Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef_0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, 1) :|: 0 < X₁
t₄: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ < X₂
t₅: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁₁: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂)
t₉: l6(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: 0 < X₀
t₁₀: l6(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: X₀ ≤ 0
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₈: l8(X₀, X₁, X₂) → l6(nondef_0, X₁, X₂)

Preprocessing

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l6

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l7

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l8

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef_0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, 1) :|: 0 < X₁
t₄: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ < X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₅: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₁: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂)
t₉: l6(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₀: l6(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l8(X₀, X₁, X₂) → l6(nondef_0, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁

MPRF for transition t₅: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+3 {O(n)}

MPRF:

l4 [X₁+2-X₂ ]
l7 [X₁+1-X₂ ]
l8 [X₁+1-X₂ ]
l6 [X₁+1-X₂ ]

MPRF for transition t₉: l6(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

l4 [X₁+1-X₂ ]
l7 [X₁+1-X₂ ]
l8 [X₁+1-X₂ ]
l6 [X₁+1-X₂ ]

MPRF for transition t₁₀: l6(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

l4 [X₁+1-X₂ ]
l7 [X₁+1-X₂ ]
l8 [X₁+1-X₂ ]
l6 [X₁+1-X₂ ]

MPRF for transition t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

l4 [X₁+1-X₂ ]
l7 [X₁+1-X₂ ]
l8 [X₁-X₂ ]
l6 [X₁-X₂ ]

MPRF for transition t₈: l8(X₀, X₁, X₂) → l6(nondef_0, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

l4 [X₁+1-X₂ ]
l7 [X₁+1-X₂ ]
l8 [X₁+1-X₂ ]
l6 [X₁-X₂ ]

All Bounds

Timebounds

Overall timebound:5⋅X₁+18 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₁+3 {O(n)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₉: X₁+2 {O(n)}
t₁₀: X₁+2 {O(n)}
t₇: X₁+2 {O(n)}
t₈: X₁+2 {O(n)}

Costbounds

Overall costbound: 5⋅X₁+18 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₁+3 {O(n)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₉: X₁+2 {O(n)}
t₁₀: X₁+2 {O(n)}
t₇: X₁+2 {O(n)}
t₈: X₁+2 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 1 {O(1)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 2⋅X₁+5 {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}
t₆, X₂: 4⋅X₁+10 {O(n)}
t₁₁, X₁: 3⋅X₁ {O(n)}
t₁₁, X₂: 4⋅X₁+X₂+10 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 2⋅X₁+5 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 2⋅X₁+5 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₁+5 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 2⋅X₁+5 {O(n)}