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) :|: X₀ < 100
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 100 ≤ X₀
t₁: l2(X₀, X₁) → l1(0, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 50
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 50 ≤ X₀
t₆: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Eliminate variables {X₁} that do not contribute to the problem

Found invariant 100 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant 100 ≤ X₀ for location l4

Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3

Cut unsatisfiable transition t₁₆: l1→l4

Cut unreachable locations [l4; l5] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₄: l0(X₀) → l2(X₀)
t₁₅: l1(X₀) → l3(X₀) :|: X₀ < 100 ∧ 0 ≤ X₀
t₁₇: l2(X₀) → l1(0)
t₁₈: l3(X₀) → l1(X₀+1) :|: X₀ < 50 ∧ X₀ ≤ 99 ∧ 0 ≤ X₀
t₁₉: l3(X₀) → l1(X₀-1) :|: 50 ≤ X₀ ∧ X₀ ≤ 99 ∧ 0 ≤ X₀

Analysing control-flow refined program

Found invariant X₀ ≤ 50 ∧ 2 ≤ X₀ for location n_l1___6

Found invariant X₀ ≤ 98 ∧ 49 ≤ X₀ for location n_l1___4

Found invariant X₀ ≤ 98 ∧ 49 ≤ X₀ for location n_l3___3

Found invariant X₀ ≤ 99 ∧ 2 ≤ X₀ for location n_l3___5

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location n_l1___2

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___8

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___9

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location n_l3___1

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___7

Found invariant X₀ ≤ 50 ∧ 2 ≤ X₀ for location n_l1___6

Found invariant X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l1___4

Found invariant X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l3___3

Found invariant X₀ ≤ 50 ∧ 2 ≤ X₀ for location n_l3___5

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location n_l1___2

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___8

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___9

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location n_l3___1

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___7

Time-Bound by TWN-Loops:

TWN-Loops: t₁₂₇ 512 {O(1)}

TWN-Loops:

entry: t₁₃₄: n_l3___7(X₀) → n_l1___6(X₀+1) :|: X₀ < 50 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ < 50 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [X₀ ≤ 50 ∧ 2 ≤ X₀ ∧ X₀ ≤ 99 ∧ 2 ≤ X₀] , (X₀) -> (X₀+1) :|: 0 ≤ X₀ ∧ X₀ < 100 ∧ X₀ ≤ 99 ∧ 0 ≤ X₀ ∧ X₀ ≤ 99 ∧ 0 ≤ X₀ ∧ X₀ < 100 ∧ X₀ ≤ 99 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ < 50
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < 0 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ < 99 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ 1 < 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ 1 < 0 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 0 < X₀ ∧ X₀ < 99 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ 1 < 0
∨ 1 < 0 ∧ 0 < X₀ ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < 99 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ 1 < 0
∨ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ X₀ < 50 ∧ 0 < 1 ∧ 1 < 0 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 < 1 ∧ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 50 ∧ 0 < 1 ∧ X₀ < 99 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ 1 < 0
∨ X₀ < 50 ∧ 0 < 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₀ < 50 ∧ 0 < X₀ ∧ 1 < 0 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 < X₀ ∧ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 50 ∧ 0 < X₀ ∧ X₀ < 99 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ 1 < 0
∨ X₀ < 50 ∧ 0 < X₀ ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ X₀ < 50 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 50 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < 99 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 50 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ 1 < 0
∨ X₀ < 50 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀ ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₀ < 50
alphas_abs: 50
M: 0
N: 1
Bound: 102 {O(1)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: X₀ ≤ 99
alphas_abs: 99
M: 0
N: 1
Bound: 200 {O(1)}
Stabilization-Threshold for: X₀ < 100
alphas_abs: 100
M: 0
N: 1
Bound: 202 {O(1)}

relevant size-bounds w.r.t. t₁₃₄:
X₀: 2 {O(1)}
Runtime-bound of t₁₃₄: 1 {O(1)}
Results in: 512 {O(1)}

512 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃₃ 512 {O(1)}

relevant size-bounds w.r.t. t₁₃₄:
X₀: 2 {O(1)}
Runtime-bound of t₁₃₄: 1 {O(1)}
Results in: 512 {O(1)}

512 {O(1)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₅, X₀: 99 {O(1)}
t₁₇, X₀: 0 {O(1)}
t₁₈, X₀: 50 {O(1)}
t₁₉, X₀: 98 {O(1)}