Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I, J, K
Locations: f0, f12, f22, f29, f35, f37, f43, f48, f58, start
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f12(X₀, X₁, 0, X₁, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ X₀
t₂₁: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f58(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₁
t₁: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f12(X₀, X₁, X₂, X₃, 1+X₄, J, I, X₇) :|: J ≤ I ∧ X₄ ≤ X₀
t₂: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f12(X₀, X₁, J, X₄, 1+X₄, I, K, X₇) :|: 1+K ≤ I ∧ X₄ ≤ X₀
t₁₉: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁
t₂₀: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₈: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f35(X₀, X₁, X₂, X₁, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₃: f22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f22(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, J) :|: X₄ ≤ X₀
t₁₇: f22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₄: f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f29(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, J) :|: X₄ ≤ X₀
t₁₆: f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₂: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f0(X₀, 1+X₁, 0, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₂ ∧ X₂ ≤ 0
t₅: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ 0
t₆: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂
t₁₅: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f0(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₃
t₁₁: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f37(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, 0) :|: X₃ ≤ X₀
t₇: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, J) :|: 1+I ≤ 0 ∧ X₃ ≤ X₀
t₈: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, J) :|: 1 ≤ I ∧ X₃ ≤ X₀
t₉: f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f43(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: X₄ ≤ X₀
t₁₄: f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f48(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₃: f48(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f37(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₀: f48(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f48(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: X₄ ≤ X₀
t₂₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Cut unsatisfiable transition [t₃: f22→f22; t₄: f29→f29; t₁₀: f48→f48]

Eliminate variables [X₅; X₆; X₇] that do not contribute to the problem

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f29

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f48

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f35

Found invariant X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ for location f37

Found invariant X₀ ≤ X₁ for location f58

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f43

Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f12

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f22

Cut unsatisfiable transition [t₆₇: f43→f43]

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: I, J, K
Locations: f0, f12, f22, f29, f35, f37, f43, f48, f58, start
Transitions:
t₅₁: f0(X₀, X₁, X₂, X₃, X₄) → f12(X₀, X₁, 0, X₁, X₄) :|: 1+X₁ ≤ X₀
t₅₂: f0(X₀, X₁, X₂, X₃, X₄) → f58(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₅₃: f12(X₀, X₁, X₂, X₃, X₄) → f12(X₀, X₁, X₂, X₃, 1+X₄) :|: J ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₅₄: f12(X₀, X₁, X₂, X₃, X₄) → f12(X₀, X₁, J, X₄, 1+X₄) :|: 1+K ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₅₅: f12(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₅₆: f12(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₅₇: f12(X₀, X₁, X₂, X₃, X₄) → f35(X₀, X₁, X₂, X₁, X₄) :|: 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀
t₅₈: f22(X₀, X₁, X₂, X₃, X₄) → f29(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅₉: f29(X₀, X₁, X₂, X₃, X₄) → f35(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆₀: f35(X₀, X₁, X₂, X₃, X₄) → f0(X₀, 1+X₁, 0, X₃, X₄) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆₁: f35(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆₂: f35(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆₃: f37(X₀, X₁, X₂, X₃, X₄) → f0(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₆₄: f37(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, 1+X₃, X₄) :|: X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₆₅: f37(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1+I ≤ 0 ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₆₆: f37(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ I ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄
t₆₈: f43(X₀, X₁, X₂, X₃, X₄) → f48(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆₉: f48(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, 1+X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₇₀: start(X₀, X₁, X₂, X₃, X₄) → f0(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₅₁: f0(X₀, X₁, X₂, X₃, X₄) → f12(X₀, X₁, 0, X₁, X₄) :|: 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f0: [X₀-X₁]
• f12: [X₀-1-X₁]
• f22: [X₀-1-X₁]
• f29: [X₀-1-X₁]
• f35: [X₀-1-X₁]
• f37: [X₀-1-X₁]
• f43: [X₀-1-X₁]
• f48: [X₀-1-X₁]

MPRF for transition t₅₃: f12(X₀, X₁, X₂, X₃, X₄) → f12(X₀, X₁, X₂, X₃, 1+X₄) :|: J ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₄+1 {O(n)}

• f0: [1+X₀-X₄]
• f12: [1+X₀-X₄]
• f22: [1+X₀-X₄]
• f29: [1+X₀-X₄]
• f35: [1+X₀-X₄]
• f37: [1+X₀-X₄]
• f43: [1+X₀-X₄]
• f48: [1+X₀-X₄]

MPRF for transition t₅₄: f12(X₀, X₁, X₂, X₃, X₄) → f12(X₀, X₁, J, X₄, 1+X₄) :|: 1+K ≤ I ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₄+1 {O(n)}

