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) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₁ < X₃
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₂, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 1
t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: 1 < X₀

Preprocessing

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4

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) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₂, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 1 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: 1 < X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁

Chain transitions t₉: l4→l1 and t₄: l1→l4 to t₉₄: l4→l4

Chain transitions t₈: l4→l1 and t₄: l1→l4 to t₉₅: l4→l4

Chain transitions t₈: l4→l1 and t₆: l1→l2 to t₉₆: l4→l2

Chain transitions t₉: l4→l1 and t₆: l1→l2 to t₉₇: l4→l2

Chain transitions t₇: l4→l1 and t₆: l1→l2 to t₉₈: l4→l2

Chain transitions t₇: l4→l1 and t₄: l1→l4 to t₉₉: l4→l4

Chain transitions t₇: l4→l1 and t₅: l1→l2 to t₁₀₀: l4→l2

Chain transitions t₈: l4→l1 and t₅: l1→l2 to t₁₀₁: l4→l2

Chain transitions t₉: l4→l1 and t₅: l1→l2 to t₁₀₂: l4→l2

Chain transitions t₃: l3→l1 and t₅: l1→l2 to t₁₀₃: l3→l2

Chain transitions t₃: l3→l1 and t₆: l1→l2 to t₁₀₄: l3→l2

Chain transitions t₃: l3→l1 and t₄: l1→l4 to t₁₀₅: l3→l4

Analysing control-flow refined program

Cut unsatisfiable transition t₉₆: l4→l2

Cut unsatisfiable transition t₉₇: l4→l2

Cut unsatisfiable transition t₁₀₀: l4→l2

Cut unsatisfiable transition t₁₀₃: l3→l2

Cut unsatisfiable transition t₁₀₄: l3→l2

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4

MPRF for transition t₉₄: l4(X₀, X₁, X₂, X₃) -{2}> l4(X₀, X₁-1, X₂, X₃) :|: 1 < X₀ ∧ 1 < X₁ ∧ X₁ < 1+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₉₅: l4(X₀, X₁, X₂, X₃) -{2}> l4(X₀, X₁-1, X₂, X₃) :|: X₀ < 1 ∧ 1 < X₁ ∧ X₁ < 1+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₉₉: l4(X₀, X₁, X₂, X₃) -{2}> l4(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 < 1+X₁ ∧ 1+X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂+X₃ {O(n)}

Analysing control-flow refined program

Cut unsatisfiable transition t₅: l1→l2

Cut unsatisfiable transition t₆: l1→l2

Cut unsatisfiable transition t₂₅₇: n_l1___6→l2

Cut unsatisfiable transition t₂₅₈: n_l1___4→l2

Cut unsatisfiable transition t₂₅₉: n_l1___5→l2

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___6

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___2

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___5

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l4___7

MPRF for transition t₂₃₃: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 < X₀ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₃₇: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ 1 < X₀ ∧ 1 < X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₃₄: n_l1___5(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₃₈: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ X₀ < 1 ∧ X₀ < 1 ∧ 1+X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₃₅: n_l1___6(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF for transition t₂₃₉: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: X₁ < X₃ ∧ 2 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ 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, l3, l5, n_l1___4, n_l1___5, n_l1___6, n_l4___1, n_l4___2, n_l4___3, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂₃₆: l1(X₀, X₁, X₂, X₃) → n_l4___7(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₂, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₂₅₅: n_l1___4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₃₃: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 < X₀ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₅₆: n_l1___5(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₃₄: n_l1___5(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₆₀: n_l1___6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₃₅: n_l1___6(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₃₇: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ 1 < X₀ ∧ 1 < X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₃₈: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ X₀ < 1 ∧ X₀ < 1 ∧ 1+X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₃₉: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: X₁ < X₃ ∧ 2 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₄₀: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₂₄₁: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ X₀ < 1 ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₂₄₂: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁

CFR: Improvement to new bound with the following program:

new bound:

2⋅X₃+6⋅X₂+4 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l5, n_l1___4, n_l1___5, n_l1___6, n_l4___1, n_l4___2, n_l4___3, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂₃₆: l1(X₀, X₁, X₂, X₃) → n_l4___7(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₂, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₂₅₅: n_l1___4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₃₃: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 < X₀ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₅₆: n_l1___5(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₃₄: n_l1___5(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₆₀: n_l1___6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₃₅: n_l1___6(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₃₇: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ 1 < X₀ ∧ 1 < X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₃₈: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ X₀ < 1 ∧ X₀ < 1 ∧ 1+X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₃₉: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: X₁ < X₃ ∧ 2 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₄₀: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₂₄₁: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ X₀ < 1 ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₂₄₂: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁

