Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀-1, X₁+1) :|: 1 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 1 ≤ X₁

Preprocessing

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀-1, X₁+1) :|: 1 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0

MPRF for transition t₁: l1(X₀, X₁) → l1(X₀-1, X₁+1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

MPRF for transition t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

2⋅X₁+X₀ {O(n)}

MPRF:

l2 [X₁ ]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅X₁+X₀ {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅X₁+X₀ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀+X₁ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₁+X₀ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁+X₀ {O(n)}