Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: f0, f10, f14, f25, f6
Transitions:
t₀: f0(X₀, X₁, X₂, X₃) → f6(E, 0, X₂, X₃)
t₂: f10(X₀, X₁, X₂, X₃) → f14(X₀, X₁-1, X₀-1, X₃) :|: 1 ≤ X₁
t₇: f10(X₀, X₁, X₂, X₃) → f6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₆: f14(X₀, X₁, X₂, X₃) → f10(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₃: f14(X₀, X₁, X₂, X₃) → f14(X₀, X₁, X₂-1, 0) :|: 1 ≤ X₂
t₄: f14(X₀, X₁, X₂, X₃) → f14(X₀-1, 1+X₁, X₂-1, E) :|: 1+E ≤ 0 ∧ 1 ≤ X₂
t₅: f14(X₀, X₁, X₂, X₃) → f14(X₀-1, 1+X₁, X₂-1, E) :|: 1 ≤ E ∧ 1 ≤ X₂
t₁: f6(X₀, X₁, X₂, X₃) → f10(X₀-1, 1+X₁, X₂, X₃) :|: 1 ≤ X₀
t₈: f6(X₀, X₁, X₂, X₃) → f25(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0

Preprocessing

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

Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f14

Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location f6

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f10

Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location f25

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars: E
Locations: f0, f10, f14, f25, f6
Transitions:
t₁₈: f0(X₀, X₁, X₂) → f6(E, 0, X₂)
t₁₉: f10(X₀, X₁, X₂) → f14(X₀, X₁-1, X₀-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₀: f10(X₀, X₁, X₂) → f6(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₁: f14(X₀, X₁, X₂) → f10(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₂: f14(X₀, X₁, X₂) → f14(X₀, X₁, X₂-1) :|: 1 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₃: f14(X₀, X₁, X₂) → f14(X₀-1, 1+X₁, X₂-1) :|: 1+E ≤ 0 ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₄: f14(X₀, X₁, X₂) → f14(X₀-1, 1+X₁, X₂-1) :|: 1 ≤ E ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₅: f6(X₀, X₁, X₂) → f10(X₀-1, 1+X₁, X₂) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₂₆: f6(X₀, X₁, X₂) → f25(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location f6_v1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location f14_v7

Found invariant 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f14_v6

Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f14_v2

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f10_v4

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location f10_v6

Found invariant 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f14_v3

Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location f25

Found invariant 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f14_v4

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f10_v3

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location f10_v2

Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location f6

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f10_v1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location f10_v7

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f6_v2

Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f14_v1

Found invariant 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f14_v5

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f10_v5

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: 1 {O(1)}

Sizebounds

t₁₈, X₁: 0 {O(1)}
t₁₈, X₂: X₂ {O(n)}
t₂₀, X₁: 0 {O(1)}
t₂₀, X₂: 1 {O(1)}
t₂₁, X₂: 1 {O(1)}
t₂₅, X₁: 1 {O(1)}
t₂₅, X₂: X₂+1 {O(n)}
t₂₆, X₁: 0 {O(1)}
t₂₆, X₂: X₂+1 {O(n)}