Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 39
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: 40 ≤ X₀
t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₅: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ 0
t₆: l2(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁
t₇: l3(X₀, X₁) → l1(X₀+1, X₁)
t₈: l4(X₀, X₁) → l1(X₀+2, X₁)
t₉: l5(X₀, X₁) → l7(X₀, X₁)
t₁: l6(X₀, X₁) → l1(0, X₁)
Preprocessing
Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l2
Found invariant 40 ≤ X₀ for location l7
Found invariant 40 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l4
Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: 40 ≤ X₀ ∧ 0 ≤ X₀
t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₅: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₆: l2(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₇: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l4(X₀, X₁) → l1(X₀+2, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀
t₉: l5(X₀, X₁) → l7(X₀, X₁) :|: 40 ≤ X₀
t₁: l6(X₀, X₁) → l1(0, X₁)
MPRF for transition t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:
new bound:
1560 {O(1)}
MPRF:
l2 [1521-39⋅X₀ ]
l3 [1521-39⋅X₀ ]
l4 [1521-40⋅X₀ ]
l1 [1560-39⋅X₀ ]
MPRF for transition t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:
new bound:
1522 {O(1)}
MPRF:
l2 [1522-39⋅X₀ ]
l3 [1521-39⋅X₀ ]
l4 [1444-37⋅X₀ ]
l1 [1522-39⋅X₀ ]
MPRF for transition t₅: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:
new bound:
40 {O(1)}
MPRF:
l2 [40-X₀ ]
l3 [39-X₀ ]
l4 [38-X₀ ]
l1 [40-X₀ ]
MPRF for transition t₆: l2(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:
new bound:
1522 {O(1)}
MPRF:
l2 [1522-39⋅X₀ ]
l3 [1483-38⋅X₀ ]
l4 [1444-39⋅X₀ ]
l1 [1522-39⋅X₀ ]
MPRF for transition t₈: l4(X₀, X₁) → l1(X₀+2, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:
new bound:
40 {O(1)}
MPRF:
l2 [40-X₀ ]
l3 [39-X₀ ]
l4 [40-X₀ ]
l1 [40-X₀ ]
Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l2
Found invariant 40 ≤ X₀ for location l7
Found invariant 40 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l4
Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 39 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 39+X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ for location l3
Found invariant 1 ≤ 0 for location l2
Found invariant 1 ≤ 0 for location l7
Found invariant 1 ≤ 0 for location l5
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₇ 6724 {O(1)}
TWN-Loops:
entry: t₁: l6(X₀, X₁) → l1(0, X₁)
results in twn-loop: twn:Inv: [0 ≤ X₀ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀+1,X₁) :|: X₀ ≤ 39 ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
entry: t₈: l4(X₀, X₁) → l1(X₀+2, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₀ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀+1,X₁) :|: X₀ ≤ 39 ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
Termination: true
Formula:
0 < X₁ ∧ X₁ < 0 ∧ 1 < 0
∨ 0 < X₁ ∧ X₁ < 0 ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₁ ∧ X₁ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
∨ 0 < X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 < 0
∨ 0 < X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
∨ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ < 0 ∧ 1 < 0
∨ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ < 0 ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
Stabilization-Threshold for: X₀ ≤ 39
alphas_abs: X₀+39
M: 0
N: 1
Bound: 2⋅X₀+80 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: 0 {O(1)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 84 {O(1)}
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
Termination: true
Formula:
0 < X₁ ∧ X₁ < 0 ∧ 1 < 0
∨ 0 < X₁ ∧ X₁ < 0 ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₁ ∧ X₁ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
∨ 0 < X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 < 0
∨ 0 < X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
∨ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ < 0 ∧ 1 < 0
∨ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ < 0 ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ < 39 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 39 ∧ 39 ≤ X₀
Stabilization-Threshold for: X₀ ≤ 39
alphas_abs: X₀+39
M: 0
N: 1
Bound: 2⋅X₀+80 {O(n)}
relevant size-bounds w.r.t. t₈:
X₀: 41 {O(1)}
Runtime-bound of t₈: 40 {O(1)}
Results in: 6640 {O(1)}
6724 {O(1)}
All Bounds
Timebounds
Overall timebound:11412 {O(1)}
t₀: 1 {O(1)}
t₂: 1560 {O(1)}
t₃: 1 {O(1)}
t₄: 1522 {O(1)}
t₅: 40 {O(1)}
t₆: 1522 {O(1)}
t₇: 6724 {O(1)}
t₈: 40 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 11412 {O(1)}
t₀: 1 {O(1)}
t₂: 1560 {O(1)}
t₃: 1 {O(1)}
t₄: 1522 {O(1)}
t₅: 40 {O(1)}
t₆: 1522 {O(1)}
t₇: 6724 {O(1)}
t₈: 40 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: 39 {O(1)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: 81 {O(1)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: 39 {O(1)}
t₄, X₁: 0 {O(1)}
t₅, X₀: 39 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 39 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: 40 {O(1)}
t₇, X₁: 0 {O(1)}
t₈, X₀: 41 {O(1)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 81 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}