WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalndloopstart(Ar_0) -> Com_1(evalndloopentryin(Ar_0)) (Comp: ?, Cost: 1) evalndloopentryin(Ar_0) -> Com_1(evalndloopbbin(0)) (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopbbin(Fresh_0)) [ Ar_0 + 2 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ 9 >= Fresh_0 ] (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= Ar_0 + 3 ] (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ Ar_0 >= B ] (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= 10 ] (Comp: ?, Cost: 1) evalndloopreturnin(Ar_0) -> Com_1(evalndloopstop(Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(evalndloopstart(Ar_0)) [ 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) evalndloopstart(Ar_0) -> Com_1(evalndloopentryin(Ar_0)) (Comp: 1, Cost: 1) evalndloopentryin(Ar_0) -> Com_1(evalndloopbbin(0)) (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopbbin(Fresh_0)) [ Ar_0 + 2 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ 9 >= Fresh_0 ] (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= Ar_0 + 3 ] (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ Ar_0 >= B ] (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= 10 ] (Comp: ?, Cost: 1) evalndloopreturnin(Ar_0) -> Com_1(evalndloopstop(Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(evalndloopstart(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalndloopstart) = 2 Pol(evalndloopentryin) = 2 Pol(evalndloopbbin) = 2 Pol(evalndloopreturnin) = 1 Pol(evalndloopstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalndloopreturnin(Ar_0) -> Com_1(evalndloopstop(Ar_0)) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= 10 ] evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= Ar_0 + 3 ] evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ Ar_0 >= B ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalndloopstart(Ar_0) -> Com_1(evalndloopentryin(Ar_0)) (Comp: 1, Cost: 1) evalndloopentryin(Ar_0) -> Com_1(evalndloopbbin(0)) (Comp: ?, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopbbin(Fresh_0)) [ Ar_0 + 2 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ 9 >= Fresh_0 ] (Comp: 2, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= Ar_0 + 3 ] (Comp: 2, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ Ar_0 >= B ] (Comp: 2, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= 10 ] (Comp: 2, Cost: 1) evalndloopreturnin(Ar_0) -> Com_1(evalndloopstop(Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(evalndloopstart(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalndloopstart) = 9 Pol(evalndloopentryin) = 9 Pol(evalndloopbbin) = -V_1 + 9 Pol(evalndloopreturnin) = -V_1 + 9 Pol(evalndloopstop) = -V_1 + 9 Pol(koat_start) = 9 orients all transitions weakly and the transition evalndloopbbin(Ar_0) -> Com_1(evalndloopbbin(Fresh_0)) [ Ar_0 + 2 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ 9 >= Fresh_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalndloopstart(Ar_0) -> Com_1(evalndloopentryin(Ar_0)) (Comp: 1, Cost: 1) evalndloopentryin(Ar_0) -> Com_1(evalndloopbbin(0)) (Comp: 9, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopbbin(Fresh_0)) [ Ar_0 + 2 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ 9 >= Fresh_0 ] (Comp: 2, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= Ar_0 + 3 ] (Comp: 2, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ Ar_0 >= B ] (Comp: 2, Cost: 1) evalndloopbbin(Ar_0) -> Com_1(evalndloopreturnin(Ar_0)) [ B >= 10 ] (Comp: 2, Cost: 1) evalndloopreturnin(Ar_0) -> Com_1(evalndloopstop(Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(evalndloopstart(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 19 Time: 0.466 sec (SMT: 0.452 sec)