MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalgcdstart(Ar_0, Ar_1) -> Com_1(evalgcdentryin(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_1, Ar_0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb5in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb6in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb5in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0 - Ar_1, Ar_1)) (Comp: ?, Cost: 1) evalgcdbb6in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0, Ar_1 - Ar_0)) (Comp: ?, Cost: 1) evalgcdreturnin(Ar_0, Ar_1) -> Com_1(evalgcdstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalgcdstart(Ar_0, Ar_1)) [ 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) evalgcdstart(Ar_0, Ar_1) -> Com_1(evalgcdentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_1, Ar_0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb5in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb6in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb5in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0 - Ar_1, Ar_1)) (Comp: ?, Cost: 1) evalgcdbb6in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0, Ar_1 - Ar_0)) (Comp: ?, Cost: 1) evalgcdreturnin(Ar_0, Ar_1) -> Com_1(evalgcdstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalgcdstart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalgcdstart) = 1 Pol(evalgcdentryin) = 1 Pol(evalgcdreturnin) = 0 Pol(evalgcdbb7in) = 1 Pol(evalgcdbb4in) = 1 Pol(evalgcdbb5in) = 1 Pol(evalgcdbb6in) = 1 Pol(evalgcdstop) = -1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ Ar_1 = Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalgcdstart(Ar_0, Ar_1) -> Com_1(evalgcdentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_1, Ar_0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb5in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb6in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb5in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0 - Ar_1, Ar_1)) (Comp: ?, Cost: 1) evalgcdbb6in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0, Ar_1 - Ar_0)) (Comp: ?, Cost: 1) evalgcdreturnin(Ar_0, Ar_1) -> Com_1(evalgcdstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalgcdstart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 1, Cost: 1) evalgcdstart(Ar_0, Ar_1) -> Com_1(evalgcdentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_1, Ar_0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb5in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb6in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb5in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0 - Ar_1, Ar_1)) (Comp: ?, Cost: 1) evalgcdbb6in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0, Ar_1 - Ar_0)) (Comp: 3, Cost: 1) evalgcdreturnin(Ar_0, Ar_1) -> Com_1(evalgcdstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalgcdstart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol evalgcdbb5in: X_1 - X_2 - 1 >= 0 For symbol evalgcdbb6in: -X_1 + X_2 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalgcdstart(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalgcdreturnin(Ar_0, Ar_1) -> Com_1(evalgcdstop(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalgcdbb6in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0, Ar_1 - Ar_0)) [ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalgcdbb5in(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_0 - Ar_1, Ar_1)) [ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb6in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb4in(Ar_0, Ar_1) -> Com_1(evalgcdbb5in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalgcdbb7in(Ar_0, Ar_1) -> Com_1(evalgcdbb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdbb7in(Ar_1, Ar_0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalgcdentryin(Ar_0, Ar_1) -> Com_1(evalgcdreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalgcdstart(Ar_0, Ar_1) -> Com_1(evalgcdentryin(Ar_0, Ar_1)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 2.517 sec (SMT: 2.450 sec)