MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_1, Ar_1, 0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 - 1, Ar_3)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_3, Ar_1, Ar_4 - 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_1, Ar_1, 0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 - 1, Ar_3)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_3, Ar_1, Ar_4 - 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = 2 Pol(evalfentryin) = 2 Pol(evalfbb7in) = 2 Pol(evalfbbin) = 2 Pol(evalfreturnin) = 1 Pol(evalfbb3in) = 2 Pol(evalfbb6in) = 2 Pol(evalfbb5in) = 2 Pol(evalfbb4in) = 2 Pol(evalfbb2in) = 2 Pol(evalfstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_1, Ar_1, 0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_2 >= 0 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 - 1, Ar_3)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_3, Ar_1, Ar_4 - 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfbb2in: X_2 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfbb3in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfbb4in: X_2 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfbb5in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfbb6in: X_5 >= 0 /\ X_4 + X_5 + 1 >= 0 /\ X_3 + X_5 >= 0 /\ -X_3 + X_5 >= 0 /\ X_2 + X_5 >= 0 /\ X_1 + X_5 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_4 + 1 >= 0 /\ X_3 + X_4 + 1 >= 0 /\ X_2 + X_4 + 1 >= 0 /\ X_1 + X_4 + 1 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfbb7in: -X_1 + X_2 >= 0 For symbol evalfbbin: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfreturnin: -X_1 + X_2 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_3, Ar_1, Ar_4 - 1, Ar_3, Ar_4)) [ Ar_4 >= 0 /\ Ar_3 + Ar_4 + 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_3 + 1 >= 0 /\ Ar_2 + Ar_3 + 1 >= 0 /\ Ar_1 + Ar_3 + 1 >= 0 /\ Ar_0 + Ar_3 + 1 >= 0 /\ -Ar_0 + Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 - 1, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ F >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ F >= 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= F + 1 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 0 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_1, Ar_1, 0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 6*V_2 + 3 Pol(evalfstart) = 6*V_2 + 3 Pol(evalfreturnin) = 6*V_1 + 3 Pol(evalfstop) = 6*V_1 + 3 Pol(evalfbb6in) = 6*V_4 + 3 Pol(evalfbb7in) = 6*V_1 + 3 Pol(evalfbb5in) = 6*V_1 + 1 Pol(evalfbb2in) = 6*V_1 + 2 Pol(evalfbb3in) = 6*V_1 + 2 Pol(evalfbb4in) = 6*V_1 + 2 Pol(evalfbbin) = 6*V_1 + 3 Pol(evalfentryin) = 6*V_2 + 3 orients all transitions weakly and the transitions evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ F >= 1 ] evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= F + 1 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 - 1, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_1 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_3, Ar_1, Ar_4 - 1, Ar_3, Ar_4)) [ Ar_4 >= 0 /\ Ar_3 + Ar_4 + 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_3 + 1 >= 0 /\ Ar_2 + Ar_3 + 1 >= 0 /\ Ar_1 + Ar_3 + 1 >= 0 /\ Ar_0 + Ar_3 + 1 >= 0 /\ -Ar_0 + Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 6*Ar_1 + 3, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 - 1, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 6*Ar_1 + 3, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ F >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_3 ] (Comp: 6*Ar_1 + 3, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 6*Ar_1 + 3, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ F >= 1 ] (Comp: 6*Ar_1 + 3, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_2, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= F + 1 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 0 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_1, Ar_1, 0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 4.212 sec (SMT: 3.999 sec)