Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ < X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 0 < X₁
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ < X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 0 < X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Chain transitions t₆: l3→l1 and t₄: l1→l4 to t₆₁: l3→l4
Chain transitions t₅: l3→l1 and t₄: l1→l4 to t₆₂: l3→l4
Chain transitions t₅: l3→l1 and t₃: l1→l4 to t₆₃: l3→l4
Chain transitions t₆: l3→l1 and t₃: l1→l4 to t₆₄: l3→l4
Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₆₅: l2→l4
Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₆₆: l2→l4
Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₆₇: l2→l3
Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₆₈: l3→l3
Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₆₉: l3→l3
Analysing control-flow refined program
Cut unsatisfiable transition t₆₁: l3→l4
Cut unsatisfiable transition t₆₃: l3→l4
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₆₈: l3(X₀, X₁, X₂, X₃) -{2}> l3(1+X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 0 < 1+X₀ ∧ 1+X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF for transition t₆₉: l3(X₀, X₁, X₂, X₃) -{2}> l3(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 1 < X₀ ∧ X₀ < 1+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
Analysing control-flow refined program
Cut unsatisfiable transition t₁₆₄: n_l1___4→l4
Cut unsatisfiable transition t₁₆₅: n_l1___3→l4
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___4
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l3___5
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___2
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1
Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l3___1
MPRF for transition t₁₄₈: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₃ ∧ X₀ < X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 2+X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 < X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF for transition t₁₅₁: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2+X₀ ≤ X₃ ∧ 0 < X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₁₄₉: n_l1___4(X₀, X₁, X₂, X₃) → n_l3___2(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 < X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF for transition t₁₅₂: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___3, n_l1___4, n_l3___1, n_l3___2, n_l3___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₅₀: l1(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₀ ∧ X₀ < X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁₆₃: n_l1___3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₄₈: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₃ ∧ X₀ < X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 2+X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 < X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₆₆: n_l1___4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₄₉: n_l1___4(X₀, X₁, X₂, X₃) → n_l3___2(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 < X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₅₁: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2+X₀ ≤ X₃ ∧ 0 < X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁₅₂: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₅₃: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₂ < X₃ ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₅₄: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₂ < X₃ ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
2⋅X₃+4⋅X₂+3 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___3, n_l1___4, n_l3___1, n_l3___2, n_l3___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₅₀: l1(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₀ ∧ X₀ < X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁₆₃: n_l1___3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₄₈: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₃ ∧ X₀ < X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 2+X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 < X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₆₆: n_l1___4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₄₉: n_l1___4(X₀, X₁, X₂, X₃) → n_l3___2(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 < X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₅₁: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2+X₀ ≤ X₃ ∧ 0 < X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁₅₂: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₅₃: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₂ < X₃ ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₅₄: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₂ < X₃ ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:2⋅X₃+4⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄₈: X₂+1 {O(n)}
t₁₄₉: X₂+X₃+1 {O(n)}
t₁₅₀: 1 {O(1)}
t₁₅₁: X₂ {O(n)}
t₁₅₂: X₂+X₃+1 {O(n)}
t₁₅₃: 1 {O(1)}
t₁₅₄: 1 {O(1)}
t₁₆₃: 1 {O(1)}
t₁₆₆: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₃+4⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄₈: X₂+1 {O(n)}
t₁₄₉: X₂+X₃+1 {O(n)}
t₁₅₀: 1 {O(1)}
t₁₅₁: X₂ {O(n)}
t₁₅₂: X₂+X₃+1 {O(n)}
t₁₅₃: 1 {O(1)}
t₁₅₄: 1 {O(1)}
t₁₆₃: 1 {O(1)}
t₁₆₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₇, X₀: 5⋅X₂+X₃+3 {O(n)}
t₇, X₁: 6⋅X₁ {O(n)}
t₇, X₂: 6⋅X₂ {O(n)}
t₇, X₃: 6⋅X₃ {O(n)}
t₁₄₈, X₀: X₂ {O(n)}
t₁₄₈, X₁: X₁ {O(n)}
t₁₄₈, X₂: X₂ {O(n)}
t₁₄₈, X₃: X₃ {O(n)}
t₁₄₉, X₀: 2⋅X₂+X₃+2 {O(n)}
t₁₄₉, X₁: X₁ {O(n)}
t₁₄₉, X₂: X₂ {O(n)}
t₁₄₉, X₃: X₃ {O(n)}
t₁₅₀, X₀: X₂ {O(n)}
t₁₅₀, X₁: X₁ {O(n)}
t₁₅₀, X₂: X₂ {O(n)}
t₁₅₀, X₃: X₃ {O(n)}
t₁₅₁, X₀: X₂ {O(n)}
t₁₅₁, X₁: X₁ {O(n)}
t₁₅₁, X₂: X₂ {O(n)}
t₁₅₁, X₃: X₃ {O(n)}
t₁₅₂, X₀: 2⋅X₂+X₃+2 {O(n)}
t₁₅₂, X₁: X₁ {O(n)}
t₁₅₂, X₂: X₂ {O(n)}
t₁₅₂, X₃: X₃ {O(n)}
t₁₅₃, X₀: X₂ {O(n)}
t₁₅₃, X₁: X₁ {O(n)}
t₁₅₃, X₂: X₂ {O(n)}
t₁₅₃, X₃: X₃ {O(n)}
t₁₅₄, X₀: X₂+1 {O(n)}
t₁₅₄, X₁: X₁ {O(n)}
t₁₅₄, X₂: X₂ {O(n)}
t₁₅₄, X₃: X₃ {O(n)}
t₁₆₃, X₀: 0 {O(1)}
t₁₆₃, X₁: 2⋅X₁ {O(n)}
t₁₆₃, X₂: 2⋅X₂ {O(n)}
t₁₆₃, X₃: 2⋅X₃ {O(n)}
t₁₆₆, X₀: 3⋅X₂+X₃+3 {O(n)}
t₁₆₆, X₁: 2⋅X₁ {O(n)}
t₁₆₆, X₂: 2⋅X₂ {O(n)}
t₁₆₆, X₃: 2⋅X₃ {O(n)}