Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀)
t₁: l1(X₀) → l1(X₀-1) :|: 2 ≤ X₀
t₂: l1(X₀) → l1(X₀-1)

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀)
t₁: l1(X₀) → l1(X₀-1) :|: 2 ≤ X₀
t₂: l1(X₀) → l1(X₀-1)

MPRF for transition t₁: l1(X₀) → l1(X₀-1) :|: 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

Analysing control-flow refined program

Found invariant 1 ≤ X₀ for location n_l1___1

MPRF for transition t₄₆: l1(X₀) → n_l1___1(X₀-1) :|: 2 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l1___1 [X₀-2 ]
l1 [X₀-1 ]

MPRF for transition t₄₄: n_l1___1(X₀) → n_l1___1(X₀-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

n_l1___1 [X₀ ]
l1 [X₀ ]

MPRF for transition t₄₅: n_l1___1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l1___1 [X₀ ]
l1 [X₀-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}