Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ X₂ < 0
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ 0 < X₂
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ < 0
t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ 0 < X₂
t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
t₁₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₂
t₁₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₅
t₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(2⋅X₅, 2⋅X₅, X₂, X₃, X₄, X₅, X₆)
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₅
t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0
Preprocessing
Cut unsatisfiable transition t₁₀: l1→l4
Cut unsatisfiable transition t₁₁: l1→l4
Cut unsatisfiable transition t₁₃: l1→l4
Cut unsatisfiable transition t₁₄: l1→l4
Cut unsatisfiable transition t₁₅: l1→l4
Cut unsatisfiable transition t₁₆: l1→l4
Eliminate variables {X₃,X₄,X₆} that do not contribute to the problem
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₃ for location l5
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ for location l1
Found invariant 0 ≤ X₃ for location l4
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₃₆: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₃₇: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, X₁, X₂, X₃) :|: X₂ < 0 ∧ X₂ < 0 ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀
t₃₈: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, X₁, X₂, X₃) :|: 0 < X₂ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀
t₃₉: l1(X₀, X₁, X₂, X₃) → l4(X₁-1, X₁-1, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀
t₄₀: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀
t₄₁: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, nondef.0, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀
t₄₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃
t₄₃: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 0 ≤ X₃
t₄₄: l5(X₀, X₁, X₂, X₃) → l4(2⋅X₃, 2⋅X₃, X₂, X₃) :|: 0 ≤ X₃
t₄₅: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₄₆: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃
t₄₇: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ < 0
MPRF for transition t₃₉: l1(X₀, X₁, X₂, X₃) → l4(X₁-1, X₁-1, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 2:
new bound:
32⋅X₃+1 {O(n)}
MPRF for transition t₃₇: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, X₁, X₂, X₃) :|: X₂ < 0 ∧ X₂ < 0 ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₃⋅X₃+132⋅X₃+4 {O(n^2)}
MPRF for transition t₃₈: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, X₁, X₂, X₃) :|: 0 < X₂ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₃⋅X₃+132⋅X₃+4 {O(n^2)}
MPRF for transition t₄₀: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
MPRF for transition t₄₁: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, nondef.0, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
MPRF for transition t₄₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ of depth 1:
new bound:
1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
Chain transitions t₄₁: l3→l1 and t₃₉: l1→l4 to t₉₅: l3→l4
Chain transitions t₄₁: l3→l1 and t₃₈: l1→l4 to t₉₆: l3→l4
Chain transitions t₄₁: l3→l1 and t₃₇: l1→l4 to t₉₇: l3→l4
Chain transitions t₄₂: l4→l2 and t₄₀: l2→l3 to t₉₈: l4→l3
Chain transitions t₉₈: l4→l3 and t₉₇: l3→l4 to t₉₉: l4→l4
Chain transitions t₉₈: l4→l3 and t₉₆: l3→l4 to t₁₀₀: l4→l4
Chain transitions t₉₈: l4→l3 and t₉₅: l3→l4 to t₁₀₁: l4→l4
Chain transitions t₉₈: l4→l3 and t₄₁: l3→l1 to t₁₀₂: l4→l1
Analysing control-flow refined program
Eliminate variables {Temp_Int₃₇₃,X₂} that do not contribute to the problem
Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₂ for location l5
Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀ for location l1
Found invariant 0 ≤ X₂ for location l4
Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀ for location l3
MPRF for transition t₁₂₁: l4(X₀, X₁, X₂) -{4}> l4(X₁-1, X₁-1, X₂) :|: X₂ ≤ X₀ ∧ Temp_Int₃₆₈ ≤ 0 ∧ 0 ≤ Temp_Int₃₆₈ ∧ Temp_Int₃₆₈ ≤ 0 ∧ 0 ≤ Temp_Int₃₆₈ ∧ 0 ≤ X₂ of depth 2:
new bound:
32⋅X₂+1 {O(n)}
MPRF for transition t₁₁₉: l4(X₀, X₁, X₂) -{4}> l4(X₀-1, X₁, X₂) :|: X₂ ≤ X₀ ∧ Temp_Int₃₆₁ < 0 ∧ Temp_Int₃₆₁ < 0 ∧ 0 ≤ X₂ of depth 1:
new bound:
3360⋅X₂⋅X₂+364⋅X₂+9 {O(n^2)}
MPRF for transition t₁₂₀: l4(X₀, X₁, X₂) -{4}> l4(X₀-1, X₁, X₂) :|: X₂ ≤ X₀ ∧ 0 < Temp_Int₃₆₅ ∧ 0 < Temp_Int₃₆₅ ∧ 0 ≤ X₂ of depth 1:
new bound:
