≤ X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 for location f20_v3

Found invariant 7 ≤ X₀ for location f11_v1

Found invariant 7 ≤ X₀ for location f14_v3

Found invariant 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 2 ≤ X₀ for location f20_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: inf {Infinity}
t₂₇: inf {Infinity}
t₂₈: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: inf {Infinity}
t₂₇: inf {Infinity}
t₂₈: inf {Infinity}

Sizebounds

t₂₈, X₀: 4 {O(1)}