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
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ < 0
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₀ < 0
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Preprocessing
Cut unsatisfiable transition t₆: l3→l1
Cut unsatisfiable transition t₇: l3→l1
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l1
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ 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 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀₈: n_l1___6→l4
Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ for location n_l1___6
Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___4
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ for location n_l1___9
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l3___3
Found invariant 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l1___2
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___11
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___8
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l1___5
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___1
Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l3___10
Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ for location n_l3___7
MPRF for transition t₈₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
X₃+2 {O(n)}
MPRF:
n_l3___1 [X₁ ]
n_l1___2 [X₁+1 ]
MPRF for transition t₈₇: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
X₃+2 {O(n)}
MPRF:
n_l3___1 [X₁+1 ]
n_l1___2 [X₁+1 ]
MPRF for transition t₈₆: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₂+2 {O(n)}
MPRF:
n_l3___8 [X₀ ]
n_l1___9 [X₀+1 ]
MPRF for transition t₉₅: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+2 {O(n)}
MPRF:
n_l3___8 [X₀+1 ]
n_l1___9 [X₀+1 ]
MPRF for transition t₈₃: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
3⋅X₂+5 {O(n)}
MPRF:
n_l3___4 [X₀ ]
n_l3___7 [X₀ ]
n_l1___6 [X₀+1 ]
MPRF for transition t₈₄: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
3⋅X₂+7 {O(n)}
MPRF:
n_l3___4 [X₀+1 ]
n_l3___7 [X₀+1 ]
n_l1___6 [X₀+2 ]
MPRF for transition t₉₂: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
3⋅X₂+5 {O(n)}
MPRF:
n_l3___4 [X₀+1 ]
n_l3___7 [X₀ ]
n_l1___6 [X₀+1 ]
MPRF for transition t₉₄: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
3⋅X₂+6 {O(n)}
MPRF:
n_l3___4 [X₀ ]
n_l3___7 [X₀+1 ]
n_l1___6 [X₀+1 ]
MPRF for transition t₈₂: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
6⋅X₃+3 {O(n)}
MPRF:
n_l3___3 [X₁ ]
n_l1___5 [X₁+1 ]
MPRF for transition t₉₁: n_l3___3(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
6⋅X₃+3 {O(n)}
MPRF:
n_l3___3 [X₁+1 ]
n_l1___5 [X₁+1 ]
CFR: Improvement to new bound with the following program:
new bound:
14⋅X₂+14⋅X₃+37 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l1___5, n_l1___6, n_l1___9, n_l3___1, n_l3___10, n_l3___11, n_l3___3, n_l3___4, n_l3___7, n_l3___8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₇₉: l1(X₀, X₁, X₂, X₃) → n_l3___10(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈₀: l1(X₀, X₁, X₂, X₃) → n_l3___11(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0
