Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₁, X₁, 1, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 101 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 100
t₃: l3(X₀, X₁, X₂, X₃) → l3(X₀+11, X₁, X₂+1, X₃) :|: X₀ ≤ 100
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 101 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l7(X₀-10, X₁, X₂-1, X₃) :|: 2 ≤ X₂
t₁₀: l5(X₀, X₁, X₂, X₃) → l6(X₀-10, X₁, X₂-1, X₃) :|: 101 ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 100
t₁₂: l6(X₀, X₁, X₂, X₃) → l4(X₀+11, X₁, X₂+1, X₃)
t₆: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀-10) :|: 101 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂
t₇: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 100
t₈: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ 2
t₉: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂

Preprocessing

Eliminate variables {X₃} that do not contribute to the problem

Found invariant X₂ ≤ 1 ∧ 100+X₂ ≤ X₁ ∧ 100+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 102 ≤ X₁+X₂ ∧ 102 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 101 ≤ X₁ ∧ 202 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 101 ≤ X₀ for location l2

Found invariant 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 91 ≤ X₀+X₂ ∧ X₀ ≤ 99+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 200 ∧ X₀ ≤ 100 ∧ 91 ≤ X₀ for location l6

Found invariant 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ for location l7

Found invariant 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ for location l5

Found invariant X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1

Found invariant 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 102 ≤ X₀+X₂ ∧ X₀ ≤ 109+X₂ ∧ X₁ ≤ 100 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 211 ∧ X₀ ≤ 111 ∧ 101 ≤ X₀ for location l4

Found invariant 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ X₀ ≤ 109+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 211 ∧ X₀ ≤ 111 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₂₈: l0(X₀, X₁, X₂) → l1(X₁, X₁, 1)
t₂₉: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₃₀: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₃₁: l3(X₀, X₁, X₂) → l3(X₀+11, X₁, X₂+1) :|: X₀ ≤ 100 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ X₀ ≤ 109+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 211 ∧ X₀ ≤ 111
t₃₂: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ X₀ ≤ 109+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 211 ∧ X₀ ≤ 111
t₃₃: l4(X₀, X₁, X₂) → l7(X₀-10, X₁, X₂-1) :|: 2 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 102 ≤ X₀+X₂ ∧ X₀ ≤ 109+X₂ ∧ X₁ ≤ 100 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 211 ∧ X₀ ≤ 111 ∧ 101 ≤ X₀
t₃₄: l5(X₀, X₁, X₂) → l6(X₀-10, X₁, X₂-1) :|: 101 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₃₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₃₆: l6(X₀, X₁, X₂) → l4(X₀+11, X₁, X₂+1) :|: 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 91 ≤ X₀+X₂ ∧ X₀ ≤ 99+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 200 ∧ X₀ ≤ 100 ∧ 91 ≤ X₀
t₃₇: l7(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₃₈: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₃₉: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 2 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₄₀: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀

MPRF for transition t₃₁: l3(X₀, X₁, X₂) → l3(X₀+11, X₁, X₂+1) :|: X₀ ≤ 100 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ X₀ ≤ 109+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 211 ∧ X₀ ≤ 111 of depth 1:

new bound:

X₁+112 {O(n)}

MPRF:

l3 [112-X₀ ]

MPRF for transition t₃₃: l4(X₀, X₁, X₂) → l7(X₀-10, X₁, X₂-1) :|: 2 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 102 ≤ X₀+X₂ ∧ X₀ ≤ 109+X₂ ∧ X₁ ≤ 100 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 211 ∧ X₀ ≤ 111 ∧ 101 ≤ X₀ of depth 1:

new bound:

200⋅X₁+26599 {O(n)}

MPRF:

l6 [200⋅X₂+1981-20⋅X₀ ]
l4 [200⋅X₂+1890-19⋅X₀ ]
l7 [200⋅X₂+1890-19⋅X₀ ]
l5 [200⋅X₂+1981-20⋅X₀ ]

MPRF for transition t₃₄: l5(X₀, X₁, X₂) → l6(X₀-10, X₁, X₂-1) :|: 101 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

X₁+114 {O(n)}

MPRF:

l6 [X₂ ]
l4 [X₂-1 ]
l7 [X₂ ]
l5 [X₂ ]

MPRF for transition t₃₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

190⋅X₁+25319 {O(n)}

MPRF:

l6 [190⋅X₂+1821-20⋅X₀ ]
l4 [190⋅X₂+1740-19⋅X₀ ]
l7 [190⋅X₂+1740-19⋅X₀ ]
l5 [190⋅X₂+1831-20⋅X₀ ]

MPRF for transition t₃₆: l6(X₀, X₁, X₂) → l4(X₀+11, X₁, X₂+1) :|: 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 91 ≤ X₀+X₂ ∧ X₀ ≤ 99+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 200 ∧ X₀ ≤ 100 ∧ 91 ≤ X₀ of depth 1:

new bound:

