Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 5 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 5
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 10
t₅: l3(X₀, X₁) → l1(X₀, X₁) :|: 10 ≤ X₀
t₆: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₀ ≤ X₁ for location l1

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l4

Found invariant 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 5 < X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 5 ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 10 ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀, X₁) :|: 10 ≤ X₀ ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀
t₆: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ 5

Analysing control-flow refined program

Cut unsatisfiable transition t₁₃₆: n_l1___3→l4

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 17 ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 5 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ X₀ ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l1___3

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 14 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 17 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 6 ≤ X₀ for location n_l3___2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 14 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l4

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l3___1

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 17 ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 5 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ X₀ ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l1___3

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 14 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 17 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 6 ≤ X₀ for location n_l3___2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 14 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l4

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l3___1

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 17 ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 5 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ X₀ ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l1___3

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 14 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 17 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 6 ≤ X₀ for location n_l3___2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1

Found invariant X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 14 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l4

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l3___1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₂₄ 134 {O(1)}

TWN-Loops:

entry: t₁₂₉: n_l3___5(X₀, X₁) → n_l1___4(X₀-1, X₁) :|: 5 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 10 ∧ X₁ ≤ X₀ ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 9 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 17 ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 5 ≤ X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 17 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 8 ∧ 6 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: X₀ < 10 ∧ X₀ ≤ X₁ ∧ 5 < X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 10 ∧ 5 < X₀ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 10
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁

Termination: true
Formula:

0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < 0 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 1 ∧ 6 < X₀ ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0
∨ 0 < 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ X₀ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < 1 ∧ X₀ < X₁ ∧ 1 < 0 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ X₀ < X₁ ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀ < X₁ ∧ 6 < X₀ ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0
∨ 0 < 1 ∧ X₀ < X₁ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ 0 < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 6 < X₀ ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0
∨ 0 < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1 < 0
∨ X₀ < 10 ∧ 0 < 1 ∧ 1 < 0 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ 0 < 1 ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 10 ∧ 0 < 1 ∧ 6 < X₀ ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0
∨ X₀ < 10 ∧ 0 < 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ X₀ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₀ < 10 ∧ X₀ < X₁ ∧ 1 < 0 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ X₀ < X₁ ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 10 ∧ X₀ < X₁ ∧ 6 < X₀ ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0
∨ X₀ < 10 ∧ X₀ < X₁ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ < 10 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 10 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 6 < X₀ ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 10 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0
∨ X₀ < 10 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₀ < 10
alphas_abs: 10+X₀
M: 0
N: 1
Bound: 2⋅X₀+22 {O(n)}
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 6 ≤ X₀
alphas_abs: 6+X₀
M: 0
N: 1
Bound: 2⋅X₀+14 {O(n)}
Stabilization-Threshold for: 5 < X₀
alphas_abs: 5+X₀
M: 0
N: 1
Bound: 2⋅X₀+12 {O(n)}

relevant size-bounds w.r.t. t₁₂₉:
X₀: 8 {O(1)}
X₁: 9 {O(1)}
Runtime-bound of t₁₂₉: 1 {O(1)}
Results in: 134 {O(1)}

134 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₂₇ 134 {O(1)}

relevant size-bounds w.r.t. t₁₂₉:
X₀: 8 {O(1)}
X₁: 9 {O(1)}
Runtime-bound of t₁₂₉: 1 {O(1)}
Results in: 134 {O(1)}

134 {O(1)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: X₁+8 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+8 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₄, X₀: 8 {O(1)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₁+8 {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: X₁+8 {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}