• f0: [1+X₀-X₄]
• f12: [1+X₀-X₄]
• f22: [1+X₀-X₄]
• f29: [1+X₀-X₄]
• f35: [1+X₀-X₄]
• f37: [1+X₀-X₄]
• f43: [1+X₀-X₄]
• f48: [1+X₀-X₄]

MPRF for transition t₅₅: f12(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f0: [X₀-X₁]
• f12: [X₀-X₁]
• f22: [X₀-1-X₁]
• f29: [X₀-1-X₁]
• f35: [X₀-1-X₁]
• f37: [X₀-1-X₁]
• f43: [X₀-1-X₁]
• f48: [X₀-1-X₁]

MPRF for transition t₅₆: f12(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f0: [X₀-X₁]
• f12: [X₀-X₁]
• f22: [X₀-1-X₁]
• f29: [X₀-1-X₁]
• f35: [X₀-1-X₁]
• f37: [X₀-1-X₁]
• f43: [X₀-1-X₁]
• f48: [X₀-1-X₁]

MPRF for transition t₅₇: f12(X₀, X₁, X₂, X₃, X₄) → f35(X₀, X₁, X₂, X₁, X₄) :|: 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f0: [1+X₀-X₁]
• f12: [1+X₀-X₁]
• f22: [X₀-X₁]
• f29: [X₀-X₁]
• f35: [X₀-X₁]
• f37: [X₀-X₁]
• f43: [X₀-X₁]
• f48: [X₀-X₁]

MPRF for transition t₅₈: f22(X₀, X₁, X₂, X₃, X₄) → f29(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f0: [1+X₀-X₁]
• f12: [1+X₀-X₁]
• f22: [1+X₀-X₁]
• f29: [X₀-X₁]
• f35: [X₀-X₁]
• f37: [X₀-X₁]
• f43: [X₀-X₁]
• f48: [X₀-X₁]

MPRF for transition t₅₉: f29(X₀, X₁, X₂, X₃, X₄) → f35(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f0: [X₀-X₁]
• f12: [X₀-X₁]
• f22: [X₀-X₁]
• f29: [X₀-X₁]
• f35: [X₀-1-X₁]
• f37: [X₀-1-X₁]
• f43: [X₀-1-X₁]
• f48: [X₀-1-X₁]

MPRF for transition t₆₀: f35(X₀, X₁, X₂, X₃, X₄) → f0(X₀, 1+X₁, 0, X₃, X₄) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f0: [X₀-X₁]
• f12: [X₀-X₁]
• f22: [X₀-X₁]
• f29: [X₀-X₁]
• f35: [X₀-X₁]
• f37: [X₀-X₁]
• f43: [X₀-X₁]
• f48: [X₀-X₁]

MPRF for transition t₆₁: f35(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f0: [1+X₀-X₁]
• f12: [1+X₀-X₁]
• f22: [1+X₀-X₁]
• f29: [1+X₀-X₁]
• f35: [1+X₀-X₁]
• f37: [X₀-X₁]
• f43: [X₀-X₁]
• f48: [X₀-X₁]

MPRF for transition t₆₂: f35(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f0: [1+X₀-X₁]
• f12: [1+X₀-X₁]
• f22: [1+X₀-X₁]
• f29: [1+X₀-X₁]
• f35: [1+X₀-X₁]
• f37: [X₀-X₁]
• f43: [X₀-X₁]
• f48: [X₀-X₁]

MPRF for transition t₆₃: f37(X₀, X₁, X₂, X₃, X₄) → f0(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f0: [X₀-X₁]
• f12: [X₀-X₁]
• f22: [X₀-X₁]
• f29: [X₀-X₁]
• f35: [X₀-X₁]
• f37: [X₀-X₁]
• f43: [X₀-X₁]
• f48: [X₀-X₁]

MPRF for transition t₆₄: f37(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, 1+X₃, X₄) :|: X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

104⋅X₀⋅X₁+40⋅X₁⋅X₁+60⋅X₀⋅X₄+60⋅X₁⋅X₄+64⋅X₀⋅X₀+106⋅X₀+60⋅X₄+82⋅X₁+42 {O(n^2)}

• f0: [0]
• f12: [0]
• f22: [0]
• f29: [0]
• f35: [0]
• f37: [1+X₄-X₃]
• f43: [X₄-X₃]
• f48: [X₄-X₃]

MPRF for transition t₆₅: f37(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1+I ≤ 0 ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

104⋅X₀⋅X₁+40⋅X₁⋅X₁+60⋅X₀⋅X₄+60⋅X₁⋅X₄+64⋅X₀⋅X₀+106⋅X₀+60⋅X₄+82⋅X₁+42 {O(n^2)}

• f0: [0]
• f12: [0]
• f22: [0]
• f29: [0]
• f35: [0]
• f37: [1+X₄-X₃]
• f43: [X₄-X₃]
• f48: [X₄-X₃]

