Initial Problem

Start: l0
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: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l2(0, O, P, 3, N, 0, O, P, 3, N, 2, X₁₁, X₁₂) :|: N ≤ 7 ∧ 1 ≤ N
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l3(O, P, N, Q, 2, O, P, N, Q, 2, 4, X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ T ∧ T ≤ 7 ∧ 1 ≤ U ∧ U ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l3(O, P, N, Q, 7, O, P, N, Q, 7, 4, X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ T ∧ T ≤ 7 ∧ 1 ≤ U ∧ U ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: X₁₁ ≤ R ∧ X₁₂ ≤ S ∧ 1 ≤ T ∧ T ≤ 7 ∧ 1 ≤ U ∧ U ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(O, P, N, 2, Q, O, P, N, 2, Q, 1, X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l2(0, O, P, N, Q, 0, O, P, N, Q, 2, X₁₁, X₁₂) :|: 1 ≤ X₁₁ ∧ P+1 ≤ X₁₁ ∧ 1 ≤ X₁₂ ∧ O+1 ≤ X₁₂ ∧ Q ≤ 7 ∧ N ≤ 7 ∧ 1 ≤ Q ∧ 1 ≤ N

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: l0
Program_Vars: X₀, X₁
Temp_Vars: N, O, P, Q, R, S, T, U
Locations: l0, l1, l2, l3
Transitions:
t₁₇: l0(X₀, X₁) → l1(X₀, X₁)
t₁₈: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₁₉: l1(X₀, X₁) → l2(X₀, X₁) :|: N ≤ 7 ∧ 1 ≤ N
t₂₀: l2(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₁: l2(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ T ∧ T ≤ 7 ∧ 1 ≤ U ∧ U ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₂: l2(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ T ∧ T ≤ 7 ∧ 1 ≤ U ∧ U ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₃: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ R ∧ X₁ ≤ S ∧ 1 ≤ T ∧ T ≤ 7 ∧ 1 ≤ U ∧ U ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₄: l3(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₅: l3(X₀, X₁) → l2(X₀, X₁) :|: 1 ≤ X₀ ∧ P+1 ≤ X₀ ∧ 1 ≤ X₁ ∧ O+1 ≤ X₁ ∧ Q ≤ 7 ∧ N ≤ 7 ∧ 1 ≤ Q ∧ 1 ≤ N

Chain transitions t₂₅: l3→l2 and t₂₂: l2→l3 to t₁₅₀: l3→l3

Chain transitions t₁₉: l1→l2 and t₂₂: l2→l3 to t₁₅₁: l1→l3

Chain transitions t₁₉: l1→l2 and t₂₁: l2→l3 to t₁₅₂: l1→l3

Chain transitions t₂₅: l3→l2 and t₂₁: l2→l3 to t₁₅₃: l3→l3

Chain transitions t₁₉: l1→l2 and t₂₀: l2→l1 to t₁₅₄: l1→l1

Chain transitions t₂₅: l3→l2 and t₂₀: l2→l1 to t₁₅₅: l3→l1

Analysing control-flow refined program

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___2

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___3

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

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)}