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: X₁₁, X₁₂
Temp_Vars: N, O, P, Q, R, S, T, U
Locations: l0, l1, l2, l3
Transitions:
t₁₈: l0(X₁₁, X₁₂) → l1(X₁₁, X₁₂)
t₂₀: l1(X₁₁, X₁₂) → l1(X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₁₉: l1(X₁₁, X₁₂) → l2(X₁₁, X₁₂) :|: N ≤ 7 ∧ 1 ≤ N
t₂₁: l2(X₁₁, X₁₂) → l1(X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₂: l2(X₁₁, X₁₂) → l3(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
t₂₃: l2(X₁₁, X₁₂) → l3(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
t₂₅: l3(X₁₁, X₁₂) → l1(X₁₁, X₁₂) :|: X₁₁ ≤ R ∧ X₁₂ ≤ S ∧ 1 ≤ T ∧ T ≤ 7 ∧ 1 ≤ U ∧ U ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₆: l3(X₁₁, X₁₂) → l1(X₁₁, X₁₂) :|: 1 ≤ R ∧ R ≤ 7 ∧ 1 ≤ S ∧ S ≤ 7 ∧ 1 ≤ Q ∧ Q ≤ 7 ∧ O ≤ 1 ∧ 0 ≤ O
t₂₄: l3(X₁₁, X₁₂) → l2(X₁₁, X₁₂) :|: 1 ≤ X₁₁ ∧ P+1 ≤ X₁₁ ∧ 1 ≤ X₁₂ ∧ O+1 ≤ X₁₂ ∧ Q ≤ 7 ∧ N ≤ 7 ∧ 1 ≤ Q ∧ 1 ≤ N

Analysing control-flow refined program

Found invariant 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location n_l1___2

Found invariant 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location n_l2___3

Found invariant 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location n_l3___1

CFR did not improve the program. Rolling back

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: inf {Infinity}

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: inf {Infinity}

Sizebounds

t₁₈, X₁₁: X₁₁ {O(n)}
t₁₈, X₁₂: X₁₂ {O(n)}
t₁₉, X₁₁: 2⋅X₁₁ {O(n)}
t₁₉, X₁₂: 2⋅X₁₂ {O(n)}
t₂₀, X₁₁: 2⋅X₁₁ {O(n)}
t₂₀, X₁₂: 2⋅X₁₂ {O(n)}
t₂₁, X₁₁: 2⋅X₁₁ {O(n)}
t₂₁, X₁₂: 2⋅X₁₂ {O(n)}
t₂₂, X₁₁: 2⋅X₁₁ {O(n)}
t₂₂, X₁₂: 2⋅X₁₂ {O(n)}
t₂₃, X₁₁: 2⋅X₁₁ {O(n)}
t₂₃, X₁₂: 2⋅X₁₂ {O(n)}
t₂₄, X₁₁: 2⋅X₁₁ {O(n)}
t₂₄, X₁₂: 2⋅X₁₂ {O(n)}
t₂₅, X₁₁: 2⋅X₁₁ {O(n)}
t₂₅, X₁₂: 2⋅X₁₂ {O(n)}
t₂₆, X₁₁: 2⋅X₁₁ {O(n)}
t₂₆, X₁₂: 2⋅X₁₂ {O(n)}