Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E, F
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(2, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₀, X₂) :|: X₀ ≤ 10
t₄: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 11 ≤ X₀
t₃: l2(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂)
t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, F) :|: E+1 ≤ D

Preprocessing

Eliminate variables {F,X₁,X₂} that do not contribute to the problem

Found invariant 2 ≤ X₀ for location l2

Found invariant 2 ≤ X₀ for location l1

Found invariant 11 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: D, E
Locations: l0, l1, l2, l3
Transitions:
t₁₁: l0(X₀) → l1(2)
t₁₂: l1(X₀) → l2(X₀) :|: X₀ ≤ 10 ∧ 2 ≤ X₀
t₁₃: l1(X₀) → l3(X₀) :|: 11 ≤ X₀ ∧ 2 ≤ X₀
t₁₅: l2(X₀) → l1(X₀+1) :|: 2 ≤ X₀
t₁₄: l2(X₀) → l2(X₀) :|: E+1 ≤ D ∧ 2 ≤ X₀

MPRF for transition t₁₂: l1(X₀) → l2(X₀) :|: X₀ ≤ 10 ∧ 2 ≤ X₀ of depth 1:

new bound:

13 {O(1)}

MPRF:

l2 [10-X₀ ]
l1 [11-X₀ ]

MPRF for transition t₁₅: l2(X₀) → l1(X₀+1) :|: 2 ≤ X₀ of depth 1:

new bound:

52 {O(1)}

MPRF:

l2 [4 ]
l1 [3 ]

Analysing control-flow refined program

Found invariant X₀ ≤ 10 ∧ 2 ≤ X₀ for location l2

Found invariant 2 ≤ X₀ for location l1

Found invariant 11 ≤ X₀ for location l3

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 13 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: 52 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 13 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: 52 {O(1)}

Sizebounds

t₁₁, X₀: 2 {O(1)}
t₁₂, X₀: 10 {O(1)}
t₁₃, X₀: 22 {O(1)}
t₁₄, X₀: 10 {O(1)}
t₁₅, X₀: 22 {O(1)}