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)
Analysing control-flow refined program
Cut unsatisfiable transition t₁₄₇: n_l1___3→l4
Cut unsatisfiable transition t₁₄₆: n_l1___4→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 t₁₃₀: 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:
n_l3___1 [X₀ ]
n_l1___3 [X₀+1 ]
MPRF for transition t₁₃₃: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2+X₀ ≤ X₃ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 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:
n_l3___1 [X₀ ]
n_l1___3 [X₀ ]
MPRF for transition t₁₃₁: 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+2 {O(n)}
MPRF:
n_l3___2 [X₃-X₀ ]
n_l1___4 [X₃+1-X₀ ]
MPRF for transition t₁₃₄: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 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)}
MPRF:
n_l3___2 [X₃-X₀ ]
n_l1___4 [X₃-X₀ ]
CFR: Improvement to new bound with the following program:
new bound:
2⋅X₃+4⋅X₂+4 {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
t₁₃₂: 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)
t₁₄₅: 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
t₁₃₀: 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
t₁₄₈: 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
t₁₃₁: 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
t₁₃₃: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2+X₀ ≤ X₃ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 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
t₁₃₄: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 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
t₁₃₅: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁, X₂, X₃) :|: X₂ < X₃ ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 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
t₁₃₆: 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+14 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁₃₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₁₃₀: X₂+1 {O(n)}
t₁₄₅: 1 {O(1)}
t₁₃₁: X₂+X₃+2 {O(n)}
t₁₄₈: 1 {O(1)}
t₁₃₃: X₂ {O(n)}
t₁₃₄: X₂+X₃+1 {O(n)}
t₁₃₅: 1 {O(1)}
t₁₃₆: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₃+4⋅X₂+14 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁₃₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₁₃₀: X₂+1 {O(n)}
t₁₄₅: 1 {O(1)}
t₁₃₁: X₂+X₃+2 {O(n)}
t₁₄₈: 1 {O(1)}
t₁₃₃: X₂ {O(n)}
t₁₃₄: X₂+X₃+1 {O(n)}
t₁₃₅: 1 {O(1)}
t₁₃₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, 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)}
t₁₃₂, X₀: X₂ {O(n)}
t₁₃₂, X₁: X₁ {O(n)}
t₁₃₂, X₂: X₂ {O(n)}
t₁₃₂, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, 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)}
t₁₃₀, X₀: X₂ {O(n)}
t₁₃₀, X₁: X₁ {O(n)}
t₁₃₀, X₂: X₂ {O(n)}
t₁₃₀, X₃: X₃ {O(n)}
t₁₄₅, X₀: 0 {O(1)}
t₁₄₅, X₁: 2⋅X₁ {O(n)}
t₁₄₅, X₂: 2⋅X₂ {O(n)}
t₁₄₅, X₃: 2⋅X₃ {O(n)}
t₁₃₁, X₀: 2⋅X₂+X₃+2 {O(n)}
t₁₃₁, X₁: X₁ {O(n)}
t₁₃₁, X₂: X₂ {O(n)}
t₁₃₁, X₃: X₃ {O(n)}
t₁₄₈, X₀: 3⋅X₂+X₃+3 {O(n)}
t₁₄₈, X₁: 2⋅X₁ {O(n)}
t₁₄₈, X₂: 2⋅X₂ {O(n)}
t₁₄₈, X₃: 2⋅X₃ {O(n)}
t₁₃₃, X₀: X₂ {O(n)}
t₁₃₃, X₁: X₁ {O(n)}
t₁₃₃, X₂: X₂ {O(n)}
t₁₃₃, X₃: X₃ {O(n)}
t₁₃₄, X₀: 2⋅X₂+X₃+2 {O(n)}
t₁₃₄, X₁: X₁ {O(n)}
t₁₃₄, X₂: X₂ {O(n)}
t₁₃₄, X₃: X₃ {O(n)}
t₁₃₅, X₀: X₂ {O(n)}
t₁₃₅, X₁: X₁ {O(n)}
t₁₃₅, X₂: X₂ {O(n)}
t₁₃₅, X₃: X₃ {O(n)}
t₁₃₆, X₀: X₂+1 {O(n)}
t₁₃₆, X₁: X₁ {O(n)}
t₁₃₆, X₂: X₂ {O(n)}
t₁₃₆, X₃: X₃ {O(n)}