WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalNestedSinglestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSingleentryin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSingleentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(Ar_2 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestart(Ar_0, Ar_1, Ar_2)) [ 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) evalNestedSinglestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSingleentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalNestedSingleentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(Ar_2 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalNestedSinglestart) = 2 Pol(evalNestedSingleentryin) = 2 Pol(evalNestedSinglebb5in) = 2 Pol(evalNestedSinglebb2in) = 2 Pol(evalNestedSinglereturnin) = 1 Pol(evalNestedSinglebb4in) = 2 Pol(evalNestedSinglebb3in) = 2 Pol(evalNestedSinglebb1in) = 2 Pol(evalNestedSinglestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestop(Ar_0, Ar_1, Ar_2)) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalNestedSinglestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSingleentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalNestedSingleentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(Ar_2 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalNestedSinglestart) = V_2 + 2 Pol(evalNestedSingleentryin) = V_2 + 2 Pol(evalNestedSinglebb5in) = -V_1 + V_2 + 2 Pol(evalNestedSinglebb2in) = V_2 - V_3 + 2 Pol(evalNestedSinglereturnin) = -V_1 + V_2 + 2 Pol(evalNestedSinglebb4in) = V_2 - V_3 + 1 Pol(evalNestedSinglebb3in) = V_2 - V_3 + 1 Pol(evalNestedSinglebb1in) = V_2 - V_3 + 1 Pol(evalNestedSinglestop) = -V_1 + V_2 + 2 Pol(koat_start) = V_2 + 2 orients all transitions weakly and the transition evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalNestedSinglestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSingleentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalNestedSingleentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: Ar_1 + 2, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(Ar_2 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalNestedSinglestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSingleentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalNestedSingleentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(0, Ar_1, Ar_2)) (Comp: 3*Ar_1 + 7, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalNestedSinglebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: 2*Ar_1 + 4, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: Ar_1 + 2, Cost: 1) evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: Ar_1 + 2, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: Ar_1 + 2, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: Ar_1 + 2, Cost: 1) evalNestedSinglebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2)) (Comp: 2*Ar_1 + 4, Cost: 1) evalNestedSinglebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: 3*Ar_1 + 6, Cost: 1) evalNestedSinglebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglebb5in(Ar_2 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalNestedSinglereturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalNestedSinglestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 14*Ar_1 + 35 Time: 0.832 sec (SMT: 0.807 sec)