All Bounds

Timebounds

Overall timebound:2⋅X₃+6⋅X₂+16 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₁₀: 1 {O(1)}
t₂₃₃: X₂+1 {O(n)}
t₂₃₄: X₂ {O(n)}
t₂₃₅: X₂+X₃+2 {O(n)}
t₂₃₆: 1 {O(1)}
t₂₃₇: X₂ {O(n)}
t₂₃₈: X₂ {O(n)}
t₂₃₉: X₂+X₃+1 {O(n)}
t₂₄₀: 1 {O(1)}
t₂₄₁: 1 {O(1)}
t₂₄₂: 1 {O(1)}
t₂₅₅: 1 {O(1)}
t₂₅₆: 1 {O(1)}
t₂₆₀: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+6⋅X₂+16 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₁₀: 1 {O(1)}
t₂₃₃: X₂+1 {O(n)}
t₂₃₄: X₂ {O(n)}
t₂₃₅: X₂+X₃+2 {O(n)}
t₂₃₆: 1 {O(1)}
t₂₃₇: X₂ {O(n)}
t₂₃₈: X₂ {O(n)}
t₂₃₉: X₂+X₃+1 {O(n)}
t₂₄₀: 1 {O(1)}
t₂₄₁: 1 {O(1)}
t₂₄₂: 1 {O(1)}
t₂₅₅: 1 {O(1)}
t₂₅₆: 1 {O(1)}
t₂₆₀: 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: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₁₀, X₀: 6⋅X₀+1 {O(n)}
t₁₀, X₁: 2⋅X₁+3⋅X₂+X₃+3 {O(n)}
t₁₀, X₂: 8⋅X₂ {O(n)}
t₁₀, X₃: 8⋅X₃ {O(n)}
t₂₃₃, X₀: X₀ {O(n)}
t₂₃₃, X₁: X₂ {O(n)}
t₂₃₃, X₂: X₂ {O(n)}
t₂₃₃, X₃: X₃ {O(n)}
t₂₃₄, X₀: X₀ {O(n)}
t₂₃₄, X₁: X₂ {O(n)}
t₂₃₄, X₂: X₂ {O(n)}
t₂₃₄, X₃: X₃ {O(n)}
t₂₃₅, X₀: 1 {O(1)}
t₂₃₅, X₁: 2⋅X₂+X₃+2 {O(n)}
t₂₃₅, X₂: X₂ {O(n)}
t₂₃₅, X₃: X₃ {O(n)}
t₂₃₆, X₀: X₀ {O(n)}
t₂₃₆, X₁: X₂ {O(n)}
t₂₃₆, X₂: X₂ {O(n)}
t₂₃₆, X₃: X₃ {O(n)}
t₂₃₇, X₀: X₀ {O(n)}
t₂₃₇, X₁: X₂ {O(n)}
t₂₃₇, X₂: X₂ {O(n)}
t₂₃₇, X₃: X₃ {O(n)}
t₂₃₈, X₀: X₀ {O(n)}
t₂₃₈, X₁: X₂ {O(n)}
t₂₃₈, X₂: X₂ {O(n)}
t₂₃₈, X₃: X₃ {O(n)}
t₂₃₉, X₀: 1 {O(1)}
t₂₃₉, X₁: 2⋅X₂+X₃+2 {O(n)}
t₂₃₉, X₂: X₂ {O(n)}
t₂₃₉, X₃: X₃ {O(n)}
t₂₄₀, X₀: X₀ {O(n)}
t₂₄₀, X₁: X₂ {O(n)}
t₂₄₀, X₂: X₂ {O(n)}
t₂₄₀, X₃: X₃ {O(n)}
t₂₄₁, X₀: X₀ {O(n)}
t₂₄₁, X₁: X₂ {O(n)}
t₂₄₁, X₂: X₂ {O(n)}
t₂₄₁, X₃: X₃ {O(n)}
t₂₄₂, X₀: 1 {O(1)}
t₂₄₂, X₁: X₂+1 {O(n)}
t₂₄₂, X₂: X₂ {O(n)}
t₂₄₂, X₃: X₃ {O(n)}
t₂₅₅, X₀: 2⋅X₀ {O(n)}
t₂₅₅, X₁: 0 {O(1)}
t₂₅₅, X₂: 2⋅X₂ {O(n)}
t₂₅₅, X₃: 2⋅X₃ {O(n)}
t₂₅₆, X₀: 2⋅X₀ {O(n)}
t₂₅₆, X₁: 0 {O(1)}
t₂₅₆, X₂: 2⋅X₂ {O(n)}
t₂₅₆, X₃: 2⋅X₃ {O(n)}
t₂₆₀, X₀: 1 {O(1)}
t₂₆₀, X₁: 3⋅X₂+X₃+3 {O(n)}
t₂₆₀, X₂: 2⋅X₂ {O(n)}
t₂₆₀, X₃: 2⋅X₃ {O(n)}