Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: f0, f12, f27, f42, f55, f66
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f12(G, G, G, 0, X₄, X₅)
t₁: f12(X₀, X₁, X₂, X₃, X₄, X₅) → f12(X₀, X₁, X₂, 1+X₃, G, X₅) :|: 1+X₃ ≤ X₂
t₁₁: f12(X₀, X₁, X₂, X₃, X₄, X₅) → f27(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃
t₂: f27(X₀, X₁, X₂, X₃, X₄, X₅) → f27(X₀, X₁, X₂, X₃, X₄, G) :|: 1+H ≤ 0
t₃: f27(X₀, X₁, X₂, X₃, X₄, X₅) → f27(X₀, X₁, X₂, X₃, X₄, G)
t₁₀: f27(X₀, X₁, X₂, X₃, X₄, X₅) → f42(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f42(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+H ≤ G
t₅: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f42(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f55(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: f55(X₀, X₁, X₂, X₃, X₄, X₅) → f55(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+H ≤ G
t₇: f55(X₀, X₁, X₂, X₃, X₄, X₅) → f55(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: f55(X₀, X₁, X₂, X₃, X₄, X₅) → f66(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables [X₀; X₁; X₄; X₅] that do not contribute to the problem

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f42

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f55

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f27

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f66

Found invariant 0 ≤ X₁ for location f12

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: G, H
Locations: f0, f12, f27, f42, f55, f66
Transitions:
t₂₇: f0(X₀, X₁) → f12(G, 0)
t₂₈: f12(X₀, X₁) → f12(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁
t₂₉: f12(X₀, X₁) → f27(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₀: f27(X₀, X₁) → f27(X₀, X₁) :|: 1+H ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₁: f27(X₀, X₁) → f27(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₂: f27(X₀, X₁) → f42(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₃: f42(X₀, X₁) → f42(X₀, X₁) :|: 1+H ≤ G ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₄: f42(X₀, X₁) → f42(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₅: f42(X₀, X₁) → f55(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₆: f55(X₀, X₁) → f55(X₀, X₁) :|: 1+H ≤ G ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₇: f55(X₀, X₁) → f55(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₈: f55(X₀, X₁) → f66(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f42

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f55

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f27

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f66

Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location f12

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f12_v1

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f27_v1

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f42

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f55

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f27

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f66

Found invariant 0 ≤ X₁ for location f12

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f42

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f55

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f27

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f66

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f42_v1

Found invariant 0 ≤ X₁ for location f12

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f42

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f55

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f27

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f55_v1

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location f66

Found invariant 0 ≤ X₁ for location f12

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: inf {Infinity}
t₃₁: inf {Infinity}
t₃₂: 1 {O(1)}
t₃₃: inf {Infinity}
t₃₄: inf {Infinity}
t₃₅: 1 {O(1)}
t₃₆: inf {Infinity}
t₃₇: inf {Infinity}
t₃₈: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: inf {Infinity}
t₃₁: inf {Infinity}
t₃₂: 1 {O(1)}
t₃₃: inf {Infinity}
t₃₄: inf {Infinity}
t₃₅: 1 {O(1)}
t₃₆: inf {Infinity}
t₃₇: inf {Infinity}
t₃₈: 1 {O(1)}

Sizebounds

t₂₇, X₁: 0 {O(1)}