10⋅X₁+1342 {O(n)}

MPRF:

l6 [10⋅X₂+101-X₀ ]
l4 [10⋅X₂+101-X₀ ]
l7 [10⋅X₂+101-X₀ ]
l5 [10⋅X₂+101-X₀ ]

MPRF for transition t₃₇: l7(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

10⋅X₁+1149 {O(n)}

MPRF:

l6 [10⋅X₂-9 ]
l4 [10⋅X₂-19 ]
l7 [10⋅X₂-9 ]
l5 [10⋅X₂-9 ]

MPRF for transition t₃₈: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

10⋅X₁+1332 {O(n)}

MPRF:

l6 [10⋅X₂+90-X₀ ]
l4 [10⋅X₂+91-X₀ ]
l7 [10⋅X₂+91-X₀ ]
l5 [10⋅X₂+90-X₀ ]

MPRF for transition t₃₉: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 2 ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

10⋅X₁+1333 {O(n)}

MPRF:

l6 [10⋅X₂+91-X₀ ]
l4 [10⋅X₂+92-X₀ ]
l7 [10⋅X₂+92-X₀ ]
l5 [10⋅X₂+91-X₀ ]

MPRF for transition t₄₀: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ 99+X₂ ∧ 92 ≤ X₀+X₂ ∧ X₀ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 9+X₀ ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

10⋅X₁+1343 {O(n)}

MPRF:

l6 [10⋅X₂+101-X₀ ]
l4 [10⋅X₂+102-X₀ ]
l7 [10⋅X₂+102-X₀ ]
l5 [10⋅X₂+101-X₀ ]

All Bounds

Timebounds

Overall timebound:442⋅X₁+58647 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}
t₃₁: X₁+112 {O(n)}
t₃₂: 1 {O(1)}
t₃₃: 200⋅X₁+26599 {O(n)}
t₃₄: X₁+114 {O(n)}
t₃₅: 190⋅X₁+25319 {O(n)}
t₃₆: 10⋅X₁+1342 {O(n)}
t₃₇: 10⋅X₁+1149 {O(n)}
t₃₈: 10⋅X₁+1332 {O(n)}
t₃₉: 10⋅X₁+1333 {O(n)}
t₄₀: 10⋅X₁+1343 {O(n)}

Costbounds

Overall costbound: 442⋅X₁+58647 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}
t₃₁: X₁+112 {O(n)}
t₃₂: 1 {O(1)}
t₃₃: 200⋅X₁+26599 {O(n)}
t₃₄: X₁+114 {O(n)}
t₃₅: 190⋅X₁+25319 {O(n)}
t₃₆: 10⋅X₁+1342 {O(n)}
t₃₇: 10⋅X₁+1149 {O(n)}
t₃₈: 10⋅X₁+1332 {O(n)}
t₃₉: 10⋅X₁+1333 {O(n)}
t₄₀: 10⋅X₁+1343 {O(n)}

Sizebounds

t₂₈, X₀: X₁ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: 1 {O(1)}
t₂₉, X₀: X₁ {O(n)}
t₂₉, X₁: X₁ {O(n)}
t₂₉, X₂: 1 {O(1)}
t₃₀, X₀: X₁ {O(n)}
t₃₀, X₁: X₁ {O(n)}
t₃₀, X₂: 1 {O(1)}
t₃₁, X₀: 12⋅X₁+1232 {O(n)}
t₃₁, X₁: X₁ {O(n)}
t₃₁, X₂: X₁+113 {O(n)}
t₃₂, X₀: 111 {O(1)}
t₃₂, X₁: X₁ {O(n)}
t₃₂, X₂: X₁+113 {O(n)}
t₃₃, X₀: 101 {O(1)}
t₃₃, X₁: X₁ {O(n)}
t₃₃, X₂: 11⋅X₁+1459 {O(n)}
t₃₄, X₀: 91 {O(1)}
t₃₄, X₁: X₁ {O(n)}
t₃₄, X₂: 11⋅X₁+1459 {O(n)}
t₃₅, X₀: 100 {O(1)}
t₃₅, X₁: X₁ {O(n)}
t₃₅, X₂: 11⋅X₁+1459 {O(n)}
t₃₆, X₀: 111 {O(1)}
t₃₆, X₁: X₁ {O(n)}
t₃₆, X₂: 11⋅X₁+1459 {O(n)}
t₃₇, X₀: 101 {O(1)}
t₃₇, X₁: X₁ {O(n)}
t₃₇, X₂: 1 {O(1)}
t₃₈, X₀: 100 {O(1)}
t₃₈, X₁: X₁ {O(n)}
t₃₈, X₂: 11⋅X₁+1459 {O(n)}
t₃₉, X₀: 101 {O(1)}
t₃₉, X₁: X₁ {O(n)}
t₃₉, X₂: 2 {O(1)}
t₄₀, X₀: 101 {O(1)}
t₄₀, X₁: X₁ {O(n)}
t₄₀, X₂: 11⋅X₁+1459 {O(n)}