Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁-10, X₀-1) :|: X₁ ≤ 110
t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁-10, X₀-1) :|: X₀ ≤ 1
t₁₀: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁-10, X₀-1) :|: 3 ≤ X₀
t₁₁: l1(X₀, X₁, X₂, X₃) → l5(X₀-1, X₁-10, X₂, X₃) :|: 111 ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₁₆: l2(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 101 ≤ X₁
t₃: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 100
t₁₂: l4(X₀, X₁, X₂, X₃) → l5(X₃, X₂+1, X₂, X₃) :|: 101 ≤ X₂
t₁₃: l4(X₀, X₁, X₂, X₃) → l5(X₃, X₂+11, X₂, X₃) :|: 101 ≤ X₂ ∧ X₂ ≤ 100
t₁₄: l4(X₀, X₁, X₂, X₃) → l5(X₃+1, X₂+1, X₂, X₃) :|: X₂ ≤ 100 ∧ 101 ≤ X₂
t₁₅: l4(X₀, X₁, X₂, X₃) → l5(X₃+1, X₂+11, X₂, X₃) :|: X₂ ≤ 100
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₅: l6(X₀, X₁, X₂, X₃) → l3(X₀+1, X₁+11, X₂, X₃)
t₁: l7(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 101 ≤ X₀
t₂: l7(X₀, X₁, X₂, X₃) → l3(1, X₀, X₂, X₃) :|: X₀ ≤ 100
Preprocessing
Cut unsatisfiable transition t₉: l1→l4
Cut unsatisfiable transition t₁₃: l4→l5
Cut unsatisfiable transition t₁₄: l4→l5
Found invariant 1 ≤ X₀ for location l2
Found invariant X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ for location l6
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 1 ≤ X₀ for location l8
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1
Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 92 ≤ X₂+X₃ ∧ X₂ ≤ 99+X₃ ∧ 102 ≤ X₁+X₃ ∧ X₁ ≤ 109+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ 101 ∧ 10+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 212 ∧ X₂ ≤ 98+X₀ ∧ 91 ≤ X₂ ∧ 192 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ 93 ≤ X₀+X₂ ∧ X₁ ≤ 111 ∧ X₁ ≤ 108+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 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, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁-10, X₀-1) :|: X₁ ≤ 110 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁-10, X₀-1) :|: 3 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₁: l1(X₀, X₁, X₂, X₃) → l5(X₀-1, X₁-10, X₂, X₃) :|: 111 ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₆: l2(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 1 ≤ X₀
t₃: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 1 ≤ X₀
t₁₂: l4(X₀, X₁, X₂, X₃) → l5(X₃, X₂+1, X₂, X₃) :|: 101 ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 92 ≤ X₂+X₃ ∧ X₂ ≤ 99+X₃ ∧ 102 ≤ X₁+X₃ ∧ X₁ ≤ 109+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ 101 ∧ 10+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 212 ∧ X₂ ≤ 98+X₀ ∧ 91 ≤ X₂ ∧ 192 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ 93 ≤ X₀+X₂ ∧ X₁ ≤ 111 ∧ X₁ ≤ 108+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₅: l4(X₀, X₁, X₂, X₃) → l5(X₃+1, X₂+11, X₂, X₃) :|: X₂ ≤ 100 ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 92 ≤ X₂+X₃ ∧ X₂ ≤ 99+X₃ ∧ 102 ≤ X₁+X₃ ∧ X₁ ≤ 109+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ 101 ∧ 10+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 212 ∧ X₂ ≤ 98+X₀ ∧ 91 ≤ X₂ ∧ 192 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ 93 ≤ X₀+X₂ ∧ X₁ ≤ 111 ∧ X₁ ≤ 108+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l6(X₀, X₁, X₂, X₃) → l3(X₀+1, X₁+11, X₂, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 101 ≤ X₀
t₂: l7(X₀, X₁, X₂, X₃) → l3(1, X₀, X₂, X₃) :|: X₀ ≤ 100
MPRF for transition t₃: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+101 {O(n)}
