Initial Problem

Start: eval_non_linear19_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_non_linear19_bb0_in, eval_non_linear19_bb1_in, eval_non_linear19_bb2_in, eval_non_linear19_bb3_in, eval_non_linear19_bb4_in, eval_non_linear19_bb5_in, eval_non_linear19_start, eval_non_linear19_stop
Transitions:
t₁: eval_non_linear19_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb1_in(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₂: eval_non_linear19_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁
t₃: eval_non_linear19_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb3_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: X₀ ≤ X₁
t₄: eval_non_linear19_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb3_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: X₁ ≤ 0
t₅: eval_non_linear19_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb1_in(2⋅X₀, 3⋅X₁, (X₂)², X₃, X₄, X₅, X₆)
t₆: eval_non_linear19_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃
t₇: eval_non_linear19_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0
t₈: eval_non_linear19_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb3_in(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆)
t₉: eval_non_linear19_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_non_linear19_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location eval_non_linear19_bb1_in

Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_non_linear19_bb2_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₂ for location eval_non_linear19_bb3_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ for location eval_non_linear19_stop

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location eval_non_linear19_bb4_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ for location eval_non_linear19_bb5_in

Problem after Preprocessing

Start: eval_non_linear19_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_non_linear19_bb0_in, eval_non_linear19_bb1_in, eval_non_linear19_bb2_in, eval_non_linear19_bb3_in, eval_non_linear19_bb4_in, eval_non_linear19_bb5_in, eval_non_linear19_start, eval_non_linear19_stop
Transitions:
t₁: eval_non_linear19_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb1_in(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₂: eval_non_linear19_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₃: eval_non_linear19_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb3_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₄: eval_non_linear19_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb3_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: X₁ ≤ 0 ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₅: eval_non_linear19_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb1_in(2⋅X₀, 3⋅X₁, (X₂)², X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₆: eval_non_linear19_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₃ ≤ X₂
t₇: eval_non_linear19_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₃ ≤ X₂
t₈: eval_non_linear19_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb3_in(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₃ ≤ X₂
t₉: eval_non_linear19_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 0
t₀: eval_non_linear19_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear19_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

TWN: t₅: eval_non_linear19_bb2_in→eval_non_linear19_bb1_in

Show Graph

Termination: true
Formula:

TWN - Lifting for [2: eval_non_linear19_bb1_in->eval_non_linear19_bb2_in; 5: eval_non_linear19_bb2_in->eval_non_linear19_bb1_in] of 2⋅log(X₀)+2⋅log(X₅)+log(X₄)+16 {O(log(n))}

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location eval_non_linear19_bb1_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ for location eval_non_linear19_stop

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location eval_non_linear19_bb3_in_v1

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ for location eval_non_linear19_bb5_in

Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_non_linear19_bb2_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location eval_non_linear19_bb3_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location eval_non_linear19_bb4_in_v2

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ for location eval_non_linear19_bb4_in_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅log(X₅)+3⋅log(X₄)+16 {O(log(n))}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅log(X₅)+3⋅log(X₄)+16 {O(log(n))}
t₆: inf {Infinity}
t₇: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅log(X₅)+3⋅log(X₄)+16 {O(log(n))}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅log(X₅)+3⋅log(X₄)+16 {O(log(n))}
t₆: inf {Infinity}
t₇: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₆ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: 2^(2⋅log(X₅))⋅2^(3⋅log(X₄))⋅65536⋅X₄ {O(EXP)}
t₂, X₁: 3^(2⋅log(X₅))⋅3^(3⋅log(X₄))⋅43046721⋅X₅ {O(EXP)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: 2^(2⋅log(X₅))⋅2^(3⋅log(X₄))⋅65536⋅X₄+X₄ {O(EXP)}
t₃, X₁: 3^(2⋅log(X₅))⋅3^(3⋅log(X₄))⋅43046721⋅X₅+X₅ {O(EXP)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₁: X₅ {O(n)}
t₄, X₂: X₆ {O(n)}
t₄, X₃: X₆ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₅, X₀: 2^(2⋅log(X₅))⋅2^(3⋅log(X₄))⋅65536⋅X₄ {O(EXP)}
t₅, X₁: 3^(2⋅log(X₅))⋅3^(3⋅log(X₄))⋅43046721⋅X₅ {O(EXP)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₀: 2^(2⋅log(X₅))⋅2^(3⋅log(X₄))⋅65536⋅X₄+2⋅X₄ {O(EXP)}
t₆, X₁: 3^(2⋅log(X₅))⋅3^(3⋅log(X₄))⋅43046721⋅X₅+2⋅X₅ {O(EXP)}
t₆, X₄: 3⋅X₄ {O(n)}
t₆, X₅: 3⋅X₅ {O(n)}
t₆, X₆: 3⋅X₆ {O(n)}
t₇, X₀: 131072⋅2^(2⋅log(X₅))⋅2^(3⋅log(X₄))⋅X₄+4⋅X₄ {O(EXP)}
t₇, X₁: 3^(2⋅log(X₅))⋅3^(3⋅log(X₄))⋅86093442⋅X₅+4⋅X₅ {O(EXP)}
t₇, X₄: 6⋅X₄ {O(n)}
t₇, X₅: 6⋅X₅ {O(n)}
t₇, X₆: 6⋅X₆ {O(n)}
t₈, X₀: 2^(2⋅log(X₅))⋅2^(3⋅log(X₄))⋅65536⋅X₄+2⋅X₄ {O(EXP)}
t₈, X₁: 3^(2⋅log(X₅))⋅3^(3⋅log(X₄))⋅43046721⋅X₅+2⋅X₅ {O(EXP)}
t₈, X₄: 3⋅X₄ {O(n)}
t₈, X₅: 3⋅X₅ {O(n)}
t₈, X₆: 3⋅X₆ {O(n)}
t₉, X₀: 131072⋅2^(2⋅log(X₅))⋅2^(3⋅log(X₄))⋅X₄+4⋅X₄ {O(EXP)}
t₉, X₁: 3^(2⋅log(X₅))⋅3^(3⋅log(X₄))⋅86093442⋅X₅+4⋅X₅ {O(EXP)}
t₉, X₄: 6⋅X₄ {O(n)}
t₉, X₅: 6⋅X₅ {O(n)}
t₉, X₆: 6⋅X₆ {O(n)}