MPRF for transition t₆₆: f37(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ I ∧ X₃ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₄ of depth 1:

new bound:

102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+102⋅X₀+54⋅X₄+80⋅X₁+40 {O(n^2)}

• f0: [0]
• f12: [0]
• f22: [0]
• f29: [0]
• f35: [0]
• f37: [2+X₀-X₃]
• f43: [1+X₀-X₃]
• f48: [1+X₀-X₃]

MPRF for transition t₆₈: f43(X₀, X₁, X₂, X₃, X₄) → f48(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+100⋅X₀+54⋅X₄+78⋅X₁+38 {O(n^2)}

• f0: [0]
• f12: [0]
• f22: [0]
• f29: [0]
• f35: [0]
• f37: [1+X₀-X₃]
• f43: [1+X₀-X₃]
• f48: [X₀-X₃]

MPRF for transition t₆₉: f48(X₀, X₁, X₂, X₃, X₄) → f37(X₀, X₁, X₂, 1+X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+101⋅X₀+55⋅X₄+78⋅X₁+38 {O(n^2)}

• f0: [X₀-X₄]
• f12: [X₀-X₄]
• f22: [X₀-X₄]
• f29: [X₀-X₄]
• f35: [X₀-X₄]
• f37: [1+X₀-X₃]
• f43: [1+X₀-X₃]
• f48: [1+X₀-X₃]

Cut unsatisfiable transition [t₆₃: f37→f0; t₁₆₇: f37→f0]

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f29

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f48_v1

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f35

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f37

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f43_v1

Found invariant X₀ ≤ X₁ for location f58

Found invariant X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ for location f37_v1

Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f12

Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location f22

All Bounds

Timebounds

Overall timebound:200⋅X₁⋅X₁+282⋅X₀⋅X₄+282⋅X₁⋅X₄+314⋅X₀⋅X₀+514⋅X₀⋅X₁+285⋅X₄+410⋅X₁+527⋅X₀+208 {O(n^2)}
t₅₁: X₀+X₁ {O(n)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₄+1 {O(n)}
t₅₄: X₀+X₄+1 {O(n)}
t₅₅: X₀+X₁ {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₅₇: X₀+X₁+1 {O(n)}
t₅₈: X₀+X₁+1 {O(n)}
t₅₉: X₀+X₁ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁+1 {O(n)}
t₆₂: X₀+X₁+1 {O(n)}
t₆₃: X₀+X₁ {O(n)}
t₆₄: 104⋅X₀⋅X₁+40⋅X₁⋅X₁+60⋅X₀⋅X₄+60⋅X₁⋅X₄+64⋅X₀⋅X₀+106⋅X₀+60⋅X₄+82⋅X₁+42 {O(n^2)}
t₆₅: 104⋅X₀⋅X₁+40⋅X₁⋅X₁+60⋅X₀⋅X₄+60⋅X₁⋅X₄+64⋅X₀⋅X₀+106⋅X₀+60⋅X₄+82⋅X₁+42 {O(n^2)}
t₆₆: 102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+102⋅X₀+54⋅X₄+80⋅X₁+40 {O(n^2)}
t₆₈: 102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+100⋅X₀+54⋅X₄+78⋅X₁+38 {O(n^2)}
t₆₉: 102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+101⋅X₀+55⋅X₄+78⋅X₁+38 {O(n^2)}
t₇₀: 1 {O(1)}

Costbounds

Overall costbound: 200⋅X₁⋅X₁+282⋅X₀⋅X₄+282⋅X₁⋅X₄+314⋅X₀⋅X₀+514⋅X₀⋅X₁+285⋅X₄+410⋅X₁+527⋅X₀+208 {O(n^2)}
t₅₁: X₀+X₁ {O(n)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₄+1 {O(n)}
t₅₄: X₀+X₄+1 {O(n)}
t₅₅: X₀+X₁ {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₅₇: X₀+X₁+1 {O(n)}
t₅₈: X₀+X₁+1 {O(n)}
t₅₉: X₀+X₁ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁+1 {O(n)}
t₆₂: X₀+X₁+1 {O(n)}
t₆₃: X₀+X₁ {O(n)}
t₆₄: 104⋅X₀⋅X₁+40⋅X₁⋅X₁+60⋅X₀⋅X₄+60⋅X₁⋅X₄+64⋅X₀⋅X₀+106⋅X₀+60⋅X₄+82⋅X₁+42 {O(n^2)}
t₆₅: 104⋅X₀⋅X₁+40⋅X₁⋅X₁+60⋅X₀⋅X₄+60⋅X₁⋅X₄+64⋅X₀⋅X₀+106⋅X₀+60⋅X₄+82⋅X₁+42 {O(n^2)}
t₆₆: 102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+102⋅X₀+54⋅X₄+80⋅X₁+40 {O(n^2)}
t₆₈: 102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+100⋅X₀+54⋅X₄+78⋅X₁+38 {O(n^2)}
t₆₉: 102⋅X₀⋅X₁+40⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+62⋅X₀⋅X₀+101⋅X₀+55⋅X₄+78⋅X₁+38 {O(n^2)}
t₇₀: 1 {O(1)}