t₁₀₆: n_l1___2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₈₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₀₇: n_l1___5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₈₂: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₈₃: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₈₄: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₁₀₉: n_l1___9(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₈₅: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₈₆: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₈₇: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₈₈: n_l3___10(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₈₉: n_l3___10(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₉₀: n_l3___11(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₉₁: n_l3___3(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₉₂: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₉₃: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ < 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₉₄: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₉₅: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀
All Bounds
Timebounds
Overall timebound:14⋅X₂+14⋅X₃+51 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₁: 1 {O(1)}
t₉: 1 {O(1)}
t₈₁: X₃+2 {O(n)}
t₁₀₆: 1 {O(1)}
t₈₂: 6⋅X₃+3 {O(n)}
t₁₀₇: 1 {O(1)}
t₈₃: 3⋅X₂+5 {O(n)}
t₈₄: 3⋅X₂+7 {O(n)}
t₈₅: 1 {O(1)}
t₈₆: X₂+2 {O(n)}
t₁₀₉: 1 {O(1)}
t₈₇: X₃+2 {O(n)}
t₈₈: 1 {O(1)}
t₈₉: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₁: 6⋅X₃+3 {O(n)}
t₉₂: 3⋅X₂+5 {O(n)}
t₉₃: 1 {O(1)}
t₉₄: 3⋅X₂+6 {O(n)}
t₉₅: X₂+2 {O(n)}
Costbounds
Overall costbound: 14⋅X₂+14⋅X₃+51 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₁: 1 {O(1)}
t₉: 1 {O(1)}
t₈₁: X₃+2 {O(n)}
t₁₀₆: 1 {O(1)}
t₈₂: 6⋅X₃+3 {O(n)}
t₁₀₇: 1 {O(1)}
t₈₃: 3⋅X₂+5 {O(n)}
t₈₄: 3⋅X₂+7 {O(n)}
t₈₅: 1 {O(1)}
t₈₆: X₂+2 {O(n)}
t₁₀₉: 1 {O(1)}
t₈₇: X₃+2 {O(n)}
t₈₈: 1 {O(1)}
t₈₉: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₁: 6⋅X₃+3 {O(n)}
t₉₂: 3⋅X₂+5 {O(n)}
t₉₃: 1 {O(1)}
t₉₄: 3⋅X₂+6 {O(n)}
t₉₅: X₂+2 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₇₉, X₀: X₂ {O(n)}
t₇₉, X₁: X₃ {O(n)}
t₇₉, X₂: X₂ {O(n)}
t₇₉, X₃: X₃ {O(n)}
t₈₀, X₀: X₂ {O(n)}
t₈₀, X₁: X₃ {O(n)}
t₈₀, X₂: X₂ {O(n)}
t₈₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₉, X₀: 3⋅X₂+2 {O(n)}
t₉, X₁: 3⋅X₃+2 {O(n)}
t₉, X₂: 5⋅X₂ {O(n)}
t₉, X₃: 5⋅X₃ {O(n)}
t₈₁, X₀: X₂ {O(n)}
t₈₁, X₁: X₃+2 {O(n)}
t₈₁, X₂: X₂ {O(n)}
t₈₁, X₃: X₃ {O(n)}
t₁₀₆, X₀: 2⋅X₂ {O(n)}
t₁₀₆, X₁: 1 {O(1)}
t₁₀₆, X₂: 2⋅X₂ {O(n)}
t₁₀₆, X₃: 2⋅X₃ {O(n)}
t₈₂, X₀: 1 {O(1)}
t₈₂, X₁: 6⋅X₃+3 {O(n)}
t₈₂, X₂: 6⋅X₂ {O(n)}
t₈₂, X₃: 6⋅X₃ {O(n)}
t₁₀₇, X₀: 1 {O(1)}
t₁₀₇, X₁: 1 {O(1)}
t₁₀₇, X₂: 12⋅X₂ {O(n)}
t₁₀₇, X₃: 12⋅X₃ {O(n)}
t₈₃, X₀: 4⋅X₂+6 {O(n)}
t₈₃, X₁: 4⋅X₃ {O(n)}
t₈₃, X₂: 4⋅X₂ {O(n)}
t₈₃, X₃: 4⋅X₃ {O(n)}
t₈₄, X₀: 4⋅X₂+6 {O(n)}
t₈₄, X₁: 4⋅X₃ {O(n)}
t₈₄, X₂: 4⋅X₂ {O(n)}
t₈₄, X₃: 4⋅X₃ {O(n)}
t₈₅, X₀: 2⋅X₂+3 {O(n)}
t₈₅, X₁: 2⋅X₃ {O(n)}
t₈₅, X₂: 2⋅X₂ {O(n)}
t₈₅, X₃: 2⋅X₃ {O(n)}
t₈₆, X₀: X₂+2 {O(n)}
t₈₆, X₁: X₃ {O(n)}
t₈₆, X₂: X₂ {O(n)}
t₈₆, X₃: X₃ {O(n)}
t₁₀₉, X₀: 1 {O(1)}
t₁₀₉, X₁: 2⋅X₃ {O(n)}
t₁₀₉, X₂: 2⋅X₂ {O(n)}
t₁₀₉, X₃: 2⋅X₃ {O(n)}
t₈₇, X₀: X₂ {O(n)}
t₈₇, X₁: X₃+2 {O(n)}
t₈₇, X₂: X₂ {O(n)}
t₈₇, X₃: X₃ {O(n)}
t₈₈, X₀: X₂ {O(n)}
t₈₈, X₁: X₃+1 {O(n)}
t₈₈, X₂: X₂ {O(n)}
t₈₈, X₃: X₃ {O(n)}
t₈₉, X₀: X₂+1 {O(n)}
t₈₉, X₁: X₃ {O(n)}
t₈₉, X₂: X₂ {O(n)}
t₈₉, X₃: X₃ {O(n)}
t₉₀, X₀: X₂+1 {O(n)}
t₉₀, X₁: X₃ {O(n)}
t₉₀, X₂: X₂ {O(n)}
t₉₀, X₃: X₃ {O(n)}
t₉₁, X₀: 1 {O(1)}
t₉₁, X₁: 6⋅X₃+3 {O(n)}
t₉₁, X₂: 6⋅X₂ {O(n)}
t₉₁, X₃: 6⋅X₃ {O(n)}
t₉₂, X₀: 4⋅X₂+6 {O(n)}
t₉₂, X₁: 4⋅X₃ {O(n)}
t₉₂, X₂: 4⋅X₂ {O(n)}
t₉₂, X₃: 4⋅X₃ {O(n)}
t₉₃, X₀: 1 {O(1)}
t₉₃, X₁: 6⋅X₃+2 {O(n)}
t₉₃, X₂: 6⋅X₂ {O(n)}
t₉₃, X₃: 6⋅X₃ {O(n)}
t₉₄, X₀: 4⋅X₂+6 {O(n)}
t₉₄, X₁: 4⋅X₃ {O(n)}
t₉₄, X₂: 4⋅X₂ {O(n)}
t₉₄, X₃: 4⋅X₃ {O(n)}
t₉₅, X₀: X₂+2 {O(n)}
t₉₅, X₁: X₃ {O(n)}
t₉₅, X₂: X₂ {O(n)}
t₉₅, X₃: X₃ {O(n)}