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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, 100, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 51 < X₁
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 51
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-1, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃)

Preprocessing

Eliminate variables {X₂,X₃} that do not contribute to the problem

Found invariant X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀ for location l6

Found invariant X₁ ≤ 50 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ 50 ≤ X₀ for location l7

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 50 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ 50 ≤ X₀ for location l4

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 0 ≤ X₀ for location l3

Cut unsatisfiable transition t₂₀: l1→l4

Cut unreachable locations [l4; l7] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l5, l6
Transitions:
t₁₈: l0(X₀, X₁) → l2(X₀, X₁)
t₁₉: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < X₁ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁) → l1(0, 100)
t₂₂: l3(X₀, X₁) → l5(X₀, X₁) :|: 51 < X₁ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 0 ≤ X₀
t₂₃: l3(X₀, X₁) → l6(X₀, X₁) :|: X₁ ≤ 51 ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 0 ≤ X₀
t₂₅: l5(X₀, X₁) → l1(X₀+1, X₁-1) :|: X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 0 ≤ X₀
t₂₆: l6(X₀, X₁) → l1(X₀-1, X₁+1) :|: X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀

Analysing control-flow refined program

Found invariant X₁ ≤ 99 ∧ X₁ ≤ 98+X₀ ∧ X₀+X₁ ≤ 100 ∧ 99 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 98+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___12

Found invariant X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l6___6

Found invariant X₁ ≤ 52 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 48 ≤ X₀ for location n_l3___4

Found invariant X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 2 ≤ X₀ for location n_l1___9

Found invariant X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 99 ∧ X₁ ≤ 98+X₀ ∧ X₀+X₁ ≤ 100 ∧ 99 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 98+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l5___10

Found invariant X₁ ≤ 99 ∧ X₁ ≤ 98+X₀ ∧ X₀+X₁ ≤ 100 ∧ 99 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 98+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___11

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___14

Found invariant X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 2 ≤ X₀ for location n_l3___8

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l5___13

Found invariant X₁ ≤ 52 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 48 ≤ X₀ for location n_l1___5

Found invariant X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 2 ≤ X₀ for location n_l5___7

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l3___1

Found invariant X₁ ≤ 52 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 48 ≤ X₀ for location n_l5___3

MPRF for transition t₂₄₀: n_l1___9(X₀, X₁) → n_l3___8(X₀, 100-X₀) :|: X₁ ≤ 100 ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ 100 < 2⋅X₁ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ X₁ ≤ 100 ∧ 101 ≤ 2⋅X₁ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ X₁ ≤ 99 ∧ 51 ≤ X₁ ∧ 0 ≤ X₀ ∧ 2⋅X₀ < 100 ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 2 ≤ X₀ of depth 1:

new bound:

296 {O(1)}

MPRF:

n_l3___8 [98-2⋅X₀ ]
n_l5___7 [98-2⋅X₀ ]
n_l1___9 [2⋅X₁-100 ]

MPRF for transition t₂₄₅: n_l3___8(X₀, X₁) → n_l5___7(X₀, 100-X₀) :|: 51 ≤ X₁ ∧ X₁ ≤ 99 ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ X₀ < 49 ∧ 0 ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 2 ≤ X₀ of depth 1:

new bound:

51 {O(1)}

MPRF:

n_l3___8 [49-X₀ ]
n_l5___7 [48-X₀ ]
n_l1___9 [49-X₀ ]

MPRF for transition t₂₅₀: n_l5___7(X₀, X₁) → n_l1___9(X₀+1, 99-X₀) :|: 51 < X₁ ∧ X₁ ≤ 99 ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 48 ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₀+X₁ ∧ X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 2 ≤ X₀ of depth 1:

new bound:

51 {O(1)}

MPRF:

n_l3___8 [49-X₀ ]
n_l5___7 [49-X₀ ]
n_l1___9 [49-X₀ ]

Found invariant X₁ ≤ 99 ∧ X₁ ≤ 98+X₀ ∧ X₀+X₁ ≤ 100 ∧ 99 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 98+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___12

Found invariant X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l6___6

Found invariant X₁ ≤ 52 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 48 ≤ X₀ for location n_l3___4

Found invariant X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 2 ≤ X₀ for location n_l1___9

Found invariant X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 99 ∧ X₁ ≤ 98+X₀ ∧ X₀+X₁ ≤ 100 ∧ 99 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 98+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l5___10

Found invariant X₁ ≤ 99 ∧ X₁ ≤ 98+X₀ ∧ X₀+X₁ ≤ 100 ∧ 99 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 98+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___11

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___14

Found invariant X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 2 ≤ X₀ for location n_l3___8

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l5___13

Found invariant X₁ ≤ 52 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 48 ≤ X₀ for location n_l1___5

Found invariant X₁ ≤ 98 ∧ X₁ ≤ 96+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 2 ≤ X₀ for location n_l5___7

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ X₀+X₁ ≤ 100 ∧ 100 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 51 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 100 ∧ 51 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 49 ≤ X₀ for location n_l3___1

Found invariant X₁ ≤ 52 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 100 ∧ 52 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ X₀ ≤ 48 ∧ 48 ≤ X₀ for location n_l5___3

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: inf {Infinity}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₀: 49 {O(1)}
t₁₉, X₁: 100 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₁, X₁: 100 {O(1)}
t₂₂, X₀: 48 {O(1)}
t₂₂, X₁: 100 {O(1)}
t₂₃, X₀: 49 {O(1)}
t₂₃, X₁: 51 {O(1)}
t₂₅, X₀: 49 {O(1)}
t₂₅, X₁: 99 {O(1)}
t₂₆, X₀: 48 {O(1)}
t₂₆, X₁: 52 {O(1)}