Sizebounds

t₅₁, X₀: X₀ {O(n)}
t₅₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₁, X₂: 0 {O(1)}
t₅₁, X₃: 4⋅X₀+7⋅X₁ {O(n)}
t₅₁, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₂, X₀: 3⋅X₀ {O(n)}
t₅₂, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₅₂, X₃: 160⋅X₁⋅X₁+228⋅X₀⋅X₄+228⋅X₁⋅X₄+252⋅X₀⋅X₀+412⋅X₀⋅X₁+365⋅X₄+420⋅X₁+564⋅X₀+X₃+250 {O(n^2)}
t₅₂, X₄: 4⋅X₀+7⋅X₄+4 {O(n)}
t₅₃, X₀: X₀ {O(n)}
t₅₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₃, X₃: 10⋅X₀+7⋅X₁+9⋅X₄+6 {O(n)}
t₅₃, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₄, X₃: 6⋅X₀+9⋅X₄+6 {O(n)}
t₅₄, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₅, X₃: 10⋅X₀+7⋅X₁+9⋅X₄+6 {O(n)}
t₅₅, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₆, X₃: 16⋅X₀+18⋅X₄+7⋅X₁+12 {O(n)}
t₅₆, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₇, X₃: 4⋅X₀+6⋅X₁ {O(n)}
t₅₇, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₈, X₀: X₀ {O(n)}
t₅₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₈, X₃: 14⋅X₁+26⋅X₀+27⋅X₄+18 {O(n)}
t₅₈, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₉, X₀: X₀ {O(n)}
t₅₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₉, X₃: 14⋅X₁+26⋅X₀+27⋅X₄+18 {O(n)}
t₅₉, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₀, X₀: X₀ {O(n)}
t₆₀, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₀, X₂: 0 {O(1)}
t₆₀, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₆₀, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₁, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₆₁, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₂, X₀: X₀ {O(n)}
t₆₂, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₂, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₆₂, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₃, X₃: 160⋅X₁⋅X₁+228⋅X₀⋅X₄+228⋅X₁⋅X₄+252⋅X₀⋅X₀+412⋅X₀⋅X₁+338⋅X₄+400⋅X₁+534⋅X₀+232 {O(n^2)}
t₆₃, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₄, X₃: 114⋅X₀⋅X₄+114⋅X₁⋅X₄+126⋅X₀⋅X₀+206⋅X₀⋅X₁+80⋅X₁⋅X₁+169⋅X₄+200⋅X₁+267⋅X₀+116 {O(n^2)}
t₆₄, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₅, X₃: 114⋅X₀⋅X₄+114⋅X₁⋅X₄+126⋅X₀⋅X₀+206⋅X₀⋅X₁+80⋅X₁⋅X₁+169⋅X₄+200⋅X₁+267⋅X₀+116 {O(n^2)}
t₆₅, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₆, X₃: 114⋅X₀⋅X₄+114⋅X₁⋅X₄+126⋅X₀⋅X₀+206⋅X₀⋅X₁+80⋅X₁⋅X₁+169⋅X₄+200⋅X₁+267⋅X₀+116 {O(n^2)}
t₆₆, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₈, X₃: 114⋅X₀⋅X₄+114⋅X₁⋅X₄+126⋅X₀⋅X₀+206⋅X₀⋅X₁+80⋅X₁⋅X₁+169⋅X₄+200⋅X₁+267⋅X₀+116 {O(n^2)}
t₆₈, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₉, X₀: X₀ {O(n)}
t₆₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₉, X₃: 114⋅X₀⋅X₄+114⋅X₁⋅X₄+126⋅X₀⋅X₀+206⋅X₀⋅X₁+80⋅X₁⋅X₁+169⋅X₄+200⋅X₁+267⋅X₀+116 {O(n^2)}
t₆₉, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₇₀, X₀: X₀ {O(n)}
t₇₀, X₁: X₁ {O(n)}
t₇₀, X₂: X₂ {O(n)}
t₇₀, X₃: X₃ {O(n)}
t₇₀, X₄: X₄ {O(n)}