3360⋅X₂⋅X₂+364⋅X₂+9 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₄₃: l4→l6
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ for location n_l2___6
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___9
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ for location n_l1___4
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ for location n_l3___5
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___11
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___3
Found invariant 0 ≤ X₃ for location l5
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___2
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4
Found invariant X₃ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ 1+X₀ for location n_l4___8
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___1
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___10
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l4___7
MPRF for transition t₂₀₈: n_l1___1(X₀, X₁, X₂, X₃) → n_l4___7(X₁-1, X₁-1, 0, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₃+2 {O(n)}
MPRF for transition t₂₀₉: n_l1___1(X₀, X₁, X₂, X₃) → n_l4___8(X₀-1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ < 0 ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₃+2 {O(n)}
MPRF for transition t₂₁₀: n_l1___1(X₀, X₁, X₂, X₃) → n_l4___8(X₀-1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₃+2 {O(n)}
MPRF for transition t₂₁₈: n_l2___3(X₀, X₁, X₂, X₃) → n_l3___2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₃+2 {O(n)}
MPRF for transition t₂₂₁: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___1(X₀, X₁, NoDet0, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₃+2 {O(n)}
MPRF for transition t₂₂₄: n_l4___7(X₀, X₁, X₂, X₃) → n_l2___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
6⋅X₃+2 {O(n)}
MPRF for transition t₂₁₁: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___7(X₁-1, X₁-1, 0, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
12⋅X₃+8 {O(n)}
MPRF for transition t₂₁₂: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___8(X₀-1, X₁, X₂, X₃) :|: X₂ < 0 ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₃⋅X₃+128⋅X₃+32 {O(n^2)}
MPRF for transition t₂₁₃: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___8(X₀-1, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₃⋅X₃+128⋅X₃+32 {O(n^2)}
MPRF for transition t₂₁₉: n_l2___6(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₃⋅X₃+128⋅X₃+34 {O(n^2)}
MPRF for transition t₂₂₂: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁, NoDet0, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₃⋅X₃+128⋅X₃+34 {O(n^2)}
MPRF for transition t₂₂₅: n_l4___8(X₀, X₁, X₂, X₃) → n_l2___6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
336⋅X₃⋅X₃+320⋅X₃+74 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:5440⋅X₃⋅X₃+788⋅X₃+33 {O(n^2)}
t₃₆: 1 {O(1)}
t₃₇: 1088⋅X₃⋅X₃+132⋅X₃+4 {O(n^2)}
t₃₈: 1088⋅X₃⋅X₃+132⋅X₃+4 {O(n^2)}
t₃₉: 32⋅X₃+1 {O(n)}
t₄₀: 1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
t₄₁: 1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
t₄₂: 1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
Costbounds
Overall costbound: 5440⋅X₃⋅X₃+788⋅X₃+33 {O(n^2)}
t₃₆: 1 {O(1)}
t₃₇: 1088⋅X₃⋅X₃+132⋅X₃+4 {O(n^2)}
t₃₈: 1088⋅X₃⋅X₃+132⋅X₃+4 {O(n^2)}
t₃₉: 32⋅X₃+1 {O(n)}
t₄₀: 1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
t₄₁: 1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
t₄₂: 1088⋅X₃⋅X₃+164⋅X₃+6 {O(n^2)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
Sizebounds
t₃₆, X₀: X₀ {O(n)}
t₃₆, X₁: X₁ {O(n)}
t₃₆, X₂: X₂ {O(n)}
t₃₆, X₃: X₃ {O(n)}
t₃₇, X₀: 36⋅X₃+3 {O(n)}
t₃₇, X₁: 34⋅X₃+1 {O(n)}
t₃₇, X₃: X₃ {O(n)}
t₃₈, X₀: 36⋅X₃+3 {O(n)}
t₃₈, X₁: 34⋅X₃+1 {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₉, X₀: 34⋅X₃+2 {O(n)}
t₃₉, X₁: 34⋅X₃+1 {O(n)}
t₃₉, X₂: 0 {O(1)}
t₃₉, X₃: X₃ {O(n)}
t₄₀, X₀: 36⋅X₃+3 {O(n)}
t₄₀, X₁: 34⋅X₃+1 {O(n)}
t₄₀, X₃: X₃ {O(n)}
t₄₁, X₀: 36⋅X₃+3 {O(n)}
t₄₁, X₁: 34⋅X₃+1 {O(n)}
t₄₁, X₃: X₃ {O(n)}
t₄₂, X₀: 36⋅X₃+3 {O(n)}
t₄₂, X₁: 34⋅X₃+1 {O(n)}
t₄₂, X₃: X₃ {O(n)}
t₄₃, X₀: 106⋅X₃+8 {O(n)}
t₄₃, X₁: 102⋅X₃+3 {O(n)}
t₄₃, X₃: 3⋅X₃ {O(n)}
t₄₄, X₀: 2⋅X₃ {O(n)}
t₄₄, X₁: 2⋅X₃ {O(n)}
t₄₄, X₂: X₂ {O(n)}
t₄₄, X₃: X₃ {O(n)}
t₄₅, X₀: 106⋅X₃+X₀+8 {O(n)}
t₄₅, X₁: 102⋅X₃+X₁+3 {O(n)}
t₄₅, X₃: 4⋅X₃ {O(n)}
t₄₆, X₀: X₀ {O(n)}
t₄₆, X₁: X₁ {O(n)}
t₄₆, X₂: X₂ {O(n)}
t₄₆, X₃: X₃ {O(n)}
t₄₇, X₀: X₀ {O(n)}
t₄₇, X₁: X₁ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₃: X₃ {O(n)}