Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂
Temp_Vars: N, O, P, Q, R, S, T, U
Locations: f0, f1, f2, f4
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 0 ≤ O
t₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f2(0, O, P, 3, N, 0, O, P, 3, N, 2, X₁₁, X₁₂) :|: N ≤ 7 ∧ 1 ≤ N
t₄: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 0 ≤ O
t₇: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f4(O, P, N, Q, 2, O, P, N, Q, 2, 4, X₁₁, X₁₂) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ T ≤ 7 ∧ U ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 1 ≤ T ∧ 1 ≤ U ∧ 0 ≤ O
t₈: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f4(O, P, N, Q, 7, O, P, N, Q, 7, 4, X₁₁, X₁₂) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ T ≤ 7 ∧ U ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 1 ≤ T ∧ 1 ≤ U ∧ 0 ≤ O
t₅: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: Q ≤ 7 ∧ T ≤ 7 ∧ U ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ T ∧ 1 ≤ U ∧ 0 ≤ O ∧ X₁₁ ≤ R ∧ X₁₂ ≤ S
t₆: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 0 ≤ O
t₂: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → f2(0, O, P, N, Q, 0, O, P, N, Q, 2, X₁₁, X₁₂) :|: N ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ N ∧ 1+O ≤ X₁₂ ∧ 1+P ≤ X₁₁ ∧ 1 ≤ Q ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₂

Preprocessing

Eliminate variables [X₀; X₁; X₂; X₃; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀] that do not contribute to the problem

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: N, O, P, Q, R, S, T, U
Locations: f0, f1, f2, f4
Transitions:
t₁₇: f0(X₀, X₁) → f1(X₀, X₁)
t₁₈: f1(X₀, X₁) → f1(X₀, X₁) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 0 ≤ O
t₁₉: f1(X₀, X₁) → f2(X₀, X₁) :|: N ≤ 7 ∧ 1 ≤ N
t₂₀: f2(X₀, X₁) → f1(X₀, X₁) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 0 ≤ O
t₂₁: f2(X₀, X₁) → f4(X₀, X₁) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ T ≤ 7 ∧ U ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 1 ≤ T ∧ 1 ≤ U ∧ 0 ≤ O
t₂₂: f2(X₀, X₁) → f4(X₀, X₁) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ T ≤ 7 ∧ U ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 1 ≤ T ∧ 1 ≤ U ∧ 0 ≤ O
t₂₃: f4(X₀, X₁) → f1(X₀, X₁) :|: Q ≤ 7 ∧ T ≤ 7 ∧ U ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ T ∧ 1 ≤ U ∧ 0 ≤ O ∧ X₀ ≤ R ∧ X₁ ≤ S
t₂₄: f4(X₀, X₁) → f1(X₀, X₁) :|: Q ≤ 7 ∧ R ≤ 7 ∧ S ≤ 7 ∧ O ≤ 1 ∧ 1 ≤ Q ∧ 1 ≤ R ∧ 1 ≤ S ∧ 0 ≤ O
t₂₅: f4(X₀, X₁) → f2(X₀, X₁) :|: N ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ N ∧ 1+O ≤ X₁ ∧ 1+P ≤ X₀ ∧ 1 ≤ Q ∧ 1 ≤ X₀ ∧ 1 ≤ X₁

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f2_v1

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

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₃, X₀: X₀ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₄, X₀: X₀ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}