MPRF for transition t₅: l6(X₀, X₁, X₂, X₃) → l3(X₀+1, X₁+11, X₂, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+101 {O(n)}
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
11⋅X₀+1324 {O(n)}
MPRF for transition t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁-10, X₀-1) :|: X₁ ≤ 110 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
10⋅X₀+1222 {O(n)}
MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁-10, X₀-1) :|: 3 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
10⋅X₀+1213 {O(n)}
MPRF for transition t₁₁: l1(X₀, X₁, X₂, X₃) → l5(X₀-1, X₁-10, X₂, X₃) :|: 111 ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
10⋅X₀+1039 {O(n)}
MPRF for transition t₁₂: l4(X₀, X₁, X₂, X₃) → l5(X₃, X₂+1, X₂, X₃) :|: 101 ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 92 ≤ X₂+X₃ ∧ X₂ ≤ 99+X₃ ∧ 102 ≤ X₁+X₃ ∧ X₁ ≤ 109+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ 101 ∧ 10+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 212 ∧ X₂ ≤ 98+X₀ ∧ 91 ≤ X₂ ∧ 192 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ 93 ≤ X₀+X₂ ∧ X₁ ≤ 111 ∧ X₁ ≤ 108+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+103 {O(n)}
MPRF for transition t₁₅: l4(X₀, X₁, X₂, X₃) → l5(X₃+1, X₂+11, X₂, X₃) :|: X₂ ≤ 100 ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 92 ≤ X₂+X₃ ∧ X₂ ≤ 99+X₃ ∧ 102 ≤ X₁+X₃ ∧ X₁ ≤ 109+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ 101 ∧ 10+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 212 ∧ X₂ ≤ 98+X₀ ∧ 91 ≤ X₂ ∧ 192 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ 93 ≤ X₀+X₂ ∧ X₁ ≤ 111 ∧ X₁ ≤ 108+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
10⋅X₀+1230 {O(n)}
All Bounds
Timebounds
Overall timebound:54⋅X₀+6339 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+101 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+101 {O(n)}
t₆: 11⋅X₀+1324 {O(n)}
t₇: 1 {O(1)}
t₈: 10⋅X₀+1222 {O(n)}
t₁₀: 10⋅X₀+1213 {O(n)}
t₁₁: 10⋅X₀+1039 {O(n)}
t₁₂: X₀+103 {O(n)}
t₁₅: 10⋅X₀+1230 {O(n)}
t₁₆: 1 {O(1)}
Costbounds
Overall costbound: 54⋅X₀+6339 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+101 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+101 {O(n)}
t₆: 11⋅X₀+1324 {O(n)}
t₇: 1 {O(1)}
t₈: 10⋅X₀+1222 {O(n)}
t₁₀: 10⋅X₀+1213 {O(n)}
t₁₁: 10⋅X₀+1039 {O(n)}
t₁₂: X₀+103 {O(n)}
t₁₅: 10⋅X₀+1230 {O(n)}
t₁₆: 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: 1 {O(1)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀+102 {O(n)}
t₃, X₁: 12⋅X₀+1111 {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀+102 {O(n)}
t₄, X₁: 111 {O(1)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀+102 {O(n)}
t₅, X₁: 12⋅X₀+1111 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀+102 {O(n)}
t₆, X₁: 111 {O(1)}
t₆, X₂: X₂+201 {O(n)}
t₆, X₃: 3⋅X₀+X₃+306 {O(n)}
t₇, X₀: 1 {O(1)}
t₇, X₁: 110 {O(1)}
t₇, X₂: 2⋅X₂+201 {O(n)}
t₇, X₃: 2⋅X₃+3⋅X₀+306 {O(n)}
t₈, X₀: X₀+102 {O(n)}
t₈, X₁: 110 {O(1)}
t₈, X₂: 100 {O(1)}
t₈, X₃: X₀+102 {O(n)}
t₁₀, X₀: X₀+102 {O(n)}
t₁₀, X₁: 111 {O(1)}
t₁₀, X₂: 101 {O(1)}
t₁₀, X₃: X₀+102 {O(n)}
t₁₁, X₀: 1 {O(1)}
t₁₁, X₁: 101 {O(1)}
t₁₁, X₂: X₂+201 {O(n)}
t₁₁, X₃: 3⋅X₀+X₃+306 {O(n)}
t₁₂, X₀: X₀+102 {O(n)}
t₁₂, X₁: 102 {O(1)}
t₁₂, X₂: 101 {O(1)}
t₁₂, X₃: X₀+102 {O(n)}
t₁₅, X₀: X₀+102 {O(n)}
t₁₅, X₁: 111 {O(1)}
t₁₅, X₂: 100 {O(1)}
t₁₅, X₃: 2⋅X₀+204 {O(n)}
t₁₆, X₀: X₀+1 {O(n)}
t₁₆, X₁: X₁+110 {O(n)}
t₁₆, X₂: 3⋅X₂+201 {O(n)}
t₁₆, X₃: 3⋅X₀+3⋅X₃+306 {O(n)}